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STRUCTURAL, ENGINEERING 
 
 BOOK TWO 
 
 CONCRETE 
 
 EDWARD GODFREY 
 
 STRUCTURAL, ENGINEER 
 
 FOR 
 
 ROBERT W. HUNT <fc CO. 
 
 CHICAGO PITTSBUEG NEW YOBK LONDON 
 
 PRICE, $2.50 
 
 FTJBIJSHED BY THE AUTHOR 
 
 PITTSBURG, PA. 
 
 ^YRIGHT 1908 
 OF V 1 BY 
 
 KlQWABD GODFREY 
 
5> 
 
 Introduction. 
 
 This book is written to point the way to sound engineer- 
 ing in concrete by enunciating the principles thereof and 
 by laying bare the falsity of much that passes for good en- 
 gineering in this comparatively new branch of construction. 
 The aim is to teach, not by example or model or system, 
 but by laying stress on the principles that should govern in 
 all design. One of the evils of following systems or models 
 is that the adherent to a system is apt to use it where it 
 is not appropriate and to hold to it, without alteration to suit 
 the case, for fear that alteration improvement would be 
 interpreted as confession of imperfection in the system. 
 Principles are, or should be, of general application. 
 
 There are four general divisions to the book, as follows : 
 
 (1) The first part consists of information relative to 
 the materials used in making concrete and reinforced con- 
 crete. 
 
 (2) The second part (pages 182 to 255 incl.), consists 
 of articles by the author which were published in Engineer- 
 ing News (New York) in 1906, together with letters criti- 
 cising the same, written by different engineers, with the 
 author's replies to these. There are three of these articles. 
 The one on Beams and Slabs was published in Engineer- 
 ing News, March 15, 1906; the one on Columns and Foot- 
 ings was published July 12, 1906; the one on Retaining 
 Walls was published Oct. 18, 1906. The letters to the edi- 
 tor and the author's replies appeared in various issues in 
 1906. 
 
 (3) The third part (pages 258 to 413 incl.), consists of 
 articles by the author which were published in Concrete 
 Engineering (Cleveland, O.), in 1907, together with letters 
 from engineers and the author's replies. There are eight 
 of these articles, and they appeared serially, beginning with 
 the issue of Concrete Engineering, Jan. i, 1907, and being 
 distributed through the larger number of the issues of that 
 year. One article (Domes, etc.), will probably appear in 
 the March, 1908, issue. 
 
(4) The last part of the book consists of cuts showing 
 piers, small arches, culverts, etc., as illustrating current 
 practice. These are taken, with the consent of the pub- 
 lishers, from Engineering News, Engineering Record, Rail- 
 road Gazette, and Street Railway Journal, to whom the 
 author hereby makes grateful acknowledgment. 
 
 There is some repetition in the book in the matter of the 
 derivation of formulas for beams and columns, because of 
 the fact that two of the articles in Concrete Engineering are 
 on the same subject as articles in Engineering News. The 
 repetition could not conveniently be avoided in this com- 
 pilation. 
 
 Because some parts of the book are elementary in char- 
 acter does not signify that it is written for the tyro. There 
 have been enough examples of flagrant blunders in public 
 utterances and in design on the part of seasoned designers 
 and eminent engineers to justify emphasis on ground prin- 
 ciples that these utterances and designs violate. 
 
 No attempt has been made to carry thiough the book a 
 uniform nomenclature. Values needed in any equation will 
 be found close to it in the reading matter. The author has 
 found attempted standard nomenclature extremely annoy- 
 ing. A practical engineer has not the time, when he wishes 
 to make use of a formula, to read an entire book in order 
 to make sure of the meaning of values in the formulas, and 
 he is only wasting time when he must refer back to other 
 chapters for their meaning. It is one of the greatest faults 
 of books of reference, and text books that must often be 
 used for reference, that formulas are set down with a view 
 of their correctness, solely, the convenience of the user in 
 applying them being ignored. 
 
 Attention is called to "Some Theses" in the section which 
 follows. In the author's opinion so many of what ought 
 to be well-known principles of mechanics are flagrantly vio- 
 lated in much current design, that the "investigations" and 
 causes assigned when failures occur resemble the quibbling 
 at a murder trial to determine whether the poison adminis- 
 tered to a sick man, with "design," was the direct cause of 
 death or the disease from "which he suffered. Studied dis- 
 regard of the greater menaces and magnifying of the lesser 
 is not peculiar to investigations of concrete failures, how- 
 ever. Volumes have been published in the few months 
 since the Quebec Bridge disaster on lattice bars and com- 
 pression members. Some engineers hold that a left hand 
 bottom chord member, that had been observed to be bowed, 
 
 2 
 
 21451ft 
 
was the initial point of failure. Others say that it was the 
 corresponding right hand chord member, which was never 
 under suspicion, as this alone would account for the fact 
 that the top chord of the bridge was thrown to the right 
 a progressive amount (10 feet or so at the pier and 50 feet 
 out where the traveler was located). Still others would 
 have both members give way at once, to account for the 
 failure of the bridge to lie down on the crippled side. The 
 calculated unit stress in these chords at the time of failure 
 is said to have been 12 ooo Ibs. A quiescent lead of this 
 intensity would not, by anything known to engineers at the 
 present time, cause these members to fail. Fourteen 
 months before this disaster the author tried in vain (by 
 a letter to an engineering journal, which they declined to 
 publish) to utter a public warning, pointing out the men- 
 ace of erecting this bridge with an immense traveler lack- 
 ing sway bracing, or braced, if at all, with wire ropes, 
 which would stretch excessive amounts. This traveler, at 
 the time of failure, held about 500 tons of steel more than 
 200 feet in the air, and no sway bracing, visible in any pho- 
 tographs, was used between the two bents. Beside the 
 roadway the vertical posts of the trusses had light lattice 
 in planes normal to the truss, which would offer but slight 
 resistance to swaying, if the traveler should lean against 
 the top chord of the truss. In the course of tying up for 
 the night (the wreck happened close to quitting time) 
 it would be a very natural sequence of events, that the 
 workmen should take a block from the left side of the 
 traveler and attach it to the truss at the right side, intend- 
 ing to make X-bracing thus, and that the tightening up of 
 the line should start the top-heavy traveler to moving to 
 the right. The truss would be inadequate .o stop it, and 
 with just a little motion of the top chord the vertical posts 
 of the truss would crush, doubling up on themselves. The 
 same side force would bend in S-shape the two bottom 
 chord members in the anchor arm which were located at 
 the bottom ends and the junction of the first heavy diag- 
 onal and first heavy post of the anchor arm, causing them 
 to fail at once, which they undoubtedly did, and alike, as 
 they also did. This hypothesis, which accounts for every 
 feature of the wreck so far made public, was ignored for 
 the untenable one, from all present engineering knowledge, 
 that two compression members, on opposite sides of a 
 structure, under about one half of their ultimate strength 
 or less, quietly gave way simultaneously. The prediction 
 is here ventured that when this bridge is re-erected, the 
 traveler will be braced. 
 
A Survey of the Field of Concrete 
 Design and Construction, in which 
 will be Found some Theses. 
 
 If the author were to write a history of reinforced con- 
 crete, he would be inclined to take his cue from the writ- 
 ers of school histories for juvenile instruction and make it 
 a record of battles and mortalities. His own recollection 
 of school histories is that they are not much more than a 
 list of wars and their battles. It is hard to conceive what 
 moral or intellectual benefit a child receives from loading 
 his memory with names and dates of the battles and their 
 casualities that exhibit the workings of the passions of 
 men. In the matter of a new form of construction battles 
 are inevitable. The passions of men exhibit themselves 
 here as elsewhere ; but the battles are with men who control 
 older forms of construction, and little can be learned or 
 gained by recording them. There are casualties from an- 
 other cause, however, the record of which would be in- 
 structive. Reference is made to disasters that have resulted 
 from errors in design or construction. A detailed record 
 of these, with a correct statement of the fault, would be 
 of great value. In many cases, however, if the truth were 
 written, it would be a simple statement of dangerous con- 
 ditions and of results that a study of these conditions would 
 lead one to anticipate. 
 
 Accidents, of course, have played some part as the 
 cause of failures, carelessness and ignorance have played 
 a larger part. Among the causes assigned to failures in 
 reinforced concrete the one most heard is "green concrete." 
 This serves the purpose to the builder that "heart failure" 
 serves to the physician. It is easier to blame the failure 
 on some ignorant or dead workman who pulled out the 
 props too soon, than to get down to the root of things 
 and discover some vitally weak part of the design, that, 
 even allowing months for the concrete to harden would 
 have a factor of safety of but a little over one. 
 
 4 
 
Another thing that is set down as the cause of many 
 failures is poor concrete. There is no doubt that failures 
 have resulted both from the removal of forms before the 
 concrete has hardened and from criminal use of poor con- 
 crete. More often there can be found faults enough in de- 
 sign to cast suspicion back to one who ought to be posses- 
 sed of more intelligence than the workmen who are em- 
 ployed to carry out the design. 
 
 The importance of good materials and their proper 
 manipulation cannot be too strongly emphasized, unless that 
 emphasis obscures other conditions just as vital to the 
 safety of the structure. 
 
 Many of the faults in design very often met with are 
 pointed out elsewhere in this book; some of the most glar- 
 ing will be mentioned here at the risk of reiteration. 
 
 When a column is made of such light section that in 
 wood (which is both stronger in compression and immense- 
 ly tougher than concrete) it would appear too slender; and 
 when that column is made of plain concrete in which there 
 are some longitudinal rods ; and when it is true that such 
 columns under a central load have been known to fail un- 
 der less compression than others of plain concrete devoid 
 of steel, the concrete in each being identical ; failure is the 
 most natural thing to look for, and that of an inclusive 
 and disastrous kind. In Bulletin No. 10 of the Illinois Ex- 
 periment Station, page 14, column 8, a plain concrete col- 
 umn 9" x 9" by 12 ft. long stood an ultimate crushing 
 strength of 2004 Ibs. per sq. in. Column 2, identical in 
 size and having 4-%" rods embedded in the concrete, stood 
 1577 Ibs. per sq. in. This is not an exceptional case. Other 
 series of tests have shown the same thing. It appears to 
 be the rule. Nevertheless, one reading the literature of re- 
 inforced concrete would be led to conclude that small lon- 
 gitudinal steel rods embedded in concrete columns add 
 largely to the strength of the columns. Authority can be 
 found for including in the strength of a column these 
 slender rods that would not stand alone and that the sur- 
 rounding concrete supports in a very imperfect way. 
 
 5 
 
Authority can also be found for including in a hooped col- 
 umn, apart from the compressive strength of the concrete, 
 the strength of an imaginary column of steel, that is some 
 function of a coil or set of hoops, which could have no 
 strength whatever as a column except through the medium 
 of the concrete, already given a value for its compressive 
 strength. This assumed column of steel is purely imagin- 
 ary. When phantom columns are relied upon to carry ma- 
 terial loads, failure should not cause any comment. It is 
 just as rational to make some of the links of a chain strong- 
 er than the others and then expect the strength of the 
 chain to be greater, as it is to call the strength of a hooped 
 column the sum of the compressive strength of an imagin- 
 ary steel column, some function of the binding hoops or 
 spiral, and of the concrete column. The latter is the only 
 real column. All of the compression must go through it, 
 and, while the compressive strength of the concrete is 
 greater in flat discs between hoops that increased compres- 
 sive strength is dependent upon the flatness of the discs 
 and is not dependent upon the section of the reinforcement, 
 as the formula would make it appear. 
 
 Much misapprehension exists as to the action of concrete 
 in compression. In tension a bundle of independent fibres 
 will carry a heavy stress. In compression a bundle of in- 
 dependent shafts of slender proportions would be of little 
 use to carry a load. A material that is weak in tension can- 
 not be very strong in compression in long members be- 
 cause of the tendency of the material to spread laterally and 
 the need of tenacity to prevent this spread. Flat discs are 
 very much stronger than cubes and cubes are stronger and 
 more reliable than shafts a few diameters in length. Again 
 shafts carrying loads not centrally placed are much weaker 
 than the latter. Perfectly central application of the load on 
 a column is something scarcely possible outside of a test- 
 ing laboratory. Concrete, except in hooped columns, should 
 not be called upon to take more than about 200 to 350 Ibs. 
 per sq. in. This applies to columns having only longitudinal 
 rods. It also applies to reinforced concrete chimneys where 
 
 6 
 
there is hooping; for the hooping in a chimney does not 
 act like that in a column ; it is merely to tie the concrete 
 together, acting like the horizontal rods in a wall. It also 
 applies to an arch under full thrust. In beams concrete is 
 confined on all but the upper side ; the extreme fibre stress 
 in beams may therefore be much greater than in unconfined 
 compression members. Unit stresses of 500 to 600 Ibs. per 
 sq. in. may be safely employed in beams. 
 
 When concrete fails in compression, spalls break off 
 around the edge. It is plainly seen that in a flat disc these 
 spalls are but a small fraction of the area in compression, 
 hence in such cases as a thin mortar joint heavy compres- 
 sive stresses can be withstood. The same is true of the 
 discs between two consecutive rings or coils in a hooped 
 column. In cubes the spalls bear a larger relation to the 
 total area, and in shafts the entire surface may spall off 
 making the failure one in shear. The fallacy of using 
 compressive unit values, found by testing cubes, to deter- 
 mine the strength of concrete shafts with or without rein- 
 forcement of longitudinal rods, is therefore apparent. 
 
 Shear in steel rods embedded in concrete at 10,000 Ibs- 
 or 12,000 Ibs. per sq. in. is one of the most blatant absurdi- 
 ties to be met with in literature on the subject of rein- 
 forced concrete and in building codes. It is totally un- 
 necessary, even in an all steel structure, to specify a shear- 
 ing unit on pins, for the reason that, if the bearing of the 
 parts on the pin are properly proportioned, and the bend- 
 ing moment is not excessive, the section will of necessity 
 be ample for the shear. Steel is thirty times as strong as 
 concrete in bearing; hence there is something less than 
 one-thirtieth of a reason for specifying any unit shear on 
 the steel rods in concrete. If so-called shear rods are pro- 
 portioned on the basis of 10,000 Ibs. per sq. in., they are 
 about as irrationally proportioned as they could be. Loose 
 stirrups could not take hold of a horizontal rod to receive 
 this shear, except through the medium of the concrete; 
 and, if the concrete takes the shear, there is no reason why 
 
it should be imparted to the steel rods, since it must go 
 back to the concrete again at the upper part of the beam. 
 
 T-beams, with their narrow stems and insufficient hori- 
 zontal shearing area in a plane above the bottom rods, offer 
 another example of irrational design. The apparent rein- 
 forcement supplied by vertical or diagonal shear rods is 
 enlarged upon elsewhere. 
 
 As pointed out, wood is very much stronger than con- 
 crete. Wood will stand an ultimate load of 10,000 Ibs. per 
 sq. in. or more in tension and may safely take 800 to 1200 
 Ibs. per sq. in. in compression. To make a reinforced con- 
 crete member capable of taking tensile stresses equal to 
 what sound wood will take there should be 10 or 15% of 
 steel reinforcement in a member of the same size. To 
 reinforce a square member in bending, as with rods near 
 each corner, so that it will be as strong as sound wood 
 for transverse loading, as in a column taking swaying 
 forces, it would require 5 or 10% of steel reinforcement. 
 Reinforcements in such amounts are prohibitive; it is 
 evident then that concrete members should be of larger di- 
 mensions than members in wood to perform the same office. 
 
 Reinforced concrete viaducts having bents composed of 
 two inclined posts and a bottom strut, with the cross 
 girder joining the tops of the posts, are not good construc- 
 tion. In wood such bents would be condemned for lack 
 of diagonal bracing. Even in material of the toughness 
 of steel such bents would not be attempted, unless diago- 
 nal bracing interfered with the headroom desired; in this 
 case extra stiff columns would be used. More failures of 
 structures have been caused by lack of proper bracing than 
 from any other cause. The experience in the concrete en- 
 gineering field should make all builders avoid, as dangerous, 
 construction that depends for lateral stiffness upon long 
 columns and lacks diagonal bracing. In the light of ex- 
 perience and intelligent interpretation of tests, as well as 
 rational analysis, the building of such construction only 
 invites disaster. 
 
 Reinforced concrete does not lend itself to efficient or 
 8 
 
economic construction in open work resembling steel trusses 
 or bents. Girders or bents should be solid or nearly so. 
 Circular openings may be used rationally to save weight. 
 
 A common form of reinforced concrete column footing 
 consists of a square flat block having rods lying near the 
 bottom, spaced uniformly, parallel to the sides. Some of 
 these rods are entirely outside of the column or shaft 
 carrying the load, that is, they do not lie under it and would 
 therefore serve to intensify the stress in rods that do lie 
 under the shaft. This is another example of irrational de- 
 sign. 
 
 There are a number of rudiments of popular but errone- 
 ous notions exhibited in much reinforced concrete design. 
 One of these concerns sharp bends in rods. A hog chain 
 or a king-post or queen-post truss are common forms of 
 supporting otherwise weak beams. A bent rod is thrown 
 under a beam, and at the bend a post is used to support 
 the beam at one or two intermediate points. In reinforced 
 concrete beams for test and in actual construction it is very 
 common to see rods similarly bent, and the appearance 
 is that of the trussed beam just referred to. With this the 
 popular eye would be satisfied, but when search is made 
 for something that corresponds to the post in the trussed 
 beam, nothing is found but a trifling amount of concrete 
 that occurs at the bend. To heighten the absurdity the 
 so-called truss rod ends at or near the support with no end 
 anchorage whatever. It is as though the truss rod in a 
 trussed wooden or steel beam were simply brought up and 
 laid under the end of the beam without an end nut to take 
 the pull. A hook on the end of such a truss rod would 
 correspond to a hook in a rod embedded in concrete. Both 
 are weak and inefficient. 
 
 Sharp bends in heavy rods are very common; nothing 
 could be more irrational. 
 
 It is a structural fault in a design when steel work is 
 so disposed that there must, be some slip before the part can 
 take its full stress. Such details are: loose stirrups around 
 rods, splices in heavy rods made by lapping them and 
 
 9 
 
binding them together, kinks or short bends in rods, etc. 
 
 Another concession to popular and erroneous ideas is 
 in the use of arches where flat slab construction would be 
 better. There used to be a bicycle manufactured that had 
 a curve in one of the parts of the frame. Advertisements 
 pointed out this weakening curve as a special element of 
 strength, because it bore some relation to an arch. Seg- 
 mental floor arches, lacking abutments and shallow where 
 they need the greatest depth, and small arches of high rise, 
 pressing horizontally against uncertain earth fill, are ex- 
 amples of the persistence of popular ideas. 
 
 When a beam may be severed from its supporting col- 
 umn or girder by the mere cracking of a surface of con^ 
 crete and the pulling out of a short length of rod, and when 
 this beam is an integral part of the only system of bracing 
 in a structure, as in the case of a building where cross 
 walls are not used to take up sway, it is reasonable to 
 expect that wind or other lateral force, acting with the load 
 on the beam will crack the beam and pull out the rod. 
 
 If reinforced concrete is to be used in high buildings to 
 replace steel cage buildings, good features of steel frame 
 buildings must not be overlooked. Specifications for steel 
 work rightly restrict and forbid reliance upon tension on 
 rivet heads to support vertical loads. But this very ele- 
 ment is of utmost importance in holding together and brac- 
 ing such steel structures as office buildings and mill build- 
 ings. Far too many reinforced concrete structures, lacking 
 a unifying element tying the various parts together, have 
 ingloriously failed, and far too many laborers and foremen 
 have been made to take blame that should have been at- 
 tributed to ignorance of designers. It is of utmost import- 
 ance that the parts of a reinforced concrete building be 
 tied together. This should be done by use of continuous 
 or spliced rods. The best way to accomplish this is to use 
 round rods and to splice them with sleeve-nuts. 
 
 Nowhere in engineering is there more evidence of a dis- 
 position to cover up ignorance with elaborate cloaks o 
 arithmetic fabric than in reinforced concrete design. This 
 
 10 
 
is exhibited in complex formulas for the design of beams, 
 in the flat plate theory, in arch calculations, in column for- 
 mulas, in calculations for temperature stresses and gener- 
 ally where concrete and steel design is treated. Some of 
 these have already been referred to. The most discredit- 
 able feature about it all is that structures that have fallen 
 down have been shown by some of these applications of 
 arithmetic to be quite safe. 
 
 Another thing in evidence is erroneous formulas and mis- 
 applied methods of calculation. 
 
 An illustration of what elaborate theory accomplishes in 
 beam design is seen from the following example, taken at 
 random. In Bulletin No. 14, Engineering Experiment Sta- 
 tion, University of Illinois, page n, test beam 57 shows a 
 calculated unit stress in the steel of 39,800 Ibs. This is 
 worked out by a formula with many terms and all of the 
 commonly made assumptions that bring in the relative 
 moduli of elasticity of steel and concrete. The test load 
 is 11,730 Ibs. at third points on a 12-ft. span. Adding to 
 the moment that this would give the dead load moment 
 due to the weight of the 8" x 11" beam there is found to 
 be a total moment of 300,900 in.-lb. Taking the neutral 
 axis of this beam at the middle of the depth of the con- 
 crete, as the rods are I in. above the bottom, the effective 
 depth is 8 I/6 inches. The stress on the steel is 36,800 Ibs., 
 or on three %-in. rods, 40,000 per sq. in. This is one-half 
 of one per cent, more than the unit stress found by the 
 elaborate formula. The results are thus practically ident- 
 ical in this case at least. 
 
 The flat plate theory, as worked out for such homogene- 
 ous material as steel plates, is given in all its elaborateness, 
 as applicable to reinforced concrete slabs supported on all 
 sides, by a number of writers. In the theory of the flat 
 plate, as usually treated a factor enters that does not find 
 a parallel in the ordinary theory of flexure. At the center 
 of the plate the extreme fibre stress at top and bottom is 
 of the same intensity in all directions, in the two respective 
 planes. Because of this fact the upper layer is capable of 
 
 11 
 
resisting a greater intensity of stress than it would take 
 with the stress in one direction only and the material not 
 confined laterally. The fibres in compression in a flat 
 plate are confined on all sides, including, to some extent, 
 the side on which the pressure is applied. In the case of 
 the fibres in tension there is not this assistance from con- 
 jugate stress. It is not clear, therefore, why Poisson's ra- 
 tio should be applied to flat plates, since the tension on the 
 free side would be the critical stress. The term represent- 
 ing fibre stress in the flat plate theory as commonly given 
 is not the true fibre stress but a fictitious unit stress re- 
 sulting from the application of Poisson's ratio. The actual 
 fibre stress is almost cut in half by this application. Ad- 
 vocates of the flat plate formula do not seem to have con- 
 sidered the question of converting this fictitious extreme 
 fibre-stress in all directions into actual stress in reinforc- 
 ing steel rods in two or more directions. They further 
 do not make it clear why all of the complexity and uncer- 
 tainty of the flat plate theory for steel plates should be re- 
 sorted to to solve flat slabs in reinforced concrete, a mater- 
 ial not at all contemplated in such formulas as Grashofs. 
 
 Some prominence has been given recently to a solution 
 of the flat slab supported on four sides, which starts with 
 the assertion that a flat square slab supported on all four 
 sides fractures along a diagonal. Assuming that the bend- 
 ing moment is greatest along the diagonal of a rectangular 
 slab a formula is derived for the magnitude of this bend- 
 ing moment, which is naturally a mathematical certainty, 
 just as the bending moment along the diameter of a cir- 
 cular plate is a mathematical certainty. But the variation 
 of intensity of this moment along the diagonal is entirely 
 ignored, or rather the intensity is taken to be constant. 
 There is just as much error in taking this moment as uni- 
 form along the diagonal of a rectangle as there is in taking 
 the intensity of the moment along the diameter of a flat 
 circular plate as uniform. It may be true that a flat slab, 
 either square or rectangular, supported on four sides, will 
 break on a diagonal line. This is proof of one thing, name- 
 12 
 
ly, that the greatest intensity of bending moment is at the 
 center of the slab ; for, as both diagonals are identically con- 
 ditioned, either may be the one to fail, and th'eir only com- 
 mon point is the center of the slab. It is not conceivable 
 that the same intensity of bending moment extends clear to 
 the corner of the slab. A crack once started in a diagonal 
 direction would naturally extend into the corner and even 
 over the support, merely on account of the brittleness of 
 the material. This would be no evidence of constant in- 
 tensity of bending moment along the fracture ; much less 
 force is needed to continue a crack once started than to 
 start the same. 
 
 The author brought out a formula for square slabs sup- 
 ported on four sides and reinforced in two directions, in 
 Concrete Engineering, Feb. I, 1907. This formula is appli- 
 cable to the materials considered and rational in its deri- 
 vation. It has the sanction of Professors Maurer and Tur- 
 neaure, as it appears in their book recently published. , 
 
 In the design of arches the elastic theory has been em- 
 phasized and very forcibly recommended. This is a theory 
 for the investigation of an arch already proportioned. It 
 could not be used to find the proportions needed. One way 
 recommended to arrive at a trial proportion for an arch 
 is to take the dimensions of existing arches and judge it 
 therefrom. An inspection of a table of the proportions of 
 existing arches reveals the fact that they are hopelessly at 
 variance with each other. The elastic theory requires that 
 the moment of inertia of the arch at all sections be known. 
 The moment of inertia of a combination of concrete and 
 steel can be assumed, or arrived at by assumptions, but not 
 definitely known. The elastic theory, as usually employed, 
 assumes fixed ends to the arch. This is an extravagant 
 assumption and one not warranted by the conditions. In 
 small models it would be possible to make mass enough in 
 the abutments to effect fixed ends in the arch span. In 
 large arches it requires massive abutments to resist over- 
 turning from the simple thrust alone. If to this, mass must 
 be added to make the ends of the arch fixed, an unwarrant- 
 
 13 
 
ed waste of material results. The concrete needed to add 
 a few inches to the depth of an arch ring and thus increase 
 by a large percentage its stiffness would be insignificant in 
 results if added to the abutments. The thrust, if the arch 
 be considered hinged at the ends, is practically the same 
 as if it be considered fixed ended, so that the amount of 
 mass in the abutments due to assumption of fixed endedness 
 is simply extra material that could be more economically 
 employed in the arch ring. 
 
 The elastic theory has application to steel arches for two 
 reasons, (i) The moment of inertia of a steel arch can be 
 definitely calculated. (2) The unstressed arch fits the abut- 
 ments upon which it rests, being very accurately built there- 
 for. This theory is inapplicable to stone or concrete arches 
 for the obverse of these reasons. The shrinkage of con- 
 crete in setting precludes any possibility of determining 
 exactly what would correspond to the moment of inertia 
 of a reinforced concrete section, that is, a coefficient from 
 which the deflection could be calculated. This same shrink- 
 age makes it impossible to build a concrete arch of any 
 kind that will be free from shrinkage stresses, and an arch 
 in which there are unknown initial stresses should not be 
 made the subject of exact calculation based on the ab- 
 sence of initial stress. Inaccuracy in stone arches has the 
 same result as shrinkage in concrete arches in that the 
 arch is subject to some initial stress. In addition to this 
 stone arches cannot take any tension. 
 
 In the inelastic theory the presumption of accuracy is not 
 made, and there is not the false security which elaborate 
 calculations tend to give. It is more in keeping with the 
 materials of stone and concrete arches. A system of blocks 
 fitted to each other along the lines of an arch will carry 
 certain fixed loads without tending to open any of the 
 joints, when these blocks follow the line of what is called 
 the equilibrium polygon. When other loads are brought 
 on the arch, as the live load, the equilibrium polygon under- 
 goes certain changes which would tend to open joints at 
 sections whose location is moderately well known. If the 
 14 
 
arch blocks be conceived to be cemented together into one 
 mass and to be tied together by steel rods, the rods will 
 take the tension. Reasonable assumptions to arrive at the 
 probable intensity of the tension are all that the materials 
 and methods of manufacture in reinforced concrete arches 
 justify. 
 
 The literature on stone and concrete arches is unsatisfac- 
 tory being in large part excessively theoretical and unprac- 
 tical from many standpoints. Semi-elliptical and basket- 
 handle arches are commonly held out as examples. Such 
 curves are unsuitable for ordinary arches, because they 
 presuppose heavy horizontal pressure of the fill or demand 
 the same to prevent large moments at the sharpening of 
 the curve. Only sand or semi-liquid mud can exert such 
 pressure (except as a wedging force, as back of a retain- 
 ing wall) and neither of these materials is desirable as a 
 fill. If the arch is the roof of a tunnel under a stream, 
 the semi-ellipse or semi-circle are consistent curves. There 
 is a general lack of appreciation on the part of writers and 
 builders, of the fact that horizontal pressure in earth, while 
 it is a possibility, is not necessarily exhibited. There are 
 many proofs of this, but they pass unnoticed. Ordinary 
 earth could be supported on a system of vertical props 
 capped with horizontal lagging pieces in approximate arch 
 shape. Unless earth will loosen in large chunks, there is 
 scarcely anything to fear from horizontal pressure. This 
 action is not possible in the fill over an arch. Horizontal 
 pressure in such case is scarcely a possibility. Of course 
 horizontal motion against earth would meet with more or 
 less resistance, but this is passive and not active. 
 
 Another phase of the impracticable nature of data on 
 arches is seen in the blanket formulas for depth at crown. 
 These often have no relation to the load to be carried, 
 whether heavy or light traffic. Some of them give the 
 depth of ring in terms of the radius of the curve of the 
 intrados, and usually the rise is taken from the point where 
 the intrados begins to curve away from the face of the 
 abutment. These details of outline have no significance as 
 
 15 
 
determining the stresses but are only, architectural features. 
 The curve of the intrados may have only a remote relation 
 to the real curve of the arch, which is the curve of the cen- 
 tral line of the arch ring. 
 
 In another respect literature on arches is unsatisfactory. 
 This concerns live load stresses. In designing girders and 
 trusses in steel, the live load can be placed at the exact point 
 where it will give the maximum stress in any member. To 
 do this, using the elastic theory in arches, would introduce 
 frightful arithmetic complications. No systematic attempt 
 seems to have been made heretofore to determine the posi- 
 tion of concentrated loads to give the maximum effect on 
 stone and concrete arches. 
 
 Further it has not been recognized in treatment of arches 
 that there is a rise for any given span and loading and fill 
 which fits the conditions, that is, a point where, if the rise 
 is diminished, the thickness of arch ring (for thrust) will 
 be unnecessarily great to take care of eccentric loading; 
 and if the rise be increased the thickness needed (for 
 thrust) is not enough to take care of unbalanced loading. 
 This is the natural economic rise for any span. 
 
 Calculated stresses in concrete arches due to tempera- 
 ture changes are void of meaning. If a concrete arch could 
 be made apart from the site and then placed bodily in its 
 intended position, and if it fit exactly that position, calcu- 
 lated temperature stresses might have a meaning. It is 
 impossible to place concrete in such way that its normal 
 unstressed shape fits exactly on the supports. It is equally 
 impossible to determine the intensity of stresses due to 
 shrinkage. If then the original condition of .stress cannot 
 be known, it is idle to make elaborate calculations as to the 
 effect of expansion and contraction due to change in tem- 
 perature. In steel work arches can be made to fit the sup- 
 ports, and temperature stress calculations have a meaning. 
 A liberal factor of safety is eminently better to cover ig- 
 norance than the most ingenious mathematical fabric ever 
 devised. 
 
 When a dam fails, elaborate theories are put forth to ac- 
 16 
 
count for its overturning, when calculations show that the 
 horizontal pressure of the water is not sufficient to tip it 
 over. Suction on the down-stream face is one of these bug 
 bears. There has been found to be a pressure somewhat 
 below the atmosphere under a falling sheet of water where 
 the stream contracts, and this is seized on to account for 
 the great force that would be necessary to overturn a mass 
 of masonry. Or in the matter of strength shearing forces 
 in vertical or horizontal planes are blamed for the failure. 
 In technical literature on the subject, so far as the author's 
 somewhat indifferent search has shown, there is no mention 
 of the uplifting tendency of water that percolates under the 
 dam, supplying nearly or quite half enough upward force to 
 lift the masonry of the dam. This force, in a gravity dam 
 designed to resist both the uplift and the lateral force of 
 the water, is 42% of the total overturning force or 72% of 
 the horizontal Iforce. A system of design that ignores forces 
 of such magnitude as these and magnifies trifles is not a 
 safe system even for a temporary structure, to say nothing 
 of the danger in a permanent structure upon which hang 
 so much life and property. 
 
 A scheme for reinforced concrete retaining walls, consist- 
 ing of a curtain wall and a bottom slab joined at intervals 
 by ribs or counterforts, has been much used in recent years. 
 Two errors in design characterize many of the designs 
 that have been described in engineering periodicals and in 
 books. One of these concerns reinforcement of the bottom 
 slab. Complete reinforcement, uniformly distributed for 
 the full width of slab, is used near both top and bottom 
 surfaces. No analysis of the forces can show need of such 
 wasteful rise of steel. In the matter of reinforcing the rib 
 or counter-fort the apparent and expressed method is to 
 treat it as a beam with increased tensile stress from ends 
 toward middle of the inclined edge. This is far from cor- 
 rect. The stress in the reinforcing rods is imparted at their 
 ends and failure to use positive end anchorages is a struc- 
 tural blunder. 
 
 In formulas for reinforced concrete chimneys much un- 
 17 
 
necessary complication is sometimes introduced by making 
 the neutral axis out of the center of the section. There is 
 no good reason, based on known facts, for assuming the 
 neutral axis anywhere but in the center of the section. 
 
 There is much misapprehension in the matter of inter- 
 pretation of tests. Some published tests are not worthy 
 of the name of tests. They are made for the purpose of 
 "proving" the miraculous strength of some system, and the 
 load is improperly placed or is placed on only a portion of 
 the floor. Tests of shear in concrete are referred to at 
 length elsewhere. Some recent tests were reported that 
 purported to give the adhesion of steel to concrete. The 
 entire resisting moment of reinforced concrete beams (with 
 a short lever arm) was attributed (so far as tension was 
 concerned) to the reinforcing steel rods, no allowance being 
 made for the tensile strength of the concrete, a real though 
 uncertain quantity. By using smaller and smaller rods such 
 tests could be made to "prove" the adhesion of steel to 
 concrete any desired amount; for even with no rods what- 
 ever, the plain concrete would take a certain bending mo- 
 ment. In one very important respect the lesson learned 
 from tests is a perverted one. Reference is made to the 
 test of practical use of a structure. There is no more mis- 
 leading notion than the one that because a structure stands 
 and performs its office it is therefore safe. Structures have 
 collapsed after standing for decades, and this under no 
 unusual conditions. Given a structure that has attained al- 
 most its full strength, and suppose that this structure fails 
 when the forms are removed. What would be the factor 
 of safety in such a structure (or in another similarly built), 
 if it reached a strength 10 or 20% greater and was capable 
 of standing up when the forms were removed? 
 
 As to the unit tension allowed on steel, this is also elab- 
 orated elsewhere. Units above 10,000 to 13,000 1'bs. per sq. 
 in. are too high, though they are very generally recom- 
 mended. At these units the concrete will generally retain 
 its integrity. Not that steel can always be stressed to this 
 amount without cracking the concrete, but, if there is 
 
 18 
 
enough concrete surrounding the steel, the tensile strength 
 of the concrete will aid the steel to the extent, for safe 
 loads, that the elongation will not crack the concrete. A 
 design that contemplates cracks in the concrete under safe 
 loads cannot be classed as good engineering. The cause 
 that will produce a crack at one point may produce others 
 at other points and thus break up and wear out the struc- 
 ture. 
 
 In the matter of the consistency of concrete there are 
 still some users that insist on "moist earth" mixtures for 
 all purposes, even reinforced concrete and parts that ought 
 to be impermeable. Also it is very generally recommended 
 that materials be heated before use in cold weather. A very 
 significant letter appears in Eng. News, Jan. 30, 1908 from 
 Mr. E. A. Mollan. He describes some concrete that was 
 made with sand and stone that had been dried out by the 
 heat of the sun. This concrete had no cohesion and was 
 worthless. When, subsequently, the same materials were 
 wetted down concrete made therewith (using the same 
 cement as before) was of good quality. Builders who make 
 use of stoves to heat and dry the sand and stone for con- 
 crete are commended to a study of this case. 
 
 19 
 
Cement. 
 
 There are two kinds of cement in common use, namely,. 
 Rosendale or natural cement and Portland cement. To- 
 this may be added, also, slag cement or puzzolan cement. 
 
 Rosendale cement is made by burning a limestone con- 
 taining the carbonates of lime and magnesia and clay at 
 about the temperature of the lime-kiln or 1000 to 2000- 
 degrees F. It is ground to a powder between mill stones 
 after burning. The color is usually brown. Rosendale 
 cement is used to some extent in foundations for street 
 pavements and in some massive concrete work. It should 
 not be used in reinforced concrete work or in work where 
 strength is to be an important characteristic. 
 
 Portland cement is made by mixing clay and limestone 
 (or other argillaceous and calcareous substances) in the 
 proper proportions, and burning the mixture at a high, 
 heat (above 2000 F.), and grinding the clinker to a pow- 
 der. The color is usually gray or greenish gray. There 
 are four different kinds of Portland cement manufactured 
 in the United States as distinguished by the materials.- 
 from which the cement is manufactured. These com- 
 binations are: i. Argillaceous limestone, or cement rock,, 
 and limestone. 2. Marl and clay. 3. Hard limestone and 
 shale or clay. 4. Slag and limestone. 
 
 There is a kind of cement called slag cement, or puzzo- 
 lan cement. This is made by first granulating the slag 
 by chilling the molten slag in water, then drying and mix- 
 ing with slaked lime, then grinding. This is an inferior ce- 
 ment and is only good in locations where it will be con- 
 stantly wet. The color of slag cement is light lilac. Slag 
 cement should not be confused with true Portland cement 
 made from slag and limestone. The latter is made by 
 burning to a clinker a mixture of crushed limestone and 
 chilled blast furnace slag and then grinding this clinker 
 as the clinker of other Portland cement is ground. A 
 description of the manufacture of this kind of cement is 
 given in Engineering News, Sept. 27, 1900. 
 
 20 
 
These cements are all what are called hydraulic cements, 
 that is, they will set or become hard under water. They 
 are unlike common lime in this respect, as they do not re- 
 quire the presence of air to acquire their cementing qual- 
 ity. The presence of water is necessary to the hardening 
 of cement, and cement will harden both in fresh or salt 
 water. Unlike lime, also, the clinker from which cement 
 is manufactured is inert. The unground lumps are like 
 cinders, and they are therefore useless in this state. It 
 is only when the clinker is ground very fine that it is fit 
 for use as a cement. This is the reason why fine grinding 
 is essential in all hydraulic cement. 
 
 An average analysis of good Portland cement is about 
 as follows: Lime, 64%; Silica, 21%; Alumina, 8^%; 
 Magnesia, 2^%; Iron Oxide, 2^/2%; Other ingredients, 
 i%%. A variation one way or the other of 2% or so in 
 the amount of lime and silica does not make much dif- 
 ference in the cement. The magnesia should not exceed 
 about 2 or 3%. There is not so much regularity in the 
 composition of Rosendale or in slag cement as there is 
 in Portland cement. There is generally much less lime 
 and more silica and magnesia in Rosendale than in Port- 
 land. 
 
 Portland cement is superior to Rosendale for every pur- 
 pose, for a given volume of cement, though the latter 
 for many uses meets the requirements of the case/ Nat- 
 ural or Rosendale cement sets quicker than Portland ce- 
 ment, though Portland cement soon overtakes and passes 
 the natural cement. The quick-setting property of natural 
 cement may be turned to advantage in work that is to re- 
 ceive its load soon after placing. By using a larger quan- 
 tity of natural cement than would be needed in Portland 
 cement the necessary strength may be attained in a short 
 period. 
 
 Natural and Puzzolan cements will not stand extreme 
 changes in temperature as well as Portland cement. 
 
 When sand and cement are mixed and ground together, 
 the mixture can be ground finer than it is possible, with 
 
the same means, to grind the cement alone. It can in 
 fact be ground so fine that nearly all of it will pass through 
 a sieve having 200 meshes to the inch. On account of the 
 extreme fine grinding, and possibly also on account of the 
 activity of the sand in this finely divided state, the cement 
 is stronger than the same amount of ordinary cement 
 would be. If the installation of a grinding mill is practi- 
 cable on a large piece of work, where the cost of cement 
 is high, there may be a saving in thus grinding a mixture 
 of cement and sand in order to reduce the amount of ce- 
 ment required. The grinding of a mixture of cement and 
 sand is patented. 
 
 The weight of Portland cement is 85 to 100 Ibs. per cu. 
 ft., depending upon whether it is loose or compact. A 
 barrel of cement is considered, by some specifications, as 
 equal to four cubic feet. This, at 375 Ibs. per standard 
 barrel, is about 94 Ibs. per cu. ft. 
 
 The tests commonly made on cement are given else- 
 where in this book. A few notes on the method of mak- 
 ing these tests and the importance of the tests would not 
 be out of place here. Some additional tests will also be 
 mentioned. 
 
 To determine whether or not a cement is hydraulic mold 
 a brick i"xi%"x8", and after the initial set place it 
 under water upon supports near the ends, having the one- 
 inch dimension vertical. If the cement is hydraulic the 
 brick will retain its shape, if not, it will give way between 
 the supports. 
 
 A simple test for soundness of cement, or freedom from 
 tendency to shrink or expand during setting, is to take a 
 cylindrical lamp chimney and fill it for a certain distance 
 with well compacted cement paste, marking the end of the 
 flat surface. If the cement shrinks, it will show by the 
 mark, and if it swells, it will break the chimney. 
 
 The swelling of cement during setting is usually due 
 to the slaking of free lime. When the cement is used 
 fresh from the mill it is apt to have some free lime in it. 
 Seasoning for several weeks after grinding, if the cement 
 
 22 
 
is finely ground, will air slake this lime and render the 
 cement more sound. On the other hand too long expos- 
 ure to the air will destroy the activity of the cement and 
 may render it useless. Moist air is especially destructive 
 on the cement. It should therefore be stored in a dry 
 place. Air generally affects cement by causing it to cake 
 in the sacks, and the hard lumps that cannot be easily 
 broken with the shovel will be useless as cement. Good 
 cement may be somewhat lumpy, but the lumps should be 
 such that they can be easily broken with the fingers. 
 
 The test for fineness of cement is important, because the 
 finer a cement is ground the stronger that cement will be. 
 Not only is the activity of the cement increased by fine 
 grinding, but the fine particles are necessary to fill small 
 voids in the sand and thus render the mortar or concrete 
 dense. 
 
 The test for specific gravity is made to determine wheth- 
 er or not the cement is properly burned and also to de- 
 lect adulterants. If Portland cement is under-burned, its 
 specific gravity will be low, and if it is over-burned, its 
 specific gravity will be high. Specific gravity tests are apt 
 to be misleading, because of the fact that the cement ab- 
 sorbs some C O 2 and water from the air and thus its 
 specific gravity is reduced. Cements having different de- 
 grees of calcination, if tested when fresh-burned, or if 
 heated red hot before testing, to drive off absorbed C O 2 
 and water, appear, according to Mr. David B. Butler, 
 (Eng. Record, Vol. 55, p. 176) to have very close to the 
 same specific gravity. Mr. Butler's tests, however, do not 
 discredit the value of the specific gravity determination to 
 detect adulterants. Natural cement or slag used as adul- 
 terants will lower the specific gravity. 
 
 The conclusions in a paper by Prof. R. K. Meade and Mr. 
 S. C. Hawk, read before the American Society for Test- 
 ing Materials in June, 1907, drawn from a series of tests 
 made by them, are as follows : 
 
 "(0 That the specific gravity test is of no value what- 
 ever in detecting underburning, as underburned cement 
 
 23 
 
will show a specific gravity much higher than that set by 
 the standard specifications. Underburned cement is read- 
 ily and promptly detected by the soundness test and no 
 others are needed for this purpose. 
 
 "(2) The value of the specific gravity test as an indi- 
 cation of adulteration is much exaggerated. While a 
 large admixture of any light adulterant with the cement 
 would be shown there is at the same time much slag ce- 
 ment and also Rosendale cement which could be mixed 
 with cement in large quantities without lowering the speci- 
 fic gravity below the limit of our standard specifications. 
 
 "(3) That low specific gravity is usually caused by 
 seasoning of the cement or the clinker, either of which 
 improves the product. 
 
 "(4) That the proposition to ignite the cement sample- 
 which falls below specifications and determine the speci- 
 fic gravity upon the ignited portion is of no value because 
 adulterated cements also have their specific gravity very 
 much raised by such ignition. 
 
 "(5) That the requirements for specific gravity should 
 be omitted from the standard specifications or at least 
 that the clause which infers that low specific gravity is 
 caused by underburning and adulteration should be omit- 
 ted and that in its place there should be inserted one stat- 
 ing that low specific gravity may, but does not necessarily 
 imply adulteration as it is in most cases due to seasoning 
 of the cement or storage of the clinker before grinding, 
 both of which are beneficial to the product." 
 
 Specific gravity of cement is usually determined by im- 
 mersion in benzine or turpentine. 
 
 The addition of a small quantity of unburned granu- 
 lated slag, before grinding, to cement made from slag" 
 is not considered an adulteration, as it neutralizes the 
 effect of any free lime that may be in the cement. 
 
 Cement that shows excessively high tensile strength in 
 short time tests is liable to be adulterated with sulphates, 
 which hasten the settling but render the cement weak after 
 a long time. 
 
 24 
 
In making pats or bricquetts for test the paste should 
 be mixed thoroughly for five minutes, rubbing the mix- 
 ture under pressure. Regularity should be observed in 
 placing the mortar in the molds. Pressure should be 
 used, and as near the same pressure as possible for dif- 
 ferent tests. A difference in the amount of tamping or 
 pressure may make a very great difference in the strength 
 of tensile tests. 
 
 Soundness of cement is of more importance in rich mix- 
 tures than in lean mixtures. Cement that will stand the 
 28-day test for soundness, but fail under the accelerated 
 test by boiling or steaming, may be satisfactory in ordin- 
 ary concrete. Cement that will stand both the accelerated 
 and the 28-day test is to be preferred. Cement that shows 
 up well in the accelerated test is not necessarily a good 
 cement. The presence of sulphates seems to counteract 
 the expansive effect of free lime. Gypsum or sulphate of 
 lime is generally added by manufacturers of cement to re- 
 tard the set. Sulphate of lime to the extent of more than 
 two per cent, by weight is not allowed in any cement by 
 the U. S. Army engineers ; not more than one per cent. 
 is allowed in cement to be used in sea water. 
 
 Cement that shows up well in the tensile test after seven 
 days and then shows little or no gain at 28 days is to be 
 looked upon with suspicion. 
 
 The tests given in cement specifications are to be made 
 in a laboratory equipped for the purpose. Simple tests 
 may be made on the work, that will in some cases be 
 sufficient to determine the general character of the ce- 
 ment. Pats and balls of cement or mortar can be made 
 use of to gage the setting qualities and soundness. By 
 pressure of the thumbnail the setting quality may be 
 estimated and by dropping the hardened specimens a 
 rough idea may be had of the strength. 
 
 Puzzolan or slag cement may be detected by taking a 
 pat and boiling it for several hours and then breaking it. 
 The fresh fracture will be bluish green. 
 
 The following is quoted from "Professional Papers of 
 
 25 
 
the Corps of Engineers, U. S. Army. No. 28." "Puzzolan 
 cement never becomes extremely hard like Portland, but 
 Puzzolan mortars and concretes are tougher or less brit- 
 tle than Portland. The cement is well adapted for use in 
 sea water, and generally in all positions where constantly 
 exposed to moisture, such as in foundations of buildings, 
 sewers and drains, and underground works generally, and 
 in the interior of heavy masses of masonry or concrete. 
 It is unlit for use when subjected to mechanical wear, 
 attrition or blows. It should never be used where it may 
 be exposed for long periods to dry air, even after it has 
 well set. It will turn white and disintegrate, due to the 
 oxidation of its sulphides at the surface under such ex- 
 posure. Sulphuretted hydrogen, which is often evolved 
 upon decomposition of the sulphides in Puzzolan cement, 
 is injurious to iron and steel. Such metals, if used in 
 connection with Puzzolan cement, should be protected, 
 or an allowance be made for deterioration by an increase 
 of section." 
 
 Cement is considered by most authorities to be a sub- 
 stance which attains its hardness by a process of crystalli- 
 zation, taking up the water used in mixing to form a hy- 
 drate of a crystalline structure. The author believes, 
 with Dr. William Michaelis of Germany that cement does 
 not crystallize in hardening, but that it is a colloid. The 
 author believes that the nature of cement is more nearly 
 represented by ordinary glue than by any crystalline sub- 
 stance, and that what crystallization takes place is inci- 
 dental and not a necessary accompaniment of the harden- 
 ing process. Cement clinker is inert : it does not slake like 
 quicklime; it must be first ground to a powder to have 
 any cementing quality. It is only the impalpable powder 
 of this so-called cement that is really cement. The rest 
 is inert, like the clinker. Pure neat cement, used alone, 
 would not get very hard and would not be very strong. 
 Laitance, or the slime that rises to the surface in a ce- 
 ment mixture in an excess of water, is the nearest thing 
 to pure cement that is usually encountered. So-called 
 
 2Q 
 
neat cement is a mixture of small particles of inert clink- 
 er and a dust that is fine enough for water to act upon 
 and turn into a colloid or gellatinous substance, which, 
 when lodged in between small grains of an inert hard sub- 
 stance, holds these grains together in an artificial stone. 
 The inert hard substance may be grains of sand or the 
 coarser grains of ground cement clinker, too coarse to 
 have cementing properties. 
 
 The foregoing statements are radically different from 
 the commonly accepted belief regarding cement. They 
 therefore call for some facts to substantiate them. No 
 attempt will be made to discuss the chemistry of cement, 
 except to cite some admitted facts that bear in a general 
 way on its chemical action. 
 
 It is well known that fine grinding improves the strength 
 of cement. It is also known that there is a point beyond 
 which fine grinding diminishes the strength of cement 
 when made into neat briquettes and pulled. It is also 
 known that this same finely, ground cement, that is weak- 
 er in neat tests than coarser cement, is stronger in ce- 
 ment and sand tests than the other. 
 
 Another fact well known is that when a broken piece 
 of china is to be mended by glue, or when two pieces of 
 wood are to be glued together, the parts must be pressed 
 firmly together and as much of the glue squeezed out as 
 possible; and the strength of the mended part is greater 
 than that of the glue itself by which it was mended. 
 
 Lime mortar, even before it has had time to be acted 
 upon by the carbon dioxide, is stronger in tension than 
 the lime paste. 
 
 Melted sulphur is used sometimes as a cement, usually, 
 however, alone. In Engineering News, Vol. 51, p. 231, 
 Mr. Alexander Potter describes some tests on melted sul- 
 phur as a cement for sewer pipe, mixed with sand. He 
 finds it to be an excellent material for that purpose. In 
 his tests he found plain sulphur to resist tension with an 
 ultimate strength of about 100 Ibs. per sq. in. Sulphur and 
 sand mixed hot, I of sulphur to I of sand stood 650 Ibs. 
 
 27 
 
per sq. in. ; 5 of sulphur to 7 of sand stood 670 Ibs. per sq. 
 in. ; 2 of sulphur to i of sand stood 400 Ibs. per sq. in. 
 Mr. Potter found that fine sand such as quicksand gives 
 better results than coarser sand. These strengths were 
 shown as soon as the sulphur was cold. This is analogous 
 to the action of Portland cement. When very finely 
 ground, it has an overdose of cement and not sufficient 
 inert substance to be cemented together. When sand 
 is added till a balanced mixture is formed, the mortar 
 is strong. Sometimes sand and cement tests pull up 
 stronger than neat cement. Cement reground with sand 
 is made much finer and will take in more sand to form a 
 balanced mixture. The mixture may be unbalanced by 
 having too much cement, as in the sulphur tests, where 
 more sand added makes the specimen stronger; or it may 
 be unbalanced by having too much inert substance to have 
 the interstices filled by the cement, as in lean mixtures of 
 sand and cement. 
 
 That Portland cement is a mixture of a cementing sub- 
 stance (the finest powder) and an inert substance may be 
 shown by the following experiment. Take a little cement 
 and mix it in about ten times its volume of hot water. 
 Let this boil for several hours, adding more water as re- 
 quired. At the end of this time stir up the mixture and 
 pour it rapidly into a tumbler. Almost immediately there 
 will be a settlement of part of the cement, which is of a 
 dark color. Upon this there will settle a light colored 
 part of the cement, leaving the water comparatively clear. 
 A distinct line will separate the dark colored and the light 
 colored parts. The upper layer will be slimy at first then 
 gellatinous, and will finally (in a week or two) attain a 
 slaty hardness. Upon drying it becomes like chalk and 
 has little cohesion. The lower layer, which in an experi- 
 ment by the author was about equal in volume to the up- 
 per layer, is like sand and has little cohesion. It can be 
 crumbled in the fingers. The upper layer is the slime or 
 laitance or true cement that is liberated in an excess of 
 water, when concrete is mixed. The fineness of the grinding 
 
 23 
 
will no doubt gage the relative amounts of inert and ac- 
 tive substance in the cement. In a repetition of this ex- 
 periment the cement was allowed to settle in a glass, and 
 the water was poured off. The separated cement was then 
 mixed together into a mortar and allowed to harden. 
 It hardened into a cohesive and hard lump. 
 
 By the use of cold water and long continued agitation 
 a partial separation can be effected, but enough of the fine 
 dust seems to adhere to the inert particles to cement them 
 together. The light and dark colors will be present but 
 they will not be so clearly defined. 
 
 Some tests presented in a paper by Messrs. Henry S. 
 Spackmand and Robert W. Lesley, read before the As- 
 sociation of American Portland Cement Manufacturers at 
 their annual convention in 1907 (See Eng. Record, Dec. 
 21, 1907, p. 691,) prove very conclusively that a large 
 part of commercial Portland cement is inert on account 
 of not being fine enough to have any activity. Briquettes 
 of neat cement were made and at periods of from 7 days 
 up were tested. At 28 days they stood a tensile test of 
 752 Ibs. per sq. in. These broken briquettes were then 
 dried and reground. This material was used as cement 
 and made into briquettes, which stood, at 28 days, 253 Ibs. 
 per sq. in. These broken briquettes were dried, reground, 
 and used again as cement. The briquettes stood 163 Ibs. 
 per sq. in. at 28 days. Tests were made at other periods, 
 and mortar tests were made with sand. The above illus- 
 trates what the tests demonstrate. In the words of the 
 experimenters "These experiments clearly show that 
 even after cement has been twice gaged with water and 
 allowed to harden under water, all the cementing and hy- 
 draulic qualities are not destroyed." It is clear that the 
 regrinding of the briquettes broke up particles that were 
 not fine enough to be active at the first and second gagings. 
 
 The paper above referred to describes other experiments 
 
 that further strengthen the conclusion that the finest 
 
 ground Portland cement is composed largely of inert 
 
 clinker, too coarse to be active. Quoting the paper again. 
 
 29 
 

 "Portland cement which had passed the 20O-mesh sieve 
 was further separated by elutriation into the following 
 parts : (A) Material that settled out in 30 seconds ; 
 (B) Material that remained in suspension for 30 seconds, 
 but settled out in one minute; (C) Material that re- 
 mained in suspension for more than one minute. The ce- 
 ment thus divided into three portions according to size 
 was treated with water in tightly stoppered tubes. "A" 
 was only slightly acted upon by water, even after two 
 years contact with it. "B" was only acted upon by water 
 after three or four months, and only a portion became 
 fully hydrated. "C" was acted upon almost immediately, 
 swelling up and forming a very voluminous jelly." [Elu- 
 triation is shaking up in dry kerosene and allowing to set- 
 tle. The amount of this cement that settled in 30 seconds 
 is not stated. In another sample 45.18 per cent, settled in 
 this time.] 
 
 When a substance crystallizes, the crystals assume a 
 definite volume and have not the property of swelling to 
 a larger volume or of occupying less space. Further, these 
 crystals have the property of exerting pressure to reach 
 that given volume, as exhibited in crystals that form in 
 the pores of soft stone swelling with such force as to crack 
 the stone. Sound cement will not swell with force as 
 crystallizing substances do. It is true that cement that 
 hardens under water will swell slightly, but the same ce- 
 ment hardening in the air will shrink, proving the lack 
 of definite volume in the hardened cement. On the other 
 hand cement that is not confined by the inert particles 
 pressing against it can be made to swell to fill a space 
 much larger than its original volume. The minute grains 
 of cement, if they are finely broken up, have the property 
 of swelling to many times their size by the absorption of 
 water and hardening in water or in air. If abundance of 
 water be present, the grains will swell up to a larger size 
 and make a more dense and a stronger mortar; and, if 
 the water be present for a sufficient time, the cement 
 will unite with some of it and harden in this larger vol- 
 
 30 
 
time. Upon being taken out of the water after being 
 thoroughly hardened the cement does not then contract 
 in drying out, but the surplus water dries out of the min- 
 ute pores in some such way as a cork that has been soaked 
 in hot water dries out, though the water would not pass 
 through the pores of the cork in a liquid state. 
 
 The amount of water permanently retained by the ce- 
 ment in an ordinary concrete mixture or in mortars of 
 about i :3 is about 16 to 18 per cent, of the weight of the 
 cement. In neat cement only about 8 to 12 per cent, is re- 
 tained. This is further evidence of the fact that the hard- 
 ening of cement is not a crystallizing process. Crystals 
 have a definite amount of water in their composition. It 
 is evidence also that the pure cement will swell and ab- 
 sorb water in proportion to the space to be filled and the 
 amount of water present, as the voids in mortar are much 
 greater than in neat cement ; also the amount of water 
 present, even in mealy concrete, is greater than needed in 
 neat cement mortar. These facts would further seem to 
 vitiate the contention of those who say that only the bare 
 amount of water for the needs of the cement should be 
 used in the mixing, since cement under varying conditions 
 will combine with different amounts of water. 
 
 When cement is mixed with a meagre amount of water, 
 the grains do not have the conditions present that promote 
 free swelling to fill the voids. The result is that the mor- 
 tar or concrete is porous, that is, full of large pores that 
 allow the passage of water. It is an erroneous belief that 
 the impermeability of concrete is promoted by using a 
 meagre amount of water in mixing and tamping this con- 
 crete. 
 
 It is well known that concrete can be made quite good 
 that is deposited in water and it is well known that speci- 
 mens that are kept in water after setting will, upon hard- 
 ening, be very much better and stronger than like speci- 
 mens hardened in air. It is not clear why authorities, 
 in the face of these facts, warn against the use of plenty; 
 of water in the mixing. 
 
 31 
 

 Dr. William Michaelis, in a paper read at the annual 
 meeting of the Association of German Portland Cement 
 Manufacturers at Berlin in Feb. 1907 (See Cement and 
 Engineering News, Aug. 1907) describes a piece of arti- 
 ficial stone made of Portland cement and 10 or 20 per 
 cent, of asbestos fiber. The mixture was stirred a long 
 time, as paper pulp is stirred, and then pressed to expel 
 the surplus water. The volume of the stone was many 
 times that of the volume of the cement used in the mix- 
 ture, showing that the cement had swollen by the absorp- 
 tion of water to attain this volume. Dr. Michaelis says 
 of this stone that it is rightly named eternite, for it is 
 practically everlasting. The stone resembles slate. There 
 is a company that makes this kind of artificial stone for 
 shingles. According to those who advocate a mealy mix- 
 ture for concrete this stone would be expected to be por- 
 ous and totally unfit for shingles on account of the large 
 excess of water used in making it. The presence of the 
 asbestos fiber and the long continued agitation hold the 
 grains of cement apart and allow them to swell by the ab- 
 sorption of water. 
 
 Pure cement when placed in water will swell to many 
 times its volume measured as a dry powder, if not confined. 
 In commercial neat cement, however, the particles of in- 
 ert clinker act to confine the pure cement and prevent the 
 swelling. If there is plenty of water in the mixture, and 
 the cement is well mixed through the mass, the cement 
 will swell to fill the voids and will bind together the in- 
 ert particles making a stronger and better concrete than 
 can be made by a mealy mixture, even with pressure ap- 
 plied in the manufacture. If the swollen cement dries 
 out before it has hardened, the concrete will shrink. This 
 is the reason why cement or concrete hardened in water 
 will swell, and, if hardened in the air, it will shrink. This 
 is the cause of shrinkage cracks in work that has not been 
 kept moist during hardening. 
 
 Tests for soundness or constancy of volume in neat 
 cement may be misleading, because of the fact that the 
 
 32 
 
best cement, that is, the finest ground cement and, other 
 things being equal, that most suitable for concrete, may 
 show the poorest results. The greater proportion of very 
 fine flour gives the better cement a tendency to swell, 
 whereas, a cement containing less fine . flour and more 
 inert clinker might show greater constancy of volume. 
 
 Cements that do not. show up well in neat tests for 
 constancy of volume may be quite sound in mortar or 
 concrete, though of course the cause of swelling in a test 
 may be the presence of free lime or magnesia and may 
 have no relation to the fineness of grinding. 
 
 lame. 
 
 Lime, while it is not ordinarily used in making concrete, 
 is of importance because of its use in mortar and be- 
 cause it may be made use of in decreasing the permeabil- 
 ity of cement concrete, also because it is one of the con- 
 stituents in the manufacture of slag cement. 
 
 Common lime is made by roasting or burning lime- 
 stone, or carbonate of calcium. The roasting reduces the 
 carbonate to oxide of calcium or quick-lime. Quick-lime 
 usually contains from 5 to 10 per cent of impurities. The 
 impurities retard the process of slaking, so that lime should 
 be slaked several days before it is used in mortar, so as 
 to be thoroughly slaked when placed in the wall. The 
 swelling of lime in slaking would be detrimental to the 
 strength of the wall. Lime may be slaked and packed in 
 barrels for an indefinite length of time, or it may be kept 
 in the mixing boxes covered with sand. It is when lime 
 mortar is exposed to the air and absorbs carbon di-oxide 
 therefrom that it becomes hardened and that it acts to 
 cement together the bricks or stone of a wall. Kept in 
 the form of a paste, with only the surface of the mass 
 exposed to the air, this absorption of carbon di-oxide will 
 not take place to any great extent. Quick-lime, if ex- 
 posed to the air, will absorb not only moisture, but car- 
 bon di-oxide as well. Air slaked lime will make weak 
 
 33 
 
mortar on account of the premature absorption of the 
 C O 2 and the formation of what is commonly known as 
 whiting. Lime should therefore be fresh-burned. 
 
 Neat lime would be of little use as a cementing mater- 
 ial on account of its weakness and the necessity of its 
 being in thin layers to enable the air to have access to it. 
 It should be used only to fill the voids in some material 
 such as sand or brick dust. 
 
 A barrel of lime will make about eight cubic feet of 
 stiff paste. The weight of a barrel of lime is 230 pounds. 
 This is three bushels or 3.75 cu. ft.. 
 
 Lime comes in lumps, as it needs no grinding after 
 burning, on account of the fact that the action of the 
 water in slaking breaks up the lumps into a powder. If 
 the lime is found in a powder, it indicates that it is air 
 slaked. The slaking of lime requires about two parts 
 by weight of water to one of lime. 
 
 Fat or rich lime is lime made from pure or nearly pure 
 carbonate of calcium. Dolomite is a limestone contain- 
 ing magnesia. Lime made therefrom is poor or meagre, 
 that is, slow in slaking and not fat or rich. 
 
 Hydrated lime is a product lately come into extended 
 use for the various purposes for which slaked lime may 
 be used. This is a very fine white powder produced by 
 slaking in a rotary pan quick-lime that has been broken up 
 into small lumps. Sufficient water is used to slake the 
 lime and still leave it hot enough to drive off the surplus 
 water, leaving a dry powder. This powder is sifted or 
 screened to remove unburned or unslaked lime and any 
 coarse particles. The hydrated lime is sold in sacks. 
 This is used in mortars : in the manufacture of sand-lime 
 bricks and of slag cement ; in hard wall plasters, either 
 mixed with Portland cement or gypsum products ; as an 
 addition to Portland cement mortar to make it more 
 easily worked and to retard the settling; in rendering con- 
 crete more dense and waterproof. 
 
 The action of lime in the manufacture of what are called 
 sand-lime brick is quite different from its action in or- 
 
 34 
 
dinary mortar. Part of the sand used in making sand- 
 lime brick is very finely ground, and thus rendered ac- 
 tive in some such way as the inert clinker from which 
 hydraulic cement is made is rendered active by grinding. 
 The bricks are cured in steam under pressure and the 
 presence of C O 2, instead of being necessary, is undesir- 
 able. The chemical action is between the lime and the 
 finely powdered sand. 
 
 Sand. 
 
 Sand is the term commonly applied to small particles 
 of quartz; it is also used to designate small particles of 
 stone such as crusher dust or very small gravel. The 
 maximum size of grains admitted under the term sand 
 is sometimes as large as % in., while sometimes finer 
 sand is required. Ordinarily about one-sixteenth of an 
 inch is the maximum size of grain. 
 
 Standard sand, used in making mortar tests, is crushed 
 quartz that passes a sieve with 20 meshes to the inch and 
 is retained on a sieve of 30 meshes to the inch. 
 
 Sand with angular grains is called sharp sand. Bank 
 sand is usually a sharp sand, while river and sea sand 
 generally have rounded grains on account of the wearing 
 of the particles on each other. Formerly specifications 
 generally called for sharp sand. The sharpness of sand has 
 been found to have but little relation to its value in ce- 
 ment mortar or in concrete, and sharp sand is not so 
 often demanded. The most important quality in sand is 
 the grading of the sizes of grains from coarse to fine. 
 
 If spheres of equal size and having radii of unity be 
 stacked so as to have the least percentage of voids, each 
 may be considered as enclosed in a solid having 12 faces, 
 each of which is a rhombus whose long diagonal is 2 and 
 whose short diagonal is the square root of 2. The vol- 
 ume of the sphere is 74.05 per cent, of that of the solid. 
 The voids, therefore, in a stack of spheres placed as com- 
 pactly as possible would be nearly 26 per cent As sand 
 
 35 
 
is composed of more or less rounded grains, we would 
 look for a percentage of voids approaching this. How- 
 ever, on account of the friction it is difficult to compact 
 sand of grains sifted to a uniform size to a density show- 
 ing less than about 44 per cent, of voids. It is found 
 that the voids in compacted sand of varying sized grains 
 amount to about 30 per cent. The percentage in ordin- 
 ary sand varies between 30 and 45. 
 
 In general sand having a large sized maximum grain, 
 that is, coarse sand, is a stronger sand for mortar or con- 
 crete than fine sand. Many fine sands are unfit for use 
 in mortar and concrete. Such sands could be improved 
 by the addition of a coarse sand, using a quantity of 
 each in the mixture for mortar or concrete. By making 
 several mixtures and comparing tests therefrom with a 
 standard a satisfactory sand may be obtained, and fine 
 sand that might be available and cheap could, by the pur- 
 chasing of some coarse sand, be made use of to advantage. 
 If only fine sand is available, its weakness may be counter- 
 acted by the use of a larger proportion of cement. 
 
 Sand containing much mica is apt to be weak, as mica 
 will not adhere well to the cement. 
 
 Sand should not contain much foreign substance of a 
 soft nature, such as clay or silt. If this foreign sub- 
 stance is in the shape of lumps, it is especially bad, as 
 these will make weak spots in the concrete. Lumps should 
 be eliminated by sifting in preference to washing. Fine 
 particles of clay in sand, found naturally in the same and 
 thoroughly mixed through the mass, do little or no harm. 
 Clay has been found by some experimenters to reduce the 
 strength and by others to increase it. The reason for 
 this discrepency is no doubt found in the difference in 
 the nature of the clay. If the clay is added to the sand, 
 the probabilities are that it will weaken the mortar, un- 
 less the clay is first finely ground. If the clay is found 
 in the sand naturally, it will probably add to the strength, 
 because it is then more apt to be in a finely ground state. 
 It is only when the clay is in the finest kind of a powder, 
 
or, if moist, in a finely divided state, and thoroughly 
 mixed through the mass that it has a beneficial effect on 
 the mortar. 
 
 Many tests have shown sand containing 5 to 10 per 
 cent, or more of fine clay to be stronger in a mortar than 
 clean sand. A little clay increases the density of the 
 mortar. Sand containing more than 10 or 15 per cent, 
 of clay or silt should be used only after thorough tests 
 and not at all on such work as reinforced concrete. The 
 ultimate effect of the clay on the life of the concrete is a 
 matter of doubt, even though short time tests do show an 
 increase of strength because of its presence. In mas- 
 sive concrete the sand may contain 10 to 15 per cent, of 
 clay and still be suitable. In reinforced concrete it should 
 contain no more than 5 or 10 per cent. In concrete blocks 
 no more than 5 per cent, should be allowed. Trie richer 
 the mixture, in general, the greater the detrimental effect 
 of foreign substances in the sand. Clay is less harmfull 
 in coarse sand than in fine sand. It helps to fill the 
 voids in coarse sand, while it holds the particles of sand 
 apart in fine sand. 
 
 If sand is found to contain an excess of clay, it can 
 be washed to remove the clay. Washing, however, be- 
 sides being expensive is liable to take out the fine grains 
 of sand, which are of great importance, as these fill the 
 small voids and make the concrete dense and strong. 
 The washing of sand may be done by use of an inclined 
 trough with a gate at the low end. Sand is placed at 
 the high end and played upon with a hose. The clean 
 sand settles at the low end of the trough, and the dirty 
 water flows over the gate. Sand should be tested, washed 
 and unwashed, to determine whether washing is profit- 
 able. 
 
 If sand is ignited, clay will be broken up, and to some 
 extent burnt, and thus rendered less harmful on account 
 of being more durable. This, too, would be an expensive 
 operation. 
 
 Dirt in sand is to be viewed with suspicion. Natural 
 
 37 
 

 sands are seldom found mixed with soil, unless it be for 
 a small depth on the top of the bed. The dirt may have 
 been incorporated into the sand as a result of handling. 
 At the site the sand should not be laid in the dirt, as the 
 last of it, when shoveled up may contain an excessive 
 amount of dirt and be the cause of a weak batch of con- 
 crete. 
 
 Good clean sand may be mixed with sand containing 
 an undesirable amount of clay and the mixture made 
 acceptable by this means. This would be preferable, in 
 some cases to washing and losing the fine particles. 
 
 The best material for good strong concrete is coarse, 
 clean sand. 
 
 Sea sand contains alkaline salts which induce efflor- 
 escence. These should be dissolved out with fresh water. 
 
 Stone dust or screenings are sometimes found superior 
 to sand in mortar tests. 
 
 Dry sand weighs ordinarily from 90 to loo Ibs. per cu. 
 ft. A common weight assumed for ordinary sand is 2600 
 Ibs. per cu. yd. Sand having very large and very small 
 grains may weigh as much as 117 Ibs. per cu. ft. or more 
 than 3000 Ibs. per cu. yd. 
 
 The specific gravity of quartz is 2.65, hence a solid 
 block of one cu. ft. would weigh 165 Ibs. The voids In 
 quartz sand may be calculated from the weight per cu. ft. 
 by noting the per cent, that it falls short of 165. Pure 
 sand weighing 100 Ibs. per cu. ft. has close to 40 per cent, 
 of voids. 
 
 Besides its use as a constituent of concrete and mor- 
 tar sand is used in casting artificial stone blocks. For 
 this purpose the sand is made use of just as in a foun- 
 dry. It is found to absorb the surplus water In the mix- 
 ture, and this keeps the mold moist. 
 
 
 38 
 
Aggregates. 
 
 The term aggregate is used by the author to mean the 
 solid inert part of concrete not included in the term 
 sand, and not, as used by some writers, to include the 
 sand. This is the rational use of the term. There is 
 need of a single word to apply to the third term in the 
 ratio of a concrete mixture, on account of the variety of 
 substances that may be employed. A 1 :2 14 concrete means 
 in America a mixture of one part, by volume, of ce- 
 ment to two parts of sand (whether this be siliceous 
 sand or rock screenings) to four parts of aggregate. 
 This use of the term is very common and convenient. 
 Anyone who would force a different meaning to a term 
 in common use, because of fancied perversion of its true 
 meaning, is commended to the work of restoring the 
 word manufactured to its true meaning, "hand made." 
 
 The aggregates used in concrete are usually gravel, 
 broken stone, and cinders. Besides these shells, broken 
 bricks, and slag are sometimes employed. 
 
 Gravel, when it comes in assorted sizes, is a very good 
 material for concrete from several standpoints. First, it 
 is usually hard and durable stone that has withstood at- 
 trition, and is the result of natural selection. Second, 
 the stones, being round, will, if graded in size, make a 
 dense mixture, and the denser the mixture of a given 
 material the stronger the concrete. Third, gravel will 
 resist fire better than many other kinds of stone. The 
 round, smooth surface of gravel is not as good a surface 
 for the cement to take hold of, and for this reason bro- 
 ken stone concrete may be stronger, though it may not be 
 as dense as gravel concrete. However, the density of 
 gravel often overcomes this, and gravel concrete is some- 
 times stronger than stone concrete. Some experimenters 
 have found gravel to be stronger than broken stone in 
 concrete. The surface of gravel concrete cannot be tooled 
 as well as that of broken stone concrete, Because the 
 gravel stones break out under the force of the tool. 
 39 
 
Crushed gravel is sometimes used in concrete. This is 
 a very good material, if the gravel is a good clean vari- 
 ety. 
 
 Gravel is apt to be mixed with dirt, either in the form 
 of lumps of coal or of slimy covering on the stones, or, 
 as in the case of sand, in the form of an admixture of 
 clay, mud, or silt. Such gravel should be washed or re- 
 jected. The objection to the washing of sand does not 
 apply with the same force to gravel, as the gravel is not 
 required to contain the very v iine particles that should be 
 a constituent of all good sand. 
 
 Broken stone should be hard and durable. Concrete 
 cannot be strong if made of weak stone. The stones 
 should not have incipient cracks, so that they will crush 
 under the rammer. They are best to be nearly cubical, 
 at least not in flat flakes, as such stones will not pack well. 
 The stone should be uniform, that is ; there should not 
 be just a few of the largest size of stones, or an excess 
 of the same; also there should not be an excess of dust, 
 say not over 15 per cent, of very small particles. The 
 whole pile, as well as different deliveries should be well 
 mixed, so that different batches of concrete will be as 
 near alike as possible. There should not be over one 
 per cent, of rotten stone. Unloading of the stone is apt to 
 separate the large stones from the small ones. Dumping 
 in dirty places may result in a large quantity of dirt 
 getting into a batch of concrete. 
 
 The kinds of stone generally used are trap, limestone, 
 and sandstone. Trap is the best of these, as it is harder 
 and stronger than the others and is a better fire resistant. 
 Hard limestone is good and durable, except as to its abil- 
 ity to withstand fire. It will calcine or turn to lime un- 
 der heat. Sandstone is not as strong as the others. 
 
 In an aggregate such as gravel and broken stone used 
 in concrete strength and density are desired. These are 
 closely related. The mixture that will pack the closest 
 will give the strongest concrete in a given quality of 
 stone. The voids in broken stone usually run from 40 to 
 
 40 
 
5o per cent, of the volume. These voids must be filled 
 up with mortar, or the mixture of sand and cement in 
 the concrete. The smaller the amount of voids the better 
 will be the concrete. Tests have shown the unexpected 
 in the matter of the sizes of the broken stone or gravel, 
 namely; that ftie mixture that has the largest maximum 
 size of stones, if the sizes are properly graded, will be 
 the densest and strongest. Many specifications, particu- 
 larly earlier ones, read as though it were a serious fault 
 to have sizes of stones too large to pass through a given 
 sized "ring," and many of these same specifications re- 
 quire also that screenings be rejected from the mixture. 
 Both of these requirements are detrimental to the strength 
 of the concrete. A mixture in which the medium size of 
 stones predominates will not be a dense mixture; the 
 exclusion of large stones and very small ones tends to 
 produce this very condition. It is well known that stones 
 of large size have less surface for a given weight, hence 
 there is less surface to cover with cement in concrete of 
 large aggregates, besides less voids to fill. However, 
 there are practical reasons for limiting the maximum size 
 of stones in most concrete work. Some of these are the 
 danger of air spaces forming under large stones and of 
 their arching and leaving voids not filled with mortar. 
 
 Given an aggregate having a certain maximum size 
 of stones, the densest and best mixture will be found 
 when about one-third of the weight is composed of pieces 
 less than one-tenth of the maximum dimension, and one- 
 third is composed of pieces between one-tenth and one- 
 half of the maximum, and one-third is composed of pieces 
 more than one-half of the maximum. For example, sup- 
 pose a mixture has stones that will measure not over one- 
 inch maximum size. One-third of this mixture should 
 pass through a sieve having 10 meshes to the inch, and 
 two-thirds of the total should pass through a sieve hav- 
 ing two meshes to the inch. There should be graded 
 sizes in all the aggregate, from the largest to the smallest 
 
 41 
 

 size, to fill the graded sizes of voids that will of necessity 
 occur. 
 
 In general, in a concrete mixture, an aggregate having 
 a large maximum size of stones demands a sand of large 
 maximum size of grains, while an aggregate having a 
 smaller maximum size of stones should have a sand of 
 small maximum size of grains. Thus, if the maximum 
 size of stones is 2*/& in., the maximum size of sand grains 
 may be *A in., and if the maximum size of stones is ^ 
 in., that of the grains of sand may be 1/16 in. This con- 
 sistency should be observed in order to have graded sizes 
 in the entire mixture. 
 
 Rock dust was formerly considered objectionable in an 
 aggregate. It is now generally recognized that this is 
 very valuable in concrete, as it fills the smaller voids and 
 makes the concrete more dense. Of course, if this dust 
 is rotten stone ground up, it should be screened out. If 
 the rock dust is not uniformly distributed it may be best 
 to screen it out and use it as sand. 
 
 The aggregate for small work should have small sizes 
 of stone. In reinforced concrete beams and columns the 
 maximum size of stones should generally be % in. to I in. 
 In arches a good size, if no small meshes are employed in 
 the steel reinforcement, is 2 in. to 2 1 /& in. The reason 
 that the stones should be small is so that they will pack 
 around the reinforcement and not leave voids. In walls 
 and heavy work large sized stones are not objectionable. 
 Rubble concrete, sometimes called cyclopean concrete, is 
 concrete in which large stones are embedded. These may 
 be almost any size convenient to handle. They should 
 not be placed near the surface or close to each other. 
 Rubble concrete is used in massive work. In some con- 
 crete work large boulders are placed against the forms 
 for appearance, to give a rustic look. 
 
 The weight of broken limestone per cu. ft. is about 85 
 to 95 Ib. or about 2300 to 2600 Ib. per cu. yd. Gravel and 
 broken trap weigh 2800 to 3000 Ib. per cu. yd. 
 
 42 
 
Cinders are often made use of in concrete. Cinder con- 
 crete is very useful in filling in between the sleepers in 
 buildings. It could also be made use of in filling in the 
 spandrel of a stone or concrete arch. If the cinders are 
 well burned and free from lumps of coal, cinder concrete 
 makes an excellent fire protection. It is light in weight 
 and porous and a very poor conductor of heat. It has 
 the further advantage that nails can be driven into it 
 with ease for a month or two after it has set. Cinder 
 concrete is not very strong. Cinders usually contain much 
 sulphur. Steel laid in cinders, if moisture be present 
 will rapidly corrode, on account of the formation of sul- 
 phuric acid, due to oxidation of the sulphur and addition 
 of water. Iron or steel pipe laid in a cinder fill should 
 be surrounded by concrete or at least by clay. Cinder 
 concrete 1 :2 14, mixed wet, is probably as good a protec- 
 tion for steel as stone concrete. Cinders for concrete 
 should be clean. It is sometimes necessary to wash them 
 and to sift out the ashes as well as to break up the large 
 clinkers. 
 
 In some localities there are large deposits of shells, 
 which, mixed with sand and cement, make a good con- 
 crete. Tests of any such substances should be made to 
 determine the best mixture and the strength. 
 
 Slag is used to some extent in making concrete. Or- 
 dinary broken slag does not seem to be a desirable aggre- 
 gate on account of its unstable chemical composition. 
 This is especially true of fresh slag. Seasoning may dis- 
 solve out the undesirable chemical compounds. When 
 molten slag is run into water, it is granulated, and much 
 of the objectionable sulphur is washed out. Pulverized 
 and mixed with slaked lime alone this granulated slag 
 can be made into bricks or blocks. 
 
 Crushed marble is employed in the manufacture of some 
 brands of artificial stone. This may be mixed with ce- 
 ment alone. 
 
 43 
 
Mortar. 
 
 Mortar may be lime and sand, neat cement, cement and 
 sand, or cement, lime and sand. 
 
 Lime mortar is made of one part of lime paste to about 
 3 or 4 parts of sand. The New York Building Code gives 
 1 :4 as the proportion. The volume of the resulting mortar 
 is about equal to that of the sand. Common lime mortar 
 will not set in water. It takes a long time for it to set 
 in a damp place. If air is excluded, it will never set. 
 Nevertheless some water is required in the setting process, 
 and lime mortar suddenly dried will be killed. Hence 
 it is well to moisten bricks before they are laid in lime 
 mortar, especially if they are porous. Lime mortar should 
 not be used in very thick walls or in very thick joints; 
 also it is unsuitable for making concrete. The reason for 
 this is twofold: in the first place air must have access to 
 the mortar to harden it; in the second place the small ten- 
 sile strength of the mortar makes it weak to resist lateral 
 flow, and it is consequently of little use in overcoming 
 compression in a mass. The ultimate tensile strength of 
 lime mortar is about 20 to 50 Ibs. per sq. in. The com- 
 pressive strength depends largely upon the thinness of 
 the joints. Cubes of mortar, when tested in compression 
 stand but little; but, when the sand is confined in joints 
 between bricks or stone, the adhesive strength of the ce- 
 menting lime is taxed less, hence a greater crushing 
 strength can be withstood. The report of tests made in 
 1884 at the Watertown Arsenal show cubes of lime mor- 
 tar to stand 120 Ibs. per sq. in. in crushing. The same 
 report shows brick piers built with lime mortar to stand 
 from about 1000 Ibs. to 2000 Ibs. per sq. in. The strength 
 of a wall laid in lime mortar will be gaged not so much 
 by the strength of the brick as by that of the mortar, 
 since lime mortar, even confined in joints, is only about 
 one-tenth to one-fifth as strong as ordinary brick. Lime 
 mortar requires about a month to set sufficiently to re- 
 ceive any considerable load, but it continues to harden 
 
 44 
 
indefinitely. In plasters, gypsum or plaster of Paris is 
 often added to hasten the setting. Dry and thoroughly 
 set lime mortar weighs about no Ibs. per en. ft. 
 
 Lime mortar is greatly improved by adding cement, 
 either Rosendale or Portland. The strength is increased, 
 and the time of setting is shortened. On the other hand 
 cement mortar for brick or stone work is improved by 
 the addition of lime. It is made easier to work with the 
 trowel ; it does not set up so quickly, giving more time 
 to place it; the adhesive value is improved on such sur- 
 faces as concrete blocks. A common mixture is that of 
 equal volumes of I to 3 lime mortar and i to 3 cement 
 mortar. The mixture of the two mortars is called cement 
 and lime mortar. Lime paste or hydrated lime may be 
 added to cement mortar without being first mixed with 
 sand. The addition of 10 to 25 per cent, of lime paste 
 to cement mortar will decrease its permeability and makes 
 it more adherent to old concrete and to concrete blocks. 
 Lime paste is used in making some artificial stone, of 
 sand and cement, to increase the density. 
 
 The addition of 10 to 20 per cent, of hydrated lime does 
 not destroy the hydraulic property of Portland cement. 
 Cement mortar to which lime is added will attain greater 
 strength when stored in water, after a day or two in 
 air, than when kept in air only. Mr. H. B. Nichols, in a 
 letter in Eng. News, Dec. 5, 1907, describes some tests 
 on adding lime paste to I -.3 Portland cement mortar and 
 i :2 natural cement mortar. It was found that from 4 to 
 20 per cent, of lime paste added to natural cement mor- 
 tar increased the strength on an average 25 per cent. 
 Percentages of lime below 20 did not seriously weaken 
 Portland cement mortar; greater percentages did weaken 
 it. The briquettes required to be kept in air 48 hours 
 before being stored in water. Lime increased the adhesion 
 of mortar very materially. 
 
 Tests from the Government report above referred to 
 for blocks of cement and lime mortar, one part cement 
 mortar and two of lime mortar, showed a strength in 
 45 
 
compression of 175 to 200 Ibs. per sq. in., Portland and 
 Rosendale cement showing about equal strength. Brick 
 piers in similar mortar showed a compressive strength of 
 about 1500 Ibs. per sq. in. 
 
 Cement without sand, or neat cement, is not very often 
 made use of. It is, however, useful in setting anchor 
 bolts in drilled holes in stone work and is considered bet- 
 ter than lead or sulphur for this purpose. The ultimate 
 adhesive strength is about 400 to 500 Ibs. per sq. in. of 
 surface of bolt in contact with cement. Blocks of neat 
 Portland cement about 2 years old showed a compressive 
 strength of about 5000 Ibs. per sq. in. Broad, flat blocks 
 showed a strength two or three times as great (Govt. 
 Report, 1884), showing that in joints between bricks the 
 crushing strength of neat Portland cement is ten to fif- 
 teen thousand pounds per sq. in., or about the strength 
 of good hard brick. 
 
 A series of tests that serve to show not only the ten- 
 sile strength of neat cement of the average American 
 brand but also the quality of the cement and the strength 
 of 1 13 mortar is that made in 1900 by the Dept. of Public 
 Works of Philadelphia on 8 different brands of Ameri- 
 can Portland cement. In all over 4000 tests were made. 
 The averages of the results from the different brands are 
 as follows : 
 
 99.4% passed through a No. 50 sieve. 
 
 90.3% passed through a No. 100 sieve. 
 
 75.6% passed through a No. 200 sieve. 
 
 Specific gravity, 3.124. 
 
 Time of initial set, 73.6 minutes. 
 
 Time of hard set, 358.2 minutes. 
 
 Rise of temp, of paste in setting, 5.4 degrees. 
 
 46 
 
Ultimate Tensile Strength. Pounds per Square Inch. 
 
 1 13 Std. 
 Quartz Sand 
 Neat. 
 
 1 day 449 88 
 7 days 724 234 
 
 28 days 792 311 
 
 2 mos. 792 323 
 
 3 mos. 803 327 
 
 4 mos. 831 329 
 6 mos. 818 333 
 
 A later summary of average results of cement tests 
 made in the Philadelphia laboratories is the following 
 given by Mr. E. S. Lamed in a paper read before the A. 
 A. P. C. M., Atlantic City, N. J. Sept. 1907. 
 
 Proportions Tensile Strength, Ib. per sq. in. 
 
 
 
 
 7 
 
 28 
 
 2 
 
 3 
 
 4 
 
 6 
 
 12 
 
 
 
 
 days 
 
 days 
 
 mos. 
 
 mos. 
 
 mos. 
 
 mos. 
 
 mos. 
 
 Neat 
 
 cement 
 
 710 
 
 768 
 
 760 
 
 740 
 
 732 
 
 758 
 
 768 
 
 i to 
 
 i 
 
 mortar 
 
 590 
 
 692 
 
 690 
 
 680 
 
 680 
 
 685 
 
 695 
 
 i to 
 
 2 
 
 mortar 
 
 370 
 
 458 
 
 460 
 
 455 
 
 453 
 
 458 
 
 460 
 
 I to 
 
 3 
 
 mortar 
 
 208 
 
 300 
 
 310 
 
 310 
 
 3io 
 
 310 
 
 308 
 
 i to 
 
 4 
 
 mortar 
 
 130 
 
 2TO 
 
 230 
 
 230 
 
 230 
 
 232 
 
 232 
 
 i to 
 
 5 
 
 mortar 
 
 80 
 
 150 
 
 185 
 
 195 
 
 195 
 
 195 
 
 197 
 
 The above tabulation was interpolated from the dia- 
 gram of cement mortar tests prepared by Mr. W. Purves 
 Taylor. The results of the neat tests and the 1 13 mortar 
 tests (i. e. one part cement to three parts crushed quartz, 
 by weight) are averaged from over 100,000 tests, while the 
 other results are based on from 300 to 500 tests. (See 
 Concrete, Oct. 1907.) 
 
 One volume of Portland cement, measured loose, mixed 
 with one-third of a volume of water will shrink to .78 
 of a volume of stiff cement paste. A volume of Rosen- 
 dale cement and .4 of a volume of water will make about 
 the same amount of paste as the Portland. It takes 6.75 
 bbl. of cement to make one cu. yd., measured loose, hence 
 
 47 
 
a cu. yd. of cement paste would require 8.65 bbl. of ce- 
 ment. This is on the basis of 4 cu. ft to a barrel of ce- 
 ment. A bag or quarter barrel of cement is accepted by 
 many engineers as a cubic foot. Sample bags should be 
 measured and weighed to see that this holds true. 
 
 The office of cement in mortar is to fill the voids in 
 the sand and at the same time cement the particles to- 
 gether. The voids in sand are about one-third of the vol- 
 ume. A mixture of one part of cement to three of sand 
 will therefore give a correct proportion on this basis and 
 result in a volume of mortar not much if any, more than 
 that of the sand. This is the common mixture for ce- 
 ment mortar. The richer the mortar in cement the great- 
 er will be its tensile strength. The compressive strength 
 does not increase in the same proportion, but depends some- 
 what on the thinness of the joints. For brick work or 
 cut stone work there is no advantage in using richer mor- 
 tar than i -.3 if the wall is to be in compression only. In 
 concrete or rubble work richer mortar by its greater ten- 
 sile strength prevents lateral failure under compressive 
 stresses. 
 
 Richer mortar than i :3 will occupy more space than the 
 volume of the sand. One volume of average sand can be 
 estimated to give one volume of 1 13 mortar ; 0.9 volume 
 of sand can be estimated to give one volume of i :2 mortar ; 
 0.7 volume of sand will give one volume of 1:1 mortar. 
 One cu. yd. of 1 13 mortar will require about 2*/4 bbl. of 
 Portland cement ; one cu. yd. of 1 12 mortar will require 
 about 3 bbl. of cement; one cu. yd. of 1:1 mortar will re- 
 quire about 4.7 bbl. of cement. 
 
 Mortars are generally mixed by volume in actual con- 
 struction. In laboratory tests, for greater accuracy, the 
 quantities are usually measured by weight. 
 
 Brick work with %" joints requires about one-eighth 
 of the volume in mortar. For %" to W joints about 20 
 per cent, will be mortar. Ashlar masonry requires about 
 6 to 8 per cent, of the volume in mortar, and rubble ma- 
 sonry requires 25 to 40 per cent, of mortar. 
 48 
 
The amount of water required is about one-fourth the 
 volume of the cement in neat cement or about one-half 
 of the volume of the cement in sand and cement mortar. 
 
 Portland and Rosendale cements may be mixed in any 
 proportion in mortar. If equal quantities of each be used, 
 the strength will be about the mean between that of the 
 separate mortars, but it will set in about the time re- 
 quired for Rosendale cement. 
 
 As in the case of lime mortar, mortar made of cement 
 and sand will stand much greater crushing load in the 
 thin joints of a brick wall than in cubes. The strength 
 in the thin joint is sometimes many times as much as the 
 same mortar in a cube. Good 1 13 Portland cement mortar 
 in thin joints will generally withstand the pressure that 
 will crush the strongest brick or stone. 
 
 Mortar made with crusher dust, that is, stone dust that 
 results in the crushing of stone, was found by Govern- 
 ment tests to be superior in tensile strength both to sand 
 and crushed quartz. In the report of the Chief of Engin- 
 eers, U. S. A., for 1902 (See Eng. News, Apr. 2, 1903) 
 the following results of tests are shown. 
 First Series of Tests. 
 
 Sand 
 I 
 
 2 
 
 3 
 
 i 
 
 2 
 
 3 
 I 
 
 2 
 
 3 
 
 of 
 
 Tests 
 
 > 
 
 
 
 i 
 
 '3 
 
 
 
 i Period 
 
 Age 
 
 
 
 24 hrs. 
 
 7 da. 
 
 i mo. 
 
 3 mo. 
 
 6 mo. 
 
 i yr. 
 
 14 
 
 
 103 
 
 370 
 
 397 
 
 
 376 
 
 381 
 
 355 
 
 36 
 
 
 105 
 
 241 
 
 274 
 
 
 294 
 
 290 
 
 291 
 
 12 
 
 
 79 
 
 397 
 
 544 
 
 
 6o 7 
 
 628 
 
 602 
 
 14 
 
 53 
 
 243 
 
 282 
 
 266 
 
 259 
 
 227 
 
 36 
 
 65 
 
 169 
 
 198 
 
 207 
 
 192 
 
 185 
 
 12 
 
 37 
 
 267 
 
 395 
 
 494 
 
 512 
 
 484 
 
 
 
 
 
 i:5 
 
 
 
 14 
 
 31 
 
 187 
 
 221 
 
 211 
 
 190 
 
 161 
 
 36 
 
 36 
 
 132 
 
 155 
 
 159 
 
 145 
 
 144 
 
 12 
 
 25 
 
 211 
 
 336 
 
 428 
 
 421 
 
 416 
 
 49 
 
Second Series of Tests. 
 No. of No. of Tests, 1 13 
 
 Sand Each Period 
 
 Age 
 
 
 
 
 
 24 hrs. 
 
 7 da. 
 
 i mo. 
 
 3 mo. 
 
 6 mo. 
 
 i 
 
 12 
 
 62 
 
 302 
 
 425 
 
 449 
 
 436 
 
 2 
 
 12 
 
 58 
 
 224 
 
 289 
 
 310 
 
 310 
 
 3 
 
 12 
 
 III 
 
 399 
 
 505 
 
 603 
 
 593 
 
 I 
 
 12 
 
 17 
 
 153 
 
 283 
 
 329 
 
 325 
 
 2 
 
 12 
 
 23 
 
 136 
 
 193 
 
 220 
 
 234 
 
 3 
 
 12 
 
 60 
 
 287 
 
 411 
 
 453 
 
 501 
 
 f3b?r 12 9 103 189 244 263 
 
 2 12 7 85 130 168 184 
 
 3 12 34 212 322 377 429 
 
 Notes. No. i, standard crushed quartz; No. 2, Plum 
 Island sand; No. 3, crusher dust. Proportions are of 
 Portland cement to sand by volume. In first series of 
 tests mortar was quite wet; in second series consistency 
 was medium. Values in table are ultimate tensile strength 
 in Ibs. per sq. in. 
 
 Some tests given by Mr. G. J. Griesenauer in Eng. News, 
 Apr. 16, 1903 show limestone screenings to be superior 
 to sand in bricquettes tested in various periods from 
 seven days to one year. Bricquettes made of screenings 
 as lean as 1 13 showed greater tensile strength at the end 
 of one year, in some cases, than neat Portland cement. 
 
 Unlike lime mortar cement mortar will set in fresh 
 water or sea water or entirely excluded from air or water, 
 except the water used in mixing. Some substances, how- 
 ever, will cause cement mortar or concrete to disintegrate 
 while setting. Water containing the discharge from a 
 pulp mill was found in one case to cause setting concrete 
 to become absolutely worthless. (See Eng. News, Feb. 5, 
 1903). Manure, especially if it be wet, will rot concrete 
 while it is setting, but does not seem to affect concrete 
 that is set and hardened. (See Eng. News, Jan. I, 1903, 
 
 oO 
 
p. ii ; Jan. 29, 1903, p. 104; Feb. 5, 1903, p. 127). Manure 
 is sometimes used and recommended to prevent concrete 
 from freezing. This is bad practice, if the manure is 
 placed in contact with the concrete. It is not only liable 
 to rot setting concrete, but it will discolor it. Weak acids 
 will attack the lime in mortar or concrete that is setting. 
 
 The effect of oil on concrete is not well understood. 
 In Eng. News, Vol. 53, p. 279 and Vol. 58, p. 16, some 
 tests are reported which show that most oils have a de- 
 leterious effect on concrete. Concrete or mortar that is 
 setting is especially susceptible to the weakening influ- 
 ence of oils. Animal and vegetable fats and oils are the 
 most harmful, excepting such drying oils as boiled linseed. 
 This latter, while it penetrates concrete to some extent 
 does not appear to weaken it. Petroleum does not seem 
 to injure concrete. Mr. H. T. Poe, Jr. in Engineering 
 Record, Vol. 55, p. 222 tells of a reservoir painted inside 
 with coal tar which was used for fuel oil and gave satis- 
 faction. An experimental tank of 1 :2 14 concrete, not 
 treated, with fuel oil in 9 months showed no disintegra- 
 tion and no leaks, only discoloring of concrete for 1^4 in. 
 (Eng. Record, Vol. 55, p. 9.) Tanks not treated were also 
 found to be unaffected by petroleum and petroleum pro- 
 ducts by Mr. J. L. Gray (Eng. Record, Vol. 55, p. 313.) 
 See Eng. News, Vol. 57, p. 13, where test of i :2 14 con- 
 crete tank filled with fuel oil gave satisfactory results. 
 Oil penetrated concrete less than % in. See also Eng. 
 News, Vol. 53, p. 279, and Eng. Record, Vol. 51, p. 357. 
 
 Alternate freezing and thawing during setting destroys 
 weaker mortars, such as lime mortar or Rosendale cement 
 mortar. Some experimenters have reported that it does 
 not affect the strength of Portland cement mortar. It 
 is the general opinion, however, that it is harmful to any 
 setting mortar or concrete. Freezing delays the setting 
 of mortar, but if thawing does not occur until the mortar 
 is set, it does not seem to weaken it. The setting of mor- 
 tar is sometimes entirely suspended due to its being 
 frozen. Upon thawing the setting resumes. Concrete in 
 
 51 
 
foundations has been found, after having stood for some 
 time in freezing weather, to quake; then, after having 
 time to set in warmer temperature, it has become good 
 and hard. Freezing is particularly harmful when there 
 is a mortar finish on concrete poorer in cement, or where 
 the facing is a richer mixture than the body of a wall. 
 The rich mortar is apt to break off from the main body. 
 Brick walls in mortar should not be run up too fast in 
 freezing weather. The heavy load coming upon the lower 
 parts of walls thus built have caused many failures on 
 account of the fact that the mortar had frozen and not 
 set. When the frozen mortar thawed it was almost in the 
 condition of fresh mortar. Failures have also occurred 
 in concrete work on account of the fact that centers were 
 removed from work that was frozen and not set. 
 
 In a paper by Messrs. P. L. Barker and H. A. Seymonds, 
 published in Eng. News, May 2, 1895, a number of testa 
 are given on the strength of cement mortars subjected to 
 freezing temperature. These experimenters found that 
 Portland cement mortar suffers no surface disintegration 
 under any condition of freezing, but the strength is di- 
 minished, sometimes very materially; Rosendale cement 
 mortar disintegrates on the surface, but seems to acquire 
 greater strength in the part not disintegrated ; the cohesion 
 of Rosendale cement mortar is destroyed by immersion 
 in water which freezes around it; salt used in mixing 
 water (about 7 per cent.) helps Rosendale cement mor- 
 tar to resist surface disintegration, but appears to dimin- 
 ish the strength ; a mixture of Portland and Rosendale 
 cements was found to combine the good points of each, 
 namely, to resist surface disintegration and not to lose its, 
 strength due to freezing; lime mortar kept frozen until 
 it had time enough to set was not injured, but when al- 
 ternately frozen and thawed it disintegrated. 
 
 Salt in the water is sometimes used to prevent freezing 
 of mortar. On exposed walls salt is liable to produce 
 effloresence and to disfigure the wall. Moist salt is 
 known to corrode steel, so that concrete in which steel is 
 
 52 
 
embedded, if it contains salt and becomes wet, may cor- 
 rode the steel. Whether or not the steel is safe from cor- 
 rosion if the concrete is kept dry is a matter of uncer- 
 tainty. Heavy walls in plain concrete do not need salt 
 in the mixture, unless it be in extremely low temperature, 
 for the cement in setting generates heat. Salt may be 
 found useful in such thin unreinforced work as sidewalks. 
 The use of such substances as salt, sugar, soft soap, etc., 
 sometimes resorted to for various purposes, seems to be 
 of doubtful benefit. At least the effect of these substances 
 is not clearly understood. 
 
 Heating the materials of mortar or concrete before mix- 
 ing is very often practiced and is very often recommended 
 to prevent freezing. Experiments have shown that it is 
 harmful to use hot or even warm materials. Mr. Wm. 
 M. Maclay, in Trans. Am. Soc. C. E., Vol. VI, 1877, de- 
 scribes tests in which the heating of ingredients of cement 
 mortar to 100 deg. F. reduced the strength to only 7 to 30 
 per cent, of that of specimens made at 40 deg. F. Experi- 
 ments made by the Austrian Society of Engineers and 
 Architects (See Eng. News, Vol. 31, p. 253) led to the con- 
 clusion that mortar mixed with warm water shows about 
 the same deterioration in freezing temperature as when 
 cold water is used. 
 
 The only warrant for the use of hot materials seems to 
 be the very doubtful one that it is often done. The only 
 evidence that it is not harmful as practiced appears to be 
 the negative evidence that no failures have been traced to 
 the use of hot materials. Pleat increases the activity of ce- 
 ment, and quick setting of mortar, that is, setting during 
 the process of placing, is detrimental to its strength. 
 Heat drives off water the presence of which is necessary 
 to the proper hardening of the cement. Concrete bricks 
 or blocks are sometimes steam cured, but in this case, 
 the heat is applied after the concrete is placed in the 
 forms and not before it is handled in a plastic state. The 
 steam immersion would not take away water from the 
 concrete, but would rather add to that already there by 
 
 53 
 
condensation, unless the blocks were heated by other means 
 hotter than the steam. In doing concrete work in hot 
 weather it is desirable to keep the materials cool and the 
 concrete protected from the direct rays of the sun. These 
 adverse conditions should not be artificially produced in 
 cold weather. 
 
 The safest and best materials for concrete are good, 
 clean, hard broken stone or gravel, good clean coarse 
 sand, finely ground Portland cement of known quality, 
 and good clean fresh water. The best temperature for 
 these materials is as cool as they can be kept without Be- 
 ing below freezing. 
 
 As stated, water for use in making mortar or concrete 
 should be clean. It should not be water from coal mines. 
 It should not contain sewage or rotting substances. It 
 should not contain waste from pulp mills and should not 
 be acid in reaction. Sea water for concrete is doubtful. 
 It should not be used, if fresh water can be obtained. 
 
 The mixing of mortar should be thorough. If done by 
 hand, the sand should be placed on the mixing board and 
 spread out to an even thickness of about 2 or 3 inches. 
 Upon this the cement should be evenly spread and the 
 dry materials turned over three or four times with shovels. 
 Water is then added. It should not be dashed on so as 
 to wash away the cement. After the addition of the water 
 the mortar should be> turned until the pile is uniform 
 throughout both in color and in consistency. 
 
 Machine mixing, both of mortar and concrete, generally 
 results in a more uniform product than hand mixing. 
 There are two general classes of mixers, namely, batch 
 mixers and continuous mixers. In the batch mixer the 
 materials for one-half to one cubic yard are put in at 
 once, and this is turned over until all are uniformly mixed, 
 then the whole is discharged. In a continuous mixer the 
 various materials are fed regularly into the mixer, and 
 concrete is discharged continuously. 
 
 Thorough mixing and uniformity of product are the 
 prime essentials. There should be in any given quantity, 
 
 54 
 
say a shovelful or a wheelbarrow full, just the amount 
 called for of the several materials. If 1 :2 14 concrete is 
 called for, there should be one part of cement, two parts 
 of sand, and four parts of broken stone or gravel in 
 each such quantity throughout. This is true of the amount 
 of water used as well as other ingredients. Each batch 
 and every part of the batch should be of the same con- 
 sistency. If this thoroughness and uniformity are not 
 maintained, the resulting concrete will not be homogene- 
 ous. 
 
 In a batch mixer it is not difficult to secure uniformity 
 as to amounts of ingredients in each batch, if a careful 
 man is placed in charge. There are, however, practical 
 difficulties in measuring the materials. One of these is 
 the fact that the most convenient thing to haul sand and 
 stone from the pile is a wheelbarrow, and it is very diffi- 
 cult to gage the capacity of a wheelbarrow or to get work- 
 men to load one the same amount at each trip. 
 
 It is quite evident that to make three or four different 
 streams discharge proportionate amounts of materials, as 
 must be done in a continuous mixer, is fraught with 
 many difficulties and difficulties that are harder to over- 
 come than the measuring of material before they are put 
 into a batch mixer. Continual vigilance is necessary in 
 order to make sure that none of the various streams be- 
 come clogged or fail to discharge their proper amounts of 
 material. 
 
 Cement mortar should not be mixed in large batches, 
 if it will require long to use up the batch. It should be 
 fresh mixed and used as soon after mixing as possible, 
 as it begins to take on its initial set in a short time. If 
 it is necessary to leave mortar stand a while, it should be 
 re-tempered, adding a little water if necessary, before it is 
 used. It is said that re-tempered mortar will adhere bet- 
 ter to old concrete surfaces or to concrete blocks than 
 fresh mortar. For the same reason re-tempered concrete 
 might be found useful in joining to old work or to con- 
 crete that has partially set. 
 
 55 
 
Re-tempering of mortar and concrete are usually pro- 
 hibited because of the uncertainties attending the prac- 
 tice. 
 
 Rosendale cement mortar and concrete are injured to 
 a greater extent by re-tempering or by delay in placing 
 than Portland cement mortar and concrete. This is be- 
 cause Rosendale cement takes its initial set in a shorter 
 time than Portland. Experiments reported by Mr. Thos. 
 S. Clark and published in Eng. Record, Dec. 27, 1902, show 
 that Rosendale cement, neat and with sand, if re-tempered 
 by adding water, after allowing to stand for one hour, is 
 reduced in tensile strength about 50 per cent, for long- 
 time tests. For tests which set but a few days greater 
 weakness than this was shown for neat cement though 
 not so much difference for tests with sand. The same 
 report states that no marked difference was shown in the 
 case of Portland cement re-tempered after one hour. It 
 is probable, however, that Portland cement re-tempered 
 after several hours standing would show similar weak- 
 ness. 
 
 Continuous mixing of cement mortar for several hours 
 seems to cause it to retain its life, that is; it seems to re- 
 tard its setting. Some experiments reported by Mr. G. 
 Y. Skeels, in Eng. News, Nov. 6, 1902, show that the ten- 
 sile strength of Portland cement bricquettes of 15 days 
 standing, after continuous mixing for 9 or 10 hours was 
 reduced only about one-quarter from the freshly mixed 
 cement. Similar results were found both for neat ce- 
 ment and i to 2 mortar. 
 
 Concrete deposited under water has been found to be 
 better if allowed to stand a few hours after mixing, as 
 the cement will not leech out so readily. 
 
 One part of brick dust, one part of quick lime, and two 
 parts of sand, mixed dry and tempered with water will 
 make a hydraulic mortar. 
 
 Grout is the name given to thin or liquid mortar. It 
 is used for filling in joints or spaces which cannot other- 
 wise be reached. Cast bases for columns are usually left 
 
 56 
 
rough on the bottom surface, and holes are provided in 
 the bottom plate for grouting. The grout is prevented 
 from running away by banking up sand around the edge 
 of the base. Grout may be used to strengthen walls in 
 which the mortar has washed out. It may also be used 
 in making concrete by first placing broken stone or gravel 
 and then pouring the grout into the interstices. A fill of 
 broken stone or a gravel bed in which there is little or no 
 sand may be consolidated by filling the voids with grout. 
 
 The method referred to in the last paragraph of pouring 
 grout under the base of a column may be used to ad- 
 vantage also for bridge shoes. It is a good plan to wedge 
 up a bridge shoe an inch or two above the surrounding 
 masonry (allowance being made for this in the plans), 
 and then after having built a dam of sand around the 
 edge, to fill in under the shoe with grout. This keeps 
 water from lying around the bridge shoe. 
 
 In Eng. News, Aug. 8, 1907, p. 145, there is a short de- 
 scription of repairs made on a bridge pier in Germany 
 that had been cracked horizontally below the water level 
 and displaced by the action of an ore steamer. The outer 
 edges of the crack were sealed by means of wooden wedges 
 and oakum, and in addition a strip of canvas was placed 
 around the pier and bound thereto. Grout was pumped 
 into the crack, by means of air pressure and grouting 
 drums, through pipes provided for this purpose. The 
 grout was a i to I mixture of Portland cement and sand, 
 mixed dry and then tempered with an equal volume of 
 water. 
 
 Concrete. 
 
 Concrete is a mixture of mortar and some aggregate, 
 hence what has been said concering mortar and its char- 
 acteristics has application in a large measure to concrete. 
 The mortar with its contained cement, acts to hold the 
 aggregate together making of the whole an artificial stone. 
 An ideal concrete is one in which the cement fills or more 
 
 57 
 
than fills the voids in the sand to form the mortar and 
 the mortar fills the voids in the broken stone or other 
 aggregate. Proportions in this country are nearly always 
 given in bulk or volume. 
 
 The voids in broken stone are about 40 to 50 per cent, 
 of the bulk. Concrete composed of one part of mor- 
 tar to two of broken stone would therefore be about right. 
 The volume will be practically equal to that of the broken 
 stone. A common mixture for walls and other heavy 
 work is one part of cement, 3 parts of sand, and 6 parts 
 of broken stone. For reinforced concrete a richer mortar 
 is desirable, because of the fact that the covering of the 
 steel with cement must be assured, and because the small- 
 er size of broken stone demands more cement to cover the 
 parts of the aggregate. The standard mixture for rein- 
 forced concrete is i part of Portland cement, 2 parts of 
 sand, and 4 parts of broken stone or gravel. 
 
 Leaner mixtures are sometimes used in heavy work 
 where large sized aggregates can be employed. Such pro- 
 portions as 1:3:7, 1:4:8, or even 1:5:10 could be used 
 where strength is not an essential characteristic. In- 
 cluded in the volume of the stone there could be large 
 stones, say a foot or so across. These should be separated 
 from each other and from the surface. 
 
 In general as few different mixtures of concrete as pos- 
 sible should be specified on one contract, and the line of 
 separation should be well defined, so as to avoid confusion. 
 The body of a pier or abutment could be of i :3 :6 con- 
 crete and the coping, because of the need of stronger con- 
 crete to take the bridge seats, could be of 1 :2 -.4 concrete. 
 Some steel reinforcement in the coping of such a pier 
 would not be out of place, to tie it together and prevent 
 cracking in the entire pier. It would not be well to call 
 for beams of one mixture and slabs or columns of an- 
 other, though column footings and columns might be of 
 different mixtures if one were plain and the other rein- 
 forced. 
 
 58 
 
In ordinary work it is best to specify standard mix- 
 tures for the concrete and to see that the materials are 
 regular, the sand and aggregate well graded in size and 
 uniformly mixed. It would not be discreet to leave to 
 the contractor the determination of the proportion of in- 
 gredients. On special work or very large contracts, where 
 the engineer is given discretion, he may determine the 
 mixtures that suit more accurately the materials to be 
 used. The percentage of voids may be ascertained by 
 taking a vessel of known capacity and filling it with the 
 aggregates. Then by weighing it before and after filling 
 level full of water the volume of water may be found 
 from the known weight per cubic foot of water, namely, 
 62.4 Ib. The percentage that this volume of water is of 
 the full capacity of the vessel is the percentage of voids in 
 the aggregate. The same may be done with the sand. By 
 using about 10 per cent, more cement than the voids in 
 the sand and 10 per cent, more sand than the voids in 
 the broken stone a mixture will be effected that is most 
 economical for the given materials. 
 
 For quartz sand the voids may be found by weighing 
 a known volume. The specific gravity of quartz is 2.65, 
 and the weight per cu. ft. is 165.4 Ibs. If then a cu. ft. of 
 sand weighs say 100 Ibs. the difference, or 65.4 Ibs. repre- 
 sents the voids. Dividing 65.4 by 165.4 we have 40 as the 
 percentage of voids. 
 
 One way that is recommended for finding the proper 
 mixture of sand and stone or sand and gravel is based 
 on the fact that, other things being equal, the denser the 
 mixture the stronger will be the concrete. The operation 
 is that of finding the mixture that has the maximum 
 weight for a given volume. A common galvanized ' iron 
 pail and spring balances may be used for the purpose. 
 The bucket is filled half full of water, and a batch of the 
 sand and aggregate at a trial proportion is thoroughly 
 mixed and slowly dropped from a shovel. The surplus 
 water is allowed to flow over. Without tamping the 
 bucket is filled level full. The mixture that weighs the 
 
 oi) 
 

 most will give the densest and strongest concrete, and on 
 account of having the least percentage of voids it will re- 
 quire the least amount of cement. 
 
 Sometimes concrete is made of cement, sand, gravel, 
 and broken stone, the gravel being intermediate in size 
 between the sand and the broken stone. Good dense con- 
 crete may be made of this combination, if suitable propor- 
 tions are determined. 
 
 Concrete is sometimes made of sand and cement only, 
 there being a large quantity of sand in proportion to the 
 cement, say I of cement to 7 or 8 of sand. This does not 
 make good concrete. The voids in the sand cannot be filled 
 by so small a proportion of cement. 
 
 Concrete may be mixed by hand or by machinery. 
 When hand mixed the following is probably the most ap- 
 proved method. First the sand is dumped on the mixing 
 board and spread out to a thickness of about three inches. 
 Over this the cement is dumped and spread out evenly. 
 This dry sand and cement is then turned over with shovels 
 two or three times, and the pile is leveled off. On this 
 the broken stone or gravel, previously wetted, is dumped 
 and spread out evenly so as to cover the sand and ce- 
 ment. The full amount of water is then measured and 
 poured on. As only the aggregate is exposed, the water 
 may be poured or dashed on without particular care, since 
 the danger of washing out the cement is removed. The 
 whole should now be turned over with shovels two or 
 three times. 
 
 When concrete is mixed by machinery, all of the in- 
 gredients, including the water, are carefully measured and 
 placed in the mixer. For mixtures in which little water 
 is to be used it may be necessary* in order to get a uni- 
 form mixture, to mix the dry ingredients without any 
 water first and then add the water and continue the mix- 
 ing until this is incorporated in the mass. The number 
 of turns of the mixer, or the time required to effect an 
 intimate and thorough mixture will depend somewhat 
 upon the kind of mixer. This can be well judged by the 
 
 60 
 
uniformity of the product in color and by inspection to see 
 if the grains of sand and the stones are covered with ce- 
 ment. The whole mass should have the color of the ce- 
 ment. Concrete not well mixed will have patches of bare 
 sand and stones. Regularity both in the proportion of 
 the ingredients and in the amount of mixing are very im- 
 portant in any concrete work and are of special moment 
 in reinforced concrete as well as any work that is to be 
 watertight. When the time of mixing required to give a 
 thorough mixture is ascertained, this length of time should 
 be allowed for each batch. 
 
 Usually about 10 or 15 turns of the mixer are required 
 to give a thorough mixture. The time required is from I 
 to iVz minutes. It requires about two to three minutes 
 per batch to put in the materials and take out the con- 
 crete, if the handling of materials can be expeditiously 
 done. 
 
 Lean mixtures require more mixing than rich ones, be- 
 cause it is more difficult to distribute the smaller amount 
 of cement thoroughly through the mass. Dry mixtures 
 require more mixing than wet ones. 
 
 It is well to mold a small cube of concrete from the 
 batch occasionally. These cubes will be useful in gaging 
 the kind of concrete turned out, and by the time required 
 for them to set the hardness of the work may be judged. 
 When concrete is placed in unusual conditions such a sam- 
 ple placed in the same conditions and accessible for in- 
 spection furnishes an index to the character of the placed 
 concrete. 
 
 Concrete should not be too wet or too dry. If too wet 
 it will shrink an excessive amount from drying out; if 
 too dry when placed, it will not be dense, as the mortar 
 will not run into the spaces. Formerly, when mass con- 
 crete was about all the kind made, very dry concrete was 
 generally specified, just enough water being used to satisfy 
 the needs of the cement in setting; and this was heavily 
 rammed. This is not very objectionable in mass concrete, 
 and it has some advantages. One of these is that the drier 
 
 61 
 

 concrete will attain its strength sooner than wet concrete. 
 Wet concrete is generally considered to be best for al- 
 most all purposes, though the amount of water which 
 should be used is not the same in all cases. 
 
 The chief advantage in dry concrete is its faculty of 
 setting up in a shorter time than wet concrete. When 
 a piece of construction is to receive its load soon after 
 placing the concrete, it is best to use a dry mixture, if the 
 conditions are not such as to render such a mixture harm- 
 ful for other reasons. Some concrete block manufacturers 
 take advantage, in making their blocks, of the fact that 
 dry mixtures hold up in a short time better than wet ones. 
 They use a mixture that is simply moist, so that blocks 
 can be removed from the molds about as soon as they 
 are molded. The result is that the blocks are spongy, and 
 we see houses built of the blocks turn dark gray in a 
 rain because of the absorption of water. Such use of 
 dry concrete can only serve to discredit concrete itself. 
 
 Another advantage in dry concrete is that it is less lia- 
 ble to freeze in cold weather than wet concrete. It should 
 be borne in mind that much water in concrete in cold 
 weather renders it more liable to the action of frost. 
 However, other means of preventing freezing should be 
 employed rather than the use of concrete that is too 
 dry for the purpose intended. On the other hand in very 
 warm weather an excess of water is advantageous, be- 
 cause it prevents the concrete from too rapid drying out 
 due to the heat. 
 
 Dry or mealy concrete has many disadvantages. It is 
 unfit to use in walls that are to keep out moisture. A 
 mealy concrete wall allows water to flow through it very 
 freely. It is unfit to use in clycopean or rubble concrete, 
 because it will not flow around the large stones and coat 
 them with cement. For similar reasons it is totally un- 
 fit for use in reinforced concrete work, as it will not flow 
 around the steel and coat it with cement. Because dry 
 concrete is porous there will be voids around the rein- 
 forcing steel as well as in the other parts. The steel is 
 
thus deprived of the protection which the concrete must 
 afford, if the combination is to be lasting. Concrete must 
 be wet to pack around the reinforcing steel or embedded 
 stones and to cover them with cement. Both of these 
 requisites are of prime importance in reinforced concrete. 
 Steel rods will not be gripped as firmly in a porous con- 
 crete as in a dense concrete. Dry concrete lacks cohe- 
 sion, and the cohesion of concrete has much to do with 
 the gripping of the steel. It is of special importance in 
 cinder concrete, reinforced, that a wet concrete be used, 
 so that the cement will coat the steel and protect it from 
 sulphur or other harmful agents in the cinders. 
 
 Dry concrete requires tamping; the drier the concrete, 
 generally, the heavier the tamping necessary. Dry concrete 
 for this further reason is unsuitable in reinforced concrete 
 work. Tamping around reinforcing steel is apt to displace 
 the steel as well as to disturb or spring the forms. The 
 concrete around the reinforcement should be worked into 
 the spaces by puddling rather than by tamping, and the 
 consistency of the mixture should be such as to admit of 
 this operation. As near a liquid as possible is evident- 
 ly the best consistency to effect this end, but other con- 
 siderations must be taken into account. If concrete is 
 too wet it will shrink an excessive amount on setting and 
 drying. This may give rise to shrinkage cracks or other 
 trouble that such change of volume would naturally lead 
 to. 
 
 With concrete too wet, unless the forms are very close, 
 approximating water-tightness, liquid mortar will be 
 wasted through the crevices. This is a fault sometimes 
 met with in concrete work, namely, the mortar being of 
 too watery a consistency, or the forms lacking the proper 
 tightness, not only results in a waste of mortar but leaves 
 the concrete spongy, where the mortar has leaked out. 
 This may give the appearance of dry concrete, whereas 
 the cause is just the opposite. 
 
 Another danger that may attend the use of sloppy con- 
 crete is the formation of laitance. This is a milky or 
 
 63 
 
slimy substance that sometimes gathers in the excess 
 water on the surface of concrete. It is composed of about 
 the same ingredients as the cement, but it does not hard- 
 en as the cement, remaining rather in a gellatinous state. 
 Besides taking from the cement useful elements needed in 
 the concrete, the laitance, if not removed, leaves a film 
 in the concrete where it is not bonded together as it should 
 be. 
 
 For reinforced concrete work there must tie found a 
 mean between too wet a concrete and too dry a concrete 
 that will meet the conditions. The proper mean is not a 
 mixture medium in constancy, but a very wet mixture. 
 The concrete should assume a nearly level surface. It 
 should flow sluggishly around the reinforcing steel and 
 require little or no tamping. A little shrinking in rein- 
 forced concrete is an aid rather than a detriment, because 
 the shrinking of concrete acts to grip the steel. 
 
 Other works than reinforced concrete do not generally 
 require such wet mixtures. Work that is to be water- 
 proof or nearly so should be made of a wet mixture and 
 should be puddled, as in the case of reinforced concrete, 
 to work out air bubbles and to solidify the mass. 
 
 There should not be an excess of water in the con- 
 crete base for a sidewalk, where a richer mortar finish is 
 to be put on subsequently. Tamping will bring this water, 
 and probably accompanying laitance, to the surface awd 
 the finish coat will not bond well to it. Pavers usually em- 
 ploy a rather dry mixture for the base and tamp it well. 
 However it is believed that a better pavement would re- 
 sult from the use of a wet mixture and little tamping, 
 with the finish coat floated in at the same time and with 
 as little troweling as possible. 
 
 Wet mixtures do not require as much mixing to distrib- 
 ute the cement through the mass as dry ones. However 
 the liquid state of the concrete may make an insufficient 
 amount of mixing appear to be enough; so that just as 
 much vigilance is required to insure the proper mixing. 
 
 
Dry mixtures are more liable than wet ones to ball in 
 the mixer, that is, to gather in lumps, as the materials 
 will not flow well without the lubricating water. With no 
 water whatever in the mixer there would be no cohesion 
 and the materials would mix, whereas a little water would 
 give a cohesion that may result in the balling referred to. 
 It may be necessary in some cases to mix the materials 
 dry and then add the water giving the mixer a few more 
 turns. While hand mixing in general is less satisfactory 
 than machine mixing, it is possible that in some cases for 
 very dry mixtures hand mixing will produce a better con- 
 crete. 
 
 As to the strength attained by wet and dry mixtures, 
 it is found that given a number of samples of different 
 consistency the drier mixtures will at first show greater 
 strength. After a few days the mixtures having more 
 water will attain the strength of the drier ones and be- 
 gin to surpass them. In general the more water used in 
 the mixture the longer it will be in attaining its full 
 strength. Medium and wet mixtures, after many months, 
 reach about the same strength. Very wet and very dry 
 mixtures are both weaker on long time tests than those 
 in which the consistency is not excessive. 
 
 The amount of water required in concrete depends upon 
 the porosity of the aggregate, the proportion of the in- 
 gredients, the wetness of the sand and aggregate before 
 being brought together, the fineness of the sand, (fine 
 sand requires more water than coarse sand.) and to some 
 extent on the brand of cement. If the sand and stone: 
 were thoroughly wet before mixing, the amount of water 
 would depend largely on the amount of cement in a batch, 
 as moistening of these will lessen the amount of water 
 required to be placed in the mixer. 
 
 Dry concrete is usually understood to be of the con- 
 sistency of moist earth. It will retain its shape w r hen 
 squeezed in the hand. No water will flush to the surface 
 on tamping. 
 
 65 
 
Medium concrete is of such consistency that it will not 
 quake in handling and will not quake under light tamp- 
 ing. When well or heavily tamped, the concrete will quake 
 and water will flush to the surface. 
 
 Wet concrete will quake in handling and cannot be 
 tamped very much. 
 
 In ordinary concrete mixtures dry concrete will require 
 about 5 to 6 per cent, of water (based on total weight of 
 dry materials), medium concrete will require about 6 to 8 
 per cent, of water, and wet concrete will require about 
 8 to 10 per cent. This is an average of about i, i^, and 
 i% gallons per cubic foot of concrete for the three re- 
 spective grades. Per bag of cement it takes about 3 to 4 
 gallons of water for dry concrete, 4 to 6 for medium, and 
 6 to 8 for wet. The amount of water should not be 
 specified in any case, unless the proper consistency and the 
 amount of water required therefor have been previously 
 determined by trial with the materials to be used. Some 
 materials will require amounts of water differing consid- 
 erably from the foregoing. 
 
 It is important to wet the aggregate before it is mixed 
 with the other ingredients especially in the drier mix- 
 tures and in hand mixed work, and particularly when the 
 aggregate is porous or absorbent. This wetting of the 
 aggregate in the pile allows it time to absorb water that 
 might otherwise be robbed from the cement of the con- 
 crete, if the stone is not wet previous to the mixing. 
 
 The following table gives approximately the amounts 
 of materials of average quality required to make one 
 cubic yard of concrete of the three most common mix- 
 tures. 
 
 Proportion Bbl., P. Cement Cu. Ft. Sand Cu. Ft. Stone 
 1:2:4 1.44 11.5 23.0 
 
 1:3:6 1.04 12.5 25.0 
 
 i :4 :8 .78 12.5 25.0 
 
 The measuring of the ingredients of concrete is not very 
 satisfactorily done on the average job. This is because 
 of uncertainty as to the capacity of a wheelbarrow, the 
 
commonly used means of carrying the sand and stone to 
 the mixer. An average wheelbarrow contains from 2 to 
 3% cu. ft., depending on the amount it is heaped. One 
 method of proceedure is to make a box just one foot each 
 way, inside dimensions, and fill this twice with the bro- 
 ken stone and dump it into the wheelbarrow. By observ- 
 ing the amount it is heaped each wheelbarrow load can be 
 heaped (or struck off) to the same extent. The same is 
 done with the sand, so that the appearance of two cubic 
 feet of sand may also be noted. Then two bags of ce- 
 ment are called one part, or two cubic feet, and each 
 wheelbarrow of sand or stone is called one part. For 
 hand mixing of a 1 13 :6 mixture there would be used 2 
 bags of cement, 3 wheelbarrows of sand and 6 of stone 
 or gravel. Four to six men with shovels would be needed 
 to turn this over. A half yard batch mixer could take in 
 the same quantities. 
 
 This way of measuring in wheelbarrows is not very ac- 
 curate and not very satisfactory on any but mass work, un- 
 less the loading of the wheelbarrows is carefully watched. 
 If there is an incline from the stone and sand piles to the 
 mixer, the men are less apt to overload their wheelbar- 
 rows, as two cubic feet is about all they will care to push 
 up the grade. 
 
 A more satisfactory and more accurate method of meas- 
 uring the ingredients consists in the use of a bottomless 
 box having handles projecting from the ends. Such a 
 box made of the proper size to contain a unit quantity, 
 for a batch of concrete, can be laid on the mixing board 
 and filled level full of sand once and of stone twice (or 
 two boxes could be used where the volume of stone is not 
 double that of sand.) This serves to measure the mater- 
 ials accurately, but it requires more handling to dispose 
 them, after this measuring, in an advantageous position 
 for mixing. This adds to the expense of mixing the con- 
 crete. 
 
 One method of using the bottomless boxes mentioned 
 in the last paragraph is to measure the sand first in such 
 
 t>7 
 

 a box and then spread it over the board and mix in the 
 cement dry. After this mixing the surface is leveled off 
 and the box placed upon it and filled with the stone. Thei 
 the stone is spread over the mixed sand and cement to 
 cover it and the water thrown on and the final mixing 
 done. The sides of the boxes should not be high. A 
 wheelbarrow could not be dumped over the sides of a high 
 box, and a flat box would not necessitate as much spread- 
 ing of the materials after the box is lifted as a high box. 
 The bottomless box method of measuring the materials 
 cannot be used in this same way in batch mechanical mix- 
 ers; a dumping square box, however, could be rigged up 
 from which to load wheelbarrows, and exact measurement 
 could be effected in this way. 
 
 There are other ways in which the problem of measur- 
 ing the materials is solved. The chief points of the prob- 
 lem are to effect the maximum accuracy of measurement 
 with the minimum amount of handling. It is desirable to 
 avoid high lifts of the sand and stone, either in the shovel 
 or in the wheelbarrow. It is also desirable to accomplish 
 these preliminaries to the mixing in the shortest time 
 possible. 
 
 The measuring of the cement is fortunately greatly sim- 
 plified on account of the way in which standard cements 
 are packed. A barrel of Portland cement of the stand- 
 ard size weighs 375 Ibs. and contains, when well com- 
 pacted, about 3.8 cu. ft. When put in a measure and well 
 shaken, this quantity will occupy just about 4 cu. ft. 
 Hence a standard barrel can be taken as four cubic feet. 
 Cement usually comes in bags, four of these being a bar- 
 rel of cement. A bag of cement can then be taken as a 
 cubic foot. It is important, however, to measure and 
 weigh some sample bags of the cement used on any work 
 to see that they contain a cubic foot and weigh close to 
 94 Ibs. each. If the bags are found not to contain a full 
 cubic foot, the other measures should be made on the 
 basis of the actual volume of cement in a bag, 
 
 68 
 
A bag of cement will sometimes contain lumps. These 
 should be broken up, or, if they are too refractory, they 
 should be thrown out and good cement used to make up 
 the deficiency. 
 
 A pile of stone in cold weather may sometimes contain 
 lumps of ice. These should be watched for and eliminat- 
 ed. 
 
 It is very important to have an inspector to watch the 
 mixing of concrete. He should count the bags of ce- 
 ment; keep tab on the amounts of materials; see that the 
 mixer runs long enough; see that the consistency and 
 fluidity is right; see that no blocks of wood, lumps of 
 mud or clay, paper from sacks, ice, lumps of hard ce- 
 ment, etc. go through; see that lumps of hard cement are 
 compensated for with good cement; see that the concrete 
 is well mixed, that it is uniform, that it has not balled in 
 the mixer, etc. ; see that the mixer is clean before start- 
 ing; see that the materials are running uniform, regular in 
 size and not mixed with dirt, no single wheelbarrows com- 
 posed entirely of large stones or of small stones, etc. 
 
 Materials should be moved by power wherever practi- 
 cable. They should be stored high where possible. If 
 raised to bins when delivered on the job, they may be 
 drawn out with use of little labor. This storing of the 
 materials may often be done by use of cranes. It is 
 better to handle the materials in this way than to dump 
 them on the ground and shovel them up. They will be 
 cleaner, and the stone is less liable to run irregular. 
 
 One method of raising materials to the mixer is to use 
 an incline with a gravity dumping car to material pile. 
 This is drawn up to the mixer by cable from the mixer 
 engine or other power and allowed to return by its own 
 weight 
 
Steel for Reinforced Concrete. 
 
 Steel for reinforced concrete should preferably be open 
 hearth steel, though Bessemer steel may safely be used for 
 rods and for plates and shapes that are punched if the 
 punched holes are reamed. 
 
 The ultimate strength of the steel is not a matter of 
 much importance, neither is the elastic limit, except as 
 these properties indicate uniformity in the product. It 
 should be a good grade of soft steel. It is of more import- 
 ance that it stand the bend test of soft steel than that its 
 ultimate strength and elastic limit be high. The reason 
 why high elastic limit and high ultimate strength are not 
 essential characteristics of steel embedded in concrete is 
 the simple fact that these qualities cannot be made use 
 of in proper design of reinforced concrete. This is di- 
 rectly contrary to a great amount of trade literature and 
 some technical literature. Commercial soft steel is almost 
 universally of an ultimate tensile strength of from 50,000 
 to 60,000 Ibs. per sq. in. and a strength at elastic limit of 
 30,000 to 40,000 Ibs. per sq. in. This latter is about three 
 times the safe value that ought to be allowed on the steel, 
 because above this value cracks begin to appear, and there 
 can be no justification for a design that anticipates cracked 
 beams and slabs. There is therefore ample margin of 
 safety in any good soft steel. 
 
 If high steels showed smaller elongations for a given 
 unit stress (for stress within the elastic limit) than soft 
 steels, there would be some justification for their use, as 
 they would then not stretch out as much under a given 
 stress, and the concrete would be less liable to be cracked. 
 But the modulus of elasticity is one property that is prac- 
 tically constant for all grades of steel. Even soft wrought 
 iron has a modulus of elasticity almost as great as the 
 hardest steel. The simplest conception of the modulus of 
 elasticity, designated as E, is a unit stress that would 
 stretch a piece of steel out to double its original length, 
 at the rate at which it stretches within the elastic limit. 
 
 70 
 
The modulus of elasticity of steel is about 30,000,000, if 
 then a piece of steel is stressed to 10,000 Ibs. per sq. in., 
 it will stretch one-three-thousandth of its length. Beyond 
 the elastic limit different grades of steel exhibit different 
 characteristics. Soft steels stretch out more before fail- 
 ure, while high steels and soft steels that have been rolled 
 or drawn cold or twisted cold, break without much 
 stretch or reduction of area at point of fracture. This 
 lack of stretch beyond the elastic limit is held out as a ben- 
 efit in trade literature. It is a positive detriment. If fail- 
 ure occurs in steel that will not stretch, it will be sudden 
 and without warning, whereas if the steel stretches out, 
 it will allow a beam or slab to sag before failure. Be- 
 sides giving warning of failure the sagging will in many 
 cases reduce the stress in the steel very materially. The 
 author has seen tests of slabs reinforced with soft steel 
 that sagged enormously and could not be broken. 
 
 The reason why it is important that steel stand the cold 
 bend test is because rods are very often curved and bent 
 in construction. This bending should be done cold, for if 
 the steel is heated, its internal structure is changed, and 
 annealing would be necessary to restore it. Soft steel of 
 ordinary manufacture will, in general, stand more punish- 
 ment than harder grades of steel. The threading of rods 
 and punching of plates or shapes are less liable to cause 
 incipient cracks or hardened metal in soft steel than in 
 high steel. These are also processes to which the embed- 
 ded steel may be subjected. 
 
 Special steel, while it has a high sound, does not possess 
 any needful characteristics, as an element in reinforced 
 concrete, that are not possessed by the cheap commer- 
 cial article. This is true because of the limitations of the 
 concrete. Good soft steel is not a special steel but is the 
 commonest product of the steel furnace. It is important, 
 however, that it be good and that it be soft, that is, not a 
 high carbon steel. 
 
 There should be a wide margin of safety in the amount 
 that a steel rod will bend. A piece of steel of high ulti- 
 
 71 
 
mate strength may stand a bend of 100 degrees and fail 
 if bent 105 degrees. It is clear that this steel would not 
 be fit to use where it is bent at an angle anywhere near 
 approaching this. 
 
 The best carbon steel for structural purposes is found 
 to possess an ultimate strength between 55,000 and 65,000 
 Ibs. per sq. in. Formerly two grades of steel were rec- 
 ognized in most specifications for structural steel work 
 with allowed limits that overlapped two or three thousand 
 pounds around the 60,000 mark. The result was that 
 manufacturers usually succeeded in making nearly all of 
 their structural steel within the overlap, so that it would 
 fill either specification, though a wide difference in allowed 
 unit stresses was sometimes permitted. The allowed lim- 
 its given at the beginning of this paragraph represent a 
 steel that is a mean between the older grades of soft and 
 medium steel. It is also about midway in tensile strength 
 between the very soft steel now used for rivets and the 
 higher steel used for eyebars and other forgings. It has 
 been found by experience to be satisfactory for structural 
 purposes. For reinforced concrete it satisfies every struc- 
 tural requirement, and because of its availability it is the 
 most economical material that can be used. 
 
 Tests made to see that the ultimate strength lies between 
 these limits are very useful to ascertain that the steel is 
 regular in quality. Dead soft steels may be ruined in the 
 manufacture. High steels will not stand bending. 
 
 The elastic limit of the steel should be not less than one- 
 half of the ultimate strength and the stretch in a measured 
 length of 8 inches should be not less than 24 per cent. It 
 should stand the cold and quench bend test, 180 degrees 
 flat, without fracture. In the quench bend test steel is 
 heated to a cherry red, as seen in the dark, and quenched 
 in water at ordinary temperature, before bending. 
 
 The proper use of steel in concrete is in small sections 
 well distributed throughout the mass. The bars should be 
 separated from each other to give the gripping effect of 
 the concrete full play. If they are placed in a layer close 
 
together, a cleavage joint is formed and the concrete is 
 liable to break off. This would be the case in a close coil 
 or set of rings close together or in a set of rods lying 
 close together near the bottom of a beam. Plates or 
 sheets of steel should not be used as separators or spacers 
 for rods, as these will also form cleavage planes. If heavy 
 rods are used, surrounded by comparatively little concrete, 
 the concrete is unable to grip the steel and the differen- 
 tial expansion due to change in temperature will crack the 
 concrete. Pvramids of concrete surrounding the bases of 
 out-door steel columns seldom last through a winter with- 
 out being cracked. Girders covered with a shell of con- 
 crete would be subject to the same detrimental effect of 
 differential expansion. 
 
 The steel should not be placed close to the surface of 
 the concrete. It cannot be gripped properly unless it is 
 deep enough in the concrete for the latter to take hold. 
 It cannot be protected from rust and fire unless there is 
 some concrete between the steel and these destroying ele- 
 ments. It is bad practice to lay the steel on the forms 
 and then the concrete on this. The steel is neither properly 
 protected nor gripped by such means. The depth to which 
 steel should be buried depends upon the size of the sec- 
 tion. It is manifest that the heavier the section tlie more 
 concrete is needed to grip it and to overcome differential 
 expansion. If rods are bedded deeper they will be less 
 affected by external change of temperature. Heavy rods 
 are of more importance in a structure, hence their protec- 
 tion is of more vital importance than that of light rods. 
 
 Standard sizes of rods or shapes should be used as 
 much as possible, so that they can be obtained without 
 delay from the mills. Also as few different sizes as pos- 
 sible should be employed. Simple details are essential. 
 A complex structure will be difficult to surround properly 
 with concrete. There should be no broad flat surfaces to 
 work the concrete under. 
 
 The steel work should be designed with a view of its 
 being easily placed in proper position and held there 
 
 73 
 
against the displacing tendencies due to the placing of the 
 concrete. Where rods cross, they should be wired to- 
 gether, and this should be done before the forms are 
 erected to the point that they will interfere by preventing 
 free access to the rods. Extra wires may often be used 
 to advantage to tie the rods in place. These wires may 
 serve the further purpose of holding the sides of the forms 
 from spreading. They can be cut off at the surface when 
 the forms are removed. 
 
 Rods in the bottom of a slab can be kept from lying on 
 the bottom of the form by placing small stones under them 
 just before the concrete is placed. 
 
 There is nothing better than round rods for reinforced 
 concrete for the reason that positive end anchorages can 
 be made by means of nuts and washers, or large square 
 plates having threaded holes, and because splices can be 
 made by means of sleeve nuts. Both the anchorage and 
 the splice will take nearly as much stress as the full sec- 
 tion of the rod. No other kind of anchorage or splice has 
 the same efficiency. The thread and nut detail comes into 
 play immediately without any slip. Rods laid together 
 and bound would have to slip before receiving much stress. 
 End hooks and curves are no doubt of some aid as a 
 precautionary measure ; they may show strength, after par- 
 tial straightening of the rod, before ultimate failure. A 
 hook cannot be seriously considered as an efficient end an- 
 chorage for a rod taking practically its full strength near 
 the end. 
 
 Wire cables in concrete are faulty from every standpoint 
 considered. The stretch in a wire cable, as compared 
 with a solid steel rod, as shown by tests made at Water- 
 town Arsenal in 1896 may be as much as four times that 
 of the plain steel rod under the same unit stress. The 
 safe unit allowed on wire cables (to be economical) would 
 be about four times as much as that on plain steel. Hence 
 the stretch in the steel cable may be sixteen times as much 
 as in the plain rod when consistent unit stresses are em- 
 ployed. The placing of initial tension in the cable can 
 
 74 
 
scarcely do more than take out the curving tendency due 
 to the winding of the coil. A stress of any magnitude on 
 the cable could scarcely be resisted by the supporting walls 
 or beams. 
 
 Sharp bends should not be made in steel rods under 
 stress, as the concrete cannot resist the stress at the 
 knuckle. Curves with a radius 20 times the diameter of 
 rod are permissible. 
 
 No welds should be allowed where the steel is under 
 stress approaching that allowed on the full section. If 
 rods were found to be a little too short to reach between 
 supports, it would not be harmful to weld a short piece on. 
 In general all welds in steel should be avoided. 
 
 Steel that is to be placed in concrete should be free from 
 scale and thick rust. A thin coat of rust is not objection- 
 able. It is well to let new rods rust so as to loosen the 
 mill scale. The scale should then be scraped off or brushed 
 off with wire brushes. The coating of steel with grout 
 to preserve it from rust is a doubtful expedient. The thin 
 layer of cement dries out and does not set properly. It 
 may not bond with the cement of the concrete. It is bet- 
 ter to have the fresh concrete come in contact with the 
 steel. A more intimate union is effected. 
 
 No paint should be used on any steel embedded in con- 
 crete. Grease and dirt are objectionable and should be 
 removed before the steel is placed. 
 
 Steel should be placed well in advance of the concrete, 
 so that any delay in placing it will not hold up the plac- 
 ing of the concrete. 
 
 Vertical reinforcement in hooped columns should be of 
 smooth rods so that when the concrete shrinks in setting 
 it will not be prevented from settling down. 
 
 No reliance should be placed on a short length of a rod 
 cither plain or deformed to act as anchorage. Where two 
 thin walls intersect they should be reinforced with steel. 
 If there is no special stress acting on the walls it is 
 enough to curve or bend rods around the corner. If, 
 however, there is pressure on the walls, as in the case of 
 
 75 
 
the walls of a rectangular cistern or the analogous case 
 of the bottom slab and rib or counterfort in a retaining 
 wall, the bend in the rods would be too sharp to be effec- 
 tive. In such case a short length even of a deformed rod 
 is entirely inadequate as an anchorage. The best form of 
 construction is probably a steel angle in the corner punched 
 to receive rods with nuts on the ends. 
 
 Steel rods are sometimes laid in the ground, as in the 
 case of those used to tie the shoes of steel arches together 
 in such structures as train sheds. To protect these from 
 corrosion a good plan is to wrap them in canvas soaked in 
 Portland cement grout and then to paint the canvas thick- 
 ly with grout. 
 
 Handling and Placing Concrete. 
 
 After concrete is taken from the mixer or the mixing 
 platform it should be placed as soon as possible in the 
 forms. As a rule the sooner it is placed the better. There 
 is, however, a possible exception to this rule. It is found 
 that concrete that is placed under water is less liable to 
 have the cement washed out of it, if it be allowed to stand 
 even for a period of two hours or more before being 
 placed. It should, however, be mixed again before being 
 deposited. Concrete placed under water would in general 
 be in a thick mass, so that any weakening due to partial 
 setting before being placed would not be of so much con- 
 sequence as it would be in such work as reinforced con- 
 crete. 
 
 It has been found also that retempered concrete will 
 adhere better to concrete that is set or partially set than 
 freshly mixed concrete. 
 
 Generally concrete should be placed in less than ^ hour 
 after mixing. It should not be disturbed more than abso- 
 lutely necessary after being put in place. If a receptacle 
 is used to hold the mixed concrete temporarily, the con- 
 crete should be taken out of it in the order in which it is 
 put in. If delay occurs in the placing of the concrete 
 
 76 
 
that results in leaving a batch mixed but not placed be- 
 fore the end of half an hour, generally the mixed concrete 
 should be rejected. However, if it is thoroughly re-mixed, 
 adding a little water, if necessary, it may be made quite 
 good for the purpose. It is found that retempered con- 
 crete is almost as good as freshly mixed concrete, if the 
 second mixing is well done. For walls and heavy work, 
 re-tempered concrete would not be objectionable. In col- 
 umns and floors the uniformity should not be disturbed by 
 using an occasional batch of concrete that has received a 
 different treatment from the rest of the work. 
 
 Jarring of the concrete in wheeling from the mixer to 
 the forms should be avoided. This jarring will tend to 
 separate the stone from the mortar. The runway for the 
 wheeling should be smooth. The concrete should not be 
 dropped far from the mixer, to the wheelbarrows or carts, 
 as this also separates the ingredients. 
 
 The mixer should be placed high and the ingredients 
 raised to it, so that the concrete will not have to be lifted 
 after it is discharged from the mixer. The concrete should 
 be handled as little as possible after leaving the mixer. 
 
 After the concrete is placed it should be left undisturbed 
 until it has received a hard set. To this end care must 
 be used in placing concrete beside other concrete that is 
 partially set. Jarring the projecting steel rods with the 
 buckets or carts in placing fresh concrete will impair the 
 bond of work that is partially set. Wheeling carts over 
 newly laid floors will have the same result. The work 
 should be planned so that concrete farthest from the mix- 
 er will be deposited first so as to avoid this. 
 
 Jarring the forms by the buckets or carts in which the 
 concrete is handled must also be avoided. In putting in 
 concrete piles the driving of the core for a pile near one 
 that has lately been placed may disturb the latter. Walk- 
 ing over newly laid concrete should be avoided as much 
 as possible. 
 
 The amount of concrete that should be placed at once 
 depends upon the kind of construction and the kind of 
 
concrete. Comparatively dry mixtures, which, in general, 
 should only be used in massive, unreinforced work, should 
 be placed in layers of about 6 inches of thickness and ram- 
 med. In such work concrete may be carried in half cubic 
 yard or cubic yard buckets, handled with a derrick. 
 
 In reinforced concrete, where semi-liquid concretes must 
 be employed, it is important that the concrete be poured in 
 such way and in such amounts as not to cause air pockets 
 to form. The same is true of any concrete that is to be 
 impermeable. Ramming is not essential in such concretes. 
 In fact, if the concrete is of such consistency that it can 
 be rammed, it is unsuitable for the purpose. In narrow 
 forms only small quantities should be dumped at a time. 
 The liquid concrete should be stirred and worked around 
 so as to make it flow into the corners and around the rein- 
 forcing steel. 
 
 If large quantities of concrete are placed at a time or 
 in one place in reinforced concrete work, it may cause 
 springing of the forms, or it may bend or displace the re- 
 inforcing rods or any rods that are used to brace the 
 forms. 
 
 Columns more than about twelve feet high should be 
 poured from a point half way up, so that the concrete will 
 not have so far to drop and so that puddling of the con- 
 crete around the reinforcement can better be effected. Then 
 the doors left for this purpose can be closed and the re- 
 mainder of the column poured. Special care is needed in 
 puddling the concrete in columns to make it flow around 
 the reinforcing rods. 
 
 Large quantities and thick layers of wet concrete may be 
 placed at once in mass work, if it can be done without' 
 leaving air pockets. The reason for ^comparatively thin 
 layers in rammed work is so that the ramming will be 
 effective. 
 
 Cinder concrete should be tamped lightly if at all, as 
 heavy tamping or ramming will break the cinders. A wet 
 mixture is most suitable for concrete made with cinders. 
 
 It is often necessary in exposed work to spade the con- 
 
 78 
 
crete against the forms so as to work back the large stones 
 and to bring the mortar to the surface. If thick layers 
 are deposited at once, this cannot well be done, and the 
 appearance will suffer. 
 
 If one or more batches of concrete are too wet, as ex- 
 hibited by free water on the concrete after being placed, 
 a comparatively dry batch or more should be mixed to take 
 up the surplus water. 
 
 Rammed concrete should be placed in layers approxi- 
 mately horizontal. If this kind of concrete is used in 
 arches the layers ought to be normal to the line of thrust. 
 This is difficult to do without setting up temporary forms 
 normal to the arch ring and tamping beside these. This 
 is an argument for the use of wet concrete in arches. 
 With wet concrete it is not important to have the layers 
 normal to the line of thrust except at quitting time. Where 
 it is possible, the work should be planned so that the en- 
 tire ring of an arch can be poured without intermission. 
 Another satisfactory plan is to lay successive rings end- 
 ing each against a temporary vertical partition. This could 
 be removed in a day or two, when the concrete would still 
 be green enough for the next ring to adhere pretty well 
 Another plan is to pour half of the arch ending it with a 
 vertical surface at the crown. 
 
 In exposed walls the layers should be kept higher on the 
 face especially where there is any tamping. Tamping 
 brings the cement to the surface and this makes a relative- 
 ly impervious layer. If this layer slopes out toward the 
 face, any water in the concrete will be shed outward, car- 
 rying with it any dissolved salts to the face of the wall. 
 The evaporation of this water leaves the salts as an efflor- 
 escence on the wall. 
 
 It is important that concreting be stopped, when discon- 
 tinued, at a joint where the strength is not impaired. To ef- 
 fect this the finishing surface, as stated, should be normal to 
 the line of thrust and it should not be where there is any 
 considerable shear. In a column the surface should be 
 horizontal and below the line where beams join in. It is 
 
 79 
 

 preferable to pour the columns some hours before the 
 beams and girders so as to allow some time for settlement 
 and shrinkage. It is better to pour an entire floor at once, 
 but if stops must be made, they are best made at the mid- 
 dle of the span of a beam or slab the latter being on a line 
 parallel with the beams; both should be against vertical 
 surfaces. A beam should not stop off near the support, 
 as the shear is great at such section. Where a beam and 
 slab are figured as a T beam, both should be poured at 
 once. Where the beam is figured as rectangular, it is not 
 so important that both be placed at once ; however, it is 
 better, as the full depth of beam includes part of the slab. 
 A notch could be left for the support of the slab, and thus 
 nearly all of the beam would be placed at one time. 
 
 Some engineers advocate splitting a beam or girder in 
 two in the middle, longitudinally, by a temporary vertical 
 bulkhead, when it is necessary to stop in the neighborhood 
 of a beam or girder. The author would not recommend 
 chis, but would rather leave a step the depth of the slab, 
 an inch or two wide, at the top of the beam. The slab 
 would find support on this step, and if the beam is figured 
 as a rectangular beam as it should be and not as a T 
 beam, it can borrow from the other slab for what may be 
 lacking in bond at the step. In a properly designed beam 
 carrying slabs there will, of necessity, be an excess of com- 
 pression area. It is better to rely upon this than to go to 
 the trouble and expense of fitting a bulkhead along the 
 center plane of a beam, with all of the added difficulties 
 this entails, such as narrowing up the space to work in, 
 possible displacing of the steel, different degrees of shrink- 
 age contraction in the beam, etc. 
 
 In enclosing steel work concreting should not be stopped 
 at or near a broad horizontal surface of steel, as the con- 
 crete will shrink away from the steel, and the thin crack 
 cannot be filled up. It is best to stop several inches be- 
 low or above such surfaces. 
 
 In walls, where possible, the stop should be made at 
 a horizontal or vertical bead or groove, so that the line 
 
 80 
 
at the junction of two days work will not show. There 
 are several advantages in placing walls in short lengftis 
 at a time. Vertical joints do not show up so bad as hori- 
 zontal ones, especially when these are made by use of a 
 bulkhead and are true to line. The contraction of the con- 
 crete due to setting will be equalized as the wall progresses. 
 These vertical joints will often be sufficient to take up ex- 
 pansion and contraction due to change in temperature. 
 The mixing plant can be moved from section to section, 
 thus lessening the distance through which mixed concrete 
 must be carried. 
 
 Before starting to place concrete it is important to see 
 that the forms are clean. The bottoms of boxes for beams 
 and girders and the bottoms of columns should be cleared 
 of all dirt, sawdust, shavings, blocks of wood, etc. Blocks 
 of wood may have lodged among the reinforcing rods of 
 walls or columns. These must be removed. 
 
 It is important to have the forms finished far enough 
 in advance of the placing of the concrete to insure continu- 
 ity of the concreting. 
 
 When leaving off the placing of concrete for the day 
 care should be taken to see that the finishing surface is 
 left so that the conditions of continuous work are approxi- 
 mated as near as possible. The bonding of the next days' 
 work should be made as good as the conditions will permit. 
 It is better, in general, to leave the surface rough than 
 smooth. In heavy work a bond may be made in several 
 ways. One way is to make steps in the top by setting up 
 vertical boards and tamping against them. Another way 
 is to bed large stones half in the last layer of concrete 
 allowing the other half to project into the new concrete. 
 Still another method is to lay wooden blocks in the con- 
 crete to form recesses and remove them before the next 
 day's work begins. 
 
 In reinforced concrete work and in impermeable con- 
 crete dependence must be placed more upon treatment of 
 the surface before starting to lay concrete than on rough- 
 ening it at quitting time. It is important in any work that 
 
 81 
 
the surface be clean. Also the forms should be cleaned of 
 any concrete that has been spattered on the day before. 
 Picking over the surface with picks, if it has stood long, 
 is recommended to remove the top skin. Washing the 
 surface with a hose and brooming or brushing it would 
 be sufficient, where it has not stood very long. This wash- 
 ing of the surface of the last day's placing of concrete is 
 very useful to get rid of the laitance or slime that comes 
 to the surface. It serves to lessen danger of efflorescence 
 and to make a better bond. The bond will be strengthened 
 by brushing over a thin coat of grout of neat cement or by 
 sifting neat cement on the previously moistened surface. 
 Bond to old and hardened concrete is effected by this same 
 means. 
 
 Much cement pavement work is being done in Pittsburg 
 by picking over the worn-out flag stone pavement to two 
 inches or so below the desired new level, moistening the 
 surface, dusting on neat cement and spreading the same 
 with a broom, and then laying cement mortar to the de- 
 sired level. 
 
 When concrete is placed in contact with bricks or porous 
 tile, these should be thoroughly saturated so as to im- 
 prove the bond and to prevent the absorption, by the por- 
 ous substances, of the water in the concrete. 
 
 A very good grade of concrete blocks or artificial stone 
 can be made by casting the blocks in sand as iron cast- 
 fngs are made. The mixture must be very wet, a consist- 
 ency that would be called soupy. The surplus water is 
 absorbed by the sand, and this serves to keep the block 
 moist during setting. By using a well selected aggregate, 
 such as crushed marble, crushed granite, white sand, etc., 
 excellent artificial stone can be made. The product is 
 dense and uniform, because the concrete is not dry and 
 tamped, and because varying atmospheric conditions have 
 no effect upon it while it is setting. These artificial stone 
 blocks are usually cast smooth and then tooled on the sur- 
 face by tools operated by power. A pleasing surface is 
 made by the use of carborundum wheels. If reinforced 
 
 82 
 
with steel, the blocks may be made quite thin, even down 
 to iVz or 2 ins. Blocks not reinforced, used for veneering, 
 are usually 3 or 4 in. thick. The blocks should remain 
 in the sand 4 to 6 days, and should then season for about 
 two weeks before being used. 
 
 Fine details in ornamental work will be more satisfactory 
 if cast in sand with very wet mixtures than in many other 
 kinds of molds or with dry mixtures. 
 
 Concrete blocks can be made of a medium mixture, mold- 
 ed under heavy pressure. Because of the pressure they 
 can be removed from the mold immediately. The blocks 
 are denser and better in every way than the hand tamped 
 blocks made from a dry mixture. 
 
 Large concrete blocks are often cast near the point where 
 they are to be placed in a structure in suitable forms of 
 wood or sheet steel or other material. When hardened, 
 they are lifted into place. Very heavy blocks can have 
 rings cast in them to facilitate handling. These blocks 
 may be used for breakwater construction, sea walls, arches, 
 etc. In sewer construction curved blocks can be cast and 
 the necessity of expensive arch forms and lagging avoid- 
 ed. The arch blocks can be held in place by the side 
 blocks, and little or no centering is required. In like man- 
 ner reinforced concrete slabs can be cast separately for 
 the top of a sewer, and as these exert no thrust the side 
 walls can be thinner. 
 
 The casting of reinforced concrete slabs may often be 
 found to effect a saving in the construction of sidewalks 
 and floors. These can be cast one over the other with 
 some kind of a separating medium and lifted into place 
 when hardened. 
 
 Beams and columns have likewise been cast on the 
 ground and lifted to place. In general this is a doubtful 
 expedient. The importance of the beams and columns of a 
 structure being tied together as a unit is very great, un- 
 less the walls of the structure supply all of the lateral 
 rigidity. 
 
 83 
 
Concrete piles are made both by casting them in place 
 or casting them on the ground and then driving. In the 
 first method the hole for the pile may be made by driving 
 a wooden pile and withdrawing it; or it may be made by 
 driving a collapsible core with a sheet metal shell and fill- 
 ing this shell with concrete; or it may be made by driving 
 a steel tube with a removable driving point and filling the 
 hole with concrete as this tube is drawn up. In any of 
 these methods the concrete should, in general, be well ram- 
 med so as to insure filling of the hole and the ability of 
 the pile to take a load without settlement. Piles that are 
 cast before being driven should be cast upright, if made 
 of dry concrete, so that the joint between the layers will 
 be normal to the direction of the driving. In wet concrete 
 it is not important whether the piles are cast horizontal 
 or vertical. However, unless they are well reinforced it 
 is difficult to raise long piles to the vertical position. As 
 far as practicable, the length of these piles should be 
 known before they are driven, as it is not practicable to 
 splice them, and it is difficult and expensive to cut them. 
 In driving concrete piles a hammer weighing nearly as 
 much as the pile and having a short fall is needed. The 
 blow of a light hammer will be absorbed locally and shat- 
 ter the pile. Concrete piles should stand two weeks or 
 more of good weather before being driven. Concrete 
 piles should be larger in diameter and generally fewer 
 in number than wooden piles for the same structure. 
 
 In placing concrete under water it is important that 
 it be treated in such way that the cement of the concrete 
 will not be washed out. Dropping concrete through a 
 depth of water will not only wash out some of the cement 
 but will tend to separate the ingredients. Concrete should 
 not be rammed under water, as the stirring of the water 
 will carry away cement. It should not be deposited in 
 running water. 
 
 If concrete is to be placed in water, it should be placed 
 in as large batches as possible. It should be wet concrete, 
 so as to require no ramming. It should be mixed long. 
 
 84 
 
Concrete that is mixed and allowed to stand several hours 
 and then mixed again is said to be preferable to freshly 
 mixed concrete for placing under water, as the cement is 
 partially set and is less liable to be washed out. It is 
 well to use about ten per cent, extra cement for the con- 
 crete that is to be placed under water to allow for loss. 
 
 The concrete may be lowered in steel buckets with bot- 
 tom doors that are opened when the bucket reaches the 
 bottom. Canvas sacks may also be employed. These sacks 
 are lowered with the mouth down. This is tied shut in 
 such way that it may be tripped open with a line. A bet- 
 ter way to place the concrete is to let it down through a 
 tube or tremie. This should be kept full of concrete, the 
 lower end resting on the bottom and being moved about 
 so as to distribute the concrete. 
 
 Reinforced concrete should, in general, not be placed 
 under water. Any concrete reinforced with steel that will 
 be submerged during setting and subsequently should be 
 designed so that no dependence will be placed upon the ad- 
 hesion or grip exerted between the concrete and steel. Con- 
 crete setting under water does not shrink and grip the steel 
 as that which sets in air. The rods should have nuts on 
 the ends and washer plates or some other effective end 
 anchorage. A riveted structure under water embedded in 
 concrete for its protective value, is legitimate construction, 
 if the concrete is of sufficient mass not to be cracked by 
 differential expansion. 
 
 When grout is to be used under water, as in filling inter- 
 stices in stone work, cracks in concrete, etc., neat cement 
 should be employed, as sand will separate from a mixture 
 of sand and cement in passing through water. 
 
 Concrete should not be deposited in polluted water, as 
 that containing sewage or discharge from pulp mills or 
 refuse from other washing processes. Such water com- 
 ing in contact with fresh concrete will destroy it by at- 
 tacking the setting cement. 
 
 In constructing inverts, such as the curved bottoms of 
 filter beds, sewers, etc., it is often best to omit the lag- 
 85 
 
ging as far up the side of the curve as the concrete will 
 permit without sloughing. The arch forms, however 
 should be in place to serve as guides in finishing the sur- 
 face. By omitting the lagging the concrete can be com- 
 pacted better, and a better surface finish can be obtained. 
 
 Much time and labor could be saved in the making of 
 concrete if the broken stone or gravel could be placed with- 
 out having to pass it through the mixer or having to pick 
 it all up in shovels and turn it a half a dozen times or 
 more. Such a process would not be productive of the 
 best grade of concrete because of the many chances of 
 air pockets being left and of lack of bond with the stone 
 due to failure of the grout to flow beneath the stones. 
 There are some situations, however, in which the kind of 
 concrete resulting from this process would meet all of the 
 requirements. This method of laying concrete for street 
 pavements is described in Concrete Engineering, Apr. 15, 
 1907, in a paper written by Mr. Walter E. Hassam. The 
 method there described is as follows. First the subgrade 
 is rolled to an elevation, for ordinary street paving in 
 concrete, about 6 inches below the finished surface. Then 
 broken stone of the egg size is spread to a sufficient depth 
 so that after rolling it will be 2 inches below the finished 
 grade of the street. The following is quoted from Mr. 
 Hassam's paper. 
 
 "This foundation stone is rolled or compressed until 
 thoroughly compact, and the voids reduced to a minimum. 
 It is then treated with a grout, composed of one part of 
 cement to 4 of sand. This grouting and rolling is contin- 
 ued, until all the voids are completely filled. This pro- 
 cess gives an exceedingly dense concrete, which is very 
 strong. 
 
 "For the wearing surface, there is spread upon the 
 foundation, before it has set, sufficient stone, of the stove 
 size, to bring the street to the required grade after roll- 
 ing. This stone is uniformly rolled or compressed, until 
 embedded in and united with the foundation. Then it 
 
is given a thin grouting of Portland cement and sand, 
 mixed in the proportion of I cement to 2 sand. 
 
 "The voids are thoroughly filled with grouting, and then 
 the surface is rolled until the grout flushes to the top of 
 the stone. As a finish, there is then applied a thin layer 
 of creamy cement and pea stone mixed in the propor- 
 tion of I cement, I sand and I of pea stone. 
 
 "This surface is poured on, brushed and rolled to an 
 even surface. The street is then allowed to set for at 
 least 6 days, when it is ready for traffic. The layers fol- 
 low each other so closely that the foundation does not set 
 until the whole is complete. When complete, the entire 
 road is a solid, homogeneous mass of rock and cement, 
 that will resist anything that can possibly come in contact 
 with it. 
 
 "The finished surface of the pavement presents to the 
 casual observer a smooth and fine appearance, but, on 
 close examination, it is found to be somewhat rough, so 
 there will be no slipping of horses or skidding of auto- 
 mobiles." 
 
 The above is the method of laying concrete used with 
 success in Worcester, Mass. It may be used for the con- 
 crete foundation of a brick or block pavement of any kind 
 or alone for solid concrete pavement. In a note regarding 
 these same pavements, in the Engineering Record, Vol. 
 53, p. 625, it is stated that for a cement wearing surface a 
 thick grout of sand and cement is poured over the founda- 
 tion (of rolled stone) and immediately filled with fine 
 crushed stone and rolled. 
 
 It is certain that concrete made as above described, with 
 thorottgly mixed grout, would be equal to if not superior 
 to the half mixed commercial concrete that often goes 
 into our city streets. The rolling and consequent compact- 
 ing of the broken stone before applying the grout produces 
 a foundation that is capable of supporting considerable 
 load without the aid of the cementing grout. 
 
 Other cases where concrete may be made in place, with- 
 out handling the broken stone in the mixer are in rough 
 
 87 
 
r 
 
 retaining walls or breakwaters. In these the grout may be 
 introduced by inserting steel pipes at intervals and forc- 
 ing the liquid mortar into the voids, either by gravity or 
 by air pressure. 
 
 The Setting and Hardening of 
 Concrete. 
 
 It is important that concrete be free from jar or disturb- 
 ance during setting. It should not be subject to intense 
 cold or high heat. Water in small interstices, as in the 
 body of concrete, will not freeze at 32 degrees; but it will 
 freeze at a somewhat lower temperature. If the mater- 
 ials can be kept above the freezing temperature until the 
 concrete is placed, danger of freezing is lessened by the 
 heat evolved in the cement during the process of initial 
 set; so that temperature higher than about 25 degrees can 
 be worked in without much danger. This is especially true 
 of concrete in thick masses. In thin walls or slabs the heat 
 generated will be quickly lost and protection is needed. 
 
 Protection of setting concrete may be afforded by the 
 use of tar paper or canvas or boards laid over it. A foot 
 or so of hay is good for this purpose. Two layers of can- 
 vas or tar paper, separated by boards, will give very ma- 
 terial protection. If only a single layer is used, it should 
 not be allowed to touch the concrete, but should be kept 
 out by boards. If manure is used, it should not be al- 
 lowed to come in contact with the concrete, and it should 
 not be allowed to become wet. Water that has absorbed 
 elements from the manure is apt to be injurious to the 
 setting concrete and to cause it to rot and be useless. Ce- 
 ment bags or tar paper used for protection should be well 
 lapped. 
 
 Placing of concrete in temperatures below 25 degrees 
 should be avoided where possible. If it must be done, the 
 best thing to do is to enclose the work with canvas and 
 heat the enclosed space with salamanders, or better with 
 steam. The concrete should be protected from the direct 
 
 88 
 
heat of any kind of stoves, so that it will not be dried out 
 too soon and prevented from setting. 
 
 Though concrete that has been allowed to freeze and 
 afterwards to thaw has, after having had time enough to 
 set, taken on apparently the strength of properly treated 
 concrete, it is not safe to rely on concrete thus treated 
 in any structure where strength is an essential feature. 
 Freezing should be avoided and prevented by means that 
 will not heat up the concrete and cause drying out. The 
 use of salt in the water is not recommended. Anything 
 short of a strong brine would freeze at a temperature not 
 much below 32 degrees, and the possibilities of efflorescence 
 and of corrosion of embedded steel make the use of salt 
 an undesirable risk. 
 
 While thoroughly seasoned limestone concrete may stand 
 400 to 500 degrees F. without any detriment or change of 
 structure, and other concretes may stand more, it is not 
 safe for it to be subject, while setting and hardening, to a 
 heat that will evaporate the contained water. The pres- 
 ence of water is necessary to the hardening of the cement, 
 and, if it be robbed of this water, it will suffer in strength. 
 
 Concrete that is setting will suffer from other than 
 thermal conditions which would not effect seasoned con- 
 crete. Water containing decaying organic matter, sewage, 
 the discharge from pulp mills, etc. will rot setting concrete, 
 though these substances will not, in general, have a dele- 
 terious effect on hardened concrete. Some oils will weak- 
 en setting concrete which could be safely stored in con- 
 crete tanks. 
 
 Water is necessary to the hardening of cement. The 
 water of mixing, if it be a liberal quantity, is sufficient for 
 this purpose in some cases, as when the concrete is in a 
 damp place; but it is generally best, and sometimes neces- 
 sary to the safety of the structure or the integrity of the 
 concrete, to add water during setting. Concrete should be 
 covered and protected from the rays of the sun and from 
 wind to prevent evaporation of the water. Concrete 
 blocks (the kind that are made of a concrete having the 
 
consistency of "moist earth" and tamped in molds, and 
 from which the molds are immediately removed) are 
 greatly improved and made to approach the condition of 
 good concrete, if they are immediately soaked, upon re- 
 moval from the forms, by allowing a smooth stream of 
 water under no pressure to run upon them until they will 
 take in no more. Generally these blocks are kept sprink- 
 led with a little water for several days to "cure" them. 
 It would be better to use preventive measures and fore- 
 stall the ailment by mixing them with plenty of water and 
 allowing the molds to remain until the concrete will stand 
 up. Not much can be expected of a block so porous as 
 to turn dark gray after a rain, even if cellular construc- 
 tion does keep the inside of the wall comparatively dry. 
 Disintegration is almost sure to get in its work. No nat- 
 ural stones that are not compact would be acceptable for 
 building work. 
 
 Rich mixtures of concrete need especially to be kept 
 moist during setting, as these are more apt to shrink and 
 crack on the surface or in the body of the concrete. A 
 rich mortar finish or a troweled surface should be kept 
 wet for nearly a week and protected from winds and sun 
 to insure its solidity. 
 
 Any thin coating of mortar or grout should not only be 
 put on a thoroughly saturated surface, but should be lib- 
 erally wetted for a day or two. Such coatings are apt to 
 have their water absorbed by the wall or evaporated and 
 to lose their cohesion. 
 
 When a concrete wall or pier is placed in a cofferdam, it 
 is well to let in the water around it a day after the con- 
 crete is placed. Concrete requires longer to set under 
 water than in the air, but it acquires greater strength. 
 Specimens that have hardened in water will show much 
 greater strength than those that have hardened in the air. 
 Immersion in water should be delayed until initial set 
 takes place. Moistening concrete will delay the setting to 
 some extent. This should be taken into account in gag- 
 
 00 
 
ing the time to remove the molds. Humidity in the at- 
 mosphere acts in some degree like immersion in water. 
 
 The time that should elapse between the placing of con- 
 crete and the removal of the forms depends upon a num- 
 ber of things, among which are the consistency of the con- 
 crete, the richness of the mixture, the load sustained, and 
 the temperature and atmospheric humidity. Wet concretes 
 require longer to harden than dry concretes. Lean con- 
 cretes require longer than rich ones. Concrete hardens 
 more slowly under water or in a saturated atmosphere 
 than in dry air. Low temperatures delay the setting of 
 concrete. If the temperature be below freezing, the sett- 
 ing may be suspended. Failures have resulted on account 
 of forms being removed from concrete that was frozen 
 and appeared to be hardened due to setting. 
 
 Another error apt to be made is to mistake drying for 
 setting. Drying is not a necessary accompaniment to the 
 hardening of concrete. In fact if the concrete is too warm 
 and the air too dry the early drying of the concrete that 
 will result will be detrimental to its strength. Concrete 
 should not be allowed to dry out until it has stood for 
 several days. Sidewalks should be sprinkled for four 
 or five days. They should be covered and protected from 
 currents of air. Plastered work and reinforced concrete 
 need special care in the matter of maintaining moisture 
 on the surface; otherwise shrinkage cracks will develop. 
 
 Concrete blocks need frequent and copious sprinkling, 
 which should be continued for a week or more. 
 
 Concrete receives its set when it reaches the state where 
 a change of shape cannot be produced without rupture. 
 This requires from a few minutes, in rich mortars of quick 
 setting cement, to several hours, in lean mixtures. A com- 
 mon way of determining when concrete has set is by pres- 
 sure of the thumb nail. After the set has taken place the 
 concrete continues to harden and gain strength for months 
 and sometimes for years. In ordinary weather nearly the 
 full strength is attained in six or eight weeks. Loading 
 tests may be made at this stage. Strength necessary to 
 
 91 
 
support its own weight is reached at varying periods de- 
 pending upon several conditions. 
 
 In counting the time that concrete should stand before 
 removing the forms days when the temperature is at or 
 below freezing should be counted out, or at least allow- 
 ance should be made for almost total suspension of the 
 hardening process. 
 
 It is safe to remove the forms from mass work, receiv- 
 ing at the time no load except its own weight, in from one 
 to three days ; in warm weather with dry concrete, one day, 
 in cold or wet weather or with wet concrete, more time. 
 When the concrete will bear the pressure of the thumb 
 nail without indentation, it is ready to support itself in 
 this class of work. Thin walls should stand two to five 
 days. Slabs of reinforced concrete should stand about one 
 to two weeks of good weather before being called upon to 
 support their own weight. Slabs of long span may require 
 more time than two weeks. At the same time that the slab 
 centering is removed, or even before it is taken down, the 
 forms on the sides of beams and girders can be removed, 
 leaving the supports of the bottoms in place for a longer 
 time. This will afford an opportunity to inspect the sur- 
 face of the beams and girders and to plaster up any cavi- 
 ties before the concrete is too hard. Where practicable 
 it is well to leave the shores under beams and girders for 
 three or four weeks. Large and heavy beams should be al- 
 lowed to stand longer than short ones, because the dead 
 weight is a greater fraction of the load they are designed 
 to carry. 
 
 Column forms can be removed in a week or so, if the 
 entire weight of the beams is supported by shores close 
 to the columns, otherwise three weeks or more should be 
 allowed. 
 
 Arches of small span can have the centering removed in 
 one to two weeks. Large arches should harden a month or 
 more. Where practicable it would be well to leave the 
 concreting of the spandrel wall of an arch span until the 
 arch ring has hardened and the forms are removed. The 
 
 
settling of the arch often cracks the spandrel wall and 
 gives an unsightly appearance to the bridge. 
 
 Ornamental work should have the forms removed as 
 soon as possible, so that defects can be plastered up and so 
 that swelling of the wood will have less tmie to act. 
 
 Falsework should be removed carefully, without jar to 
 the concrete either by hammering on the boards or drop- 
 ping heavy pieces on the floor below. The supports should 
 not be removed when any unusual load is on the floor. 
 Materials should not be stored on floors that are not thor- 
 oughly hardened and self supporting. 
 
 Concrete in reinforced work should ring when struck 
 with the hammer, before the supports are removed. 
 
 Finishing Concrete Surfaces. 
 
 One of the chief difficulties in connection with the use 
 of concrete is to get a surface finish that is pleasing iu 
 appearance and at the same time economical. The various 
 methods in use will be taken up with a view of showing 
 their good and bad features and their limitations. 
 
 Surfaces that are wrought in other materials than con- 
 crete will first be considered. 
 
 A common and acceptable surface finish is a veneer of 
 brick. Brick work in 4 in. thickness may be laid against 
 a concrete wall. For example, if a 13 in. wall would be 
 required, an 8 in. wall of concrete may be put up in the 
 regular way, using wooden forms, then the brick may be 
 laid outside of this. Metal bond is often used, small pieces 
 of wire or other metal being bedded in the concrete and 
 projecting out to be built into the brick work. An other 
 than metal bond is preferable. The metal is not thorough- 
 ly protected in a brick wall because of the porosity of the 
 wall. Occasional belt courses of cut stone projecting out 
 for the support of the brick work would serve to lessen 
 the height of the unsupported brick veneering and thus 
 lessen dependence on metal bond. A good method of bond- 
 ing -would be to leave vertical recesses, at intervals, about 
 
 93 
 
the width of a brick. Into these headers could be laid and 
 thus a very satisfactory bond secured. 
 
 Another way to have a brick surface is to lay up the 
 brick wall and use it as the outside of the form pouring 
 the concrete behind it. 
 
 Cut stone and artificial stone veneers may also be used 
 in the same way as brick. This is satisfactory for a wall 
 not taking much vertical load. It may lead to structural 
 weakness, if used for a pillar taking a concentrated load. 
 More than one case could be cited in large buildings, 
 where reliance upon a combination of a stone shell and a 
 core of other material in a pillar, to take a load, necessi- 
 tated the removal of the pillars and the insertion of steel 
 columns after the walls were completed. Cracks in the 
 stone veneer showed that it was taking the load, and that 
 it was not capable of withstanding it In one building 
 the core was of rubble masonry and the shell was of cut 
 stone; in another the core was of concrete and the shell 
 was of artificial stone. Both rubble masonry and con- 
 crete will shrink on account of the large proportion of 
 mortar. The cut stone and the artificial stone, with their 
 deep courses and thin mortar joints, do not shrink any 
 perceptible amounts. The result is that about all of the 
 load must be carried by the veneer. The same fault has 
 been observed, where tile facing was backed with brick. 
 In this case the cracking of the tile was attributed to 
 failure of the mortar to set because of the cold weather. 
 Settling of the brick work behind the weak tile would, 
 however, be apt to produce the same result in work set up 
 in warm weather. In construction of this sort no depend- 
 ence whatever should be placed upon the veneer in sup- 
 porting the load, and it should be built in such way as to 
 allow the core to shrink in setting. This might be effect- 
 ed by using wooden blocks a trifle higher than the stones 
 for one or more courses and removing these later and sub- 
 stituting the stone or tile. It might also be done by leav- 
 ing out the top course of stone or tile facing. Or a number 
 of the joints in the facing might be raked out, soon after 
 
the concrete backing is placed, and, after the concrete has 
 set and shrunk, these joints could be pointed. The use 
 of dry tamped concrete would lessen the shrinking. In a 
 long wall brought up slowly the shrinking will not be so 
 harmful. In a small pillar a cast iron or steel column 
 should be used in the middle. 
 
 In the present state of the art artificial stone or cut 
 stone facing is probably the best surface treatment for 
 concrete in such construction as residences and office build- 
 ings. This is partially due to the fact that concrete work- 
 ers have not developed the skill that workers in the other 
 materials possess. Brick work with the outer % in. or so 
 of mortar "raked out" (or blocked out with wooden cleats, 
 as is done in practice) makes an appropriate and pleas- 
 ing surface finish for rugged styles of architecture. 
 
 Blocks in glazed tile are made use of for external fin- 
 ish of buildings. With these it is even more important 
 that but a short height be laid at once, if concrete is poured 
 behind them, or some other precaution be employed to pre- 
 vent their receiving any of the load of the waif. These 
 tile are brittle and unreliable in supporting loads. 
 
 Thin tile can be used as an external finish by pasting 
 them on paper, as they come for pavements, and then past- 
 ing the paper, with bill posters' paste, on the inside of the 
 forms before concrete is placed. Before the forms are 
 removed they must be thoroughly flushed with water. 
 
 Boulder facing may be made on rustic walls or arch 
 spans by placing the boulders against the forms and then 
 the concrete behind them. 
 
 Of the surface finishes that are made in the concrete 
 itself there may be mentioned those that are made in the 
 concrete by aid of the forms, while it is being placed, and 
 those that require subsequent treatment. 
 
 If the concrete is simply placed against the rough sur- 
 face of sawed boards, it will have the impression of the 
 saw marks and grain and knots as well as the cracks or 
 joints. This is far from pleasing for any surface above 
 the ground. When the forms against the exposed face are 
 
 95 
 
made of planed boards, tongued and grooved, and neatly 
 jointed, the surface is greatly improved. A broad surface 
 can be relieved of its monotony by paneling. The larger 
 and rougher the surface the bolder the panels should be. 
 Long retaining walls should preferably have panels to re- 
 lieve the dead flat surface. 
 
 If the concrete is thrown indiscriminately against the 
 forms, the surface will not present a smooth appearance, 
 especially if dry concrete is used. By manipulating the 
 concrete with spades or shovels it can be given a richer 
 and smoother surface. As a layer of concrete is placed 
 a shovel is run down against the form and the larger stones 
 shoved back. This allows the mortar of the concrete to 
 flow against the form, and a surface of mortar results. 
 Sometimes a perforated shovel or spade is used for this 
 purpose, and the mortar passes through the perforations. 
 With rammed or dry concrete the spade may be used to 
 shove back the concrete and a wetter mortar poured in. 
 Of course the smoother the forms for this class of work 
 the better will be the appearance of the work. 
 
 In narrow forms it is recommended by one engineer 
 that instead of a spade a hoe be used with the blade bent 
 nearly in line with the handle. 
 
 Another way by which a mortar finish may be made is to 
 plaster the forms with cement mortar in advance of plac- 
 ing the concrete. The mortar and concrete are united by 
 tamping. 
 
 Another way to obtain a mortar finish is to place a loose 
 board against the forms and tamp the concrete behind the 
 board. The board is then removed and mortar run into 
 the space that it occupied. This is of course only appli- 
 cable to comparatively dry concrete. 
 
 Still another method is to use a sheet of steel on the 
 one side of which are riveted i" x i" angle irons to act 
 as runners and spacers. The sheet may be any convenient 
 width and length, depending on the nature and size of the 
 work. It is flared out at the upper edge to act as a hop- 
 per. The contrivance is placed with the angle irons against 
 
 96 
 
the surface to receive the mortar finish. Mortar is placed 
 on one side and concrete on the other. Then by means 
 of handles the sheet is drawn up and the concrete tamped 
 to unite the mortar and concrete. It should not be drawn 
 quite out of the concrete. There is difficulty in carry- 
 ing up a long line of this kind of concreting, especially at 
 corners and at the junction of two sheets. It cannot be 
 worked w r ell in a narrow space. 
 
 Of the foregoing methods the manipulation with the 
 spade or other similar tool against the forms is probably 
 the most satisfactory for the reasons that it can be done 
 with wet concrete and in a narrow space, and because it 
 results in a more uniform concrete. The mortar of the 
 entire mass is uniform, the only difference at the sur- 
 face being that the stones are not exposed. Separate mor- 
 tars do not bond so well. It is especially true of work done 
 in freezing weather that a mortar of a different mixture 
 from that of the concrete is apt to break away from the 
 body. 
 
 Concrete of small aggregates, as that used in reinforced 
 concrete, does not need to have the mortar brought to the 
 .surface, as a rule. The churning and puddling, which 
 should be done in any case to work out the air bubbles 
 and to work the concrete into corners and around the 
 steel, will serve to give the concrete the smooth surface 
 desired, if the mixture is the proper richness and con- 
 sistency. 
 
 In order to cover up the roughness of the boards and 
 to prevent them from adhering to the concrete, as well 
 as to prevent the knots from discoloring the concrete, a 
 filling coat is sometimes used on the wood. Soft soap 
 may be used for this purpose, applied with a brush. Lin- 
 seed oil may also be used. Fatty oils should not be used, 
 as they act on fresh concrete disintegrating and discolor- 
 ing it. Hot paraffine is sometimes used. Crude oil is a 
 very good substance to prevent adhesion of the concrete 
 to the wood. A mixture of crude oil and kerosene also 
 gives good results. 
 
 97 
 
If the wood is thoroughly wet with water before the 
 concrete is laid, there is not much danger of concrete ad- 
 hering. This wetting is to be recommended for the fur- 
 ther reason that the wood will not then absorb water from 
 the concrete. 
 
 Paper, unless it is oiled, will stick to the concrete and is 
 hard to remove. Burning may have to be resorted to. 
 
 One method used successfully to cover up the grain of 
 the wood was to paint the surface with a gloss oil and to 
 blow sand into this with a bellows. 
 
 The author does not know of any case where canvass 
 painted with linseed oil has been used as a cover for rough 
 forms, but he believes it would be an admirable material 
 for the purpose. It is waterproof and would therefore 
 not absorb water from the concrete; it would also prevent 
 the leaking of the liquid mortar that occurs at cracks or 
 joints in the wooden forms. It would probably be econom- 
 ical for the reason that it does not require planed boards 
 in the forms and it could no doubt be use'd repeatedly. 
 It would further help to keep the frost out of the concrete. 
 
 With all the means used to cover up the irregularities 
 of the wood and to make the surface smooth there will 
 still be some roughness not commercially avoidable. Some 
 treatment after removal of the forms is generally neces- 
 sary. Air pockets may occur in places where the holes 
 will be exposed. These should be plastered with a rich 
 mortar. Corners may break off in removing the forms. 
 These should also be plastered. If large chunks of con- 
 crete break away in an important part of the structure, 
 the best thing to do may be to remold the piece. Any 
 sign of extended weakness in the concrete may show 
 that a bad batch of concrete was used or that the con- 
 crete has been mistreated during setting. 
 
 If made right, the concrete surface will have a skin of 
 neat cement. It is generally desirable for appearance sake 
 to remove this, and there are several ways to do it, de- 
 pending upon the length of time that the concrete has set, 
 before it can be made accessible for treatment. The time 
 
 a 
 
that elapses from the placing of the concrete until the 
 surface can be exposed depends upon the kind of concrete 
 and the nature of the part of the structure in question. 
 
 If the surface can be exposed a few hours after the 
 concrete is placed, this cement may be removed with clean 
 water applied by means of a hose. The hose should be 
 used without a nozzle, as the pressure would gouge out 
 stones. Water may also be applied with buckets. Heavy 
 walls in dry concrete could probably have the forms re- 
 moved in half a day or so after concrete is placed, and 
 the surface could be thus treated. The forms should not 
 be removed so soon on a high section of wall. 
 
 If the concrete has set for about 24 hours, clean water 
 and scrubbing brushes will remove the outside skin of 
 cement. If about two days have elapsed, wire brushes 
 may be needed, using water to wash away the loosened 
 cement. If the concrete surface is hard, more vigorous 
 work is required to make it smooth and to take off the 
 skin of cement. Blocks of sandstone, or of concrete of 
 cement and sand, or of carborundum, with water, may be 
 used to scour the surface. These are rubbed with a cir- 
 cular motion. When a sand blast is available, this is an 
 excellent means of accomplishing the desired result. 
 
 Some preliminary treatment will usually be found to 
 be necessary, such as chipping off rough projections, as 
 those left by cracks in the mold, filing off the arrises, etc. 
 
 These scouring processes have for their object the se- 
 curing of a smooth surface. Sometimes, after the surface 
 is washed and scoured reasonably smooth, some grout of 
 cement and sand is brushed on, and by the same circular 
 motion with the bricks, this grout is worked into any 
 pores in the surface. The result, after the setting of the 
 grout is a very smooth surface. 
 
 A smooth surface is not always desirable. Some rough- 
 ness is more in keeping with the nature of the concrete 
 anH is more pleasing in appearance in many situations. 
 The washing or scrubbing off of the skin of neat cement, 
 above described, will expose the surface of tfie aggregate 
 
 99 
 
and leave the desirable dull or rough surface without any 
 further treatment. The appearance will then depend upon 
 the selection of the aggregate. If a mortar of sand and 
 cement be exposed on the finished surface, the washed 
 surface will resemble sandstone. By using white sand the 
 appearance will be that of nearly pure white sandstone. 
 Other colors can be obtained by using different colored 
 sands. 
 
 Torpedo sand, a sand having large grains, used in the 
 surface mortar, will, when the surface is washed clean of 
 the cement skin, give a good appearance. The same is 
 true of small regular sized pebbles or of small sized 
 crushed granite or limestone, screened to */i in. or so. 
 Colored granite can be used with good effect to obtain a 
 red, black, or gray surface. Colors obtained in this way 
 are more durable and uniform than those made by use 
 of coloring pigments. 
 
 The surface treatment by use of regular sized particles 
 in the aggregate and subsequent washing off of the skin 
 of cement may be carried to any size of stones, even to* 
 that of cobble stones. This style of finish in pebble size 
 is especially appropriate in park pavilions, concrete fences, 
 etc. If a dense impervious concrete is not essential, a 
 dry mixture can be used and the washing away of the 
 mortar skin dispensed with. This sort of finish on rein- 
 forced concrete arches can be employed by using the dry 
 concrete with coarse sand, or small pebbles, or 1 A in. bro- 
 ken stone for a depth of an inch or so against the forms 
 and a wet impervious concrete surrounding the steel. 
 
 Where the concrete is molded and not plastered, there 
 is an advantage in using a stiff mixture in preference to a 
 wet mixture, as the forms can be removed in a shorter 
 time, and the washing off of the cement is easier and 
 cheaper of accomplishment than when it has a harder set. 
 The lack of density and impermeability due to the dry 
 mixture would make this method less applicable to build- 
 ings whose character demands that the walls be not ab- 
 sorbent of water. 
 
 100 
 
Concrete of materials not affected by acids, such as sand, 
 gravel, granite, and trap can be treated to a surface scrub- 
 bing of a 20 per cent, solution of hydrochloric acid. This 
 will remove the cement skin, even after a hard set. The 
 acid must be immediately neutralized with alkali to pre- 
 vent penetration into the concrete, and all must be washed 
 off with clean water. The disadvantages connected with 
 this method are the high cost and the difficulty of hand- 
 ling the acid to apply it and the fact that the acid that 
 wastes and is not neutralized may penetrate into the base 
 of the structure and destroy the concrete. 
 
 This acid wash may also be used to remove efflorescence 
 from concrete surfaces. 
 
 Coloring of the surface of concrete may be effected, as 
 stated, by using naturally colored aggregates and washing 
 the surface. Pigments are also used. These are not apt 
 to be very permanent. If used in large quantities they will 
 weaken the concrete. If used in the entire body there is 
 a waste of material in that which is not exposed, and it is 
 difficult to get uniformity by any other means, unless it 
 is a case where plastering is permissible. If pigments are 
 used, it is best to mix them thoroughly with the dry ce- 
 ment. A little lamp black can be used to advantage in 
 ordinary concrete to relieve the dirty color of the concrete. 
 This could be placed in the mixer with the cement, a given 
 quantity for each bag of cement. 
 
 Concrete surfaces will not hold oil paint very well; the 
 washing off of the skin of neat cement will make them 
 more retentive. In any event oil paint is not appropriate 
 to the nature of the concrete except for interior walls and 
 ceilings. A wash of neat cement can be applied to a wall, 
 or the cement may be mixed with plaster of Paris or bet- 
 ter with marble dust. Either of the latter will give the 
 appearance of marble. In applying these the mixture 
 should not be too thin or it will crock. If it is too thick 
 it cannot be worked with the brush. An ordinary white- 
 wash brush is used in its application. It is necessary that 
 the surface be thoroughly drenched with water just before 
 
 101 
 
the application, otherwise the wall will absorb the water 
 in the cement and prevent setting. The surface must be 
 kept wet for a day or so. 
 
 Some of the things that contribute to unsightly appear- 
 ance in concrete work are the following. Their remedy 
 is evident, (i) Irregularity in the nature of the ingre- 
 dients. This applies to the stone, sand, and cement. It is 
 evident that unless the first two run uniform, there will not 
 be a uniform surface on the concrete. It is also true that 
 different brands of cement may give different colors. (2) 
 Lack of uniformity in the amounts of ingredients in each 
 batch. (3) Insufficient mixing in any or all batches of 
 concrete. (4) Dirt on the forms. (5) Want of care in 
 placing, tamping, spading, etc. 
 
 Of surfaces that face upward, vertical surfaces, and 
 those that face downward the latter are the most difficult 
 of treatment. This is of course because of the fact that 
 generally from two to four weeks must elapse after plac- 
 ing the concrete before these can be safely exposed, because 
 of the necessity of supporting the setting concrete. The 
 difficulty of reaching such surfaces makes their treatment 
 doubly expensive. A sandblast or scouring with bricks for 
 interior exposed beams and ceilings would be best. For- 
 tunately in arches and exterior girder work the under 
 side does not show up to any extent and can often be left 
 rough. 
 
 Pavements and floors are in a class by themselves and 
 offer the most satisfactory conditions for surface finish. 
 Ordinary sidewalks as commercially made are often put 
 down in the following way. After the sub-grade is tamped 
 and the layer of cinders or broken stone for drainage is 
 laid down and tamped (generally a thickness of 4 to 6 
 inches) a layer of stiff concrete is placed and rammed. 
 This is about 3 or 4 inches thick and is usually a gravel 
 concrete of about 1 13 :6 mixture. This concrete base is 
 blocked off and sand joints used to separate the blocks. 
 Then this concrete is left until the next day, when a top 
 coat of cement mortar is laid, usually a i :2 or 1 13 mixture 
 
 * 
 
of cement and sand or crushed granite }i" size and under. 
 This finishing layer is generally a rather stiff mixture. 
 When placed, it is troweled smooth and cut into blocks, 
 the cuts being directly over the sand joints in the concrete 
 base below. After hard troweling to a smooth surface a 
 toothed roller is passed over the surface to give it a some- 
 what roughened surface. The advantages in this kind of 
 pavement are largely on the contractor's side. He does 
 not waste any cement that would be in extra mortar, if 
 wet concrete were used, and some of it should flow down 
 into the base of loose stone used for drainage. Without 
 a rich top coat he obtains a rich skin on the top of the 
 pavement by troweling. Why the pavement is allowed to 
 stand a day before the top coat is laid, and the union of 
 the top coat with the base endangered, is not clear. 
 
 A better method (and the method employed by some 
 pavers) is to use a moderately wet concrete and to place 
 on this without any intermission the finish coat and to re- 
 duce the troweling to a minimum. Work expended on 
 troweling would often be better employed, if it went to- 
 ward a more thorough mixing of the mortar. If the mor- 
 tar be placed on the fresh concrete before the latter has 
 time to take on an initial set, a good bond will be effected, 
 and in no other way can such bond be assured. 
 
 Some of the faults that are very common in sidewalks 
 are pitting of the surface, mapping and hair cracks or 
 even large and growing cracks, and breaking off of pieces 
 down to the concrete base. The latter sometimes exhib- 
 its itself in the splitting away of the top coat from the 
 concrete base, and the pavement has a hollow sound. 
 
 These faults are largely the result of the method of mak- 
 ing pavements above described. Excessive troweling, es- 
 pecially in a mortar not rich in cement, draws to the sur- 
 face a skin of cement and leaves just below it sand or 
 screenings partially robbed of their cement. This neat 
 cement does not possess much resistance to wear, and when 
 it is worn off the insufficiently cemented sand or screenings 
 show up in spots or pits. Another result of much trowel- 
 103 
 
ing is that the skin of cement thus formed shrinks in set- 
 ting and causes hair cracks or mapping of the surface. 
 Sometimes large shrinkage cracks are formed, which con- 
 tinue to increase in size. Lack of proper provision for 
 expansion and contraction at the regular joints intended 
 co take up the motion may be the cause of some of the 
 large cracks observed. It is not enough to make a groove 
 at the surface of the pavement to relieve the tension. There 
 should be a complete separation of the blocks. 
 
 The splitting away of the mortar coat is the natural re- 
 sult of insufficient bonding between the concrete base and 
 the mortar finish. 
 
 In contrast with the method of laying pavements above 
 referred to the author recently observed the laying of con- 
 crete in the floor of one of the largest reinforced concrete 
 buildings in the world. While the body of the concrete 
 was fresh, the surface being quite rough, no attempt what- 
 ever having been made to make it even approximately 
 horizontal, the mortar for the top finish was poured. This 
 was of the consistency of soup. Men waded in concrete 
 6 or 8 inches deep to spread the mortar about with shovels. 
 Then the top surface was leveled off by working a straight 
 edge back and forth. In this work the concrete of the 
 body of the floor slabs while it was soft enough to allow 
 the men's feet to sink into it, did not show any water on 
 the surface for the reason that it was not tamped. 
 
 If there is an excess of water in the concrete base in 
 pavement work the bond may be impaired between this 
 and the finishing mortar. Concrete in the base almost wet 
 enough to flow, spread out to a uniform depth with rakes 
 rather than tamped to a smooth flat surface covered with 
 laitance, would present a much better opportunity for the 
 bonding of the finishing mortar. 
 
 In steps and other parts where vertical surfaces must be 
 finished off it is necessary in the ordinary methods of mak- 
 ing sidewalks, to use stiff concrete and to plaster on the 
 mortar, also a stiff mixture, as soon as the molds can be 
 removed. The necessity for using stiff concrete is to allow 
 
 104 
 
of early removal of the molds, so that plastering can be 
 done on the surface before the concrete has a hard set. 
 Generally steps are troweled to a smooth finish, though the 
 treads would be better to have a rough surface to prevent 
 slipping. 
 
 The rough surface on pavements, so desirable on steep 
 grades and in fact desirable most anywhere to overcome 
 slipperiness in cold or muddy weather, is obtained in sev- 
 eral ways. A steel trowel must not be used in the finish- 
 ing process, if any kind of rough surface is to be made. 
 In fact a steel trowel should be used sparingly in pave- 
 ments. If a smooth glossy surface is wanted, it should be 
 made by using a rich mixture and fine sand in the finish- 
 ing mortar rather than by rubbing with a steel trowel. 
 
 In the process of leveling off the pavement when the 
 mortar coat is laid a wooden straight edge is used. This 
 is worked back and forth on the side boards forming the 
 mold for the pavement until all of the high places are 
 brought down and all of the hollow places filled in. If 
 the mortar is uniform in consistency and well mixed, the 
 work could stop here, so far as the greater part of the 
 surface is concerned, and the rounding of corners and 
 marking and dividing into blocks would complete the pave- 
 ment. A strip about iVz in. wide rubbed smooth with 
 a tool for the purpose is usually made around each block. 
 The surface can be given a kind of regularity, if in man- 
 ipulating the straight edge it be moved back and forth two 
 or three inches as it is pushed forward making sinuous 
 lines along the pavement. A wooden float may be used, 
 after the surface is made horizontal by the straight edge 
 or by a trowel, where a straight edge cannot be employed. 
 The desired roughness can be made in this way. What 
 is probably the most pleasing surface appearance for pave- 
 ments is obtained by use of a wooden plate. The surface 
 is stippled with this, and by suction against it a most work- 
 manlike and artistic finish results. Another way to pro- 
 duce the rough surface is to throw the last half inch or 
 so of mortar with the trowel, a little at a time. 
 
 105 |j 
 
It is a mistake to sprinkle dry cement on the surface 
 of a pavement. 
 
 To overcome the tension due to troweling, where the 
 pavement is troweled, and to roughen the surface it may 
 be broomed or brushed with a corn brush just after trow- 
 eling. 
 
 Where a smooth troweled surface is desired the final 
 rubbing should be done a half an hour or so after the 
 mortar is laid. Less cement would then be drawn to the 
 surface, and the surface tension will be less. For smooth 
 troweling the mixture should not be very wet. 
 
 It is best to lay pavements in alternate blocks against 
 bulkheads or vertical boards placed temporarily where joints 
 are to be. Where this is not done, the concrete base should 
 be marked off in blocks and separated, while the concrete 
 is green, by making joints ^4 inch wide or so, filled with 
 sand or tar paper or other filler. The location of these 
 must be marked before the mortar finish is laid, and when 
 the latter is finished oft" it should be cut with a thin trowel 
 making a complete separation and not merely a groove. 
 Very little if any space is needed between blocks to take 
 up expansion and contraction due to change in tempera- 
 ture, but the contraction due to shrinkage in setting may 
 be enough to split the block at some other section than 
 in the groove, unless a complete separation is made. 
 
 Pavements that are not on a grade are generally given 
 a slope of ^4 in. to the foot for drainage. 
 
 There is a difference of opinion as to the proper mix- 
 ture for a mortar finish on pavements. Some engineers 
 would not use a mortar richer than 1 :2 or 1 :3 because of 
 the fact that with troweling a rich mortar will check. 
 Others specify mortar coats as rich as 1:1. If the mortar 
 is of the same richness as that used in the concrete (e. g. 
 a 1 :2 mortar for a 1 12:4 concrete) there ought to be equi- 
 librium in the mass. Mixtures of 1:1% to 1:2% with 
 granite screenings that will pass through a sieve having 
 V* in. meshes give satisfactory results. The former is 
 much used in high class pavement work. Particularly 
 106 
 
glossy surfaces are obtained by richer mixtures, using as 
 rich as I :i. Such pavements, while they may be good in 
 the interior of buildings, are too slippery for out-of-doors. 
 
 For hard smooth surfaces fine sand may be used. Fine 
 sand should only be used in a rich mixture. For a rough 
 surface or in leaner mixtures use coarse sand or screen- 
 ings. 
 
 Plastering on vertical surfaces of concrete should be 
 avoided where practicable. It is often necessary, however, 
 and when it is done, special precautions should be taken 
 to make the plaster adhere. If it is not important that the 
 body of the wall be dense and impermeable, plastering 
 will adhere better, if the concrete be made dry, on account 
 of the rough surface. There is a further advantage in 
 using dry concrete, if other considerations do not demand 
 wet concrete, namely; the forms can be removed soon 
 after the concrete is placed and before the cement has a 
 hard set. It would be well in some cases to wash or scrub 
 the surface or to pick it before applying the plaster. Lime 
 paste mixed with the cement and sand for plastering in- 
 creases the adhesion and lessens the tendency for hair 
 cracks to form on the surface. Lime delays the setting of 
 the cement and makes it easier to work. Lime paste can be 
 used in quantities up to an equal amount with the cement. 
 If a hard surface is desired, less lime would be used. In 
 this plastering, as in pavements, it is well to go over the 
 surface with a brush or broom after troweling to relieve 
 the tension of the cement. In plastering piers and abut- 
 ments the trowel marks can be removed by brushing hori- 
 zontally with a whisk broom. The surface appearance is 
 greatly improved by this means. 
 
 A simple, and inexpensive mode of plastering is what 
 is called a splatterdash coat. The mortar is thrown or 
 splashed against the surface with a paddle. An effective 
 rough surface can be made in this way. The methods 
 used on pavements to produce a rough surface, by means 
 of wooden floats and stippling, can be employed to good 
 advantage on walls. A rough surface is generally better in 
 107 
 
appearance and less liable to crack than a smooth surface. 
 
 A method recommended to secure a good bond is as fol- 
 lows. First the surface is washed, then after thorough 
 drenching with water a coat of neat cement grout is brush- 
 ed on. While this is still wet a coat of plaster about % 
 in. thick is put on. Succeeding coats of the same thick- 
 ness are applied about an hour apart until the desired 
 thickness is attained. As a finish the last mortar may be 
 thrown on, to give a rough surface. 
 
 Plastering should, in general, be resorted to only to fill 
 in holes and to smooth over rough places. A plaster coat 
 should either be very thin, that is, just enough to fill ir- 
 regularities, or it should be one to three inches thick, so 
 that it will have some strength in itself. 
 
 In making steps the forms should be of planed boards. 
 The mortar of the concrete should be worked up against 
 the forms in a manner heretofore described. Upon re- 
 moval of the forms the surface can be made smooth by 
 plastering up any holes with a I :i or 1 :2 mortar and by 
 using the same in a wash over the surface, rubbing it 
 smooth with a wooden float or with a scouring brick. 
 
 In sea walls it is well to have as smooth and dense a 
 surface as possible. This is to prevent penetration of the 
 salts. 
 
 It is said that mortar that has set up for 3 or 4 hours 
 will adhere better as a plaster and shrink less than fresh- 
 ly mixed mortar. 
 
 On a dry, hard surface a plaster coat or floor finish 
 should be 2 or 3 inches thick. 
 
 On a brick wall or on cinder concrete nails can be driv- 
 en in to anchor the plaster, or expanded metal or other 
 metal lath can be nailed on and plastering done on this 
 base. Old brick buildings can by this means be given a 
 cement finish, which, when properly done, enhances their 
 appearance very greatly. 
 
 Old wooden floors can be covered with a finish of % 
 in. or more of a concrete made with saw dust as one of 
 the aggregates. This, too, is anchored to the floor by 
 
 108 
 
means of nails driven into the wood. The use of this kind 
 of floor finish on new concrete floors has not received the 
 attention and trial it deserves, possibly on account of the 
 lack of workmen skilled in its manipulation. 
 
 Common sense and artistic judgment are probably vio- 
 lated more in the matter of the finish for cast blocks than 
 in any other line. There are probably more "rock face" 
 blocks made than any other kind, and there is nothing more 
 absurd than an imitation of rock faced stone blocks in cast 
 stone work. Cast stone or concrete blocks can never have 
 any standing so long as their very appearance holds them 
 out to be what they are not. It is legitimate to tool dress or 
 finish concrete blocks or artificial stone, but it is not legiti- 
 mate to cast in them an imitation of a dressing which they 
 do not receive. Rock faced is the name given to the finish 
 of stone that has been rough dressed. The surface is the nat- 
 ural fracture of the stone. No mason would attempt to pro- 
 duce this appearance by carving the entire surface. It 
 would not be economical in concrete blocks to break off 
 enough of the surface to produce this effect, even if the 
 concrete should possess the property of fracturing in this 
 way. Its sole beauty lies in its irregularity and in the fact 
 that it is a natural and not an artificial result. In con- 
 crete blocks regularity is necessary and painfully manifest. 
 It would be as rational to carve a human face in the rugged 
 side of a mountain of rock to enhance its beauty as it is 
 to cast a rugged face in a molded block. 
 
 A very satisfactory surface is obtained in concrete by 
 tooling. For rough work a pick may be used to break off 
 the outer skin. Light picks may be employed on the sur- 
 face while the concrete is rather green. A cheap and effec- 
 tive finish can be obtained in this way. This is especially 
 suitable for factory buildings. The picking is done, light- 
 ly, and it is said that a workman can finish 1,000 sq. ft. 
 a day. A pointed chisel may be used for the surface of 
 heavy walls. Smaller work may be crandalled. Bush ham- 
 mering is another method employed; this may be done by 
 an unskilled workman. To avoid a broad expanse of flat 
 109 
 
surface the wall should be laid off in panels. A good way 
 is to divide the surface into blocks by nailing triangular 
 strips on the forms. The V shaped grooves would not be 
 dressed, but only the flat. part. 
 
 For chisel dressing allow }4 to % in. to be removed by 
 the tool. Bush hammering on a good flat surface need not 
 cut in any measurable depth. All arrises should be round- 
 ed to about % in. radius. A file can be used for this pur- 
 pose. Dressing with hammers should not be done before 
 the concrete is a month or two old. Small stones are apt 
 to be dislodged by the process, unless they are firmly ce- 
 mented in. 
 
 On some kinds of artificial building stones a tooling ma- 
 chine of carborundum wheels is used. This can be used 
 on very green concrete, as it grinds soft and hard spots 
 alike and does not jar the stone. The surface finish is very 
 good. 
 
 Where compressed air is available, pneumatic tools for 
 crandalling or otherwise dressing the concrete surface 
 would be economical and satisfactory. 
 
 It may be found difficult to dress the surface of a con- 
 crete made of a hard gravel. The stones may be gouged 
 out of the cement before they will break. 
 
 WLhedJettftCT-riol . 
 
 Forms for Concrete Work. 
 
 ..Forms should be designed so that they will retain their 
 shape, until the concrete has hardened sufficiently to be self 
 supporting. Hemlock should not be used, except in the 
 roughest kind of work. Spruce and pine are preferable. 
 Kiln dried lumber or thoroughly seasoned lumber is not de- 
 sirable, because the dry wood will swell. Green wood is 
 also undesirable on account of liability to check and warp. 
 Partly seasoned lumber is best. 
 
 Whether or not lumber should be planed will be deter- 
 mined by the kind of surface desired. Dry concrete does 
 not require tight forms, since there will be no liquid mor- 
 110 
 
tar to run out of the cracks. For wet concrete the forms 
 should be as tight as possible. Cracks may be filled, where 
 necessary, with putty or clay or plaster of Paris. In order 
 to prevent excessive pressure and heaving of forms due 
 to swelling the boards can be planed beveled on one edge, 
 the full width being against the concrete. The narrow edge 
 of a board will then be brought in contact with the wide 
 edge of the next. Closer fit can also be secured. 
 
 For fine work it would be well to shellac the wood to 
 prevent penetration of water and consequent swelling. If 
 end grain is in contact with concrete, it should be covered 
 with shellac to prevent absorption of water. 
 
 Tongued and grooved boards are best for a smooth sur- 
 face, though they are more expensive. Boards surfaced 
 on one side and on the edges are good enough for most 
 work. 
 
 The thickness of boards used for sheathing or lagging 
 should be such as to keep deflection within limits. The 
 thickness will be determined more by the amount of deflec- 
 tion than by the extreme fibre stress produced by the load. 
 In general, to avoid springing, I in. boards should not be 
 used on wider spacing than 2 ft. between studding. The 
 span for i^ in. plank should be not more than 3 ft. and 
 that for 2 in. plank not more than 4 ft. for vertical loading. 
 Wider spacing than this can be used, where the pressure is 
 lateral, as in walls up to about 4 ft. for iVz in. plank and 
 6 ft. for 2 in. plank. 
 
 For the under side of floor slabs generally one inch 
 boards are used, with studding 16 to 24 in. apart. For col- 
 umns and the sides of beams one inch boards may also be 
 used running lengthwise and held in place by outside forms 
 made of 2 in. x 4 in. or larger sized pieces. These may 
 be spaced at intervals of about two ft. and held in place 
 by means of bolts in the case of columns or be wedged 
 against those of the next beam in the case of beams. A 
 heavy plank along the bottom of a beam would serve to 
 support the weight on the shores and allow the removal 
 of the side sheathing in advance of the bottom supports. 
 Hi 
 
Nailing should be reduced to a minimum, as the jar in 
 knocking off the forms, if nailed, is injurious to the con- 
 crete, also the wood will be rendered unfit for continued 
 use by repeated nailing. Bolts and wedges should be used 
 where possible to hold the studding in place. 
 
 Thick plank will be found more economical than thin 
 boards, if used many times, as they will hold their shape 
 better and last longer. In sewer, culvert, and arch work 
 thick lagging, say 2 in. plank is generally used. 
 
 Cutting of the wood should be avoided as much as pos- 
 sible. 
 
 Where there is much duplicate work, great saving can be 
 effected by making the forms in such way that as large 
 sections as can be conveniently handled can be made up 
 into units. These units will consist of frames, say of 2 
 in. x 4 in. pieces, to which the boards are nailed, the frame 
 to be rigid enough not to warp in handling. In high walls 
 these units are very useful. In a retaining wall, for ex- 
 ample, if one side only of the wall has studding, the other 
 side may be brought up by use of these units. If two 
 sets are employed the w r ork can proceed as follows. First, 
 one set is placed in position, being blocked the proper dis- 
 tance from the back sheathing of the wall and held there- 
 to by means of bolts passing through or by means of wires 
 drawn up taut by twisting. Then, when the concrete is 
 nearly up to the top of this row of frames, another row 
 is placed above in the same manner. When the space thus 
 formed is filled, the concrete below will probably be self 
 supporting. The first row of units can then be removed 
 and placed above the second, and so on. In the same way 
 the forms of a chimney or tank can be made in segmental 
 units for both inside and outside. With two or more sets 
 of these, say 3 or 4 ft. in depth, the work can proceed con- 
 tinuously. One set only of the units requires guides or 
 bracing to bring and hold them to line. It is generally 
 best to brace the inside. 
 
 Forms for floor slabs may also be made in units, say 
 2 or 4 pieces to a panel, or more pieces if the panels are 
 112 
 
large. Designing the floor so that the panels are uniform 
 in size will greatly facilitate the construction. 
 
 Beams and girders should be given a small camber, say 
 an inch for every 20 ft. of span. 
 
 Wires are very often used to hold forms against spread- 
 ing. These can be cut off with cutting pliers at the sur- 
 face of the concrete, or, to prevent rust stains, they may 
 be cut with a chisel below the surface and the hole plas- 
 tered up. Bolts are sometimes used for the same purpose 
 and removed with the forms. To prevent adhesion to the 
 concrete these may be run through gas pipe or tin tubes, 
 which remain in the concrete. If the gas pipe or tin tube 
 is brought out nearly to the surface and the end stuffed 
 with cloth or waste to prevent admission of concrete, thr 
 bolt may be drawn out. The waste packing can be re- 
 moved and the hole plastered up. 
 
 Wooden blocks used as spacers must be removed as con- 
 crete is placed. No wood should be left in concrete, either 
 by accident or for any structural reason. Wood buried 
 in concrete will suffer dry rot, as it cannot season. 
 
 Tie rods or bolts should not be close to the edge of the 
 concrete, as they are liable to break out pieces of con- 
 crete in removing. 
 
 In sewer work for sewers of sufficient diameter for men 
 to work in, it is a good plan, as stated elsewhere, to omit 
 lagging on the invert up to a point where it is needed to 
 prevent flowing of concrete. This affords better oppor- 
 tunity to place and compact the concrete as well as to 
 trowel the surface to a smooth finish. The ribs would be 
 in place just the same to guide in forming the sewer. 
 Loose lagging can be used on the upper part of the sewer. 
 This allows easy removal as the work advances. Loose 
 lagging on culverts and arches is often desirable. 
 
 Vertical props should, in general, be braced together. 
 This prevents accidental dislodgement and prevents sway- 
 ing of the structure. The props or shores should rest on 
 solid footings and should be so designed that they can be 
 the last pieces removed and that they can be left in place 
 113 
 

 even after the concrete is self supporting. Such a condi- 
 tion is often desirable in a building where a floor is support- 
 ed by props to a floor below, the latter being just capable of 
 self support. It may be necessary to allow the shores to 
 remain in the successive stories down to the foundation, 
 in order not to strain these floors with load they are not 
 designed to carry, until the top floor is self supporting. 
 There should be props under the girders close to columns 
 so as to relieve the green concrete of the columns of the 
 weight of the floors. 
 
 Props should have double wedges of hard wood under 
 them, so that they can be removed without jarring the 
 concrete and so that they can be eased off without removal, 
 in case it is not positively known that the concrete is thor- 
 oughly hardened. Very heavy posts as those supporting 
 long span arches could rest in sand boxes arranged with 
 gates to let out the sand and lower the posts by this means. 
 For a unit compression on posts 1,000 Ibs. per sq. in. 
 is recommended for pieces whose unsupported length is 
 ten times the least width or less, and 400 Ibs. per sq. in. 
 for pieces whose unsupported length is forty times the 
 least width. For other ratios proportionate values are to 
 be used. Lengths more than 40 times the least width 
 should be avoided. 
 
 For beams a unit of 800 Ibs. per sq. in. is recommended. 
 
 If the span in feet be divided into the coefficient C, in the 
 
 following list of common sizes, the result is the total weight 
 
 in pounds that the beam will carry as a uniformly distribut- 
 
 ed load. 
 
 2 x 4, =2840 
 
 2 x 5, C= 4440 
 
 2 x 6, C= 6400 
 
 2 x 8, C=i 1400 
 
 2 x 9, 0=14400 
 
 2 x 10, 0=17800 
 
 2 X 12, C=25600 
 
 3x14, 0=52270 
 
 114 
 
3x15, 
 4 x 16, 
 
 As an example, suppose it is desired to know the size 
 of joists required to carry a 6 in. slab of concrete on joists 
 spaced 18 in. apart, the span being 10 ft. and an accidental 
 load of 75 Ibs. per sq. ft. being provided for. The total 
 load carried by a joist is (75 + 75 or 150) x 10 x 1.5 
 2250 Ibs. Reversing the rule above given and multiplying 
 this by the span length we have C ~ 22500. Hence 2 x 12 
 joists would be needed. 
 
 The depth of beams should generally be between one- 
 tenth and one-twentieth of the span. Beams deeper than 
 one-tenth will be overstressed in shear, when strained to 
 their capacity in bending; beams shallower than about 
 one-twentieth will deflect too much under load. 
 
 In proportioning the forms allowance should be made 
 for accidental load that may be placed upon the floors in 
 the processes of construction. A uniform load of 75 Ibs. 
 per sq. ft. for slabs and of 50 Ibs. per sq. ft. for beams and 
 girders ought to cover this contingency, as well as the 
 weight of forms, except where the forms are unusually 
 heavy. 
 
 The lateral pressure of the green concrete may be taken 
 as equal to that of water, keeping in view the amount of 
 concrete that will be placed at one time. 
 
 There should be a door at the bottom of column forms 
 to allow cleaning out before concrete is placed. Also the 
 bottom board in wall forms and girder forms should be 
 placed last where practicable. 
 
 Collapsible forms for tunnels, culverts, and sewers are 
 often made use of. Sheet steel is sometimes used in place 
 of lagging of wood. Forms that are not collapsible may 
 often be removed by revolving about the vertical axis; 
 then if the lagging is loose and not nailed, the form can 
 readily be removed and placed forward. 
 
 A good and economical form for circular columns can 
 be made of sheet steel. It may be made of two semicircu- 
 lar sections, flanged and bolted together. 
 115 
 
In bracing forms wooden pieces should be used, generally 
 2x4 scantling. Wire ropes should not be employed for 
 this purpose in any case, as the stretch in these may be 
 disastrous to the structure. 
 
 In heavily battered walls, as the wing walls for an abut- 
 ment, a cover on the sloping part of the wall is generally 
 necessary. This should be removed as soon as possible 
 so that the top surface can be plastered and made inper- 
 vious. If much wet concrete is poured at a time in such 
 wall, it may be necessary to tie down the cover of the slop- 
 ing portion to prevent its being lifted by the pressure of 
 the concrete. It could be anchored by wires into the body 
 of the wall. If secured only to the side forms, the pres- 
 sure might lift these. 
 
 In footings and retaining walls, instead of having a heavy 
 batter, steps are usually preferable, with the tread sloped 
 so as to shed water. This is especially true when dry con- 
 crete is used, as it allows access to the concrete for tamp- 
 ing. 
 
 Lateral pressure of wet or of tamped concrete must not 
 be overlooked in the building and bracing of forms. The 
 sides of beam and wall forms should be held against spring- 
 ing by bolts and wedges, where practicable, or by stiff 
 braces. 
 
 A suggested scheme for slab and beam forms is as fol- 
 lows. Use a heavy plank under the girder 4 in. wider than 
 the girder. On top of this nail a one inch planed board, 
 the width of the girder, along the middle of the plank. 
 There will be a 2 in. margin on each side. One inch of this 
 will be taken up with the side boards for the girder. The 
 other inch will be used as a ledge to support the joists for 
 the slab which can be blocked up by nailing them to the 
 vertical studding for the sides of the girder. If strips be 
 nailed lightly to these joists and studding, and if the 
 sheathing for slabs and girders be nailed together with 
 cleats to form units, there will need to be but little nail- 
 ing into the wood in contact with the concrete. The heavy 
 plank under the girder should be supported by props 3 
 
 116 
 
to 6 ft. apart. For heavy girders it may be stiffened by 
 knee braces to the props or by a pair of joists nailed to the 
 side of the props. By the above described arrangement 
 the forms under the slabs and on the sides of girders may 
 fte removed and used elsewhere while the weight of the 
 girders is still on the shores. 
 
 It is important that columns be plumb and that beams 
 be straight and true to line. Before beginning to place the 
 concrete all forms should be brought to correct position 
 and true to line and securely braced. Warped and inclined 
 surfaces of walls, intended to be plane and vertical, and 
 wavy copings are very unsightly. 
 
 Sharp corners in the concrete should be avoided. The 
 arrises should generally be either chamfered off in the 
 mold or trimmed rounding when the forms are removed. 
 
 In dividing a wall into blocks the joints should be V 
 shaped, either sharp or truncated. The recess should not 
 have parallel sides, as the withdrawing of the molding 
 pieces would break off spalls of concrete; also the con- 
 crete will not as readily fill in, around the squared recess. 
 The same is true of moldings. These should not have re- 
 cesses with parallel sides. Surfaces that face upward 
 should in general, have a slope outward so as not to bind 
 on the forms and so as to allow concrete to be more easily 
 worked under the form. Further, such surfaces will turn 
 the water and absorb less. 
 
 The design of the work should be made with a view of 
 reducing to a minimum the difficulties inherent in the hand- 
 ling and placing of concrete and with an appreciation of 
 the skill of the workmen executing the plans. Moldings 
 should be as simple as possible and in conformity with the 
 construction. Small arches and buildings should have 
 light moldings and ballustrades, where any are used. Mas- 
 sive structures should have bold and massive ornamen- 
 tation. Fine details should not be attempted on out-door 
 work. These can be executed by use of lime or plaster of 
 Paris in conjunction with cement for indoor ornamenta- 
 tion. Imitations should be avoided. Broad plain surfaces 
 117 
 
should be broken up by paneling where practicable; the 
 heavier the work the more massive and bold the paneling 
 
 should be. 
 
 
 
 The Properties of Concrete 
 
 Concrete partakes of the properties of the stone or other 
 aggregate from which it is made, though these properties 
 are affected by the mortar with which the aggregate is ce- 
 mented together. The property of greatest importance is 
 the compressive strength. The compressive strength of the 
 concrete is in general less than that of the stone of the 
 aggregate. The unit compressive strength tested in cubes 
 is generally less for small cubes than for large ones. It 
 is greater for flat discs than for cubes, the flatter the disc 
 the higher the unit. 
 
 On account of the many factors that enter in the manu- 
 facture of concrete affecting its uniformity, and on account 
 of the very nature of concrete, being a non-homogeneous 
 substance, laws that are even approximately exact cannot 
 be written that will tell the compressive strength without 
 allowance for a liberal variation. If the dimensions of the 
 specimen were greatly in excess of the largest piece of the 
 aggregate, unit results would no doubt be more uniform. 
 Sand and cement in ordinary sized specimens give more 
 uniform units than concrete, because the grain of sand 
 bears so small a ratio to the size of the specimen that it is 
 possible to test. 
 
 The best that can be done in the matter of establishing 
 a unit value for concrete in compression is to take average 
 values of a large number of tests made under different 
 conditions, and in design to use a liberal factor of safety 
 to cover irregularities and imperfect work. A standard 
 concrete should be used in reinforced concrete, and uni- 
 form conditions should be striven for. The cube is prob- 
 ably the best standard for compressive strength, and its 
 size should be from 8 to 12 in. so as to minimize the 
 effect of non- uniformity. 
 
 118 
 
TESTS &// COMCRITZ CUBES 
 
 Aggregate as stated /n /$t Co/umn. 
 
 Compress/ve Strength in /As per 5q. fnch . 
 
 I. MORTAR- /PORTLAND CEMENT : / SAND 
 
 35 
 
 
 
 x3 
 
 
 
 | 
 
 Kind 
 
 Age 
 
 1 
 
 Average 
 
 
 I 
 
 of 
 
 of 
 
 3 
 
 Compr 
 
 Authority 
 
 1 
 
 Stone 
 
 Cube 
 
 ^ 
 
 Strength 
 
 
 5 
 
 
 
 ^ 
 
 
 
 /i 
 
 Trap 
 
 // fo43dd. 
 
 4 
 
 3944 
 
 U. 5. /G9S 
 
 3 
 
 
 
 7 // . 
 
 9 
 
 2442 
 
 > 9f 
 
 3 
 
 99 
 
 19 " 26 " 
 
 9 
 
 3346 
 
 99 t9 
 
 3 
 
 >-> 
 
 31 ,48> 
 
 10 
 
 3676 
 
 9 99 
 
 3 
 
 99 
 
 61 76 99 
 
 7 
 
 45 9 / 
 
 > 99 
 
 3 
 
 99 
 
 4- mo. 
 
 6 
 
 3079 
 
 99 
 
 3 
 
 Pebbles 
 
 7 to //da 
 
 4 
 
 2092 
 
 9> 
 
 3 
 
 99 
 
 21 26 " 
 
 4 
 
 3052 
 
 9 99 
 
 3 
 
 19 
 
 29 "46 99 
 
 5 
 
 3642 
 
 9 99 
 
 3 
 
 * 
 
 61 70 99 
 
 3 
 
 3793 
 
 9 
 
 3 
 
 Cinder 
 
 29 39 99 
 
 IQ 
 
 1544 
 
 
 3 
 
 99 
 
 9O 99/02 
 
 /5 
 
 2/86 
 
 
 3 
 
 2 Trap J Grave/ 
 
 Tbfr 
 
 / 
 
 /80O 
 
 
 3 
 
 99 99 
 
 23 
 
 / 
 
 3806 
 
 9 
 
 3 
 
 99 99 
 
 32 
 
 / 
 
 5O24 
 
 
 3 
 
 99 99 
 
 67 - 
 
 1 
 
 4700 
 
 
 3 
 
 2 Pebbles J6ra. 
 
 7 
 
 / 
 
 I486 
 
 
 3 
 
 99 ->9 
 
 22 99 
 
 / 
 
 2676 
 
 
 3 
 
 99 99 
 
 32 99 
 
 / 
 
 3000 
 
 
 3 
 
 99 I) 
 
 65 99 
 
 1 
 
 3800 
 
 
 3 
 
 1 Trap j Pebbles 
 ! Gravel 
 
 7 >-> 
 
 1 
 
 /52O 
 
 99 99 
 
 3 
 
 iTrapJfebbks 
 1 6 ravel 
 
 22 
 
 1 
 
 2800 
 
 99 99 
 
 3 
 
 iTrep./fkbb/es 
 1 6 rave/ 
 
 32 
 
 / 
 
 2700 
 
 99 99 
 
 3.3 
 & 
 
 BroKen 
 
 1 9 to 22 mo 
 
 64 
 
 3334 
 
 ' Rafter 
 
 119 
 
TJrsrs OM CONCRETE CUBES 
 
 Continued 
 
 IL./YIORTAR-I PORTLAND CEMENT: 2 SAND 
 
 5 
 
 
 
 \ 
 
 
 
 & 
 
 ft/net 
 
 Age 
 
 \ 
 
 Average 
 
 
 I 
 
 of 
 
 of 
 
 VO 
 
 Compr 
 
 Authority 
 
 ^^ 
 ^> 
 
 Stone 
 
 Cube 
 
 1 
 
 Strength 
 
 
 2 
 
 Trap 
 
 3 mo. 
 
 8 
 
 1964 
 
 u. 3. /see 
 
 2 
 
 99 
 
 4 99 
 
 4 
 
 2834 
 
 99 99 
 
 3 
 
 99 
 
 3 99 
 
 10 
 
 2O3O 
 
 91 99 
 
 3 
 
 99 
 
 4 99 
 
 5 
 
 2803 
 
 99 99 
 
 
 6ravel 
 
 28 da. 
 
 
 2/25 
 
 DycKerhoff 
 
 3 
 
 Cinder 
 
 39 99 
 
 3 
 
 /098 
 
 U. 5. 1898 
 
 3 
 
 99 
 
 102 99 
 
 3 
 
 /634 
 
 99 99 
 
 4 
 
 Trap 
 
 3 mo. 
 
 IO 
 
 1957 
 
 99 99 
 
 4 
 
 99 
 
 4 99 
 
 16 
 
 2244 
 
 99 99 
 
 4 
 
 Gran/te 
 
 28 da. 
 
 
 
 /607 
 
 /B99 
 
 4 
 
 Pebb/es 
 
 3 mo. 
 
 5 
 
 3206 
 
 v 1836 
 
 4 
 
 Conglomerate 
 
 7 foioda. 
 
 25 
 
 1565 
 
 99 J899 
 
 4 
 
 19 
 
 1 mo. 
 
 30 
 
 2399 
 
 99 99 
 
 4 
 
 99 
 
 3 99 
 
 30 
 
 2896 
 
 99 99 
 
 4 
 
 99 
 
 6 99 
 
 26 
 
 3796 
 
 99 99 
 
 4 
 
 Slag 
 
 52 da. 
 
 8 
 
 3392 
 
 "9 /9OO 
 
 4 
 
 99 
 
 05 99 
 
 8 
 
 4/35 
 
 99 99 
 
 4 
 
 Cinder 
 
 33 99 
 
 3 
 
 904 
 
 99 /S98 
 
 4 
 
 99 >*.*,; 
 
 98 99 
 
 3 
 
 1325 
 
 99 99 
 
 4 
 
 BricK 
 
 28 99 
 
 6 
 
 720 
 
 99 /899 
 
 4 
 
 99 
 
 3 mo. 
 
 5 
 
 275.7 
 
 99 99 
 
 4 
 
 L/mestone 
 
 6 eta. 
 
 4 
 
 1084 
 
 99 99 
 
 4 
 
 99 
 
 II to 13 da 
 
 8 
 
 1676 
 
 99 91 
 
 4 
 
 99 
 
 /9 99 2O 99 
 
 6 
 
 2O40 
 
 99 99 
 
 4 
 
 99 
 
 52 da. 
 
 5 
 
 3604 
 
 99 I9OO 
 
 A 
 
 99 
 
 85 99 
 
 5 
 
 4-256 
 
 99 99 
 
 5 
 
 Trap 
 
 3 mo. 
 
 /2 
 
 2270 
 
 9* /899 
 
 5 
 
 99 
 
 4 99 
 
 6 
 
 2321 
 
 99 99 
 
 
 Gravel 
 
 28c/a. 
 
 
 2367 
 
 DycKerhoff 
 
 5 
 
 C/nder 
 
 29 to 38 c& 
 
 /5 
 
 724 
 
 U. 5. 1898 
 
 120 
 
TSTS OA/ COMCRETI CUBES 
 
 Continued 
 
 JZ". MORTAR - 1 PORTLAND CEMENT : 2 SAND 
 
 i 
 
 
 
 I 
 
 
 
 ^ 
 
 Kind 
 
 Age 
 
 1 
 
 Average 
 
 
 S: 
 
 of 
 
 of 
 
 1 
 
 Compr 
 
 Authority 
 
 ^ 
 
 Stone 
 
 Cube 
 
 v> 
 
 5ltengfh 
 
 
 JS 
 
 
 
 1 
 
 
 
 5 
 
 Cinder 
 
 eotolOlda 
 
 15 
 
 IO&I 
 
 U. S. I89Q 
 
 ^ 
 
 O ravel 
 
 1 toZ^mo. 
 
 7 
 
 /477 
 
 BaKer 
 
 si 
 
 99 
 
 99 & 99 
 
 2 
 
 1742 
 
 99 
 
 is 
 
 99 
 
 12 "-A5 99 
 
 2 
 
 4583 
 
 99 
 
 vh 
 
 99 
 
 ?O *93O 99 
 
 6 
 
 227Q 
 
 99 
 
 | 
 
 99 
 
 3? 9936 " 
 
 3 
 
 2365 
 
 99 
 
 ^S 
 
 99 
 
 35 9936 99 
 
 2. 
 
 3497 
 
 99 
 
 6 
 
 Trap 
 
 3 mo. 
 
 /3 
 
 1869 
 
 U. 5. 1899 
 
 6 
 
 99 
 
 4- " 
 
 7 
 
 241 1 
 
 99 *9 
 
 6 
 
 Gravel 
 
 10 da. 
 
 
 694 
 
 A.W.Dow 
 
 7 
 
 Trap 
 
 3 mo. 
 
 15 
 
 1466 
 
 U.S. /899 
 
 7 
 
 $6ravel,4Sfon& 
 
 6 99 
 
 
 2OOO 
 
 EtoKer 
 
 7 
 
 99 99 
 
 32 to 37 mo. 
 
 6 
 
 4428 
 
 99 
 
 8 
 
 Trap 
 
 3 mo. 
 
 18 
 
 1163 
 
 U.S. 1899 
 
 e 
 
 99 
 
 3 99 
 
 to 
 
 8/6 
 
 99 91 
 
 5.18 
 8.93 
 
 Limestone 
 
 19 to 22 mo. 
 
 128 
 
 2678 
 
 ftaffer 
 
 Iff. MORTAR - IPopn A ND CEMENT : 3 5 A ND 
 
 5 
 
 Gravel 
 
 28 da 
 
 
 /682 
 
 DycKerhoff 
 machine mixed 
 
 5 
 
 Limestone 
 
 3 mo. 2 da. 
 
 & 
 
 4043 
 
 U.S. /900 
 hand m/xed 
 
 5 
 
 99 
 
 + 9 )> 
 
 4 
 
 3/87 
 
 U. S. /900 
 
 6 
 
 Trap 
 
 dofa. 
 
 2 
 
 858 
 
 1898 
 
 6 
 
 19 
 
 ntozoda 
 
 3 
 
 1 507 
 
 99 99 
 
 6 
 
 99 
 
 4Zda. 
 
 3 
 
 2/92 
 
 99 99 
 
 6 
 
 99 
 
 4- mo\ 
 
 15 
 
 164-8 
 
 99 99 
 
 6 
 
 Gravel 
 
 45 Gfa. 
 
 
 /628 
 
 A.W.Dow 
 
 6 
 
 99 
 
 3 mo. 
 
 
 2671 
 
 99 
 
 121 
 
TESTS ON COMCRCTZ CUBES 
 
 Continued 
 
 HI MORTAR -/PORTLAND CEMENT: 3 SAND 
 
 \ 
 
 K/r>d 
 
 Age 
 
 \ 
 
 Average 
 
 
 \ 
 
 of 
 
 of 
 
 v^ 
 
 Compr. 
 
 Auffyor/fy 
 
 fc> 
 | 
 
 Qfone 
 
 Cube 
 
 ^ 
 
 ^ 
 
 Strength 
 
 
 6 
 
 Gravel 
 
 6mo. 
 
 
 1844 
 
 A.W.Dow. 
 
 6 
 
 >? 
 
 /year 
 
 
 2824 
 
 9 + 
 
 6i 
 
 99 
 
 Z&cto. 
 
 
 1515 
 
 Dyekerhoff 
 
 6 
 
 Conglomerate 
 
 7 To IO eta. 
 
 23 
 
 1420 
 
 U. 5. t899 
 
 6 
 
 99 
 
 / mo. 
 
 28 
 
 2/74 
 
 99 
 
 6 
 
 99 
 
 3 
 
 30 
 
 2522 
 
 99 99 
 
 6 
 
 99 
 
 6 
 
 23 
 
 3//0 
 
 99 99 
 
 6 
 
 Cinder 
 
 Z9da 
 
 3 
 
 529 
 
 I89B 
 
 6 
 
 99 
 
 91 99 
 
 3 
 
 788 
 
 99 M 
 
 6 
 
 BncK 
 
 3 mo. 
 
 7 
 
 22O7 
 
 99 1899 
 
 6 
 
 ?Gr0Y.4BroK.sto. 
 
 / year 
 
 
 283.5 
 
 A. W. DOW. 
 
 6 
 
 3 99 3 99 99 
 
 10 da. 
 
 
 949 
 
 99 
 
 6 
 
 3 99 3 99 99 
 
 45 99 
 
 
 1854 
 
 99 
 
 6 
 
 3 3 " 
 
 6 mo. 
 
 
 2070 
 
 99 
 
 6 
 
 3 1 3 99 99 
 
 / year 
 
 
 2751 
 
 99 
 
 6 
 
 Limestone 
 
 
 /O 
 
 3067 
 
 Barter 
 
 6 
 
 99 
 
 7da. 
 
 
 /584 
 
 /?5% voids fi//ed 
 
 6 
 
 99 
 
 fO " 
 
 1 
 
 908 
 
 /I. W.Dow. 
 
 6 
 
 99 
 
 30 99 
 
 
 1795 
 
 iZ5%vo/d$ f///ed 
 
 6 
 
 99 
 
 45 99 
 
 / 
 
 1791 
 
 A. W. Dow. 
 
 6 
 
 99 
 
 90 " 
 
 
 2579 
 
 I25%voids f///ed 
 
 6 
 
 99 
 
 3 mo. 
 
 t 
 
 2256 
 
 A. W. Dow. 
 
 6 
 
 99 
 
 6 
 
 / 
 
 251 1 
 
 99 
 
 6 
 
 99 
 
 /year 
 
 3 
 
 2442 
 
 99 
 
 li 
 
 99 
 
 7&a. 
 
 1 
 
 /2B2 
 
 Voids filled 
 
 7? 
 
 99 
 
 30 *> 
 
 / 
 
 1672 
 
 99 99 
 
 Ik 
 
 99 
 
 9099 
 
 1 
 
 1/28 
 
 99 99 
 
 7.5 
 
 
 
 
 
 
 I&9 
 
 91 
 
 19 to 22 mo. 
 
 I2B 
 
 1872 
 
 6. W. Rafter 
 
 10 
 
 99 
 
 lofa. 
 
 1 
 
 892 
 
 75%voids filled 
 
Tesrs o/v COA/CRETZ CUBES 
 
 ______, Continued 
 
 HE MORTAR- /PORTLAND CEMENT : 3 SAND 
 
 1 
 
 VVv 
 
 tf/nd 
 
 4ge 
 
 \ 
 
 Average 
 
 
 1 
 
 of 
 
 o-T 
 
 I 
 
 Gompr 
 
 Attfhorifv 
 
 1 
 
 Stone 
 
 Cube 
 
 \ 
 ^ 
 
 Strength 
 
 
 10 
 
 Limestone 
 
 3otfa. 
 
 / 
 
 472 
 
 75% voids f/'J/ed 
 
 IO 
 
 99 
 
 90 
 
 / 
 
 919 
 
 91 99 I") 
 
 IF MORTAR- /PORTLAND CEMENT : 4 SAND 
 
 a 
 
 Trap 
 
 4- mo. 
 
 /O 
 
 /080 
 
 U B. /893 
 
 5 
 
 O rav el 
 
 2 Beta 
 
 
 1273 
 
 Dyctfer/ioff 
 
 8i 
 
 99 
 
 28 ->-> 
 
 
 1204 
 
 *><> 
 
 10 
 & 
 
 Limestone 
 
 I9fo22mo. 
 
 IO 
 
 1735 
 
 G.W Rafter 
 
 ~Y. MORTAR -/PORTLAND CEMENT : 5 SAND 
 
 10 
 
 Trap 
 
 4- mo. 
 
 12 
 
 708 
 
 U. 5. 1898 
 
 "i 5 
 
 Limestone 
 
 1 9 to 22 mo. 
 
 32 
 
 1554 
 
 6. W. Rafter 
 
 lb.4l 
 
 
 
 
 
 
 W. 'MORTAR- /PORTLAND CEMENT : 6 SAND 
 
 12 
 
 Trap 
 
 4 mo. 
 
 14 
 
 625 
 
 U. 5. 1898 
 
 12 
 
 Conglomerate 
 
 7 to /o da 
 
 25 
 
 602 
 
 * 1699 
 
 12 
 
 a 
 
 I rno. 
 
 30 
 
 993 
 
 11 99 
 
 12 
 
 99 
 
 3 
 
 30 
 
 1076 
 
 99 99 
 
 12 
 
 99 
 
 6 " 
 
 21 
 
 1408 
 
 99 99 
 
 16.66 
 
 Lim&stone 
 
 19 to 22 mo. 
 
 4 
 
 1427 
 
 &Wffaffer 
 
When exposed to ordinary conditions of weather, i :2 14 
 concrete will attain in two or three months a unit strength 
 of 2,000 to 2,500 Ibs. per sq. in. Carefully treated specimens 
 placed in water, or kept under cover and damp, attain 
 strength of 2,500 to 3,500 Ibs. per sq. in. or even 4,000 Ibs. 
 It is not possible to realize this latter in ordinary work. 
 The former represents more nearly average conditions in a 
 structure. 
 
 The table of tests on concrete cubes in the five pages 
 given herewith are taken from Municipal Engineering, 
 January, 1903. The specimens were nearly all 12 in. cubes. 
 
 The strength of concrete in cubes has only limited ap- 
 plication in the proportioning of the parts of a structure. 
 In plain concrete columns of even a few diameters in 
 length, and in columns having small longitudinal steel rods, 
 a safe unit, if based on the strength of a cube in compres- 
 sion, should have a large factor of safety to cover the un- 
 certainties. A factor of safety of eight or ten for concrete 
 in such condition would be about equivalent to a factor of 
 safety of four for concrete confined as in a reinforced con- 
 crete beam or slab, using in each case the unit determined 
 by the cube as a basis. Carefully prepared specimens load- 
 ed exactly centrally, as near as it is possible to effect this 
 condition, are not safe guides to the design of members 
 made by unskilled labor, whether or not that labor has 
 competent supervision, when the facts are such that a lit- 
 tle variation from perfect conditions makes a great varia- 
 tion in the unit stress. In beams and slabs the concrete 
 under stress is confined and braced in such a way that a 
 bad batch of concrete or poor work has not a very detri- 
 mental effect on the compressive strength. Many design- 
 ers fail utterly to appreciate the fact that in columns of 
 plain concrete, or concrete and longitudinal rods, the con- 
 crete is under entirely different conditions than in a beam 
 or slab, and that these unfavorable conditions in the con- 
 crete column are in parts of the structure whose failure 
 means a menace to the entire structure. 
 
 The tensile strength of concrete is from one- tenth to 
 124 
 
one-fifth as much as the compressive strength. It is a 
 more uncertain property than the compressive strength. 
 In general the tensile strength of concrete does not enter 
 in the computation of the structural strength of reinforced 
 concrete. It is not thereby eliminated from the problem. 
 It has an effect on the location of the neutral axis, a fact 
 very generally ignored by manufacturers of fine formu- 
 las. It has further an important bearing on the calculated 
 deflection of a beam. The tensile strength of good concrete 
 suitable for reinforced concrete, well aged, is from 200 to 
 500 Ibs. per sq. in. If a reinforced concrete beam be de- 
 signed for 500 Ibs. per sq. in. extreme fibre stress in com- 
 pression, and the concrete would stand 500 Ibs. per sq. 
 in. in tension, the beam could be conceived to act for safe 
 loads entirely as a concrete beam. Assuming a modulus 
 of elasticity of an average value, equal for both tension 
 and compression, the deflection could be computed as for 
 a timber beam. For example if the modulus of elasticity 
 is 3,000,000, the deflection at 500 Ibs. per sq. in. would be 
 (by the ordinary deflection formula), for uniform load, 
 the square of the span in inches divided by 28,800 times 
 the depth of slab or beam out to out, in inches. If then 
 the depth of slab or beam, out to out, is one-twentieth of 
 the span, the maximum deflection would be the length of 
 the span divided by 1440. If the depth is one-tenth of the 
 span, the maximum deflection would be the length of span 
 divided by 2880. 
 
 The foregoing rule will give the deflections that may 
 be looked for in reinforced concrete floors that are carry- 
 ing their loads safely without cracks on the tension side of 
 beam or slab. This is seen to be small. It will be inverse- 
 ly as the modulus of elasticity. Thus for a modulus of 
 6,000,000, it would be half as much as for 3,000,000, and 
 for 1,500,000, twice as much. If cracks occur' in the con- 
 crete, the deflection will be greater. Also if cracks occur, 
 the steel will, at the crack, carry all of the tensile stress. 
 This is doubtless what takes place in many beams, namely, 
 the concrete carries all or nearly all of the tensile stress 
 125 
 
up to the point of its ultimate strength ; but there is the 
 possibility, always present, of the concrete cracking and 
 throwing the entire tension on the steel. This assumption 
 of the action of the stresses in a reinforced concrete beam 
 does not carry with it warrant for using any less steel 
 than would be used if the concrete were totally without 
 tensile strength, neither from the standpoint of the unit 
 stress that the steel may take nor from that of the allowed 
 stretch. One crack in a beam will throw all of the stress 
 on the steel, and, if the elongation of the steel is excessive, 
 other cracks would be a natural consequence. 
 
 In the matter of the shearing strength of concrete ex- 
 perimenters have reported widely different results, varying 
 all the way from equality with the tensile strength to equal- 
 ity with the compressive strength. This wide variation 
 in the unit shear found by different observers is just what 
 might be expected in a material such as concrete, but the 
 failure to grasp its meaning on the part of engineers gen- 
 erally is not so easily understood. Elsewhere in this book 
 (Shear on Concrete and Its Bearing on the Design of 
 Beams) the author has pointed out that, according to Mer- 
 riman's well-known formula for combined shear and ten- 
 sion, if the tension on a section in shear be zero, the ten- 
 sile unit stress due to shear alone is equal to the shearing 
 unit stress. It is the simplest kind of reasoning to deduce 
 the proposition that, unless a section in shear is in com- 
 pression at the same time to overcome the tension resulting 
 from the shear, the shearing strength of the section cannot 
 exceed the tensile strength of the concrete. 
 
 The modulus of transverse strength of concrete, or the 
 calculated extreme fibre stress of a plain concrete beam in 
 bending at rupture, cannot be much more than the tensile 
 strength per sq. in. Experimenters have found it to be 
 between one and one and one-half times the unite tensile 
 strength. A safe value, where stone concrete is to be in 
 bending is about 50 Ibs. per sq. in. 
 
 The modulus of elasticity of concrete is the subject of 
 this paragraph. Modulus of elasticity is sometimes defined 
 126 
 
as the ratio of stress to strain, with stress further defined 
 as an axial load and strain the deformation (stretch or 
 shortening.) The stress would be in pounds per sq. in. 
 and the "strain" in linear dimensions. It is elementary 
 arithmetic that there can exist no such thing as a ratio be- 
 tween pounds and inches, or between any measure of 
 weight and another of length. Even if a liberal meaning 
 is applied to the ratio, it necessitates an explanation as to 
 the terms in which the "strain" must be given. This 
 forced meaning of the word strain is totally unnecessary 
 and does not possess the redeeming feature of being con- 
 venient. The language is rich enough in terms to express 
 the particular so-called strain referred to to dispense with 
 a blanket term that must be further defined to make its 
 meaning clear in any particular case. Deflection, for beams, 
 stretch or elongation, for tension members, and shortening, 
 for compression members, are sufficiently succinct to need 
 no explanatory notes. The modulus of elasticity is de- 
 fined under the heading of Steel for Reinforced Concrete, 
 and its definition will not be repeated here. The modu- 
 lus of elasticity of concrete varies from one million or less 
 to five or six million. It varies with the intensity of stress ; 
 it varies with the kind of aggregate used ; it varies with the 
 amount of water used in mixing; it varies with the atmos- 
 pheric condition during setting. An average value may 
 be loo per cent, too great or 50 per cent, too small. Added 
 to the absolute uncertainty of its value as determined in 
 plain concrete tests shrinkage of the concrete vitiates as- 
 sumptions as to relative extensions of concrete and steel 
 jointly stressed. The workability of formulas is immense- 
 ly hampered by introduction of the modulus of elasticity. 
 If this brought in any needed factor or tended to accuracy, 
 it might be justifiable. It does neither. It is merely a use- 
 less refinement of absolutely no value from any standpoint 
 whatever. 
 
 The adhesion of concrete to steel is generally stated as 
 one of the useful properties in the combination of con- 
 crete and steel. Concrete plastered on flat surfaces of steel 
 127 
 
will adhere only indifferently. When a steel rod is embed- 
 ded in concrete, and the concrete is allowed to set in the 
 air, the shrinkage which results causes the concrete to 
 grip the steel rod, and the combination of adhesion and 
 friction due to the gripping makes the rod hold in. the con- 
 crete. The force necessary to pull a rod out of concrete 
 of i :2 14 mixture, properly made, will be found to average 
 about 500 Ibs. per sq. in. of the surface of the rod em- 
 bedded, This is the unit found on ordinary commercial 
 steel. On such surfaces as that of cold rolled steel the 
 adhesion is not so great, but cold rolled steel has no place 
 in reinforced concrete construction. The surface of hot 
 rolled steel is sufficiently rough to give the above value in 
 adhesion. In the case of a unit such as this a liberal fac- 
 tor of safety should be employed, because of the fact that 
 imperfect concrete or poor work will greatly diminish the 
 available strength. A safe unit for this adhesion is 50 
 Ibs. per sq. in. Round or square rods embedded 50 diame- 
 ters in concrete at this unit would require a force of 10,000 
 Ibs. per sq. in. to strain the adhesion to 50 Ibs. per sq. in. 
 Fifty diameters is therefore a proper depth to anchor a 
 plain round or square rod beyond the point where its full 
 stress occurs. 
 
 The coefficient of expansion of concrete, for temperature 
 variations, does not differ much from that of steel. Its 
 value ranges between .0000055 an d .0000065 per degree R, 
 while that of steel is about constant at the higher value. 
 The approximate agreement between the coefficient in steel 
 and concrete is of great value in reinforced concrete con- 
 struction. If there were a large difference, change in 
 temperature would disrupt a concrete member of a struc- 
 ture in which steel were embedded. 
 
 Concrete has the useful property of being probably the 
 best preservative of steel known. Even steel that is some- 
 what rusted will, after being buried in concrete for some 
 time, often be found to be freed of its rust. It has been 
 thoroughly established that steel buried in good wet con- 
 crete will be permanently preserved. To insure the pre- 
 128 
 
servation of the steel a wet concrete is needed and one 
 that has a liberal proportion of cement. Dry, rammed con- 
 crete is porous and not a suitable constituent of reinforced 
 concrete construction. It cannot be expected to preserve 
 embedded steel. 
 
 Another valuable quality of concrete is the capacity to 
 resist fire and not only to retain its integrity and the great- 
 er part of its strength through fire, but also to act as 
 protection to steel work. There is perhaps no better fire 
 protection commercially available for steel or cast iron 
 columns than a few inches of cinder concrete, preferably 
 held together with rods or a mesh of steel of some sort. 
 Not all concretes have the same fireproof qualities. Cinder 
 concrete is one of the best, if the cinders be completely 
 burned, for the reason that the aggregate itself being un- 
 affected by heat and the sand being practically so, there 
 remains only the cement that can be attacked by the fire. 
 Also, on account of the cinder concrete being porous, its 
 conductivity is low. The concretes that are best for fire 
 resisting are those in which the aggregates are least affect- 
 ed by heat. Sand and gravel are among the best of the 
 hard stones. Broken brick would make a good fireproof 
 concrete. Sandstone and trap are also good. Granite is 
 not so good, though with the granite broken in small 
 pieces, granite concrete would stand fire better than solid 
 granite. Limestone and marble are not good fire resistants 
 on account of the fact that the heat calcines them, turn- 
 ing them into quicklime. Under the heat of a fire solid 
 stone cracks and spalls off in large chunks. Concrete, and 
 especially reinforced concrete, acts quite differently. The 
 sharp corners will spall off for a small depth, but the 
 broad surfaces will be affected by a calcination acting from 
 the surface in. The depth to which this calcination acts 
 will depend upon the time the fire lasts. It is a slow pro- 
 cess and is rendered more so by the lessened conductivity 
 of the calcined stone. A long continued fire may only affect 
 the concrete an inch or so. The driving off of the water 
 chemically combined with the cement absorbs a large 
 129 
 
amount of the heat of a fire. The water does not separate 
 from the cement until a temperature of about 500 to 700 
 degrees F. is reached, and it requires a much higher tem- 
 perature than this to complete the dehydration. Concrete 
 conducts heat so slowly that a column of ordinary size 
 would have to be in a hot fire for many hours in order 
 to have the high temperature of the fire penetrate to its 
 center. 
 
 Concrete may be used for flue linings where the tempera- 
 ture does not exceed about 600 deg. F. Neat cement tests 
 made at the Watertown Arsenal in 1902 did not show any 
 decrease in strength up to a temperature of 600 deg. F. 
 Small specimens of concrete heated in an oven until the 
 heat penetrates the interior begin to lose strength at about 
 600 deg. F. for trap concrete and at about 500 deg. F. or 
 less for limestone concrete. 
 
 In Engineering World, Jan. 4, 1907, some tests are re- 
 corded that purport to show the benefit of tile as a fire 
 protection and the fallacy of depending on concrete for the 
 purpose. As these tests have been given wide publicity, it 
 is pertinent to examine them and weigh their value. Leav- 
 ing out unimportant details and giving results in close ap- 
 proximations, the tests were as follows. A column about 
 10 in. square, of limestone concrete, at the age of 23 months 
 stood a crushing load of about 3500 Ibs. per sq. in. Another 
 column, identically made, and surrounded with 3 in. of solid 
 porous tile, laid in cement, with metal fabric in the hori- 
 zontal joints, was subjected, at the same age to a heat of 
 1500 deg. F. for three hours. Without applying any water 
 to cool the column, presumably, as no mention is made of 
 applying water, it was tested the next day and stood sub- 
 stantially the load carried by the column that was not sub- 
 jected to the fire. 
 
 Another column, identically made, w r as subjected to the 
 same heat test as the second, without protection, and at 
 the same age. After the fire test water was applied. This 
 column failed under about 700 Ibs. per sq. in. 
 
 130 
 
The points about these tests that deserve mention are 
 these: 
 
 (a) The columns were of limestone concrete, a ma- 
 terial acknowledged to be poor as a fire resistant. 
 
 (b) The tile used for protection was solid and not, as 
 very generally used, hol)o\V. 
 
 (c) The tile was reinforced in the joints with steel 
 mesh, a very unusual and expensive construction. 
 
 (d) The tile covered column was not, apparently del- 
 uged with water to test its integrity, while the concrete col- 
 umn was so treated. 
 
 (e) One hundred by 700 equals 20 by 3500; hence, if we 
 consider that a shell of concrete was totally destroyed by 
 calcination in protecting the inner core, an area of 20 
 square inches remained good for the full unit load. This 
 means that a thickness of 2% in. of concrete was needed 
 to protect the inner core, as against 3 in. of tile. To in- 
 crease the dimensions of the concrete column by 3 in. each 
 way would be very much cheaper than to add 3 in. of tile 
 of any sort, and the result is a column that is vastly more 
 rigid than would be the tile-covered column. 
 
 (f) If we make allowance for the slenderness of the 
 core remaining sound in the bare column subjected to fire, 
 the comparison in (e) would be still more favorable to 
 the concrete as a protection ; since the slender column 
 would not be expected to stand as high a unit stress as 
 the original column. 
 
 If one of these columns had been made 16 in. square, and 
 had been tested on the same basis as the tile-protected one, 
 it would no doubt have shown that much less than a 3 
 in. thickness, even of limestone concrete, would serve to 
 preserve the core. This is on account of the fact that the 
 larger core would retain for a longer time a low tempera- 
 ture, not destructive to the concrete, and would take up 
 more of the heat that would otherwise be conducted to the 
 interior. 
 
 Concrete is superior to tile as a fire protection. Tile, on 
 account of excessive expansion under high heat, will break 
 131 
 

 up, when in long elements, as surrounding columns or in 
 floor arches or in partitions. This was strikingly exhibit- 
 ed in the Baltimore and San Francisco fires. In hollow 
 blocks of tile or concrete, on account of the fact that the 
 thin shell becomes heated in a short time, the expansion 
 will tend to crack this outer shell off. It is a nice theory 
 that an air space will act as an insulator to keep excessive 
 heat from the vital structural parts, and it would hold true 
 for moderate heat. A hot lire, however, or fire and the sub- 
 sequent application of water, demands something better 
 than would be required for insulation against moderate 
 heat. In the Baltimore and San Francisco fires tile arches 
 suffered very greatly from the breaking off of the soffit or 
 the under part of the arch. Reinforced concrete, if it be 
 rationally proportioned, that is, with the beams as rectan- 
 gular beams and not T beams, as advocated in this book, 
 will have ample protection of the steel by the concrete in 
 the lower part of the rectangle, where the heat of the fire 
 is most destructive. The amount of the protection will be 
 in agreement with the size, and hence with the importance 
 in the structure, of the steel protected. 
 
 It is more economical to add an inch or two of concrete 
 in the beam or column than to fasten tile to concrete. In 
 any event the latter is easily broken off by expansion, ex- 
 posing the thinly covered steel. It is immeasurably better 
 to add concrete, even if it were not absolutely needed from 
 the standpoint of strength, for the fire protection it affords, 
 than to load a structure with material that has no other 
 use than fire protection. Such foreign material is an extra 
 load on the structure with no compensation in the way of 
 added strength, whereas a little extra thickness m the con- 
 crete adds greatly to the strength and rigidity and longevity 
 of the structure. 
 
 It is true of reinforced concrete beams in a greater 
 measure than of columns that concrete added for fire pro- 
 tection is cheaper and better than tile, because the rigidity 
 of the beams is increased in a greater proportion by a small 
 increase in thickness than would be a column. Also it is 
 132 
 
more difficult to make tile hold on the under side of a beam 
 than to make it stand up against a column. Hanging tile 
 ceilings have proven, in recent fires to be specially subject 
 to the destructive action of the heat. 
 
 Columns need protection in greater amount near the ceil- 
 ing of a room where the temperature is the highest. The 
 practice of making knee braces or brackets to the girders, 
 as often followed, is an excellent one ; as these serve the 
 double purpose of laterally bracing a building and of add- 
 ing concrete about the head of a column, where it is most 
 needed for protection. Ornamental caps, molded in the 
 concrete, also serve this purpose. 
 
 Reinforced concrete partitions are ideal as barriers 
 against the progress of fire. They will confine a fire in a 
 room as the sides of a stove confine the fire within, pro- 
 vided, of course, that the fire does not go through door 
 openings. 
 
 There are systems of floor construction that make use 
 of hollow tile in a rational way. In one of these rows of 
 tile are laid on flat forms at the ceiling level, and between 
 the rows ribs or beams are formed in reinforced concrete, 
 the tile serving to fill the space between the ribs and to 
 present a flat surface for the ceiling plastering. In such 
 construction the destruction of the tile would be of little 
 consequence. 
 
 Another system makes use of tile to fill in part or all 
 of the space between a bottom layer of rich concrete an 
 inch or two thick, reinforced with wire mesh and steel 
 rods, and a top layer, two or three inches thick of plain 
 concrete. Sometimes the tiles are separated and concrete 
 poured between them to form ribs, and other times the 
 tiles are laid close. The tiles in this construction carry the 
 horizontal shear, and the concrete above them takes the 
 compression. Being completely enclosed the hollow tiles 
 are protected from fire by the concrete with its embedded 
 wire mesh and rods. 
 
 A variation in the above described floor construction 
 omits the top layer of concrete. Such a "floor" might be 
 
 133 
 
suitable for a sloping roof, where the live load is not ex- 
 pected to be realized. It is lacking in a prime essential 
 of substantial construction in that the top flange consists 
 solely of a thin sheet of tile, made up of a great number of 
 pieces indifferently joined together by a little mortar used 
 in laying the tile. It would require an inspector watching 
 the laying of every tile to insure the filling of the joints 
 with mortar. Flushing would not fill these joints, as the 
 liquid mortar would be wasted by running into the hollows 
 of the tile, if flushing were attempted. The difficulty in 
 securing filled joints lies in the fact that the joints that 
 count are where the thin edges of the tile meet. These 
 remarks apply also to ordinary tile arches, though not with 
 equal force, since the thrust in an ordinary tile arch does 
 not approach in intensity the compression in a system of 
 hollow tile, say 5%" deep with %" "metal" having i" of 
 concrete or mortar underneath, with its embedded steel, 
 on a span of sixteen feet. These are the dimensions of a 
 floor measured by the author. 
 
 The ability of concrete to resist the passage of water 
 though it varies all the way from that of a sieve to that of 
 a good cork. The way to make concrete that will allow the 
 flow of water through it with little impediment is to mix 
 it dry, that is, with a minimum amount of water, and then 
 to ram it or not to ram it in place, as the ramming has lit- 
 tle to do with it. Ramming will bring the stones together 
 and help the adhesion; it will not get rid of the general 
 porosity. The only way to make concrete of itself water- 
 proof is to mix it very wet. Two or three inches of wet 
 concrete will hold water back better than ten or twenty 
 feet of dry rammed concrete. This would appear quite ex- 
 travagant, if it were not a fact proven true by experience. 
 The fact that by using a wet mixture in the thin walls of 
 a tank water can be completely retained is sufficient refu- 
 tation of the charge so often made that concrete is inher- 
 ently porous. 
 
 If a little cement mortar be mixed in a tumbler, the 
 water being slowly added, it will be seen that while the 
 134 
 
mixture is dry, or the consistency of "moist earth," there 
 will be bubbles in it. Ramming or compacting the mortar 
 will not serve to eliminate these bubbles but may break 
 them up. The air is imprisoned and has not the buoyancy 
 to force its way to the surface. Some of it may be forced 
 out on account of the porosity of the mortar, but the ulti- 
 mate result is only a reduction of the magnitude of the 
 pores. When more water is added, the mortar assumes a 
 liquid consistency, and the air bubbles will rise to the sur- 
 face. It is urged against liquid concrete that the excess 
 of water above that which the cement absorbs in the hard- 
 ening process, when it evaporates, will leave voids in the 
 concrete. By this reasoning it is concluded that wet con- 
 crete will be porous, and by reversing it, it is contended 
 that the proper consistency for the maximum watertight- 
 ness is that in which there is just enough water for the 
 needs of the cement in hardening. Reasoning like this 
 would make a cork a very poor thing to keep back water. 
 Cork is quite porous. It can be made to absorb hot water, 
 and it will give it off again in drying. Its substance can 
 be compressed to a fraction of its normal volume. And 
 yet it is practically perfectly water tight, while other woods 
 or barks, weighing much more and apparently much more 
 dense, do not possess this property. The best way to keep 
 water out of concrete is to put lots of water in it in the 
 manufacture. A rich concrete is necessary, for water tight- 
 ness, and a mixture that will compact well. Small gravel 
 is good for this purpose because of the density of the stones 
 themselves and because gravel has the property of packing 
 well on account of the comparatively small friction between 
 the stones. Thorough mixing is another necessity, to in- 
 corporate the cement and water and to distribute it uni- 
 formly throughout the mass. 
 
 Some clay in the sand in a finely divided state or added 
 to the mixture, if it can be thoroughly mixed through flie 
 mass, or clay in a semi-liquid state has been known for 
 some time to add to the density and watertightness of con- 
 crete. In Eng. News, Sept. 26, 1907 Mr. Richard H. Games 
 135 
 

 describes some tests in which 5 to 10% of the cement of 
 mortar was replaced with an equal quantity of dried and 
 finely ground colloidal clay intimately mixed with the ce- 
 ment. The result was a watertight product much stronger 
 than the cement mortar. 
 
 Some concretes become more impermeable with age. 
 Concrete which when new may not be quite watertight, 
 may become so by the action of water passing through it. 
 This may be due partially to uncombined silicates being 
 dissolved by the water and re-deposited, or to the swell- 
 ing of the tine cement particles in the presence of water. 
 Possibly also solid matter in suspense in the water clogs 
 up the interstices as a filter becomes clogged. 
 
 It is true that even with wet concrete pockets are lia- 
 ble to form, and poor batches may find their way into a 
 wall or tank. These can be stopped up or remedied by 
 rich mortar filling all of the pores. In a cistern built under 
 the author's supervision perfect watertightness was attained 
 by the use of wet concrete and careful plastering of all 
 holes with neat mortar while applying a wash of neat mor- 
 tar with a brush, after thoroughly wetting the surface. 
 The neat cement wash exposed at once any large pores in 
 the concrete, and these were plastered up by troweling. 
 This wash was made the consistency of thick cream. After 
 24 hours the surface was again washed with the cement 
 cream, and a third coat was applied after another interval 
 of 24 hours. In addition to this treatment the contractor 
 washed the surface with a mixture of hydrated lime and 
 soft soap. The author is of the opinion that this latter 
 did not affect the watertightness, as it appeared not to be 
 permanent. (See Eng. News, Sept. 28, 1905, p. 330). 
 
 That concrete of itself can be made practically water- 
 tight is proven by numerous tanks and sewer pipes and 
 some water pipes that have been made of concrete un- 
 treated and not "waterproofed." Tests of mortar and con- 
 crete have demonstrated their ability to withstand water 
 under pressure. In Trans. Assoc. of C. E., Cornell Uni- 
 versity, Vol. XIII; Mr, A. B. Moncrieff describes tests on 
 136 
 
blocks of concrete, 2 ft. each way, in which a water pipe 
 was embedded, the pipe being surrounded by a 5 in. bulb of 
 hemp and small rope. Some of these test blocks allowed 
 only 1-50 of a pint of water to pass through in two weeks 
 under 100 ft. head of water. At the end of 80 weeks the 
 tests were repeated with a head of 200 ft. The results 
 were about the same. 
 
 In Engineering News, June 26, 1902, p. 517, Messrs, J. 
 B. Mclntyre and A. L. True describe some tests on gravel 
 concrete 5 in. thick that had set 24 hrs. in air under a 
 damp cloth and a month in water. They found that con- 
 crete specimens containing i :i mortar, and in which the 
 mortar was 30 to 45% of the whole mass, were watertight. 
 These stood pressures as high as 80 Ibs. per sq. in. for 24 
 hrs. without leak. Some of the concrete specimens having 
 i :2 mortar and 40 to 45% of mortar in the mixture were 
 also impermeable, as well as the 1 :2 14 and 1 12.5 14 mixtures. 
 
 In Engineering Record Dec. 14, 1907, p. 661, some tests 
 are given by R. T. Surtees, C. E. Newton-le-Willows, Lan- 
 cashire, England, that show remarkable results. Some 
 plugs of concrete 5 in. thick were made in pipes and water 
 under pressure was brought to bear against them. Two 
 of these stood a pressure of 35 to 50 Ibs. per sq. in. for 
 thirty days without leakage. In a repetition of the tests one 
 specimen was allowed to set where exposed to the sun most 
 of the day, another was allowed to set in a shaded place, 
 and two others were allowed two days under a damp cloth 
 and 28 days immersed in water. The concrete of the first 
 shrunk and did not fill the pipe. The second showed a very 
 slight dampness, which soon took up. The other two were 
 perfectly watertight. The pressure on these tests was in- 
 creased to 260 Ibs. per sq. in. With pressure varying be- 
 tween 50 and 260 Ibs. for two days no sign of dampness 
 appeared on the outside. One of the blocks was cut out 
 to see how far the water had penetrated. It was seen to 
 be traceable for a distance of only iVs in. The concrete of 
 these tests was made of two mixtures, namely, I part of 
 cement, i part of sand, i part of crushed gravel, i part of 
 
 137 
 
gravel screened to % in., and a mixture of 1:1:1^:1% of 
 the same ingredients respectively. The same experimenter 
 made a reinforced concrete pipe and subjected it to 120 Ibs. 
 No sign of dampness appeared on the outside of the pipe. 
 
 Troweling increases the impermeability of concrete. 
 Troweling should be done in such positions as the top sur- 
 face of an arch and the exposed surface of a sea wall. 
 
 Concrete has been found to be suitable for tanks in which 
 to freeze water in the manufacture of ice. At the annual 
 meeting of the Am, Soc. of Refrigerating Engineers, at 
 New York, in 1907, Mr. Abram Day describes some ice 
 tanks of reinforced concrete that have been used for some 
 years with satisfaction. In some tanks Mr. Day used 1:1 13 
 concrete of trap rock and in others iVz \iVz :2Vz. He finds 
 the best size of aggregate to be s.tone about % in. to ^ in. 
 The inside of his tanks are either left rough or washed 
 with neat cement. No waterproofing is used. [See Eng. 
 News, Dec. 12, 1907, and Ice and Refrigeration, Dec. 1907 .] 
 
 Another useful property of concrete was brought out 
 at the meeting referred to in the previous paragraph. Mr. 
 John E. Starr described a nine-story cold-storage ware- 
 house built entirely of reinforced concrete, with a double 
 facing wall filled in between with cork. Additional insula- 
 tion was also provided by coating the tops of all floors 
 with cork boards, two to four inches thick. It is a remark- 
 able fact that though the inside of this house is frequent- 
 ly at as low a temperature as five below zero, R, with the 
 outside wall above 100 deg. F., no signs of cracking, due to 
 expansion, have ever been noticed. 
 
 Hollow blocks of concrete afford excellent insulation 
 against moderate heat or to retain heat in a building. 
 
 The ability of concrete to stand weather and atmospheric 
 conditions is often much better than that of the stone com- 
 posing the aggregate of the concrete. A poor stone is 
 improved by being made into concrete and surrounded and 
 protected by a mortar of sand and cement. Hard stone 
 such as granite and trap are not as durable nor as strong, 
 made into concrete, as the original stone. These stones 
 138 
 
however, make the strongest kind of concrete, and the use 
 of trap, especially, in concrete has the advantage of being 
 a means of utilizing this stone for building purposes, when 
 it would be scarcely possible to use it at all as a building 
 stone. Trap is very refractory under the dressing tool and 
 can only be employed in rough blocks. Some stones that 
 would develop planes of fracture in a structure made of 
 block stones have these planes fractured in the crusher. 
 They are therefore rendered safe against failure by crack- 
 ing. Stones that by themselves suffer surface disintegra- 
 tion would be subject to the same action, if exposed on 
 the surface, though the cement and sand of the concrete 
 will protect them very materially. If the mortar of the 
 concrete be worked to the surface, stone that would suffer 
 surface disintegration may be quite durable in concrete. 
 Slag cement should not be used for concrete that will be 
 dry, if used at all, it should be where the concrete is al- 
 ways wet. Good Portland cement concrete will be durable 
 either wet or dry. 
 
 One of the most trying situations for concrete is sea 
 water between high and low tides. Much has been writ- 
 ten on the subject of the chemical effect of the salts of 
 sea water on cement and concrete. That the deterioration 
 is a surface action almost entirely and that it is generally 
 confined to the zone between high and low tide levels 
 suggests that the action is at least partially mechanical. 
 The formation of salt crystals in the pores of the concrete, 
 by the evaporation of the salt water, by their swelling ac- 
 tion may have something to do with this surface disin- 
 tegration. 
 
 It is a fact, and one that the author has found to be 
 not generally known by practical chemists, that silicates, 
 when ground to a fine powder, glass, for example, are solu- 
 ble in acids and alkalies that do not affect the solid lumps. 
 Ground glass is even soluble in pure water. Crushed rock 
 will make soil in a very short time, whereas the same rock, 
 in large pieces, may withstand the weather a long time 
 before disintegrating. Water acts on the ground rock in 
 139 
 
a very short time. It is said that holes can be blasted in the 
 rock in certain parts of the Florida Keys and crops planted 
 in the broken stone. Cement clinker is a sort of glass. 
 When ground to a fine powder, it is partially soluble in 
 water. This can be seen by stirring cement in a large 
 quantity of water, preferably hot. A glass like scum forms 
 on top of the water after it stands a while. If allowed to 
 absorb water and to harden without being subject to con- 
 ditions that take away the water, cement will unite with 
 the water and form a permanent compound. If the 
 amount of water is stinted, as in the "moist earth" con- 
 crete mixtures so popular with many, it is impossible for 
 all of the grains of cement to find sufficient water to make 
 them into a stable compound. They remain, therefore, in 
 some degree, in the state of ground silicates, easily dis- 
 solved by water. With Portland Cement, sloppy concrete 
 and a smooth finish on the surface exposed to sea water, 
 or any wave action, is the best precaution against dissolv- 
 ing action. 
 
 The continuous washing of the surface of concrete by 
 waves of water, either salt or fresh, would be expected to 
 carry away any uncotnbihed silicates in the cement ; where- 
 as, if the water were still, the dissolved silicates would not 
 be carried away, but, as is possibly the case in still water, 
 they would be redeposited in the pores of the concrete. 
 It is probably this dissolving that is responsible for the 
 pitting and roughening of cement pavements caused by 
 rain. While this is a chemical action, the mechanical action 
 of the beating water supplies the destructive element. Dry 
 concrete and excessive troweling to give a glossy surface 
 are very commonly resorted to by pavers. It is not un- 
 common to see the same pavements pitted after some time 
 of exposure to weather. 
 
 In sewers and water pipes this is not exhibited in the 
 same way, because mud deposits in the pores and protects 
 the concrete where the scour would be the most. 
 
 Concrete subject to the action of sea waves should have 
 a coat of rich mortar plastered very smoothly. Facing con- 
 
 140 
 
Crete with granite between high and low tide levels is very 
 often practiced. This is a sure way of rendering a sea 
 wall permanent. 
 
 There is a cement called iron-ore cement, manufactured 
 in Germany, which is said to resist the action of sea water. 
 This cement is made of iron-ore and limestone instead of 
 clay and limestone. 
 
 The weight of stone concrete generally runs about 150 
 Ibs. per cu. ft. Heavy stones, such as granite and lime- 
 stone may exceed this. Sandstone concrete may weigh 
 less. Concrete mixed with a minimum amount of water 
 will weigh less than medium or wet concrete, a fact which 
 testifies' to the porosity of the former. The weight of 
 sandstone is about 150 Ibs. per cu. ft.; of granite, 170; of 
 limestone, 170. 
 
 Cinder concrete weighs about no Ibs. per cu. ft. when 
 dry. Wet cinder concrete should be calculated to weigh 
 about 125 Ibs. per en. ft. in designing the forms. 
 
 Notes on General Design and 
 Construction 
 
 Under this heading will be given some notes bearing on 
 the general design and treatment of structures that do not 
 come under the head of any of the other general subjects 
 treated. 
 
 DRAINAGE. Retaining walls and arches should be well 
 drained by a system carefully planned to perform its work. 
 Iron or steel pipes should be avoided, if the water passing 
 through them runs over the exposed face of the wall ; be- 
 cause the rust will disfigure the wall. A collapsible wooden 
 core, say of a round or square piece split longitudinally 
 on a slant, would allow the removal of the pieces separate- 
 ly. Or a box of thin wood could be used and broken up 
 on removal. Or a smooth hard wood core could be used 
 and drawn out before the concrete has a hard set. Clay 
 tiles placed in concrete make good permanent drains. In 
 
 141 
 
building a wall there should be a lot of loose stones 
 placed where water would collect and where the drain is 
 located, so that it will not clog up. It would not be out 
 of place to have a drainage system in a building. In a fire 
 damage by water is often greater than by the fire itself. 
 A fire in the upper story of a building may be extin- 
 guished by the application of water, which, if it is not 
 carried away, may run down the stairs to floors below 
 and work damage there. 
 
 PROVISION FOR EXPANSION AND CONTRACTION. Calcula- 
 tions for temperature stresses in concrete are of little if 
 any use. Shrinkage in concrete due to setting in the air 
 is a more important factor in changing its size than tem- 
 perature variation. If this were elimnated, calculations 
 for temperature changes would have some meaning. How- 
 ever the actual change in temperature, as in an arch, would 
 not be very much, especially if the arch is one having fill 
 over it. Concrete and earth are both poor conductors of 
 heat, and the range of temperature in the body of the arch 
 would not approach that which could be expected to take 
 place in a steel structure. It is usually in arches that 
 temperature stresses are the most minutely elaborated. 
 There is undoubtedly more or less uncertainty in the 
 stresses in an arch due to temperature changes, but the 
 same is true in a larger measure of the effect of shrinkage. 
 Uncertainties should be covered by a factor of safety or 
 by liberal design : it does not minimize them to attempt 
 to cover them by fictitious though elaborately calculated 
 stresses. Steel reinforcement in all parts of an arch or 
 other structure is one of the best safeguards against shrink- 
 age and temperature stresses. To build a structure so that 
 shrinkage may take place during the building is another. 
 In an arch it would be better, where possible to place the 
 entire arch ring, leaving a groove and steps for the span- 
 drel wall to be poured after the forms of the arch ring are 
 removed. In a building walls or partitions would be bet- 
 ter to be separate from the columns, let into recesses in 
 the latter and placed after the columns have set. In a long 
 
 142 
 
structure two sets of columns and girders at a dividing 
 plane would give opportunity for shrinkage to act. Pro- 
 vision for shrinkage is only a makeshift, and a useless 
 one, unless carried down to the foundation. 
 
 ARCHES IN SERIES. In a long line of arch spans it is 
 legitimate to make the piers between the adjacent spans 
 heavy enough to be rigid against live load only on any 
 span, if the arches are equal and the dead load thrust bal- 
 anced. However, there should be an occasional pier that 
 will take the full thrust of one span, so that if one span 
 should fail, the entire system will not come down. Every 
 third or fifth pier may be an abutment. Forms should not 
 be removed in a long line of arches in a span adjacent to 
 a pier that is not capable of acting as an abutment. 
 
 Box CULVERTS. Flat slab tops on box culverts are pre- 
 ferable to arches for several reasons. They do not re- 
 quire abutments but only supporting side walls. When 
 fill is being made between wooden trestle, a flat top box 
 culvert can be introduced between trestle bents, where 
 often an arch culvert and its abutments would require 
 the removal of one or two bents. 
 
 TANKS. There is not much economy, if any in using 
 a reinforced concrete tank as compared with a steel tank. 
 The shell of a steel tank can be stressed to 20,000 Ibs. 
 per sq. in. or more, and the tank will be safe and tight. 
 Many oil tanks are designed with a unit stress, on the 
 vertical section, of about 24,000 Ibs. per sq. in. Steel em- 
 bedded in concrete and stressed to these amounts would 
 crack the concrete, and of course the cracks would destroy 
 the value of the tank as a receptacle for liquids. There is 
 not much difference in cost per pound of steel ro'ds placed 
 in a rinforced concrete tank and the steel shell in place 
 and riveted. There is- therefore a large margin in favor 
 of the steel tank. There may, however, be cases where re- 
 inforced concrete tanks would be more suitable, and there 
 may be cases where they would be more economical. The 
 greater lasting quality of reinforced concrete makes it more 
 desirable in many cases than steel. Tanks with small ten- 
 
 143 
 
sion in the shell may require to be made of steel plates 
 much thicker than the mere tension would demand, so 
 that small tanks might be as cheap in reinforced concrete 
 as in steel. 
 
 CISTERNS. A cistern with an approximately flat bot- 
 tom would often be better to have the bottom somewhat 
 concave. Shrinkage cracks are less liable to occur in a 
 curved bottom, and with the bottom concave the cistern 
 can be emptied and cleaned better than with a flat bottom. 
 
 SMALL COLUMN PEDESTALS. In making small column 
 pedestals it is well to make as few different sizes in a given 
 structure as practicable, at the expense of using more con- 
 crete than is required in some of them. It simplifies the 
 form work to make duplicate sizes. Steps in the sides 
 are preferable to a batter, especially if the top is small and 
 the batter large. It is hard to pour concrete in the small 
 hole and hard to tamp it through the same. 
 
 STAIR SUPPORTS. Slabs and beams for the support of 
 stairs are to be calculated for a span equal to the hori- 
 zontal projection and not the actual length, though of 
 course the weight of the parts are found from their actual 
 dimensions. When triangular blocks are cast on a slab 
 for the steps, these should not be counted in any part 
 of the depth of slab. The slab should be proportioned for 
 a depth exclusive of these blocks. At angles, as where a 
 landing joins the slope of the stairs, there should not be 
 a sharp corner in the slab: there should be a thickening 
 of the slab, and reinforcing rods should be given gentle 
 curves, say with a radius 50 to 80 times the diameter of 
 rod. 
 
 BEAMS AND GIRDERS. As few sizes as possible of beams 
 and girders should be used, and their spacing should be 
 as regular as practicable. For economy, the deeper the 
 beam the less it will weigh, just as in wooden construction 
 and, generally, in steel work. However, deep beams loaded 
 to their capacity are apt to be weak in shear. Also deep 
 beams may be too narrow for other reasons. They may, 
 further, encroach on clearance, or they may necessitate ad- 
 
 144 
 
ditional height to a building. Girders and beams should 
 be placed at columns rather than near the columns so that 
 they will help to stiffen the building. 
 
 SHAFT HANGERS. Shaft hangers may be attached to 
 beams by means of bolts placed in the concrete having 
 the threaded end projecting to receive the hanger; or 
 threaded castings may be built in the beam, either in the 
 side or bottom, to these the hanger may be attached, or 
 timbers or steel angles may be bolted on; or pieces of 
 gaspipe may be left through the beams near the bottom 
 and bolts run through them to which timbers, or blocks 
 or longitudinal angles may be bolted; or clamps may be 
 used on the beams, held on by friction. 
 
 HOLES FOR PIPES AND WIRES. Holes should be left in 
 floors in the building of them for all pipes and wires that 
 may be placed. It would be better to leave too many than 
 not to leave any or not to leave enough. It is easy to ce- 
 ment up such holes but very difficult to cut them in hard- 
 ened concrete. 
 
 BATTERED ABUTMENTS. It is unnecessary to give abut- 
 ments a batter on the front face. It appears to be a rudi- 
 ment of some popular notion of stability that a small bat- 
 ter, say of i to 12, will add rigidity to abutments, wing 
 walls, sides of culverts (inside), etc. It does not pay for 
 the trouble. 
 
 VERTICAL PIPES. If possible vertical pipes should be lo- 
 cated where they will not run between a column and its 
 lire protection. Expansion due to heat will cause the pipes 
 to buckle and will tend to pry off the lire protection. This 
 will apply to any building where the fire protection is 
 separate from the structural column, as in cast iron or 
 steel column construction. 
 
 HEAVY GIRDERS. In general, reinforced concrete is 
 neither appropriate nor economical for very heavy girders, 
 either long span girders or short ones taking heavy con- 
 centrations. Steel girders are more suitable in such cases, 
 In very long spans the dead weight of the girder is ex- 
 cessive : in short spans carrying heavy concentrations the 
 
 145 
 

 embedment of the steel is apt to be insufficient for the 
 stress, also shearing stresses are difficult to provide for. 
 Shallow beams are best made in steel also, as concrete 
 beams shallow in depth are clumsy on account of having 
 to be so wide. 
 
 SLENDER COLUMNS. Slender columns should not be at- 
 tempted in concrete. They are better to be of cast iron or 
 of steel, protected with concrete if necessary. 
 
 REINFORCING WALLS AT CORNERS. Walls that meet at an 
 angle should be tied together at the intersection to pre- 
 vent cracking at the corner. 
 
 SCHEME FOR FLOOR SUPPORT. A very simple and efficient 
 reinforced concrete floor for either a highway or a rail- 
 road bridge can be made by running rods transversely from 
 girder to girder to act as bottom reinforcing rods in the 
 floor slab. The rods should be plain, round, threaded on 
 the ends, and should pass through the steel work, Holes 
 being left for the purpose. If the slab rests on a shelf on 
 the side of a beam or girder, the holes may be in the web 
 just above the shelf. If it is a through span, the slab rest- 
 ing on the bottom flange of the girder, some of the rivet 
 holes, say at intervals of 6 or 9 ins., may be left open. In 
 a deck span the web plate may be extended to take the 
 holes for reinforcing rods. This slab construction is ad- 
 mirable for highway bridges. The entire roadway may 
 be one continuous slab from truss to truss or girder to 
 girder, passing over the stringers, with the same rods to 
 act as reinforcement. Over this slab brick or block or 
 asphalt pavement may be laid. The lateral system on a 
 bridge with a floor of this sort need only be strong enough 
 to take care of lateral forces during erection, as the con- 
 crete slab will give ample stiffness. 
 
 SURFACE FINISH. Every contract for concrete work 
 should include a clause requiring that the exposed surface 
 be properly finished. The finish should be appropriate to 
 the nature of the work. In some cases this may mean 
 merely a washing down to remove dirt and efflorescence 
 after removal of forms. An otherwise good job of con- 
 146 
 
creting may appear very poor on account of failure to treat 
 the surface properly, and the owner may have to go to 
 considerable expense to improve the appearance of a struc- 
 ture .by reason of failure to specify the kind of finish de- 
 sired. 
 
 WATERPROOF PLASTER. A mixture, by volume, of 3 parts 
 of litharge, I part of glycerine, 48 parts of Portland ce- 
 ment, and 48 parts of sand makes a strong, adherent, and 
 dense plaster, which will repel water. Hot paraffine is 
 sometimes ironed into concrete to waterproof the surface. 
 Linseed oil, painted on until the concrete will absorb no 
 more, is also used to waterproof concrete that has not 
 been properly made and lacks density. 
 
 WHITEWASH. Whitewash for concrete surfaces should 
 be durable and adhesive. The following is recommended. 
 Slake with warm water, half a bushel of lime, covering 
 it during the process to keep in the steam ; strain the liquid 
 through a fine sieve or strainer : add a peck of salt, pre- 
 viously well dissolved in warm water, 3 Ib. of ground rice, 
 boiled to a thin paste and stirred in boiling hot water, l /2 
 Ib. of powdered Spanish whiting, and a pound of glue 
 which has been previously dissolved over a slow fire; add 
 five gallons of hot water to the mixture. Stir well and 
 let it stand for a few days, covered from the dirt. Strain 
 carefully and apply with a brush or a spray pump. It 
 should be put on hot. Coloring matter may be put in to 
 make various shades. 
 
 SOME USES OF CONCRETE. Some of the more uncommon 
 situations in which concrete can be used to advantage are 
 the following: 
 
 For props in coal mines, in place of timber. 
 
 To line steel coal or ash hoppers or bins. 
 
 For fence posts. These are usually made square and 
 tapered and have a reinforcing steel wire near each cor- 
 ner, these tied together with wires. 
 
 . For roof tiles or shingles. These may be reinforced with 
 a wire mesh or metal lath of some kind. 
 
 To protect wooden piles in sea water from toredo. To 
 
 147 
 
accomplish this the concrete may be molded into a cylin- 
 der around the pile. Steel reinforcement must be used to 
 hold the concrete from breaking off. Another method is 
 to use concrete half-cylinders surrounding the pile, or 
 sewer pipe of clay or concrete if they can be threaded over 
 the top of the pile. The space between the pile and the 
 surrounding cylinder is then filled with sand. In the event 
 of a break in the surrounding cylinder the sand will run 
 out and the damage can be detected and repaired. 
 
 Estimating Cost. 
 
 The cost of a structure is a function of the number of 
 pounds of steel or cast iron, the number of cubic feet or 
 yards of masonry, the number of bricks, the number of 
 feet of board measure, the number of square feet of pav- 
 ing, of lineal feet of handrailing, etc., that go to make up 
 the whole. An estimate of the cost requires careful calcu- 
 lating of all of these as well as a knowledge of a fair unit 
 price at which they can be put into the structure. 
 
 Cost estimates must be based on unit values. The ac- 
 curacy of the estimate will often depend upon the particu- 
 lar unit at which the estimate starts. Sometimes greater 
 accuracy will result from tracing back the unit cost of the 
 raw materials of manufacture : often such tracing is pro- 
 ductive of only confusion with no increased accuracy. For 
 example, there is nothing gained by analyzing the cost of 
 a pound of steel or a barrel of cement. These materials 
 have certain prices fixed by those who sell them. In the 
 matter of working up materials there are also arbitrary 
 elements. The cost per unit will depend upon the particu- 
 lar plant or equipment employed and its fitness to handle 
 the work most economically. 
 
 The plant or equipment needed to do a piece of work 
 should be selected with a view of the size of the work and 
 the time in which it is to be finished. Large equipment 
 cannot, in general, be used economically on a small job, 
 and small equipment cannot be used economically on a 
 
 148 
 
large job. The size of a concrete plant should be such 
 that its normal daily capacity is about equal to the amount 
 of concrete that it is desired to turn out per day. For 
 maximum economy a plant should be employed continous- 
 ly. If stops must be made to wait for forms to be put in 
 readiness, or for other causes, the concrete will cost more 
 than if the work of the concrete mixing can be carried on 
 continuously. 
 
 For small concrete jobs, such as pavement work, hand 
 mixing is more economical. Small batches may be mixed 
 with a hoe or shovels in a box. Half-yard batches should 
 be mixed on a platform by at least two men with shovels. 
 The platform may be made of a steel plate or of boards 
 placed with close joints on a frame. 
 
 A typical gang mixing and laying one-half cubic yard 
 batches is the following: I foreman, 2 men delivering 
 sand and stone, I man delivering cement, 2 men mixing 
 
 2 men delivering concrete, I man tamping. At $3 per day 
 for the foreman and $1.50 per day for each of the other 
 men the cost per day of this gang is $15. The gang should 
 turn out about 20 to 25 cu. yds. per day. This is a cost 
 of 75 cts. to 60 cts. per cu. yd. for labor. 
 
 A typical gang for mixing and laying by hand cubic- 
 yard batches is as follows : I foreman, 3 men delivering 
 sand and stone, I man delivering cement, 4 men mixing, 
 
 3 men delivering concrete, 2 men tamping. The cost of 
 this gang at the same wages as above is $22.50 per day. 
 They should turn out about 40 cubic yards per day, making 
 the cost of labor 56 cts. per cu. yd. 
 
 The above examples give about average conditions and 
 show the cost of labor on hand mixed concrete in heavy 
 work where mixing and laying can go on continuously. 
 If labor is cheap (and efficient) the unit cost may be less, 
 and vice versa. If materials can be deposited for easy 
 handling, as when they are laid close to the mixing board 
 and need only to be measured the unit cost will be reduced 
 accordingly, whereas long hauls or high lifts, either before 
 or after mixing will add to the cost very materially. If 
 149 
 
the gang cannot be continuously employed, costs may be 
 two or three times as much as the above. Concrete de- 
 posited in narrow forms will also cost more per cu. yd. 
 than in massive work. 
 
 With mechanical mixers the cost of mixing concrete will 
 be less than by hand mixing, though the extra cost of 
 skilled workers to run the engine and mixer helps to bal- 
 ance the costs. Batch mixers should turn out about 20 
 batches per hour. 
 
 Current prices for which similar work is being done in 
 localities situated about the same distance from the source 
 of supply afford a sound basis upon which to gage the 
 cost of work. It is best for the engineer not engaged in 
 the estimating of cost to the contractor or manufacturer 
 to use as a base the unit cost of work in place, rather than 
 to analyze the elements that go to make up that cost, 
 such as material, labor, freight, hauling, profit, etc. The 
 contractor's profit is an elastic factor, depending upon the 
 size of the work, the risk, and many other considerations. 
 The cost of manufacture is variable. Some shops can 
 make heavy work cheaper than others, while others can 
 handle light work more economically. It is not the pur- 
 pose here to analyze the cost in shops and mills, so much 
 as to give more general data for determining the probable 
 cost of ordinary building and bridge work, as well as to 
 point out some of the special cases where costs are apt to 
 be more or less than the average. Average costs will pre- 
 vail near the railroads and within radii of 50 or 100 miles 
 of the commercial centers. Freight rates average about 
 % to one and one-half cents per ton-mile. Long pieces 
 requiring several cars and not weighing enough to load 
 them to their normal capacity will cost more per ton than 
 materials that can be shipped in full car loads. Partial 
 carloads are charged at a minimum car load rate, say one- 
 half of the capacity of the car. Where more than one car 
 is required, one car is charged at this minimum rate and 
 each other car at one-half of this amount, if the actual 
 weight of the material shipped is not over that total. 
 
 150 
 
Hauling under ordinary conditions costs about 50 cents 
 per ton for structural material. 
 
 The actual cost of hauling crushed stone i% miles in 
 some macadam paving was found to be 26.6 cts. per ton 
 when drawn from the crusher bins and 31 cts. per ton when 
 drawn from the piles. The contract price was 32^ cts. per 
 ton. 
 
 The hire of a dumping wagon and team and driver is 
 about 4 dollars per day: that of a horse and cart and 
 driver is about three dollars per day. 
 
 The actual cost, with stone free at the quarry, of lay- 
 ing macadam pavement ( 5" layer large sized stone, rolled ; 
 2^/z" to 3" layer of medium sized stone, sprinkled and 
 rolled ; about %" of fine screenings, sprinkled and rolled) 
 was 42 cents per square yard. The average weight of 
 stone was .3 tons per sq. yd. (Eng. News, Oct. 8, 1903). 
 
 The actual cost of quarrying and crushing stone in the 
 above mentioned work was 42 cts. per ton ; in which coal 
 delivered cost 4 dollars per ton, a driller $1.75 per day, help- 
 er $1.50 per day, engineman $2 per day. 
 
 The cost of mixing materials and laying the same in 
 making the Buffalo breakwater was as follows : 
 
 Laying Materials 17.4 cts. cu. yd. 
 
 Mixing Materials 12.9 cts. cu. yd. 
 
 Placing mixed materials 14.6 cts. cu. yd. 
 
 Total 44.9 cts. cu. yd. 
 
 Sometimes the gravel and sand for a piece of work can 
 be found at or near the site, thus greatly reducing the cost 
 of concrete made of the same. 
 
 Bricks may be hauled direct from the works without the 
 expense of loading and unloading on cars. 
 
 Extra hazardous work should have something added to 
 the estimated cost to allow for the risk taken by the con- 
 tractor. Work that must be finished in a short time should 
 have the estimate increased, especially if a penalty attaches 
 for failure to complete by a specified time. If the season 
 is a poor one for the class of work, still more expense is 
 liable to be incurred. Erecting of bridges over streams in 
 
 151 
 

 flood time may be attended by serious difficulties and ex- 
 pensive delays. 
 
 Large contracts, as a rule, cost less per unit than small 
 ones. The placing and removing of the contractors plant 
 on a job often requires considerable time. If the magni- 
 tude of work does not justify bringing labor saving ma- 
 chinery to the site, the extra labor will make the smaller 
 job more expensive. Large orders of materials may be 
 placed at lower rates than small ones. 
 
 Where labor is the principal item of cost in any work, 
 less certainty can be expected in the estimate of the cost, 
 and little agreement between prices bid by contractors; 
 whereas materials that are regularly manufactured should 
 vary but little in cost. 
 
 There are some general rules that will be found very 
 useful in making a rough estimate of the cost of structures 
 and checking against large errors in more careful esti- 
 mates. The cost per square foot of area covered by a 
 building having practically one floor will be nearly con- 
 stant for different sizes of buildings of the same class. 
 Higher buildings will have a cost per cubic foot nearly 
 constant for a given class of building. For ordinary lengths 
 of spans the cost of reinforced concrete bridges per square 
 foot of floor does not vary much. 
 
 The cost per square foot of the area covered by buildings 
 of the World's Columbian Exposition for nine of .the 
 principal buildings varied between 75 cents and $2.35, and 
 averaged about $1.50. The Administration building cost 
 $9.18 per square foot. The cost per square foot under 
 roof of eleven of the principal buildings of the Louisiana 
 Purchase Exposition varied between 61 cents and $1.49 
 with an average of $1.12. Festival Hall cost $5.23 per sq. 
 ft. Fine Arts Building (central building) cost $9.88 per 
 sq. ft., U. S. Gov't. Building cost $2.31 per sq. ft. The 
 eleven buildings at St. Louis have timber framework. The 
 Chicago buildings had steel frames. The Fine Arts Build- 
 ing at St. Louis is permanent and fire-proof. The U. S. 
 
 152 
 
Gov't. Building has steel arches. The cost of the sterl 
 work alone was 65 cents per sq. ft. 
 
 The cost per square foot of floor of what is probably 
 the longest stone arch in the world; namely, the bridge 
 at Plauen, Saxony with a span of 295.2 feet, was $4.65. 
 Low cost of labor and availability of stone close to the 
 bridge made its cost much lower than such a bridge could 
 ordinarily be built for (Eng. News, Jan. 28, 1904). 
 
 Fern Hollow Bridge at Pittsburg, Pa., cost, including 
 the masonry $4.06 per sq. ft. of floor. This is a plate gir- 
 der arch with viaduct approaches. The arch span is 195 
 feet. It was estimated that a stone arch bridge would 
 have cost nearly three times as much. (Eng. News, Feb. 
 26, 1903). 
 
 The cost of a double track stone arch railroad bridge 
 of 64-foot spans at Watertown, Wis. was $4.35 per sq. ft., 
 including removal of old bridge. (See Eng. News, Vol. 
 49* P- 266). 
 
 The cost of the P. R. R. Co.'s four-track stone arch 
 bridge at Rockville, Pa. was $5.03 per square ft. 
 
 Following are the approximate costs of reinforced con- 
 crete arch bridges per square foot of roadway and side- 
 walk, end to end of abutments : 
 
 Bridge at Dayton, O., Spans 69 to 88 ft. Pavement of 
 bituminous macadam. Assuming abutments 20 ft. each, 
 cost per sq. ft. = $3.63 (Eng. News, May 19, 1904). 
 
 Bridge at Dayton, O., Spans 80 to no ft. Cost, includ- 
 ing provision for temporary traffic and removal of old 
 bridge, $3.63 per sq. ft. (R. R. Gazette, May 4, 1904). 
 
 Bridge at Forest Park, St. Louis, Span 45 ft. Macadam 
 pavement on roadway. Cost per sq. ft. $3.63. (Eng. News, 
 June n, 1903). 
 
 Bridge at Laibach, Austria. Span 108 ft. Cost $32,000 
 ($4.14 per sq. ft.) The metal work of this bridge cost 
 about $6,000 and the ornamental work $2,000. (Eng. News, 
 July 1 6, 1903). 
 
 Bridge at Brooklyn, N. Y. Skew arch. Cost $2.85 per 
 
 153 
 

 sq. ft. Contains 91,360 Ibs, of steel and 1300 cu. yds. of 
 concrete. (Eng. News, Dec. 30, 1903). 
 
 Bridge at Waterloo, Iowa. Seven spans each 72 ft. Cost 
 per sq. ft. $1.65. This does not include floors and pave- 
 ments. Bridge contains 7200 bbls. Portland cement, 5000 
 cu. yds. crushed rock, 3000 cu. yds. sand, no tons of steel 
 ribs, 6,000 cu. yds. of spandrel filling. (Eng. Record, Feb. 
 13, 1904). 
 
 Bridge at Des Moines, Iowa. Spans 100 ft. Spandrel 
 walls and arch ring faced with brick. Cost per sq. ft. 
 $4.48. (Eng. News, May 14, 1903). 
 
 Bridge at Topeka, Kan. Longest span 125 ft. Cost $4.51 
 per sq. ft. (Eng. News, Apr. 2, 1896). 
 
 Bridges at Niagara Falls. Cost of two bridges $4.60 
 per sq. ft. (Eng. Record, Feb. 16, 1901). 
 
 Bridges in Porto Rico. One bridge having i i2O-ft. 
 and 2 zoo- ft. spans and rather high piers cost $8.17 per 
 sq. ft. and one having 3 7o-ft. spans cost $5.29 per sq. ft. 
 (Eng. News, Aug. i, 1901) 
 
 Bridge at Washington Street, Dayton, O., about $3.30 
 per sq. ft. (Eng. Record, Mar. 2, 190?). 
 
 Bridge at Sandy Hill, N. Y., $2.43 per sq. ft. (Eng. Rec- 
 ord. May 4, 1907.) 
 
 Bridge at Jacksonville, $3.00 per sq. ft. (Eng. Record, 
 May 18, 1907). 
 
 Bridge at Mishawaka, $3.82 per sq. ft. (Eng. Record, July 
 7, 1906.) 
 
 Bridge at South Bend. $3.32 per sq. ft. (Eng. Record, 
 July 28, 1906.) 
 
 Bridge at Philadelphia, $6.85 per sq. ft. (Eng. Record, 
 Nov. 17, 1906.) 
 
 Bridge near Goshen, O., $4.67 per sq. ft. (Eng. Record, 
 Mar. 30. 1907.) 
 
 Bridge over Rock Creek, Washington, D. C. (Boulder- 
 faced span, illustrated in this book), $5 per sq. ft. (Eng. 
 Record, Vol. 46, p. 151.) 
 
 The cost in 1903 of a large reinforced concrete factory 
 
 154 
 
building was 6.4 cts. per cu. ft. This was for the building 
 alone, not including plumbing or furnishings. 
 
 Mr. H.-G. Tyrrell (R. : R. Gazette, Vol. 37, No. i8) made 
 comparative estimates of a large factory building designed 
 to carry 100 Ibs. per sq. ft. of live load (six stories and 
 basement), and found that a building of heavy wooden 
 interior construction with brick floors, and cast iron col- 
 umns in the lower two tiers would cost 6.2 cts. per cu. ft. 
 or 83 cts. per sq. ft. of area of floors; the same building 
 with concrete steel floors on a steel frame work would 
 cost 10.2 cts. per cu. ft. or $1.36 per sq. ft. of area of 
 floors. This did not include furnishings or stairs. 
 
 The cost of a reinforced concrete power building per cu. 
 ft. above ground was 7.7 cts. (See description, Eng. Rec- 
 ord, Apr. 15, 1905, p. 438.) The total cost of this building 
 was $225,000. 
 
 The cost of a brick building with slate roof on timber 
 will probably be from 8 to 14 cents per cubic foot of its vol- 
 ume. 
 
 The cost of a mill building with sides and roof of cor- 
 rugated iron will probably be from 75 cents to $1.50 per 
 square foot of plan. 
 
 The cost of apartment buildings and department stores 
 as usually constructed will be from 20 to 30 cents per cubic 
 foot of volume. 
 
 Office buildings will usually run from 30 to 60 cents per 
 cubic foot. 
 
 City dwellings will run from 10 to 30 cents per cubic foot. 
 
 Brick veneer dwellings will cost about 8 cents per cubic 
 foot. 
 
 Window and door frames as ordinarily made for mill 
 buildings cost about 25 cents per square foot in place es- 
 timating the dimensions out to out of frames. Galvanized 
 iron louvres of No. 18 iron cost about the same. 
 
 The cost of furnishing clips and rivets and putting up 
 corrugated" iron is about "$2.00 per square of 100 square 
 feet. 
 
 Erection of plain structural work costs 9 to 10 dollars 
 155 
 
per ton; of frame work of office buildings 10 to 12 dollars 
 per ton; of mill buildings n to 15 dollars per ton. Com- 
 plicated work of many small parts and light tonnage, such 
 as angles and tees for roof tile, may run as high as 28 to 
 30 dollars per ton to erect. Bridge truss work will cost 
 15 to 20 dollars per ton. These figures include furnish- 
 ing falsework, also the painting. 
 
 The painting of structural work costs about one dollar 
 per ton for each coat. 
 
 The driving of field rivets costs from 5 cents to 20 cents 
 each, depending upon the accessibility of the rivets and 
 the number of times that scaffolds must be moved in a day. 
 A riveting gang costs about 18 dollars a day. For ordin- 
 ary work 12 cents per rivet is a good average. 
 
 The hire of an engine and derrick is about 30 dollars 
 per week. That of an engine and concrete mixer is about 
 the same. This does not include any men to operate the 
 same. 
 
 The hire of a road roller with coal and operator is about 
 12 dollars per day. 
 
 The hire of a work train and crew, coal, etc., is about 
 $22 per day. 
 
 The cost of galvanizing structural work is about twenty 
 dollars a ton. 
 
 The cost of corrugated steel roofing or siding per square 
 of 100 square feet, at 3^ cents per pound for material and 
 $2.25 per square for erection and painting is about $11.75 
 for No. 18 and about $9.00 for No. 20. Galvanized roofing, 
 at one cent extra for galvanizing would cost about $14.50 
 for No. 18 and about $11.00 for No. 20 per square erected. 
 
 The cost of concrete-steel roofing on 1 5-foot spans is 
 about 25 to 30 cents per square foot, exclusive of covering. 
 Concrete-steel floors for ordinary loads on spans 8 to 10 
 ft. cost about the same. Heavy floors cost 30 to 40 cents 
 per sq. ft. Cement finish on floors costs 7 to 10 cents per 
 sq. ft. 
 
 The cost in 1903 of a 54 inch self-supporting steel stack 
 no ft. high of 5-16", %", and 3-16" metal, including lad- 
 
 156 
 
der, painted on outside, with base casting, but not anchor 
 bolts or foundation, was $1,200. Breeching of 3-16" metal, 
 5 ft. in diameter or oblong and same area cost $9.00 per 
 lineal foot. 
 
 The cost in 1902 of a stack 10 ft. inside diameter and 
 180 ft. high, of porous brick, was $7,375, not including 
 foundation. A 125-ft. x 6-ft. porous brick stack, includ- 
 ing foundation, will cost about $4,000. The cost in 1903 
 of a reinforced concrete stack 150 ft. high, 6 ft. inside 
 diameter, including foundation, was $3,800. The contract 
 price in 1907 of a reinforced concrete stack 166 ft. high, 
 8 ft. inside diameter, was $4,100. 
 
 The cost of a n8,ooo-gallon concrete-steel stand pipe, 
 with enclosing tower, at Hull, Mass, was about $12,000. 
 (See Eng. News, Vol. 52, p. 596.) 
 
 Mr. H. G Tyrrell, in R. R. Gazette, Dec. 30, 1904, shows 
 that the cost of the parts of single track steel trestle for 
 50 loading, towers 30 ft. between bents, at 3^5 cts. per 
 Ib. for girders, 4 cts. per Ib. for bents and bracing, and 
 $10 per cu. yd. for concrete, are as follows : 
 
 Length Cost of Steel Trestle 120 Ft. High per lin. ft. 
 intermediate j | j Traction | ] 
 
 Span Spans Bents Bracing Piers Total 
 
 30 $15.15 $45-2 $15.2 $12.0 $87.55 
 
 60 21.77 39.2 13.0 8.0 82.57 
 
 100 39.09 32.0 10.8 5.5 87.39 
 
 In Proceedings, Am. Ry. Eng. M. of W. Asso. Vol. 2, 
 p. 139 it is stated that the cost of ballasted trestle on the 
 A. T. & S. Fe Ry., 2 examples, averaged $12.66 per lin. 
 ft. divided as follows : treated piles, $5.02 ; lumber, $5.01 ; 
 bolts, $.21; cross ties, $.24; ballast, $.285; labor (all kinds), 
 $1.89; creosote, $.005. 
 
 Mr. J. C. Bland, in 1891, found the estimated contract 
 price of single track timber trestle was, in round numbers, 
 nearly equal in dollars per lineal foot to one-half of the 
 height of trestle in feet out to out of cap and sill. In this 
 the floor deck alone was $4.22 per ft. of track and piles 
 $3 each; both increased by 20% for the contractor's profit. 
 
 157 
 

 Timber in place was estimated at $52 to $55 per M. B. M., 
 contract price. 
 
 A number of examples of the cost of railroads are 
 given in R. R. Gazette, Sept. 7, and Oct. 26, 1906, as fol- 
 lows : ist case. No tunnels, few bridges, along river, con- 
 siderable cut and fill, single track, $26,300 per mile. 2d 
 case. Along river, heavy cuts, some bridges, single track, 
 $37,014 per mile. 3d case. Cuts and fills, bridges, tun- 
 nels, single track, $60,628 per mile. 4th case. Heavy cross- 
 ings, double track, $76,336 per mile. 5th case. Heavy cross- 
 ings, double track, $105,186 per mile. 6th case. Detour 
 around large city, double track, $50,000 per mile. In the 
 foregoing the cost includes preliminary surveys, clearing 
 right of way, roadbed, ties, rails, ballast, side tracks, but 
 does not include real estate, stations equipment, or signals. 
 
 Following is a list, alphabetically arranged, giving prices 
 of various materials and work, to be used as a guide in 
 estimating the cost of structures. These are taken largely 
 from current price lists and contract prices, as published 
 in engineering journals, and in general indicate prices 
 prevailing in 1904 to 1907. 
 
 ASPHALTUM: Ventura and other California asphalts, 
 $20 to $23 per ton at New York; Trinidad refined, $22 to 
 $25 per ton ; Venezuela asphalt, $25 to $60 per ton ; Ber- 
 muda asphalt, $25 to $35. 
 
 BRICK: At yards, per thousand, common soft, $5 to 
 $7; hard $7 to $9; vitrified (hard burned), paving, com- 
 mon, $8 to $12, special, $15 to $20; select red, not pressed, 
 $8 to $10, pressed, $14 to 18; Roman, $30; fire bricks, $14. 
 Freight on bricks is about $2 per thousand for 50 mile run. 
 
 BRONZE : Phosphor, in place, abt. 40 cts. Ib. 
 
 CAST IRON : Pig Iron, $19 to $22 per long ton. 
 
 Cast iron counterweights, iVz to 2 cts. per Ib. delivered. 
 
 Cast iron pipe, $33 to $38 per ton delivered; laid, $38 
 to $45 per ton. 
 
 Standard and plain castings, 2 1 /fc to 3% cts. per Ib. in 
 place. Special castings, large orders, 3 to 5 cts. per Ib. 
 in place; small orders 5 to 10 cts. 
 
 158 
 
CEMENT: Portland $1.50 to $2.00 per bbl., 400 Ibs. 
 
 Rosendale, So cts. to $i per bbl., 300 Ibs. 
 
 Large users of Portland cement pay less than $1.50 per 
 bbl. for domestic brands. On small orders freight and 
 handling increase the cost. 
 
 CEMENT FINISH: Portland, mortar % in. thick 50 
 to 80 cts. per sq. yd. 
 
 CLAY : Fireclay, dry powder $1.50 ton delivered on 
 cars; calcined fireclay, $3 to $4 ton. 
 
 For puddle $1.50 cu. yd. delivered. 
 CONCRETE: Natural cement, $3 to $5 cu. yd. in place. 
 
 Portland cement, in large mass, easily deposited, $4 to $7 
 cu. yd. Walls requiring difficult forms, $6 to $8 cu. yd. 
 Tunnels, etc. $10 to $12 cu. yd. 
 
 The cost of 1:3:6 Portland cement concrete may be 
 analyzed as follows: 
 
 i cu. yd. broken stone $2.00 
 
 l /2 cu. yd. sand 50 
 
 I bbl. cement , , 2.00 
 
 Mixing and depositing .50 
 
 Total $5.00 
 
 This is with the use of a mechanical mixer. Hand mix- 
 ing would probably cost from 70 cts. to $1.25 per cu. yd. 
 
 For detailed information on the cost of concrete struc- 
 tures on the N. C. & St. L. R. R. see paper by H. M. Jones, 
 published in part in the R R. Gazette, Oct. 21, 1904. The 
 cost to the R. R. Co. per cubic yard for culverts and walls 
 run about $6 to $7. Two examples are a little over $9. 
 
 Reinforced concrete, including steel, usually costs from 
 $10 to $20 per cu. yd. Concrete should be estimated at $5 
 to $10 per cu. yd. in place, steel at about 2.5 cts per Ib. in 
 place (plain structural steel), forms 5 to 10 cts. per sq. 
 ft. The unit cost of concrete will depend upon the diffi- 
 culty of handling and placing. 
 
 COPPER: 14 to 15 cts. Ib. 
 
 CURB: Cement and sand, 1:3, 25 to 50 cts. per lineal 
 foot, about Vz ct. per sq. in. of section per lineal foot, in 
 place. 
 
 159 
 
Sandstone and limestone, 50 cts. to $i per lineal foot, in 
 place. 
 
 Bluestone, $i to $1.50 per lineal ft. in place. 
 
 Granite, $i to $2.50, lin. ft. in place. 
 
 Curved curbs in stone 20% to 100% extra. 
 
 Resetting curb 10 to 50 cts. per ft. 
 
 DREDGING : Soft material 12 to 30 cts. per cu. yd. ; 
 gravel and hard material 30 cts. to $i cu. yd. In Eng. 
 News, Sept. 20, 1906, a report is given of some dredging 
 done by U. S. Govt. Engineers with hydraulic dredges 
 (New York Harbor) which cost only 5.274 cts. per cu. yd. 
 
 EXCAVATING: In earth, large masses, above water, 
 25 to 50 cts. cu. yd., below water, for piers, $i to $5 cu. yd. ; 
 in trench, earth, 50 cts. to $i cu. yd. ; loose rock, $i to $2 
 cu. yd. ; hard rock, $i to $3 cu. yd. 
 
 Steam shovel work costs about 12 to 20 cts per cu. yd. 
 In Eng. Record, Vol. 54, p. 732, some data are given from 
 a paper by Mr. John C. Sessor on steam shovel work on 
 the C. B. & Q. Ry. On one job of 251,711 cu. yds. 1,104 
 cu. yds. were moved per lo-hr. shift. The cost was as 
 follows : equipment, i cent ; steam shovel service, 8.9 cents ; 
 temporary trestle, 3.6 cents ; track and track work, 5 cents : 
 supervision and engineering 0.2 cents; total, 18.7 cents, 
 all per cubic yard. On another job of 188,240 cu. yds. 946 
 cu. yds. were moved per lo-hr. shift. The cost was as 
 follows: equipment, iVz cents; steam shovel service, 9.6 
 cents; temporary trestle, 3.1 cents; track and track work, 
 4.2 cents; supervision and engineering, 0.3 cents; total, 
 18.7 cents, all per cubic yard. 
 
 The I. C. R. R. estimates excavating in earth, in jobs 
 below 50,000 cu. yds., to cost 25 cts. per cu. yd., and in 
 larger jobs, 20 cts. per cu. yd. adding in both cases one 
 cent per cu. yd. per loo-ft. haul. 
 
 A committee report of the Roadmaster's and Maintain- 
 ance-of-Way Asso., published in the R. R. Gazette of Oct. 
 31, 1904, and in Eng. News of Oct. 27, 1904, gives the fol- 
 lowing as the cost of ditching cuts and widening embank- 
 ments. 
 
 160 
 
By wheelbarrows : 12.2 cts. per cu. yd. plus 31 cts. per 
 cu. yd. per 1000 ft. haul for common loam or 7.3 cts. extra 
 in bad, wet material. 
 
 By push cars: 19.1 cts. per cu. yd., where material is 
 unloaded by shovel, or 15.9 cts. where unloaded by dump- 
 ing box, or similar arrangement, plus 33.4 cts. per cu. yd. 
 per 5,000 ft. haul. 
 
 By machine ditcher: 22 to 30 cts. per cu. yd., the latter 
 figure being for a 1 5-mile haul in loam. In wet or bad 
 material add about 4.5 cts. per cu. yd. 
 
 The same report places the cost of team work with 
 scrapers at 14 to 25 cts. per cu. yd., and of ditching by 
 casting, in fair digging, where one cast will place the ma- 
 terial in suitable final location, at 10 cts. per cu. yd. Much 
 valuable information is given in this report. 
 
 FENCE: Board, 50 cts. to $1.50 per ft. 
 
 FILLING: Earth, material at hand, 20 cts. to 50 cts. 
 cu. yd. 
 
 FLAG STONE : In place $i to $3 sq. yd. 
 
 FORMS: Allow 5 to 10 cts. per sq. ft. for concrete 
 forms, depending on whether lumber is dressed or not and 
 on number of times it can be used. 
 
 FRENCH DRAIN : 50 cts. to $i lin. ft. 
 
 FUEL: Hoisting engines, etc. Allow l/3 ton of coal 
 per 10 horse power per 10 hr. shift. (Gillette.) 
 
 GRAVEL: In bank, 15 to 20 cts. cu. yd, f. o. b. cars 
 35 to 40 cts. cu. yd., freight for 50-mile run, about 75 cts. 
 cu. yd., hauling, 25 to 50 cts. cu. yd. Usual price delivered 
 about $i cu. yd. 
 
 LIME: Common, bbl. (250 Ibs.) 80 cts., finishing $i ; 
 per ton at works. $3.75, delivered, $6. 
 
 LEAD : Pig, about 4.6 cts. Ib. ; lead pipe about 5 cts. Ib. 
 
 MASONRY: Rubble, dry, $2 to $5 cu. yd., in mortar, 
 $3 to $8 cu. yd. Coursed rubble, large stones, $5 to $8. 
 
 Brick, common, $6 to $10 cu. yd., good, $10 to $15 cu. 
 yd. Laying brick, $2 to $3 cu. yd. Cost of lime mortar 
 per cu. yd. of brick work about 60 cts., of cement mortar 
 $i to $2. 
 
 161 
 
On the basis of $7.25 per M. for red brick, $2.50 per bbl. 
 for cement, $1.25 per bbl. for lime, $1.25 per cu. yd. of 
 sand, assuming a mason at 65 cts. per hr. with help at 
 37% cts. per hr. to lay 1,200 bricks in 8 hrs., a brick wall 
 13 ins. thick will cost about 40 cts. per superficial foot. 
 With pressed brick face the cost will be about 50 cts. per 
 superficial foot. 
 
 Bridge pier, sandstone or limestone, $8 to $12 cu. yd. 
 
 Ashlar, sandstone or limestone, $12 to $20 cu. yd., gran- 
 ite, $20 to $30 cu. yd. 
 
 Dressed bluestone, for steps etc., $i to $2 cu. ft. 
 
 MINERAL WOOL: Slag, ordinary, sh. ton, $19; se- 
 lected, $25; rock, ordinary, $32; selected, $40. 
 
 PAINT: Prepared, $i to $1.50 gallon. 
 
 PAVING: Asphalt In 44 cities in North America the 
 cost of asphalt paving including 4 to 6 ins. of concrete, 
 I to i% ins. of binder, and iVz to 2 ins. of surface, in 1900 
 varied between $1.43 and $3.25 per sq. yd. (See Eng. Rec- 
 ord, Vol. 43, No. 8.) It is estimated that the cost of guaran- 
 tee for the first five years is 3 cts. per yard and for the sec- 
 ond five years is 15 cts. per yard. The congresional ap- 
 propriation bill allowed $1.80 per sq. yd. to be paid for as- 
 phalt pavements in Washington, D. C. (Eng. News, Aug. 
 
 13. 1903-) 
 
 Asphalt block, $2 to $2.50 sq. yd. 
 
 The division of the cost of asphalt pavement is about 
 as follows: 2%" of surface, 67 cts. sq. yd.; 2" of binder 
 13 cts. sq. yd.; 6" of Portland cement concrete $i. Total 
 $1.80 sq. yd. 
 
 Brick, work only, 15 to 20 cts. sq. yd. 
 
 Brick, 4" of brick on 3" of sand, 65 to 85 cts. sq. yd. ; 
 4" of brick on 6" of natural cement concrete and i 1 /^" cush- 
 ion of sand, $1.20 to $1.60 sq. yd.; sidewalks, 2" of brick 
 on sand 50 to 80 cts. sq. yd. 
 
 Cobble stone, 80 cts. sq. yd. 
 
 Concrete sidewalks, finished with mortar of sand and 
 cement, granite screenings and cement, etc. 10 to 25 cts. 
 sq. ft. Mortar finish alone 5 to 15 cts. sq. ft. 
 
 162 
 
A common contract price for concrete sidewalks, small 
 jobs, is 15 to 20 cts. per sq. ft. Large paving work can be 
 done at an actual cost of about 10 cts. per sq. ft. 
 
 Macadam, stone free at quarry, 8" depth, 40 to 50 cts. 
 sq. yd. ; including cost of stone, 8" depth, 60 to 90 cts. sq. 
 yd., 12" depth, 90 cts. to $1.30 sq. yd. 
 
 Stone blocks on broken stone base, $1.50 to $2 sq. yd. 
 Stone blocks on concrete base $2 to $3.50 sq. yd. 
 Wooden blocks 4 in. creosoted yellow pine blocks on 
 one inch of sand over 6 in. of natural cement concrete 
 $2.25 to $2.35 per sq. yd. Cost of 4" creosoted yellow pine 
 blocks f. o. b. cars about $1.70 per sq. yd. 
 
 The following analyses of the cost of brick and stone 
 block paving are taken from Engineering News, July 24, 
 1902. 
 
 "The following is a summary of the cost of paving with 
 brick laid on edge, wages being 25 cts. per hour for pav- 
 ers and 15 cts. for laborers : Cost per sq. yd. 
 
 57 "pavers" at $10 per M $0.57 
 
 Hauling 1% miles over earth roads 06 
 
 Laying pavers, including labor of grouting 08 
 
 0.18 cu. ft. = 1-150 cu. yd. of grout* 05 
 
 1-36 cu. yd. sand cushion at $1.08 a cu. yd .03 
 
 Plank to protect concrete 01 
 
 Total net cost $0.80 
 
 Add about 19% for profit 15 
 
 Contract price $6-95 
 
 * I Portland to 2 sand. 
 
 'To this, of course, must be added the cost of grading 
 and cost of concrete foundation. 
 On block paving "we have for the total labor cost : 
 
 Per sq. yd. 
 Loading and unloading inclusive of lost team time $0.10 
 
 Hauling I mile .05 
 
 Distributing blocks 03 
 
 Laying 06 
 
 163 
 
Filling joints 06 
 
 Foreman at 40 cts. per hr., 30 sq. yds 013 
 
 2 water and errand boys 007 
 
 Total labor $0.30 
 
 "Cost of Medina Block Pavement. 
 
 Per sq. yd. 
 
 1/3 cu. yd. street excavation $0.15 
 
 6-in. concrete foundation 50 
 
 1-18 cu. yd sand cushion in place at $1.08 06 
 
 Medina block (6 in.) f. o. b. Albion, N. Y 1.15 
 
 Freight to Rochester 07 
 
 Unloading, hauling and laying 30 
 
 1.5 gallons tar at 10 cts. a gallon 15 
 
 1-50 cu. yd. sand for joints 02 
 
 Total $2.40 
 
 Add for contractor's profit 25 
 
 Total cost $2.65 
 
 Cost of street paving in 30 cities in Wisconsin per sq. 
 yd. (See Municipal Journal and Engineer, Nov., 1905) as- 
 phalt $1.80 to $2.19; bricks, $i to $2.19; macadam $.25 to 
 $1.30; wood block $.60 to $1.97. 
 
 All-concrete roadway paving has been found in several 
 cities to cost 14 to 18 cts. per sq. ft. At Jackson, Mich., 
 some street paving having 3 ins. of gravel ; 6 ins. of i :8 
 cement and gravel ; 4 ins. of 1 13 cement and %-in. crushed 
 granite, mixed quite wet, cost 18 cts. per sq. ft. (See Con- 
 crete Engineering, Dec., 1907, p. 205.) 
 
 PILES : Driven and cut, ordinary lengths and sizes, 
 spruce 20 to 40 cts. ft. ; white oak, 25 to 60 cts. ft. Spruce 
 30 to 40 ft. long, driven and cut, $6 to $10 each. Shorter 
 piles for trestle bents $3 to $5 in place. 
 
 PILING: (Nov., 1907) Spruce, ordinary cargoes, 6 
 to 7 cts. ft. Oak, 14-in. butt, 40 to 50 ft., 19 cts. ft. ; 50 to 
 55 ft., 22 cts. ft; 55 to 60 ft., 23 cts. ft.; 60 ft. and up, 25 
 cts. ft. 
 
 164 
 
Pine, 60 to 65 ft., $8.50 each; 70 to 75 ft. $10.50 each; 
 80 ft. and up, $16 each. 
 
 Concrete piles in place, about $i per lineal foot. 
 
 PIPE: Vitrified pipe, 8" dia., 15 cts., hauling V* ct. ft., 
 laying, ity cts. ft., cement, Vz ct. ft. = 17.5 cts. ft. in trench 
 already dug. For 12" pipe the cost is about 35 cts. per 
 ft. total. (See Eng. Record, March 10, 1906, p. 350.) 
 
 RAILING: Gaspipe, 2-rail, 50 to 75 cts. ft., 3-rail, 75 
 cts. to $1.25 ft. 
 
 A substantial bridge railing costs about $1.50 to $2.50 
 per lineal ft. Cast iron newel-posts about $10 each. 
 
 ROOFING: Four layers of felt paper covered with 
 pitch and gravel or pitch and slag 4 to 6 cts. sq. ft. 
 
 Slate, 7 to 13 cts. per sq. ft. Slag, 4 cts. Tin, 8 to 10 cts. 
 Shingle, 7 to 10 cts. per sq. ft. 
 
 Tile, Spanish $9 to $12 per square of 100 sq. ft. 
 
 SAND BLASTING: (Cleaning) Large contracts i to 
 3 cts. sq. ft. (See Eng. News, Vol. 47, Page 324.) 
 
 SAND: Building, 20 to 25 cts. cu. yd. in bank, f. o. b. 
 cars, 40 to 50 cts. cu. yd. freight for 5o-mile run, about 
 75 cts. cu. yd., hauling, 25 to 50 cts. cu. yd. Usual price 
 delivered about $1.10 cu. yd. 
 
 SEEDING: In grass $25 to $75 acre. 
 
 SEWER PIPE: Laying and cementing in trench al- 
 ready dug, small sizes, 15 to 25 cts. per ft, large sizes 50 
 cts. to $i per ft. 
 
 Cost of pipe per lineal ft., 5", 5 to 7 cts., 10", 15 to 20 cts. 
 15", 25 to 40 cts., 21", 50 to 75 cts., 30", $i to $1.70; 48", 
 
 $2 tO $3. 
 
 SHRUBS : 50 cts. to $2 each. 
 
 SODDING: In country towns, 7 to 10 cts. sq. yd., in 
 cities, 25 to 50 cts. sq. yd. 
 
 STEEL: Structural, material only, i% to 2% cts. per 
 Ib. Erected and painted, 3 to 5 cts. per Ib. 
 
 Castings, in place, 5 to 10 cts. Ib. 
 
 Rails, new, $28 ton, f. o. b. cars; old, short pieces, $14 
 to $14.50. 
 
 Scrap, structural, $14 long ton. 
 165 
 
STONE: Wholesale rates, delivered at N. Y. ; price 
 per cu. ft. 
 
 Nova Scotia, in rough, 90 cts. ; Ohio freestone, in rough, 
 85 to 90 cts. ; Minnesota freestone, in rough, 90 cts. ; Long- 
 meadow freestone, 85 cts. ; Brownstone, Portland, ct., 60 
 cts. ; Brownstone, Belleville, N. J., 75 cts. to $i ; Scotch 
 redstone, $1.05; Lake Superior redstone, $1.10; granite, 
 rough, 40 to 50 cts. ; limestone, buff and blue, 80 cts. ; por- 
 tage, $i ; Caen, $1.25 to $175; white building marble, $1.25 
 to 1.75 ; Wyoming bluestone, 90 cts. ; Euclid bluestone, 90 
 cts. ; crushed stone, $1.40 per net ton. f. o. b. cars N. Y. 
 C. (May, 1904.) 
 
 TARRED PAPER: i ply (roll 300 sq. ft.), ton, $32.50 
 to $35-50; 2 ply, roll 108 sq. ft., 55 to 6oc roll; 3 ply, roll 
 108 sq. ft., 78 to 8oc. Slater's Felt (roll 506 sq. ft.) 75c. 
 R. R. M. Stone Surfaced Roofing (roll no sq. ft.) $2.75. 
 
 TAR : Regular bbl., $2.25, oil bbl., $5.75 ; Coal tar, gal- 
 lon, 8 cts. 
 
 TIES, RAILROAD: Untreated, cedar and spruce, 40 
 to 60 cts. each ; oak and yellow pine, 60 to 80 cts. each. 
 See Trans, Am. Ry. Engineering and M. of W. Asso. Vol. 
 2 for cost of ties to 13 of the principal American rail- 
 roads. It is there shown to vary between 35^ and Si 1 /^ 
 cents each. 
 
 TOOLING: Bush hammering concrete surfaces 2 to 5 
 cts. per sq. ft. 
 
 TRANSPORTING: The cost of picking up materials 
 such as stone or sand and hauling them a moderate dis- 
 tance in wheelbarrows is about 20 to 25 cts. per cu. yd. 
 With wagons or carts the cost is about 15 to 23 cts. per 
 cu. yd, 
 
 TREATING WOOD: Cheaper processes 5 to 10 cts. 
 per cu. ft. Creosoting 20 to 60 cts. per cu. ft. 
 
 Railroad ties 20 cts. each, up. 
 
 Creosoted yellow pine in place costs, including cost of 
 wood, $65 to $80 per 1,000 ft. B. M. 
 
 TREES : $i to $5 each. 
 
 166 
 
WOOD: (Prices per thousand feet of board measure) 
 May, 1904. 
 
 Hemlock, rough, in lengths up to 20 ft. $17 to $19. 
 Lengths 22 to 40 ft. $3.25 to $7 additional. 
 
 Pine, yellow (Long Leaf) building orders, 12 ins. and 
 under, $20.50 to $22.50; 14-in. and up, $26 to $29; 1% and 
 iVz-in. wide boards, $28 to $30; 2-in. wide plank, heart 
 face, $30 to $31.50. 
 
 Yellow pine of heavy construction, in cargo lots, de- 
 livered New York City, $22 to $25. 
 
 Spruce : random cargoes, 2-in. cargoes, $18 to $21 ; 6 
 to 9-ins., cargoes $19.50 to $21.50; 10 and 12-in. cargoes, 
 $21 to $23. 
 
 The framing and placing of wood in a structure costs 
 $5 to $15 per thousand feet of board measure. 
 
 White oak timber in wharf construction costs $50 to 
 $60 per thousand feet in place. 
 
 Bridge timber in place, per thousand feet, white oak, 
 $40 to $50 ; yellow pine, $35 to $45 ; hemlock, $22 to $30. 
 
 More than half the cost of wood is generally due to 
 freight on account of the long distances between the cen- 
 ters of greatest supply and greatest consumption. 
 
 
 167 
 
Specifications for Natural and Port- 
 land Cement.* 
 
 Recommended Standard Specifications. 
 (Standard Specifications for Cement adopted by a Joint 
 Committee embracing representatives from the American 
 Society of Civil Engineers, American Society for Testing 
 Materials, American Institute of Architects, Engineer 
 Department of United States Army, Association of Port- 
 land Cement Manufacturers and American Railway En- 
 gineering and Maintenance of Way Association.) 
 General Observations. 
 
 1. These remarks have been prepared with a view of 
 pointing out the pertinent features of the various require- 
 ments and the precautions to be observed in the interpreta- 
 tion of the results of the tests. 
 
 2. The Committee would suggest that the acceptance or 
 rejection under these specifications be based on tests made 
 by an experienced person having the proper means for 
 making the tests. 
 
 3. Specific gravity is useful in detecting adulteration or 
 underburning. The results of tests of specific gravity are 
 not necessarily conclusive as an indication of the quality 
 of a cement, but when in combination with the results of 
 other tests may afford valuable indications. 
 
 4. The sieves should be kept thoroughly dry. 
 
 5. Great care should be exercised to maintain the test 
 pieces under as uniform conditions as possible. A sudden 
 change or wide range of temperature in the room in which 
 
 * The specifications and recommendations that follow 
 are taken without change, except the omission of figures 
 showing apparatus and reference to same, from Manual of 
 Recommended Practice, Edition of 1907, published by 
 American Railway Engineering and Maintenance of Way 
 Association. 
 
 168 
 
the tests are made, a very dry or humid atmosphere, and 
 other irregularities vitally affect the rate of setting. 
 
 6. Each consumer should fix the minimum requirements 
 for tensile strength to suit his own conditions. They shall, 
 however, be within the limits stated. 
 
 7. The tests for constancy of volume are divided into 
 two classes, the first normal, the second accelerated. The 
 latter should be regarded as a precautionary test only, and 
 not infallible. So many conditions enter into the making 
 and interpreting of it that it should be used with extreme 
 care. 
 
 8. In marking the pats the greatest care should be ex- 
 ercised to avoid initial strains due to molding or too rapid 
 drying out during the first twenty-four hours. The pats 
 should be preserved under the most uniform conditions pos- 
 sible, and rapid changes of temperature should be avoided. 
 
 9. The failure to meet the requirements of the accelerat- 
 ed tests need not be sufficient cause for rejection. The ce- 
 ment may, however, be held for twenty-eight days, and a 
 retest made at the end of that period. Failure to meet the 
 requirements at this time should be considered sufficient 
 cause for rejection, although in the present state of our 
 knowledge it cannot be said that such failure necessarily 
 indicates unsoundness, nor can the cement be considered 
 entirely satisfactory simply because it passes the tests. 
 
 STANDARD SPECIFICATIONS FOR CEMENT 
 
 GENERAL CONDITIONS. 
 A 11 . i- 11 u * j 
 
 1. All cement shall be inspected. 
 
 2. Cement may be inspected either at the place of manu- 
 facture or on the work. 
 
 3. In order to allow ample time for inspecting and test- 
 ing, cement shall be stored in a suitable weather-tight 
 building having the floor properly blocked or raised from 
 the ground. 
 
 4. The cement shall be stored in such a manner as to 
 permit easy access for proper inspection and identification 
 of each shipment. 
 
 5. Every facility shall be provided by the contractor and 
 
a period of at least twelve days allowed for the inspection 
 and necessary tests. 
 
 6. Cement shall be delivered in suitable packages with 
 the brand and name of manufacturer plainly marked there- 
 on. 
 
 7. A bag of cement shall contain 94 pounds of cement 
 net. Each barrel of Portland cement shall contain four 
 bags, and each barrel of Natural cement shall contain three 
 bags of the above net weight. 
 
 8. Cement failing to meet the seven-day requirements 
 may be held awaiting the results of the twenty-eight day 
 tests before rejection. 
 
 9. All tests shall be made in accordance with the meth- 
 ods proposed by the Committee on Uniform Tests of Ce- 
 ment of the American Society of Civil Engineers, presented 
 to the Society January 21, 1903, and amended January 20, 
 1904, with all subsequent amendments thereto (See adden- 
 dum to these specifications.) 
 
 10. The acceptance or rejection shall be based on the 
 following requirements : 
 
 NATURAL CEMENT. 
 
 IT. This term shall be applied to the finely pulverized 
 product resulting from the calcination of an argillaceous 
 limestone at a temperature only sufficient to drive off the 
 carbonic acid gas. 
 
 12. The specific gravity of the cement, thoroughly dried 
 at 100 C, shall not be less than 2.8. 
 
 13. It shall leave by weight a residue of not more than 10 
 per cent, on the No. 100, and 30 per cent, on the No. 200 
 sieve. 
 
 14. It shall develop initial set in not less than ten min- 
 utes, and hard set in not less than thirty minutes, nor more 
 than three hours. 
 
 15. The minimum requirements for tensile strength for 
 briquettes one inch square in cross-section shall be within 
 
 170 
 
the following limits, and shall show no retrogression in 
 strength within the periods specified:* 
 Age. Neat Cement. Strength 
 
 24 hours in moist air 50-100 Ibs. 
 
 7 days (i day in moist air, 6 days in water) . .100-200 Ibs. 
 
 28 days (i day in moist air, 27 days in water) 200-300 Ibs. 
 
 One Part Cement, three Parts Standard Sand. 
 
 7 days (i day in moist air, 6 days in water) 25- 75 Ibs. 
 28 days (i day in moist air, 27 days in water) 75-100 Ibs. 
 
 16. Pats of neat cement about three (3) in. in diameter, 
 one-half (Vz) in. thick at center, tapering to a thin edge, 
 shall be kept in moist air for a period of twenty- four hours. 
 
 (a) A pat is then kept in air of normal temperature. 
 
 (b) Another is kept in water maintained as near 70 
 F. as practicable. 
 
 17. These pats are observed at intervals for at least 28 
 days, and, to satisfactorily pass the tests, should remain 
 firm and hard and show no signs of distortion, checking, 
 cracking or disintegrating. 
 
 PORTLAND CEMENT. 
 
 18. This term shall be applied to the finely pulverized 
 product resulting from the calcination to incipient fusion 
 of an intimate mixture of properly proportioned argilla- 
 ceous and calcareous materials, and to which no addition 
 greater than 3 per cent, has been made subsequent to calci- 
 nation. , 
 
 19. The specific gravity of the cement, thoroughly dried 
 at 100 C, shall be not less than 3.10. 
 
 20. It shall leave by weight a residue of not more than 
 8 per cent, on the No. 100, and not more than 25 per cent, 
 on the No. 200 sieve. 
 
 21. It shall develop initial set in not less than thirty 
 
 * For example, the minimum requirement for the twen- 
 ty-four hour neat cement tests should show some specified 
 value within the limits of 50 and 100 pounds, and so on for 
 each period stated. 
 
 171 
 
minutes, but must develop hard set in not less than one 
 hour, nor more than ten hours. 
 
 22. The minimum requirements for tensile strength for 
 briquettes one-inch square in cross-section shall be within 
 the following limits, and shall show no retrogression in 
 strength within the periods specified.* 
 
 Age. Neat Cement. Strength. 
 
 24 hours in moist air 150-200 Ibs. 
 
 7 days (i day in moist air, 6 days in water) 450-55 Ibs. 
 
 28 days (i day in moist air, 27 days in water) 550-650 Ibs. 
 
 One Part Cement, Three Parts Standard Sand. 
 
 7 days (i day in moist air, 6 days in water) 150-200 Ibs. 
 28 days (i day in moist air, 27 days in water) 200-300 Ibs. 
 
 23. Pats of neat cement about three (3) in. in diameter, 
 one-half (%) in. thick at the center, and tapering to a thin 
 edge, shall be kept in moist air for a period of twenty-four 
 hours. 
 
 (a) A pat is then kept in air at normal temperature and 
 observed at intervals for at least 28 days. 
 
 (b) Another pat is kept in water maintained as near 
 70 F. as practicable, and observed at intervals for at least 
 28 days, :9toa? tsJ * 
 
 (c) A third pat is exposed in any convenient way in an 
 atmosphere of steam, above boiling water, in a loosely 
 closed vessel for five hours. 
 
 24. These pats, to satisfactorily pass the requirements, 
 shall remain firm and hard and show no signs of distortion, 
 checking, cracking or disintegrating. 
 
 25. The cement shall not contain more than 1.75 per 
 cent, of anhydrous sulphuric acid (SO 3 ), nor more than 4 
 per cent, of magnesia (MgO). 
 
 * For example, the minimum requirement for the twen- 
 ty-four hour neat cement tests should show some specified 
 value within the limits of 150 and 200 pounds, and so on 
 for each period stated. 
 
 172 
 
 
ADDENDUM. 
 
 ABSTRACT OF METHODS RECOMMENDED BY THE SPECIAL COM- 
 MITTEE ON UNIFORM TESTS OF CEMENT OF THE AMERI- . . 
 CAN SOCIETY OF CIVIL ENGINEERS. 
 SAMPLING. 
 
 1. The sample shall be a fair average of the contents of 
 the package; it is recommended that, where conditions per- 
 mit, one barrel in every ten be sampled. 
 
 2. All samples should be passed through a sieve having 
 twenty meshes per linear inch, in order to break up lumps 
 and remove foreign material ; this is also a very effective 
 method for mixing them together in order to obtain an 
 average. For determining the characteristics of a shipment 
 of cement, the individual samples may be mixed and the 
 average tested; where time will permit, however, it is rec- 
 ommended that they be tested separately. 
 
 3. Cement in barrels should be sampled through a hole 
 made in the center of one of the staves, midway between 
 the heads, or in the head, by means of an auger or a samp- 
 ling iron similar to that used by sugar inspectors. If in 
 bags, it should be taken from surface to center. 
 
 CHEMICAL ANALYSIS. 
 
 4. As a method to be followed for the analysis of ce- 
 ment, that proposed by the Committee on Uniformity in 
 the Analysis of Materials for the Portland Cement Indus- 
 try, of the New York Section of the Society for Chemical 
 Industry, and published in the Journal of the Society for 
 January 15, 1902, is recommended. 
 
 SPECIFIC GRAVITY. 
 
 5. The determination of specific gravity is most conven- 
 iently made with Le Chatelier's apparatus. This consists of 
 a flask of 120 cu. cm. (7.32 cu. in.) capacity, the neck of 
 which is about 20 cm. (7.87 in.) long; in the middle of this 
 neck is a bulb, above and below which are two marks ; the 
 volume between these marks is 20 cu. cm. (1.22 cu. in.) 
 The neck has a diameter of about 9 mm. (0.35 in.), and is 
 graduated into tenths of cubic centimeters above the mark. 
 
 173 
 

 6. Benzine (62 Baume naptha), or kerosene free from 
 water, should be used in making the determination. 
 
 7. The specific gravity can be determined in two ways : 
 (a) The flask is filled with either of these liquids to 
 
 the lower mark and 64 gr. (2.25 oz.) of powder, previously 
 dried at 100 C (212 F.) and cooled to the temperature 
 of the liquid, is gradually introduced through the funnel 
 [the stem of which extends into the flask to the top of the 
 bulb], until the upper mark is reached. The difference in 
 weight between the cement remaining and the original quan- 
 tity (64 gr.) is the weight which has displaced 20 cu. cm. 
 
 8. (b) The whole quantity of the powder is introduced, 
 and the level of the liquid rises to some division of the grad- 
 uated neck. This reading plus 20 cu. cm. is the volume 
 displaced by 64 gr. of the powder. 
 
 9. The specific gravity is then obtained from the for- 
 mula: 
 
 Weight of Cement 
 
 Specific Gravity = 
 
 Displaced Volume 
 
 10. The flask, during the operation, is kept immersed in 
 water in a jar, in order to avoid variations in the tempera- 
 ture of the liquid. The results should agree within o.oi. 
 
 11. A convenient method for cleaning the apparatus is 
 as follows: The flask is inverted over a large vessel, pre- 
 ferably a glass jar, and shaken vertically until the liquid 
 starts to flow freely; it is then held still in a vertical posi- 
 tion until empty ; the remaining traces of cement can be re- 
 moved in a similar manner by pouring into the flask a small 
 quantity of clean liquid and repeating the operation. 
 
 FINENESS. 
 
 12. The sieves should be circular, about 20 cm. (7.87 in.) 
 in diameter, 6 cm. (2.36 in.) high, and provided with a 
 pan 5 cm. (1.97 in.) deep, and a cover. 
 
 13. The wire cloth should be woven (not twilled) from 
 brass wire having the following diameters : 
 
 No. 100, 0.0045 in. ; No. 200, 0.0024 in. 
 
 14. This cloth should be mounted on the frames without 
 
 174 
 
distortion; the mesh should be regular in spacing and be 
 within the following limits : 
 
 No. TOO, 96 to 100 meshes to the linear inch. 
 
 No. 200, 188 to 200 meshes to the linear inch. 
 
 15. Fifty grams (1.76 oz.) or 100 gr. (3.52 oz.) should be 
 used for the test, and dried at a temperature of 100 C. 
 (2i2F.) prior to sieving. 
 
 16. The thoroughly dried and coarsely screened sample 
 is weighed and placed on the No. 200 sieve, which, with 
 pan and cover attached, is held in one hand in a slightly in- 
 clined position, and moved forward and backward, at the 
 same time striking the side gently with the palm of the 
 other hand, at the rate of about 200 strokes per minute. 
 The operation is continued until not more than one-tenth 
 of I per cent, passes through after one minute of continu- 
 ous sieving. The residue is weighed, then placed on the 
 No. loo sieve and the operation repeated. The work may 
 be expedited by placing in the sieve a small quantity of 
 large shot. The results should be reported to the nearest 
 
 tenth of i per cent. 
 r 
 
 NORMAL CONSISTENCY. 
 
 17. This best can be determined by means of. Vicat 
 Needle Apparatus, which consists of a frame, bearing a 
 movable rod with a cap at one end, and at the other a cyl- 
 inder, i cm. (0.39 in.) in diameter, the cap, rod and cylin- 
 der weighing 300 gr. (10.58 oz.). The rod, which can be 
 held in any desired position by a screw, carries an indica- 
 tor, which moves over a scale (graduated to centimeters) 
 attached to the frame. The paste is held by a conical hard- 
 rubber ring, 7 cm. (2.76 in.) in diameter at the base; 4 
 cm. (1.57 in.) high, resting on a glass plate about 10 cm. 
 (3.94 in.) square. 
 
 18. In making the determination, the same quantity of 
 cement as will be subsequently used for each batch in mak- 
 ing the briquettes [but not less than 500 gr. (17.16 oz.)] 
 is kneaded into a paste, as described in paragraph 38, and 
 quickly formed into a ball with the hands, completing the 
 operation by tossing it six times from one hand to the 
 
 175 
 
other, maintained 6 in. apart; the ball is then pressed into 
 the rubber ring, through the larger opening, smoothed off 
 and placed (on its large end) on a glass plate and the 
 smaller end smoothed off with a trowel ; the paste, confined 
 in the ring, resting on the plate, is placed under the rod 
 bearing the cylinder, which is brought in contact with the 
 surface and quickly released. 
 
 19. The paste is of normal consistency when the cyl- 
 inder penetrates to a point in the mass 10 mm. (0.39 in.) 
 below the top of the ring. Great care must be taken to fill 
 the ring exactly to the top. 
 
 20. The trial pastes are made with varying percentages 
 of water until the correct consistency is obtained. 
 
 Note. The Committee of Standard Specifications for 
 Cement inserts the following table for temporary use, to 
 be replaced by one to be devised by the Committee of the 
 American Society of Civil Engineers. 
 
 PERCENTAGE OF WATER FOR STANDARD MIXTURES. 
 
 Neat II. I I 
 
 1. 211.3 
 
 1 .4 1 1 .5||Neat 1 1 _ 1 1 1 .2 1 1 .3 ! 1 .4 1 1 .5, 
 
 18 
 19 
 
 12.0 
 12.3 
 
 10.0 
 10.2 
 
 9.0 
 9.2 
 
 8.4 
 8.5 
 
 8.0] 
 8.1 
 
 | 33 
 34 
 
 17.0 
 17.3 
 
 13.311 I.5|I0.4 
 13.6 11.7)10.5 
 
 9.6 
 9.7 
 
 20 
 
 12.7 
 
 10.4 
 
 9.3 
 
 8.7 
 
 8.2J 
 
 35 
 
 17.7 
 
 13.8 1 1.8 
 
 10.7 
 
 9.9 
 
 21 
 
 13.0 
 
 10.7 
 
 9.5 
 
 8.8 
 
 8.3 
 
 36 18.0 
 
 14.0)12.0 
 
 10.8 
 
 10.0 
 
 22 
 
 13.3 
 
 10.9 
 
 9.7 
 
 8.9 
 
 8.4 
 
 37 118.3 
 
 14.2 12.2 
 
 109 
 
 10. 1 
 
 23 
 
 13.7 
 
 1 I.I 
 
 9.8 
 
 9.1 
 
 8.5 
 
 38 |I8.7 
 
 14.4 
 
 12.3 
 
 1 I.I 
 
 10.2 
 
 24 
 
 14.0 
 
 1 1.3 
 
 10.0 
 
 9.21 8.6 
 
 39 1 19.0 
 
 14.7 
 
 12.5 
 
 11.2 
 
 10.3 
 
 25 
 
 14.3 
 
 11.6 
 
 10.2 
 
 9.3J 8.8 
 
 40 
 
 19.3 
 
 14.9 
 
 I2.7H 1.3 
 
 10.4 
 
 26 
 
 14.7 
 
 11.8 
 
 10.3 
 
 9.5! 8.9 
 
 41 
 
 19.7 
 
 15.1 
 
 12.8)11.5 
 
 10.5 
 
 27 
 
 15.0 
 
 12.0 
 
 10.5 
 
 9.6| 9.0 
 
 | 42 |20.0 15.3 
 
 13.0)11.6 
 
 10.6 
 
 28 
 
 I5.3| 12.2 
 
 10.7 
 
 9.7| 9.1 
 
 1 43 
 
 20.3115.6 
 
 13.2 
 
 1 1.7 
 
 10.7 
 
 29 
 
 I5.7JI2.5 
 
 10.8 
 
 9.9 
 
 9.2 
 
 | 44 
 
 20.7115.8 
 
 13.3 
 
 11.9 
 
 10.8 
 
 30 
 
 16.0 12.7 
 
 1 1.0 
 
 10.0 
 
 9.3 
 
 | 45 
 
 21.0(16.0 
 
 I3.5| 12.0 
 
 1 1.0 
 
 31 
 
 16.3112.9 
 
 11.2 
 
 10.1 
 
 9.4 
 
 46 
 
 21.3 16. 1 
 
 13.7112.1 
 
 II. 1 
 
 32 
 
 16.7)13.1 
 
 1 1.3)10.3 
 
 9.5 
 
 ! 
 
 ... |... 
 
 
 
 __.|_ 
 
 to I ! I to 2 | I to 3 | I to 4 I I to 5 
 
 Cement 
 
 500 
 
 333 
 
 250 
 
 | 200 
 
 167 
 
 Sand 
 
 500 
 
 667 
 
 750 
 
 ) 800 
 
 833 
 
 TIME OF SETTING. 
 
 21. For this purpose the Vicat Needle, which has al- 
 ready been described in paragraph 17, should be used. 
 
 22. In making the test, a paste of normal consistency 
 is molded and placed under the rod, as described in para- 
 
 176 
 
graph 18 ; this rod, bearing the cap at one end and the nee- 
 dle, I mm. (0.039 in.) in diameter, at the other, weighing 
 300 gr. (10.58 oz.). The needle is then carefully brought in 
 contact with the surface of the paste and quickly released. 
 
 23. The setting is said to have commenced when the 
 needle ceases to pass a point 5 mm. (0.20 in.) above the 
 upper surface of the glass plate, and is said to have termi- 
 nated the moment the needle does not sink visibly into the 
 mass. 
 
 24. The test pieces should be stored in moist air during 
 the test; this is accomplished by placing them on a rack 
 over water contained in a pan and covered with a damp 
 cloth, the cloth to be kept away from them by means of a 
 wire screen ; or they may be stored in a moist box or clos- 
 et. 
 
 25. Care should be taken to keep the needle clean, as 
 the collection of cement on the sides of the needle retards 
 the penetration, while cement on the point reduces the area 
 and tends to increase the penetration. 
 
 26. The determination of the time of setting is only ap- 
 proximate, being materially affected by the temperature of 
 the mixing water, the temperature and humidity of the air 
 during the test, the percentage of water used, and the 
 amount of molding the paste receives. 
 
 STANDARD SAND. 
 
 27. For the present, the Committee recommends the 
 natural sand from Ottawa, 111., screened to pass a sieve 
 having 20 meshes per linear inch and retained on a sieve 
 having 30 meshes per linear inch; the wires to have diam- 
 eters of 0.0165 and 0.0112 in., respectively, *. e,, half the 
 width of the opening in each case. Sand having passed the 
 No. 20 sieve shall be considered standard when not more 
 than i per cent, passes a No. 30 sieve after one minute con- 
 tinuous sifting of a 50o-gr. sample. 
 
 28. The Sandusky Portland Cement Company of San- 
 dusky, Ohio, has agreed to undertake the preparation of 
 this sand and to furnish it at a price only sufficient to cover 
 the actual cost of preparation. 
 
 177 
 
FORM OF BRIQUETTE. 
 
 29. While the form of the briquette recommended by a 
 former Committee of the Society is not wholly satisfactory, 
 this Committee is not prepared to suggest any change, 
 other than rounding off the corners by curves of %-in. 
 radius. 
 
 MOLDS. 
 
 30. The molds should be made of brass, bronze or some 
 equally non-corrodible material, having sufficient metal in 
 the sides to prevent spreading during molding. 
 
 31. Gang molds, which permit molding a number of 
 briquettes at one time, are preferred by many to single 
 molds; since the greater quantity of mortar than can be 
 mixed tends to produce a greater uniformity in the results. 
 
 32. The molds should be wiped with an oily cloth be- 
 fore using. 
 
 MIXING. 
 
 33. All proportion should be stated by weight ; the quan- 
 tity of water to be used should be stated as a percentage 
 of the dry material. 
 
 34. The metric system is recommended because of the 
 convenient relation of the gram and the cubic centimeter. 
 
 35. The temperature of the room and the mixing water 
 should be as near 21 C. (70 F.) as it is practicable to 
 maintain it. 
 
 36. The sand and cement should be thoroughly mixed 
 dry. The mixing should be done on some non-absorbing 
 surface, preferably plate glass. If the mixing must be 
 done on an absorbing surface is should be thoroughly 
 dampened prior to use. 
 
 37. The quantity of material to be mixed at one time 
 depends on the number of test pieces to be made; about 
 1,000 gr. (35.28 oz.) makes a convenient quantity to mix, 
 especially by hand methods. 
 
 38. The material is weighed and placed on the mixing 
 table, and a crater formed in the center, into which the 
 proper percentage of clean water is poured; the material 
 on the outer edge is turned into the crater by the aid of a 
 
 178 
 
trowel. As soon as the water has been absorbed, which 
 should not require more than one minute, the operation is 
 completed by vigorously kneading with the hands for an 
 additional iMj minutes, the process being similar to that 
 used in kneading dough. A sandglass affords a convenient 
 guide for the time of kneading. During the operation of 
 mixing the hands should be protected by gloves, preferably 
 of rubber. 
 
 MOLDING. 
 
 39. Having worked the paste or mortar to the proper 
 consistency, it is at once placed in the molds by hand. 
 
 40. The molds should be filled at once, the material 
 pressed in firmly with the fingers and smoothed off with 
 a trowel without ramming; the material should be heaped 
 up on the upper surface of the mold, and, in smoothing off, 
 the trowel should be drawn over the mold in such a man- 
 ner as to exert a moderate pressure on the excess material. 
 The mold should be turned over and the operation repeated. 
 
 41. A check upon the uniformity of the mixing and 
 molding is afforded by weighing the briquettes just prior 
 to immersion, or upon removal from the moist closet. 
 Briquettes which vary in weight more than 3 per cent, from 
 the average should not be tested. 
 
 STORAGE OF THE TEST PIECES. 
 
 42. During the first 24 hours ^fter molding, the test 
 pieces should be kept in moist air to prevent them from 
 drying out. 
 
 43. A moist closet or chamber is so easily devised that 
 the use of the damp cloth should be abandoned if possible. 
 Covering the test pieces with a damp cloth is objectionable, 
 as commonly used, because the cloth may dry out unequal- 
 ly, and in consequence the test pieces are not all maintained 
 under the same condition. Where a moist closet is not 
 available, a cloth may be used and kept uniformly wet by 
 immersing the ends in water. It should be kept from di- 
 rect contact with the test pieces by means of a wire screen 
 or some similar arrangement. 
 
 44. A moist closet consists of a soapstone or slate box, 
 
 179 
 
or a metal-lined wooden box the metal lining being cov- 
 ered with felt and this felt kept wet. The bottom of the 
 box is so constructed as to hold water, and the sides are 
 provided with cleats for holding glass shelves on which to 
 place the briquettes. Care should bye taken to keep the air 
 in the closet uniformly moist. 
 
 45. After 24 hours in moist air, the test pieces for lon- 
 ger periods of time should be immersed in water main- 
 tained as near 21 C. (70 F.) as practicable; they may be 
 stored in tanks or pans, which should be of non-corrodible 
 material. 
 
 TENSILE STRENGTH. 
 
 46. The tests may be made on any standard machine. A 
 solid metal clip is recommended. This clip is to be used 
 without cushioning at the points of contact with the test 
 specimen. The bearing at each point of contact should be 
 ^4-in. wide, and the distance between the centers of contact 
 on the same clip should be I 1 A in. 
 
 47. Test pieces should be broken as soon as they are 
 removed from the water. Care should be observed in cen- 
 tering the briquettes in the testing machine, as cross-strains, 
 produced by improper centering, tend to lower the break- 
 ing strength. The load should not be applied too suddenly, 
 as it may produce vibration, the shock from which often 
 breaks the briquette before the ultimate strength is reached. 
 Care must be taken that the clips and the sides of the bri- 
 quette be clean and free from grains of sand or dirt which 
 would prevent a good bearing. The load should be applied 
 at the rate of 600 Ibs. per minute. The average of the bri- 
 quettes of each sample tested should be taken as the test 
 excluding any results which are manifestly faulty. 
 
 CONSTANCY OF VOLUME. 
 
 48. Tests for constancy of volume are divided into two 
 classes: (i) Normal tests, or those made in either air or 
 water maintained at about 21 C. (70 F.), and (2) ac- 
 celerated tests, or those made in air, steam or water at a 
 temperature of 45 C. (115 F.) and upward. The test 
 pieces should be allowed to remain 24 hours in moist air 
 
 180 
 
before immersion in water or steam, or preservation in 
 air. 
 
 49. For these tests, pats about 7% cm. (2.95 in.) in di- 
 ameter, i}4 cm. (0.49 in.) thick at the center, and tapering 
 to a thin edge, should be made, upon a clean glass plate 
 [about 10 cm. (3.94 in.) square], from cement paste of nor- 
 mal consistency. 
 
 50. A pat is immersed in water maintained as near 21 
 C. (70 F.) as possible for 28 days, and observed at inter- 
 vals. A similar pat is maintained in air at ordinary tem- 
 perature and observed at intervals. 
 
 51. A pat is exposed in any convenient way in an atmos- 
 phere of steam, above boiling water, in a loosely closed 
 vessel. 
 
 52. To pass these tests satisfactorily, the pats should 
 remain firm and hard, and show no signs of cracking, dis- 
 tortion or disintegration. 
 
 53. Should the pat leave the plate, distortion may be de- 
 tected best with a straight-edge applied to the surface 
 which was in contact with the plate. 
 
 
 181 
 
The Design of Concrete-Steel 
 Beams and Slabs. 
 
 The formulas for proportioning concrete-steel beams are 
 legion, and they are far more varied than those for the 
 design of columns with which engineering literature was 
 flooded a decade or two ago. Nice formulas for the design 
 of columns were elaborated in the days before tests were 
 so common that were satisfactory in every respect, except 
 that they did not agree with the results of tests that were 
 subsequently made. Investigators later found that the 
 behavior of compression members of practical proportions 
 agreed very closely with a simple little straight line 
 formula. Even at the present time the last of these com- 
 plex formulas has not been weeded out of specifications. 
 
 Another feature of construction that has yielded to the 
 simplifying influence of development, or the developing 
 influence of simplification, relates to the ultimate and the 
 working stress of steel. The two grades of structural 
 steel, with separate unit stresses, though they are still 
 recognized in some specifications, are gradually merging 
 into one grade for all pieces subject to the ordinary pro- 
 cesses of the shop, excepting forging ; and the manufacturer 
 no longer needs to exhibit his ability to bring forth either 
 grade from the same melt, bloom, billet or finished piece. 
 
 Concrete- steel designing is young, and probably on ac- 
 count of its rapid growth the infant is afflicted with both 
 of the above-named ailments. The formulas brought out 
 rival those for retaining walls in complexity, and the units 
 recommended are about as numerous as the formulas. 
 
 The foregoing may seem an inconsistent preface to a 
 paper suggesting both formulas and unit stresses, but the 
 writer's purpose is to show the busy engineer, who does 
 not want to delve into abstruse mathematics, that formulas 
 for the design of concrete-steel beams or slabs can be 
 made as simple as those for steel beams. In fact, the 
 formulas are even more simple than formulas for steel 
 
 
in bending, if certain rules of proportioning be adopted. 
 Further, the agreement between the formulas and the 
 actual strength of the construction is about as close as in 
 steel construction, as many tests closely approximating 
 the proportions here recommended have demonstrated. 
 
 In the matter of variation from an established unit 
 stress we commonly allow steel to vary about 8 per cent 
 either way from a desired average tensile strength. We 
 should be satisfied if concrete-steel tests show as close 
 agreement with their calculated strength, especially as 
 the variation, barring the effects of careless work, will 
 probably be on the safe side in nearly every case. The 
 last-named condition obtains because of the real but un- 
 certain element of strength imparted to the combination 
 of concrete and steel by the strength possessed by the steel 
 after it has passed its elastic limit, the nominal limit of 
 ultimate strength. 
 
 There are many kinds of concrete, just as there are many 
 grades of oak. Some oak has knots and wind shakes and 
 is unfit for use in a structure, but specifications for oak 
 beams do not recognize these grades in allowing unit 
 stresses ; rather the aim is to exclude those grades unfit 
 for use by proper selection and inspection of the materials. 
 So in concrete-steel construction there should be a standard, 
 and this should be a concrete suitable for the purpose and 
 made strictly according to the requirements, as near as 
 these ends can be accomplished commercially. 
 
 It is almost universally agreed that concrete composed 
 of I part Portland cement, 2 parts sand and 4 parts small 
 hard broken stone or gravel, or of proportions closely 
 approximating these, is the most suitable mixture for the 
 concrete. For cinder concrete the same proportions, using 
 cinders in place of broken stone, may be called standard. 
 It is also common knowledge that this stone concrete, 
 when made of good materials, will sustain an ultimate 
 crushing load of about 2,000 Ibs. per in., and the cinder 
 concrete will take about 750 Ibs. per sq. in. It is pre- 
 183 
 

 sumed^in all cases that the materials and workmanship 
 are good, just as we presume that wood used in structures 
 is good and sound. 
 
 It is further almost generally agreed that the ultimate 
 strength of a concrete-steel beam is reached when the 
 steel is strained to its elastic limit and the concrete has 
 reached its ultimate strength. 
 
 The use of steel having high elastic limit and depend- 
 ence upon high safe units in consequence is indefensible. 
 The excessive stretch in the steel will crack the concrete. 
 The writer made a number of tests on the floors of a large 
 concrete-steel building, and in one case, in a bay con- 
 taining 13 beams, 91 cracks were counted in the beams when 
 the "safe" load was placed upon the floor. One beam had 
 16 cracks. Many of these appeared long before the sup- 
 posed safe load was placed. The deflection was excessive. 
 This building was designed with steel of high elastic limit, 
 and dependence was placed upon the high tensile value 
 of the steel to sustain the loads. 
 
 The theoretic elongation of the concrete, even at mod- 
 erate tensile values in the steel, corresponds to excessive 
 tensile values in the concrete; and the fact that concrete 
 in which steel is embedded has been stretched out in 
 tests without cracking to elongations that would rupture 
 plain concrete is evidence that the concrete in setting has 
 shrunk, thus putting the steel under an initial compression, 
 which must be overcome before any stretch occurs in 
 the concrete. This shrinking of concrete in setting is one 
 of its most useful properties, viewed as a medium in con- 
 crete-steel construction. Besides giving the embedded 
 steel an initial compression and thus helping its tensile 
 value, it also grips the steel, and thus takes firm hold upon 
 it, greatly aiding the adhesion of the concrete to the steel. 
 It is to be noted that this gripping of the steel, and not 
 mere adhesion due to contact, is the thing that makes 
 the union between the steel and the concrete effective. 
 This is the reason why round and square bars hold better 
 184 
 
in the concrete than flats. It is also a reason for bed- 
 ding the steel deep enough from the surface of the con- 
 crete to make the gripping effective. It further overcomes 
 the almost infinitesimal reduction in diameter in the em- 
 bedded steel when under stress below the elastic limit, so 
 that the adhesion or skin friction is not lost when the steel 
 elongates slightly. 
 
 The fact that concrete shrinks in setting further points 
 out the error in depending for compression upon steel 
 embedded in concrete, unless the concrete is merely used 
 for its protecting value. The initial compression in the 
 steel adds an uncertain amount to any calculated compres- 
 sion in the same. Steel reinforcement in the intrados of 
 segmental concrete floor arches is not rational design, as 
 the steel, to be useful, must be in compression. Steel 
 embedded in concrete columns as hoops or spirals is 
 rational, as loading the column tends to increase its 
 diameter and to put tensile stress in the steel. Also light 
 longitudinal rods, wired to these spirals to take flexure 
 in the columns, is excellent to reinforce the column against 
 eccentric or lateral forces. 
 
 Another phase of this shrinking is that very long units 
 in concrete-steel construction should not be placed at one 
 time, unless expansion joints be provided. It is the shrink- 
 ing of concrete that causes vertical cracks in plain con- 
 crete walls to appear at intervals, and makes it expedient 
 to leave expansion joints in such walls 30 ft. apart or so. 
 Steel embedded in concrete walls or other construction 
 has the effect of distributing the shrinkage stresses and 
 lessening the shrinkage cracks, and walls thus reinforced 
 can be made much longer without liability to these cracks 
 than plain walls. However, if a long reinforced wall is 
 brought up uniformly from the ground up, shrinkage 
 cracks will probably appear. If the wall be built from 
 one end to the other, allowing setting and shrinkage of 
 part of the wall before the remainder has been placed, a 
 very long wall can be made without danger of these 
 185 
 
cracks. By the same token long concrete-steel buildings 
 should be placed in alternate units, if much is to finished 
 at once, leaving the intermediate units to be placed after 
 the setting of the first; or some other provision should 
 be made to allow for the shrinkage of the concrete. 
 
 It is not the intention here to go into the subject of 
 the making of concrete, more than to say that it is abso- 
 lutely essential in this class of work that the concrete be 
 thoroughly mixed, and it should be very wet. Dry or 
 mealy concrete is totally unfit for concrete-steel work. It 
 will neither adhere to the steel nor protect it. 
 
 Tests show that a rod embedded in wet concrete will 
 resist pulling out, when the concrete has set and hardened, 
 with a force of about 500 Ibs. per sq. in. of the surface of 
 rod embedded. At 10,000 Ibs. per sq. in. on the steel and 
 50 Ibs. per sq. in. adhesion to the concrete a round or 
 square rod should be embedded 50 diameters in concrete. 
 This is very often ignored in concrete-steel beams designed 
 for buildings and prepared for test. The curve of maxi- 
 mum moments of a beam taking uniform load or a single 
 rolling load is a parabola; hence the curve of stress in the 
 reinforcing rods, assuming them to be parallel to the bot- 
 tom of the beam, is a parabola. The line representing the 
 adhesive value of a rod embedded in concrete is a straight 
 line from the end of rod to the point of maximum stress; 
 hence for the adhesive value to be at all sections greater 
 than the actual stress the straight line should be outside 
 of the parabola; that is, it should be tangent to it at 
 the support. This would make the ordinate of the straight 
 line just twice that of the parabola, or the adhesive value 
 should be double the maximum stress. Therefore, it is 
 essential in consistent design to have the beam no less 
 than loo times the diameter of rod from end to center 
 of span. In other words, the rod should be no more than 
 I -200 of the span length. 
 
 Tensile value of the concrete should not be allowed 
 under any circumstance, as one shrinkage crack may de- 
 stroy entirely this tensile value for the whole beam. 
 186 
 
As intimated, high tensile strains in the steel though 
 they may be warranted from the standpoint of high elastic 
 limit in the material, presume too far upon the extensi- 
 bility of the concrete. The elastic limit of ordinary struc- 
 tural steel, or 40,000 Ibs. per sq. in. ? is the most suitable 
 value to represent the ultimate useful strength of the steel. 
 With 2,000 Ibs. per sq. in., as the ultimate strength of 
 the concrete in compression, and with tension eliminated 
 there remains the variation of the stress in the con- 
 crete from the neutral axis up and the position of the 
 neutral axis to determine the value of the beam in flexure. 
 
 Tests have shown that the neutral axis of a concrete- 
 steel beam remains close to the middle of the depth of the 
 beam. A little calculation will show that a variation of 
 one-eighth of the depth of beam one way or the other, 
 in the standard construction here to be proposed, makes 
 a difference of about 6 per cent in the calculated resist- 
 ing moment, if the stress in the steel remains the same, 
 or about the same difference if the extreme fiber stress 
 in the concrete remains the same. Using the units here- 
 tofore given and 2,000,000 as the modulus of elasticity of 
 concrete, and substituting in one of the elaborate formulas, 
 which allows for parabolic variation of the stress in con- 
 crete from the neutral axis both ways and for tension in 
 the concrete, the neutral axis is found to be within 4 l /2 
 per cent of the middle of the depth of the beam. So that 
 the neutral axis is shown, both by theory and test, to be 
 close to the middle of the depth of the beam, and its shift- 
 ing a comparatively large fraction of the depth makes but 
 small variation in the calculated strength of the beam. 
 
 The assumption that the variation in stress in the con- 
 crete from the neutral axis to the extreme fiber is accord- 
 ing to a curve deviating somewhat from a straight line 
 is another element that complicates the formulas. Here, 
 again, fine theory arrives at conclusions that are incom- 
 patible with the known variations in ultimate compressive 
 strength of different tests made of the same materials 
 
 187 
 
under apparently the same conditions. To assume that 
 the intensity of stress in the concrete varies directly as the 
 distance from the neutral axis is sound engineering and 
 is accepted by many investigators. 
 
 In order to simplify further the calculations, it is 
 recommended that the center of the steel be one-eighth 
 of the depth from the bottom of the beam. 
 
 Referring to Fig. i, it is seen that the total compres- 
 sion in the concrete is 
 
 BD 
 
 2,000 
 
 -=500 BD 
 
 This must equal the tension in the steel. Now, if the 
 area of the steel be A, we have 40,000 A = 500 BD, or A = 
 1.25 per cent of the rectangle BD. 
 The center of gravity of the stress in the concrete is 
 
 above the neutral axis and the effective depth of beam is 
 
 3 
 
 3 8 
 
 The ultimate resisting moment is or 
 
 17 
 
 ~>=U-D 
 
 24 
 
 24 
 
 DX 500 BD or M=354 BD*. 
 
 Assuming all dimensions in inches, this moment is in 
 inch-pounds. Or, making B = 12 and dividing by 12 
 to reduce to foot-pounds, we have ultimate bending mo- 
 ment in foot-pounds per foot in width of slab or beam 
 = 354 D*. 
 
Now as to the shear. It is safe to say that any stone 
 concrete that will not stand 50 Ibs. per sq. in. as a safe 
 load in shear should not enter into the construction of 
 concrete-steel beams and slabs ; also that concrete should 
 not be stressed much above this amount in shear. The 
 horizontal shear in the beam in a section just above the 
 rods is equal at any point to the increment of stress in the 
 rods. Hence, as we have used the same unit for shear 
 and adhesion, there should be the same area across the 
 beam as that of the surface of the rods. Round rods 
 should then be spaced not less than 3.1416 times 
 their diameter apart and square rods not less than four 
 times their diameter apart; also the distance to the side 
 of beam at last bar should not be less than one-half of 
 these respective distances. With rods spaced just these 
 amounts, it will be found that the distance from center 
 of rod to bottom of beam will be 2*/2 times the diameter 
 of rod, which is an ample depth to insure gripping of the 
 steel by the concrete. Of course, rods can be given wider 
 spacing than that shown in the figure. For example, square 
 rods spaced five times their diameter apart will be two 
 diameters from the bottom of beam. 
 
 This limit in the spacing of rods is very often over- 
 looked in the designing of beams for buildings and for 
 test. The beams are made too narrow and unscientific 
 expedients are resorted to to overcome the defect. This 
 has even more force in the case of dependence upon high 
 tension steel or mechanical bond, as the greater increment 
 of stress that must be assumed demands greater area of 
 concrete to take the horizontal shear. 
 
 Again, in the matter of vertical shear at the end of 
 span. Assuming a safe bending moment as one-fourth 
 of the 354 D 2 already found, and equating to the expres- 
 sion for the bending moment in a uniformly loaded beam 
 at W Ibs. total load, we have 
 
 WL 
 g =SSD 2 ( Z=span in fecf) 
 
 189 
 

 But the allowed end shear at 50 Ibs. per sq. in. on a 
 rectangle 12 ins. wide and D ins. deep, remembering that 
 the maximum intensity of shear in a rectangular beam 
 is three-halves of the average, is 
 us 9 
 
 MM o* *"b 9.^-= X50X12 A 
 
 or total allowed load on beam = W = 800 D. 
 
 Substituting this value of W in the equation above, we 
 have 
 
 
 88 
 
 But, as D is in inches and L is in feet, the actual ratio 
 is very close to 10. Hence, when the depth is more than 
 one-tenth of the span, the full load on a beam begins to 
 overtax the shearing strength of the concrete before the 
 steel reinforcement has its proper stress. Here again 
 some investigators have erred by making short, deep test 
 beams; and, finding that they fail in shear, concluding 
 that concrete is inherently unreliable in shear; whereas 
 the real fault is in the design of the beam. 
 
 In all concrete-steel designing more or less reliance must 
 necessarily be placed upon the shearing strength of the 
 concrete. It only remains to proportion the beam or 
 slab in such way as to place the concrete where it will 
 take the shear. The best mechanical bond can do no more 
 than transmit the forces of shear in concrete into direct 
 stress in the steel or direct stress in the steel into shear 
 in the concrete. It is difficult to see how stirrups placed 
 at intervals could perform this function. 
 
 From Fig. i it is seen that the maximum depth of beam 
 is 20 times the diameter of rod. Hence the maximum 
 ultimate bending moment is 
 
 354 >~ 354 X ( 20 <*> 2 = U^foo d* 
 
 But the minimum span must be 200 d to develop the 
 
 adhesion in the rod. This is 10 times the depth, which 
 
 agrees with the limiting span for shear. Since the shorter 
 
 the span the greater the load per square foot for the same 
 
 190 
 
resisting moment, we may obtain the limiting load per 
 square foot thus : The moment in foot-pounds on a span 
 200 d -f- 12 ft long is 
 
 where w is the load per sq. ft. Equating this to 141,600 
 t/ 2 we have w 4,080. 
 
 This is the maximum ultimate load per sq. ft. that can 
 be placed upon the top surface of a concrete-steel beam 
 of stone concrete designed in the proportions here given 
 and with the units here employed. 
 
 For cinder concrete, by the same course of reasoning, 
 using 750 Ibs. per sq. in. ultimate compression and 30 
 Ibs. per sq. in. for adhesion and shear, we arrive at the 
 following results: 
 
 Maximum ultimate bending moment = 133 D 2 . 
 
 Minimum span for adhesion 333 d, or 6.26 D. 
 
 Percentage of steel reinforcement = .47. 
 
 Minimum span for shear = 6.65 X depth. 
 
 Maximum ultimate load per square foot 3,910 Ibs. 
 
 It is recommended that for quiescent loads as in build- 
 ings a factor of safety of 3^2 be used, and for rolling loads 
 a factor of 4. The minimum span lengths, or, in other 
 words, the maximum depths, should be used only in 
 extreme cases. In special cases, where the beams would 
 be clumsy, some of the rods may be curved up and anchored 
 at the ends, thus making suspension rods receiving all 
 of their stress at the ends. A rod thus placed in a curve 
 would carry the shear corresponding to its own tension, 
 leaving the concrete to take only that due to the trans- 
 ference of stress into the horizontal rods. 
 
 ' f I 
 
 ^\ ir .-- X L i 
 
 Fig. 2. 
 191 
 
Fig. 2 shows the proportions for a beam of this design. 
 The end detail of the rod should be capable of taking 
 practically all of the stress on the rod; upsetting would 
 not be necessary, however. Turning up rods at the end 
 without anchoring the ends or making them continuous 
 can scarcely be said to add any useful element of strength. 
 
 The shear carried by the curved rod will be found to 
 be equal to the stress in the rod times H -r- l / 2 L. 
 
 For slabs of short span the rules of design here given 
 would demand close spacing of steel of small diameter. 
 Steel mesh is the most suitable material, if the strands are 
 straight; or if wires or rods are used, alternate strips of 
 the slab may be considered as beams supporting strips of 
 plain concrete between, which act as fillers, or which 
 may be considered to perform the useful office of absorb- 
 ing shock. 
 
 As an example of the application of the foregoing, given 
 a floor with beams spaced 5 ft. and having a span of 20 
 ft. and these beams carried by girders of the same span; 
 all to carry 100 Ibs. per sq. ft. of live load, considered as 
 quiescent. Assume a depth of slab of 4 ins. and 3 ins. 
 spacing of rods. The rod will be l /% of the depth, or J^-in. 
 from the bottom of the slab. The safe bending moment 
 on the slab per foot of width, with the full area of the 
 steel, would be 101 X l6 = J > 616 ft.-lbs. But the total 
 moment, including 50 Ibs. per sq. ft. for weight of slab 
 is 150 X 2 S -:- 8 469 ft.-lbs. Hence in 3 ins. only 
 
 _^_ of the steel area is needed. Now, i% per 
 1616 
 
 cent of 3 X 4 = - T 5 sc l- m - anc * tne fraction of 
 this required is .044 sq. in. One-quarter-inch round rods 
 will therefore suffice. One-two-hundredth of the span is 
 .3 in. and the diameter of rods is less than this, as it should 
 be. For the beam, assume a depth of 20 ins. This includes 
 the depth of slab. Taking the dead load at 95 Ibs. per 
 sq. ft., the total moment is 5 X *95 X 2O X 2 -r- 8 == 
 48,750 ft.-lbs. The allowed moment on the beam per foot 
 192 
 
of width is 101 X 2O 2 = 40,400 ft.-lbs. The width of 
 beam should therefore be 1.21 ft., or 15 ins. Rods will 
 be 2 ins. from bottom of beam, and the area required is 
 i l /4 per cent of 300 = 3.75 sq. ins. Three i l /s-in. square 
 rods will satisfy the conditions. The maximum diameter 
 of rod allowed = 
 
 JLx240=1.2ins. 
 200 
 
 For the girders, assume a depth of 32 ins., including 
 the depth of slab. Using a dead load of 120 Ibs. per 
 sq. ft., the total maximum moment is 220 X 2O X 2 2 -f- 
 8 220,000 ft.-lbs. The allowed moment per foot width 
 of girder is 101 X 3 2 *= 103,430 ft.-lbs. The width of 
 beam required is then 25^ ins. The area of rods required 
 is i]/4 per cent of that of the beam, or 10.2 sq. ins. This 
 is very nearly made up by six rods i% ins. in diameter 
 and two I 5-16 ins. The allowed safe shear on the full 
 section of the concrete girder is 2-3 of 200 (the nominal 
 ultimate) ~ 3 l /2 (the factor of safety), or 40 Ibs. per 
 sq. in. The concrete will then take 40 X 3 2 X 2 5-5 
 32,640 Ibs. The total end shear is 44,000 Ibs. As the con- 
 crete will take just about 24 of the shear, we may turn 
 up the two i 5-i6-in. rods and anchor them at the ends, 
 as in Fig. 2. The stress in these rods will be the product 
 of their area and 2-7 of 40,000 == 30,930 Ibs. The shear 
 that they will carry is found by the method given under 
 Fig. 2 to be 1 1, 680 Ibs., which is just about the amount 
 needed to supplement the shearing strength of the concrete. 
 The diameter of the horizontal rods is just a trifle more 
 than 1-200 of the span length, and the rods can be spaced 
 a little more than ?r or 3.1416 times their diameter apart. 
 The two curved rods may be placed between horizontal 
 rods, as they give rise to no horizontal shear in the con- 
 crete; the latter merely hangs upon them as a saddle. 
 
 In a beam of the magnitude of the one just propor- 
 tioned some saving of steel could be effected by placing 
 the rods nearer to the bottom of the beam, or, say, 3 ins. 
 193 
 
from the same, and making their area inversely propor- 
 tional to the distance from center of steel to center of 
 compression in concrete. 
 
 The writer believes that the foregoing principles of de- 
 sign, while they do not show the apparent economy of 
 some special systems, would place concrete-steel designing 
 in the class of sound engineering and force recognition 
 where it is now decried. 
 
 Tests of beams thus systematically designed would show 
 where any modification of units is needed. 
 
 &' 
 
 THE DESIGN OF REINFORCED CONCRETE BEAMS 
 AND SLABS. 
 
 Sir: I have read with great interest the article by Mr. 
 Edward Godfrey on the design of reinforced concrete 
 beams and slabs in your issue of March 15, and would say 
 that he has handled the fundamental questions of the 
 subject with great clearness and ability. He has, how- 
 ever, been intent on simplifying the calculations too much 
 and thus fallen into the mistake of deriving empirical 
 formulas. It seems to the writer that it is just as easy 
 to err on one side as the other of mathematical complexity. 
 The same path which has been pursued in deriving for 
 steel beams working formulas which have stood the test 
 of experiment and experience should be followed here. 
 The fundamental assumptions, which are the solid founda- 
 tions of the mathematical edifice, must be carefully weighed 
 and made as broad and simple as possible. After having 
 done this we can proceed with full confidence that we will 
 not be led astray by a mathematical will-o'-the wisp. Where 
 fanciful and complicated formulas have been derived, the 
 fault is not to be found, as is often too hastily assumed, in 
 mathematics as such, but in the lack of judgment or com- 
 mon sense in not starting aright. Mathematics can be 
 compared to a powerful locomotive which, given a clear 
 track and a cool brain to guide it, will arrive at its desti- 
 194 
 
nation with accuracy and dispatch, but if put on a poor 
 track and in the hands of an incompetent runner, will 
 land in the wayside ditch. 
 
 The writer firmly believes that the mathematical engine 
 has been started correctly by Mr. Paul Christophe in his 
 classical work on reinforced concrete. The assumptions 
 that he starts on are carefully weighed, simple and, if I 
 may be allowed the expression, eminently sane. They are, 
 with modifications proper to the new material, the same 
 as those for the steel beam and should therefore lead to 
 as satisfactory results. As a matter of fact, numerous 
 experiments which have come to the writer's knowledge 
 bear this out. Not to go into the subject too deeply at 
 present, the writer would say that the percentage of steel 
 for stone concrete of 1.25 per cent, which Mr. Godfrey gets, 
 is excessive. Christophe demonstrates that for rectangular 
 beamr there is a certain percentage of steel with a cor- 
 responding position of neutral axis and depth of beam 
 at which both the concrete and the steel are stressed up to 
 their full respective values and which is therefore the 
 economical one to use, as both above or below this point 
 either the concrete or steel are over-stressed. Taking the 
 depth of beams the same as the distance of the center of 
 steel from the top of beam (which is the most rational 
 thing to do, we can then add as much or as little concrete 
 below as other considerations will dictate) we get for the 
 percentage 0.60, for the position of neutral axis 0.385 of 
 
 the depth h and for ^0.108 / ^ where M is the bend- 
 ing moment and e the width of beam. There are several 
 other questions which the writer would like to take up at 
 some other time. In conclusion he would say that he 
 agrees with Mr. Godfrey that correct principles of design 
 while they do not show the apparent economy of some 
 special systems, would place concrete-steel designing in 
 the class of sound engineering. There are enough in- 
 herently weak points in concrete-steel as regards work- 
 105 
 
manship and materials that we should not add further 
 uncertainties caused by strenuous inventors and adherents 
 of special systems. The latter as a rule care very little 
 for advancing the cause of good engineering as long as 
 they can make it pay and cases are liable to arise where 
 twisting and even falsification of facts may be resorted to 
 in order to keep an otherwise discredited system in ap- 
 parently good repute. Yours truly, 
 
 Henry Szlapka, 
 
 Resident Engineer, Toledo-Massillon Bridge Co. 
 342 Mint Arcade, Philadelphia, Pa., March 30, 1906. 
 
 
 Sir: I am in receipt of proof of a letter to you from 
 Mr. Henry Szlapka, criticising my article on the design 
 of reinforced concrete beams and slabs, published in your 
 issue of March 15, and desire to thank you for this op- 
 portunity to reply to the same. 
 
 The first word that strikes me as strange in this letter 
 is the word empirical, as applied to my formula. Em- 
 pirical is defined as pertaining to or derived from experi- 
 ment. In the sense that unit values, and sometimes final 
 results, in formulas for strength must be derived from 
 experiment, all such formulas might be classed under this 
 head. But as commonly employed the term means a more 
 or less scientific guess. The formula I derive is not em- 
 pirical, for it is derived from the well-known theory of 
 beams, using the strength of steel and concrete as deter- 
 mined from tests, and a position of the neutral axis deter- 
 mined from tests to locate the neutral axis (not by the 
 uncertain method of using comparative moduli of elastic- 
 ity). Mr. J. J. Harding, in a paper read before the West- 
 ern Society of Engineers, Oct. 25, 1905, says, "Experimental 
 methods are desirable for determining the position of the 
 neutral axis, as it enables one to design a beam without 
 making an assumption as to the modulus of elasticity of 
 the concrete, which may easily vary 100 per cent." 
 
 For the sake of simplicity I have eliminated some of 
 
 196 
 
the unnecessary kinks in the other formulas. For ex- 
 ample, I have represented the stress in the concrete by 
 a triangle and not by a triangle with a little segment 
 added to the hypothenuse. The strength of concrete is 
 not so well defined, even if conditions of manufacture 
 and the materials appear to be identical, as to make it 
 expedient to count in the almost insignificant segment of 
 force with all of the complexity it entails in the formula, 
 granting for the sake of the argument that the compres- 
 sion in the concrete does not vary as the distance from 
 neutral axis. Suppose it should be discovered by use of 
 exceedingly delicate instruments that steel under various 
 stresses has a sliding modulus of elasticity, then the 
 principle of the design of beams that the extension or 
 shortening of the fibers varies directly as the stress would 
 not be exactly correct, and the stress would not vary in 
 intensity exactly as the distance from the neutral axis, 
 but as the ordinates to some curve. Now there is no 
 doubt at all that some mathematician would arise, with 
 lots of time at his disposal, who would work out a gen- 
 eral formula to take this variation into account for all 
 shapes of beams. A difference in the strength of beams 
 might be found amounting to one or more per cent. The 
 strength of one bar of steel tested at two different places 
 may vary several per cent, and the opinions of two 
 engineers as to the proper factor of safety may vary still 
 more; but this does not concern the mathematician, who 
 has found a principle of mathematics violated by the com- 
 monly used "empirical" formula. Now I do not want to 
 place a practical designer like Mr. Szlapka in a class 
 with this mathematician, but I want to say that there is 
 a lot of mathematical dust thrown into the eyes of de- 
 signers who have not the time or the inclination to delve 
 into these abstruse mathematical questions, but who would 
 like at the same time to know a sound reason for using 
 a formula, and to have that formula stripped of all elements 
 
 197 
 
that complicate it without introducing any useful additional 
 element of correctness. 
 
 As to i% per cent of steel being too high, I quote from 
 Prof. A. N. Talbot in Engineering News, July-December, 
 
 1904, page 125 : "For 1:3:6 concrete, reinforcement as 
 high as i l /2 per cent for steel of 33,000 Ibs. per sq. in. 
 elastic limit * * * may be used without developing 
 the full compressive strength of the concrete." The pro- 
 portions of concrete that I recommend are 1:2:4, a much 
 stronger concrete, generally, than 1:3:6; it would allow 
 a greater percentage of steel. Again, to quote Prof. W. 
 Kendrick Hatt in "Engineering Record," Vol. 51, page 545: 
 "In the writer's tests of beams under a center load, 2 l /2 
 per cent steel failed to develop the crushing strength of 
 the concrete." In Engineering News of Feb. 15, 1906, p. 
 170, Mr. J. J. Harding states that for steel of an elastic 
 limit of 35,000 Ibs. he would use between i and i*4 per cent 
 of the area of the concrete. Mr. T. L. Condron, in a paper 
 read before the Western Society of Engineers, March 15, 
 
 1905, says: "For extra strong concrete of about i of 
 cement, 2 of sand and 4 of broken stone, the percentage 
 of reinforcing may be increased to 1.25 per cent." (This 
 in a discussion of 202 tests.) In view of the foregoing 
 conclusions from the results of tests it is hard to see the 
 force of Mr. Szlapka's bald assertion that i 1 /^ per cent is 
 excessive. 
 
 Mr. Szlapka also objects to my assumption that the 
 neutral axis is in the middle of the depth of concrete. As 
 intimated, this was done on the strength of the results 
 of tests or measurements to locate the neutral axis and 
 not by means of a fancy formula, though it is not at 
 variance with one of the most complex formulas I could 
 find. In Engineering News, July-December, 1904, pp. 
 124-125, Prof. Talbot gives plottings of the position of the 
 neutral axis. For 1.39 per cent reinforcement the distance 
 from top of beam is almost exactly 50 per cent of the depth 
 from top of concrete to steel. For 0.97 per cent it is about 
 
 198 
 
0.42 of the same depth. Prof. Talbot gives this formula 
 for finding the position: k 0.26 + 0.18 p, where k is 
 the fraction of depth from top to neutral axis, and /> 
 is the percentage of steel. For i 1 /^ per cent this would 
 be 0.485 of depth from top of concrete to steel. Prof. F. 
 E. Turneaure in Engineering News, July-December, 1904, 
 p. 215, says: "The diagrams show the neutral axis to lie 
 at first very near the center of the concrete beam. As the 
 cracks develop it moves gradually nearer to the compres- 
 sion side." 
 
 The use of the term "depth of beam" to designate the 
 distance from top of concrete to steel is merely a mat- 
 ter of nomenclature. There are good practical reasons for 
 using the outside depth of concrete as the "depth." In 
 the first place it figures in the mind of the designer as 
 the depth and governs the clearance, and it is usually in 
 round numbers. In the second place a rule such as I 
 give requiring l /% of the depth from center of steel to bot- 
 tom of beam gives sufficient concrete below the steel to 
 grip it and does not admit of skimping in this respect. 
 It is a very essential point of design that the steel be sur- 
 rounded with enough concrete to grip it effectually. This 
 is a point often overlooked in designing. 
 
 It has not been my purpose to discredit mathematics 
 but to point out the fallacy of unnecessary complication 
 in formulas for use. In the struggle for existence the 
 fittest formula has generally been found to be the simplest. 
 Yours very truly, 
 
 Edward Godfrey. 
 Monongahela Bank Building, Pittsburg, Pa., April 12, 1906. 
 
 THE DESIGN OF REINFORCED CONCRETE 
 BEAMS AND SLABS 
 
 Sir: The writer asks for the privilege of presenting a 
 reply to Mr. E. Godfrey's letter in your issue of May 3, 
 not for the sake of continuing a discussion and sparring 
 
for the last word, but because many points are raised 
 of an exceedingly practical character, on which the writer 
 earnestly seeks for light. If Mr. Godfrey's statement that 
 1% per cent is the proper amount of steel reinforcement 
 is correct, then the writer is wrong by over 100 per cent 
 and naturally feels great uneasiness over the safety of 
 numerous structures which he has designed, and which have 
 been built on his theory. His only justification must be, 
 that he has erred, not through carelessness, but through 
 unavoidable ignorance which is shared by a great number 
 of his colleagues. He would like to ask Mr. Godfrey and 
 beyond him, all practical designers who may notice this 
 letter, whether they have used a percentage of i^J or one 
 nearer 0.60 in their actual work. If they have used the 
 former, they were more fortunate than the writer in not 
 having had to meet close commercial competition. 
 
 A great number of times estimates made on the writer's 
 theory have been beaten by reputable rivals and those of 
 his designs which were executed did not differ by any 
 material amount from other plans. The sizes given by 
 his theory have usually compared closely with those by 
 other more competent designers and, moreover, have passed 
 the careful scrutiny of building inspectors. If he is 
 radically wrong, he can only regret that he did not follow 
 the advice of one of the best known bridge engineers given 
 some years ago, who told him that he was too young to 
 risk his reputation by dabbling with reinforced concrete, 
 because in the course of time such structures would develop 
 numerous flaws as yet hidden from observation. As a 
 matter of fact, a concrete engineer has to take too many 
 chances from poor materials and lack of care in execution 
 of his work to add deliberately another grave risk of 
 error from theory. Where so much uncertainty exists, he 
 must accept the best current practice, select the most 
 reasonable theory as a basis for his designs and await the 
 consequences, assured that he cannot be held morally re- 
 sponsible for defects which could not be prevented by using 
 200 
 
all due precaution. The case would be different with a 
 designer who use gross section instead of net of the steel 
 reinforcement with the intention of making his customer 
 believe he was getting more than he actually received. This 
 is a matter in which ignorance cannot be excused. 
 
 Mr. Godfrey takes up considerable space in combating 
 statements never made by the writer, which cover points 
 on which, as a matter of fact, they are in agreement, as 
 will be shown. He also talks about "mathematical dust" 
 and "bald" statements. The "mathematical locomotive" 
 naturally raises a great deal of dust in its flight through 
 spacej like its material prototype, but that is a by-product 
 which need not concern the man at the throttle. It can 
 be left to be gathered up by the poor professional mathe- 
 maticians, for whom most engineers profess such a marked 
 contempt. As to baldness, the writer does not worry 
 about being in that incipient condition himself, but feels 
 very much concerned about his statements having reached 
 that stage. 
 
 To bring matters to a definite issue the writer will 
 briefly state the fundamental assumptions of Mr. Chris- 
 tophe's theory and ask Mr. Godfrey's and others' opinion, 
 why in the present state of the art they are not the best, 
 avoiding unnecessary refinement on the one hand, and 
 being sufficient on the other to serve as a broad basis for 
 elaboration. If they are correct, the writer feels no hesita- 
 tion in following wherever they lead to. These assump- 
 tions are five in number: (i) Solidarity of concrete and 
 reinforcement, provided the latter is so arranged as to 
 assure a sufficient bond between the two; (2) invariability 
 of plane sections; (3) invariability of the coefficient of 
 elasticity of concrete in compression within the usual limits 
 of stress; (4) neglecting the action of concrete in tension; 
 (5) absence of initial stresses. 
 
 Mr.Godfrey speaks in all cases of ultimate values, whereas 
 the ordinary theory does not pretend to follow beyond 
 the elastic limit, either in steel or in concrete steel, and 
 
 201 
 
it therefore seems that results deduced from testing beams 
 to failure have little value as interpreted by our ordinary 
 formulas. Moreover, beams of rectangular section, which 
 are the only ones fully discussed in textbooks and experi- 
 mented on, are very little used in actual practice as com- 
 pared with beams of T section where the floor slab is 
 counted on for part of the compression flange. What per- 
 centage of steel would Mr. Godfrey fix on for that case? 
 
 As to the writer's definition of "depths of beam" it is 
 the only rational one to use, even if this statement is 
 bald. Take a shallow beam, say 8 ins. deep and a deep 
 one, say 36 ins., both within practical everyday limits. 
 In the one case Mr. Godfrey would get I in. and in the 
 other 4^2 ins. for the amount of concrete under steel. 
 Would he actually use these figures in a commercial de- 
 sign? This amount will rather be found to be a constant 
 and that because of a very important consideration which 
 Mr. Godfrey has not touched on. That is the protection 
 afforded against fire, and here a great diversity of opinion 
 exists. Prof. Chas. L. Norton, as quoted in Taylor & 
 Thompson's book on concrete, considers 2 ins. in all 
 beams and girders essential and most building regulations 
 call for at least that amount. However, no more than 
 i l / ins. has been used very often and passed by some 
 building departments. In a fire test of a system which 
 has never used more than that amount it was incresed 
 to 2 l /t ins., for the purpose of the test only, according to 
 the writer's best knowledge and belief. There is also 
 another point in this connection which has not been com- 
 mented on, and which deserves careful consideration. In or- 
 der to attach shafting or pipes to reinforced concrete beams, 
 many different devices have been used, among others some 
 in which a socket or similar device is in close contact with 
 the reinforcement. In case of fire, heat is thus trans- 
 mitted directly to the steel reinforcement with the result 
 of heating it rapidly and causing the concrete protection 
 to fall off, due to the unequal expansion, the concrete taking 
 202 
 
a much longer time to heat to the same temperature than 
 the steel; therefore, such devices should not be allowed, 
 or, if they are, the buildings so constructed should not 
 be held up as examples of fireproof construction. The 
 last two points mentioned have apparently been frequently 
 overlooked, but should not be slighted in the future. 
 
 If the inventor of a system is compelled to use features 
 which cannot comply with scientific requirements and tries 
 to pass them off under the sanction of the building depart- 
 ment of a prominent city, he is no better than the packer 
 of poisoned meat who uses the apparent sanction of United 
 States government inspection which, when closely investi- 
 gated, has no substantial meaning, but of which fact the 
 public knows nothing. 
 
 As stated before, there are enough unavoidable uncer- 
 tainties* in the subject without adding other difficulties of 
 our own making. In the rebuilding of San Francisco rein- 
 forced concrete will play an important part, but grave 
 fear must be entertained that unscrupulous competition 
 will result in much reckless and "skinned" work, unless 
 held in check by regulations and inspection which are 
 more than a mere name. Yours truly, 
 
 Henry Szlapka,, 
 Res. Engr. Toledo Massillon Bridge Co. 
 
 342 Mint Arcade, Phila., May 7, 1906. 
 
 The author did not reply to the above letter of Mr. 
 Szlapka. The letter does not bring out much that is new. 
 As to Christophers assumptions, No. (5) would not hold 
 in ordinary beams, as the shrinking of the concrete does 
 put initial stress in the steel, and this disturbs all assump- 
 tions about the coefficients of elasticity, including 
 No. (3), as made use of to locate the neutral axis. 
 As to the amount of concrete that is proper to use below 
 the steel, it would not be reasonable to use the same amount 
 below a wire mesh in a slab as would be needed below 
 and around a round or square bar 2 in. or so in diameter. 
 The concrete is needed to grip as well as protect the steel, 
 
 203 
 
and light sections of steel do not need as much concrete 
 to grip them as heavy sections; also light sections do not 
 need as much protection as heavy ones, because they are 
 of less importance in the structure. One inch of concrete 
 is sufficient in a shallow slab. It is totally inadequate in a 
 large beam with heavy rods. [AUTHOR.] 
 
 The Design of Reinforced Concrete 
 Columns and Footings. 
 
 INTRODUCTION. In the paper published in En- 
 gineering News of March 15, 1906, the writer derived 
 some simple formulas for the design of reinforced concrete 
 beams and slabs and some rules governing the proper pro- 
 portioning of the steel for reinforcement and the limiting 
 span length. Accepting the premises given in that paper, 
 it becomes a simple matter to design beams and slabs in 
 this comparatively new combination of materials. There 
 seems to be no voice lifted up to deny the complete safety 
 of beams thus designed to carry their loads, and no sub- 
 stantiated objection to the proposed method of design has 
 yet been raised on the side of economy the other end of 
 the see-saw that the engineer must maintain in equilibrium. 
 
 Many so-called practical tests have been made on rein- 
 forced concrete construction in place that do not merit 
 the name of tests. They are made on a small section of 
 a floor supported on all sides by the contiguous construc- 
 tion, and do not test in any adequate sense the part of the 
 floor immediately loaded. If a designer of steel construc- 
 tion should load a beam by placing a uniform load on a 
 fraction of its length and declare that from the results of 
 the "test" the beam is shown to be capable of carrying 
 that uniform load throughout, he would be promptly ruled 
 out ; and yet this is the kind of test that is commonly held 
 up as demonstrating the ability of some forms of con- 
 crete-steel design to carry enormous loads. Careful tests 
 of isolated beams have been made in large numbers, which 
 204 
 
have proven with practical agreement the correctness of 
 the premises and rules of proportion as well as the re- 
 . suiting formulas obtained by the writer in the paper above 
 referred to. 
 
 On account of inquiries and criticisms that the writer 
 has received from different sources, it is thought to be in 
 place to amplify the former paper on beams and slabs by 
 what immediately follows. 
 
 X 
 
 Fig. 1. 
 
 Tests have shown that rods of a greater diameter than 
 about i -200 of the span are apt to pull out of the concrete 
 without breaking, on account of the lack of length in con- 
 crete to grip the metal effectually. Other tests have shown 
 that beams having a greater depth than one-tenth of the 
 span and containing horizontal rods at the bottom, or 
 having rods turned up at the support and not anchored at 
 the ends, will fail when loaded to destruction, approxi- 
 mately as per sketch Fig. I. This demonstrates the in- 
 ability of the concrete in beams so designed to carry the 
 end shear, vertical and horizontal (which combine in the 
 diagonal line in the figure), when the depth exceeds one- 
 tenth of the span. 
 
 On the location of the neutral axis, theoretical methods 
 of determining its position by the relative moduli of elas- 
 ticity of steel and concrete are unsatisfactory, on account 
 of the wide variation in the modulus of elasticity of con- 
 crete as determined by compression tests. There is, how- 
 ever, a more direct method of locating this axis, and one 
 which gives more concordant results, namely, by measur- 
 ing the relative extension and shortening of the lower and 
 upper fibres in a beam under test. In a letter replying to 
 a critic on this phase of the subject the writer gave the 
 205 
 
following defense of his position, which is here repeated 
 to make this paper complete for reference: 
 
 "In Engineering News, July-December, 1904, pp. 124- 
 125, Prof. Talbot gives plottings of the position of the 
 neutral axis. For 1.39 per cent reinforcement the distance 
 from top of beam is almost exactly 50 per cent of the depth 
 from top of concrete to steel. For 0.97 per cent it is about 
 0.42 of the same depth. Prof. Talbot gives this formula 
 for finding the position: k = 0.26 + 0.18 p, where k is the 
 fraction of the depth from top to neutral axis and p is 
 the percentage of steel. For 1%. per cent this would be 
 0.485 of the depth from top of concrete to steel. Prof. 
 F. E. Turneaure in Engineering News, July-December, 1904, 
 p. 215, says: The diagrams show the neutral axis to lie 
 at first very near the center of the concrete beam. As the 
 cracks develop it moves gradually nearer to the compres- 
 sion side.' " 
 
 On the proper percentage of steel the writer's paper was 
 also criticised by the person to whom the reply in the last 
 paragraph was directed. This critic stated that 1% per 
 cent is too large a percentage of steel. This criticism is 
 correlative with the one on the location of the neutral 
 axis. A higher location of that axis means a less per- 
 centage of steel, since it affords a larger lever arm or 
 effective depth in the resisting moment. The writer's reply 
 to this criticism was as follows: "As to i% P er cen t being 
 too high, I quote from Prof. A. N. Talbot, in Engineering 
 News, July-December, 1904, page 125 : Tor 1:3:6 
 concrete, reinforcement as high as i l /2 per cent for steel 
 of 33,000 Ibs. per sq. in. elastic limit * * * may be used 
 without developing the full compressive strength of the 
 concrete.' " The proportions of concrete that I recom- 
 mend are I : 2 : 4, a much stronger concrete, generally, 
 than I : 3 : 6; it would allow a greater percentage of 
 steel. Again, to quote Prof. W. Kendrick Hatt, in "En- 
 gineering Record," Vol. 51, page 545: "In the writer's 
 tests of beams under a center load 2j4 per cent of steel 
 206 
 
failed to develop the crushing strength of the concrete." 
 In Engineering News of Feb. 15, 1906, page 170, Mr. J. J. 
 Harding states that for steel of an elastic limit of 35,000 
 Ibs. he would use between I and iJ4 per cent of the area 
 of the concrete. Mr. T. L. Condron, in a paper read be- 
 fore the Western Society of Engineers, March 15, 1905, 
 says : "For extra strong concrete of about I of cement, 
 2 of sand and 4 of broken stone, the percentage of rein- 
 forcement may be increased to 1.25 per cent." (This in a 
 discussion of 202 tests.) 
 
 The writer has been asked why he does not use the floor 
 slab in connection with the beam as top flange, making a 
 tee beam out of it. The buckle plate in a steel floor would 
 not be used as top flange of the floor beams, though it may 
 be secured firmly to the beams; and there is no good rea- 
 son for using the concrete-steel floor slab as part of the 
 beam. The slab is spread out too much for a proper dis- 
 tribution of the stresses, and it may have holes cut into it 
 for pipes, etc., thus destroying its value as beam flange. 
 Again, to include it in the calculations would add largely 
 to the percentage of steel in the lower half of the rectangle 
 of the beam. The rectangle of the concrete should not be 
 called upon to take care of more than about 1^4 P er cent 
 of steel. Practically the only saving effected by counting 
 in the slab is in the amount of concrete in the lower part 
 of the beam. The concrete is needed there to protect the 
 steel against corrosion and fire, and generally to give width 
 enough to the beam to take care of the horizontal shear. 
 
 The subject of the limiting load that a concrete-steel 
 beam of the proportions given in the former paper may 
 carry may be amplified as follows : Assuming the neutral 
 axis of a beam to remain in the middle of its depth for 
 safe loads, it is seen that the safe resisting moment of the 
 beam is directly proportional to the amount of steel. For 
 steel in less amounts than 1^4 P er cent tne stress in the 
 concrete is less than 2,000 Ibs. per sq. in. at 40,000 Ibs. 
 per sq. in. on the steel, but cases may arise where it is 
 207 
 

 more economical to increase the relative amount of con- 
 crete. If the depth of a beam be doubled, its resisting 
 moment per foot of width will be four times as great, 
 assuming that the steel is still i^4 per cent; that is, that 
 the steel is doubled also. Now, if the amount of steel in 
 the beam of double depth be divided by two, the resisting 
 moment will be one-half as great. In other words, if the 
 same rods be used in a beam of twice the depth, the re- 
 sisting moment is doubled. The weight of the concrete 
 and the depth of the beam are, of course, twice the values 
 in the original beam, and these may be objectionable, when 
 the double strength could be obtained by using a beam 1.4 
 times as deep, with i^4 per cent of steel. However, where 
 a large increase in depth and weight of concrete are not 
 objectionable, the limiting ultimate load of 4,080 Ibs. per 
 sq. ft. on the top surface of the beam may be increased 
 without necessitating the curving up and anchoring of 
 some of the rods. Thus, if the limiting beam of one-tenth 
 of the span be doubled in depth, with the same steel, it 
 will have twice the strength and also twice the shearing* 
 area at the ends; hence it will have twice the ultimate 
 capacity. In the foregoing the ratio in depth of one to 
 
 two is taken to simplify the discussion. Any other relative 
 
 
 
 :cpi anil 
 ad* 
 
 representing Grip or Adhesion of Pod 
 of Moments 
 
 
 . 
 
 depths could be taken, and it would be found that starting 
 
 with any given beam having 
 
 208 
 
 per cent of steel the 
 
strength of a deeper beam of the same width with the 
 same steel rods, placed l /% of the depth from the bottom, 
 will be directly as the depths. 
 
 DESIGN OF COLUMN AND WALL FOOTINGS. 
 In proportioning concrete-steel footings the same prin- 
 ciples of design hold; the beam, however, is a cantilever 
 and not a simple beam. 
 
 Given a wall footing with a projection p and an upward 
 pressure of the soil of S tons per square foot; in order 
 to have shearing area at the ' edge of wall to take the 
 upward pressure on the projection p, at 40 Ibs. per sq. 
 in. on the gross area, we have 
 
 144 
 or h = .35 /> S ................... (i) 
 
 That is, for every ton of soil pressure per square foot 
 there must be a height h of 0.35 times p. Square rods 
 seem to be the most suitable for footings. For the size 
 of rod, in order to have 50 diameters of the rod in con- 
 crete at the point of maximum stress it is necessary to 
 use rods of a diameter not greater than 1-50 of the pro- 
 jection p. The curve of moments and of stress in the rods 
 is a parabola which lies at all points within the straight 
 line representing the adhesion or gripping of the rod by 
 the concrete. Hence p need be no greater than 50 d. As- 
 sume that 
 
 P = 50 d ......... ......... (2) 
 
 and that the stress on steel is 12,500 Ibs. per sq. in. The 
 amount of stress on the concrete will be the same as that 
 on the steel, hence we may write for the allowed moment 
 on the section x inches in width and h inches in depth, 
 
 M=12,SQO d 2 X =8,854 d 2 h % 
 24 
 
 But h .35 p S, whence M = 3,099 p d 2 S inch-lbs. 
 For the upward pressure of S tons per sq. ft. we have 
 
 209 
 
Equating these two values of M and using for p its value 
 
 50 d we have ^ W 
 
 x = 8.93 d, or say 9 d ...... ........ ....(3) 
 
 Hence for any upward pressure the same rods would 
 be used, having a diameter 1-50 of p and spaced 9 times 
 their diameter apart. Only the height h would vary for 
 different earth pressures, as per equation (i). 
 
 The foregoing does not take into account the stress on 
 the concrete, but we have seen that when the steel does 
 not exceed i% per cent of the concrete the stress in the 
 concrete will not be excessive. When the steel in this foot- 
 ing = i% per cent of the concrete, 
 
 =8.89 </or 
 
 50 
 
 This would mean an earth pressure of only about a half 
 a ton per square foot. Hence for all practicable earth 
 pressures the amount of concrete is ample. , ' * 
 
 In square footings for columns the corners will have a 
 projection 1.4 times that of the sides. The height h 
 should be made 1.4 times that obtained by equation (i) 
 using the projection at the side. Some rods should be 
 laid diagonally, as shown in Fig. 3. 
 
 to ii Fig - 3 - 
 
 If cinder concrete be used in the wall footing, at 25 
 Ibs. per sq. in. shear on gross area, we have 
 
 p = 83 d (4) 
 
 h = .&Sp (5) 
 
 x = 8.5 d, (6) 
 
 210 
 
For a plain concrete footing in stone concrete, allowing 
 40 Ibs. per sq. in. as safe modulus of transerve strength 
 we have for the bending moment under edge of wall 
 2,000 3^ f* 
 144" 2 
 
 and for the resisting moment 52-1" both on a rectangle h 
 
 6 ' 
 
 inches deep and one inch wide. Equating these we find 
 the following to be very nearly true: 
 
 S p* = h* (7) 
 
 For a plain cinder concrete footing at 20 Ibs. per sq. 
 in. safe modulus of transverse strength, similarly we find 
 
 2$ p* = h 2 (8) 
 
 By the .foregoing we may obtain the relative cost of 
 footings plain and reinforced. Thus at two tons per sq. 
 ft. earth pressure, by eq. (i) h =. .7 p (reinforced) and 
 by eq. (7), h = 1.4 p (plain). By comparing the cost of 
 the steel reinforcement with that of the additional excava- 
 tion and concrete the relative costs of the plain and rein- 
 forced footings may be found. 
 
 DESIGN OF COLUMNS. In the design of concrete 
 columns reinforced with steel it is essential to keep in 
 mind the rational use of steel as a reinforcement in con- 
 crete, namely, to take tensile stresses. When a prism is 
 compressed longitudinally, its diameter is increased, hence 
 the outer fibers are put under annular tension. Hoops or 
 211 
 
spirals bedded near the surface of a circular column will 
 [ resist this tension and relieve the concrete. Hoops would 
 have to be welded into solid rings to be of use, but a spiral 
 may be used in long lengths. M. Considere in a series 
 of tests on hooped concrete columns found that they ex- 
 hibited great strength against compressive loads. They 
 also showed regularity in the matter of failure. Where 
 a plain concrete column would break suddenly without 
 warning, a hooped column would hold together after cracks 
 had shown partial failure to have occurred. These are 
 desirable qualities in any kind of construction. Columns 
 reinforced with longitudinal rods only did not show much, 
 if any, advantage over plain columns. Longitudinal rods, 
 however, are very useful in connection with a coil to 
 space the loops and to tie the concrete together longi- 
 tudinally, also to assist in resisting flexure in the column 
 due to eccentric or horizontal loads. 
 
 It may be shown by a little computation that the area 
 of metal required at a given unit stress to contain the liquid 
 contents of a cylinder by resisting the bursting pressure is 
 double that required to support the same load if the 
 cylinder acts as a column. M. Considere found by the 
 formulas for earth pressures that a shell filled with sand 
 is 2.4 times as effective to sustain the load as it would be 
 in the form of a column, at the same unit stress, and his 
 experiments along that line confirm his calculations. This 
 
 would mean that the lateral pressure of the sand is 
 
 4. o 
 
 times its longitudinal pressure. If, then we treat the 
 disintegrated concrete, at failure, as a substance whose 
 
 pressure against the spirals is -~ t i mes that of a liquid 
 
 confined in a cylinder, we may arrive at the tension on a 
 spiral. In the tests above referred to some very high unit 
 loads were shown at failure, while some of the tests 
 failed between two and three thousand pounds per square 
 inch. While the hoops or coils may hold the disintegrated 
 concrete together and show high unit loads before ulti- 
 212 
 
mate failure, the nature of the material as commercially 
 made does not justify a higher safe unit load than about 
 550 Ibs. per sq. in. The concrete between the spirals is 
 in no better shape to resist compression than that in a 
 beam. Using this unit load in short columns (under ten 
 diameters in length) we have for our effective liquid 
 pressure 550 -f- 4.8 =115 Ibs. per sq. in. 
 
 Let D = outside diameter of column and 1 /%D = pitch 
 of coil, in inches. 
 
 The tension on a coil = 
 
 
 
 115X X D=7.2D 2 . 
 
 2 8 
 
 Allowing 12,500 Ibs. per sq. in. on the steel we have for 
 square rods of diameter d inches 
 
 12,500 d 2 = 7.2 D 2 . 
 
 Or, d ~~]& D nearl y- 
 
 If the diameter of coil be made ^ that of the column 
 and that of the steel be made 1-40 of the same the stress 
 on steel will be practically 12,500 Ibs. per sq. in. 
 
 It is recommended that round or octagonal columns be 
 used and that the full area of the circle be included as 
 taking the load, also that square rods be used having a 
 diameter one-fortieth that of the column in a coil with a 
 pitch one-eighth that of the column. Where 1-40 D would 
 give an odd figure the nearest sixteenth or eighth may be 
 used and the pitch made five times as great. 
 
 In proportioning the longitudinal rods we may, in order 
 to establish a rule for their size, follow the method em- 
 ployed by Marsh in "Reinforced Concrete" and allow 
 them to take the outward force of the concrete between 
 the spirals. If we assume eight square rods placed verti- 
 cally inside of the coil, their clear span is 
 
 lT~""4lT~~~T(f' 
 
 The outward force from the 115 Ibs. per sq. in. of assumed 
 218 
 
liquid pressure is 115 X r D -+- 8 per inch. Being 
 fixed ended their moment is 
 
 UoXx. 
 
 Equating this to 12,500 d' z -f- 6, the resisting moment of 
 square rods of a diameter d\ we obtain 
 
 d<=^. 
 
 38 
 
 This is close to one-fortieth of the column diameter; 
 ice eight rods of the same diameter as that used in 
 
 le coil may be placed on the inside of the coil and wired 
 to the same. Where a coil ends the next should lap not 
 less than half a coil, which would be about 55 diameters. 
 
 For columns more than ten diameters in length it is 
 recommended that smaller unit loads be used, down to a 
 minimum of 370 Ibs. per sq. in. at 25 diameters. They 
 should not be any more slender than one-twenty-fifth of 
 the length. Between 10 and 25 diameters the allowed unit 
 pressure would be found by the following formula: 
 
 />=670-12 -^ 
 
 where p pressure per square inch, 
 / = length in inches, 
 
 D = diameter in inches. 
 
 It is recommended that the same reinforcement be used 
 in all columns of a given diameter, so that flexure will 
 be taken care of in long columns. 
 
 THE DESIGN OF CONCRETE STEEL BEAMS AND 
 SLABS 
 
 Sir: Referring to the papers by Mr. Edward Godfrey, 
 published in your issues of March 15 and July 12, I con- 
 tend that the formulas and rules given by Mr. Godfrey 
 are not sanctioned by practice. 
 
 Tests have shown that the adhesion between steel and 
 concrete decreases with the diameter of the rods embedded 
 
(Service Francais des Phares et Balises, etc), and fol- 
 lowing the rules given by Mr. Godfrey, to use rods of a 
 diameter no more than 1-200 of the span of the beam, the 
 designer will, in many cases, get too small rods. For| 
 example, for a beam of a span of 6 ft. the rods are to bej 
 
 .. 
 
 A good designer will never use M-in. rods in a beam. 
 Rods for beams especially should have sufficient stiffness 
 not to bend at many points under the load of the concrete. 
 If too small rods are used it will be very difficult to assure 
 their distance from the bottom. To choose the proper diam- 
 eter of the rods in each case the designer should have had 
 practical experience; otherwise he may sometimes choose 
 rods not easy to handle and which will not always allow 
 him to get into the work the reinforcement made with a 
 pencil on drawing paper in the office. 
 
 As for the space between the rods, the rule given by Mr. 
 Godfrey will induce the designer to use too large beams. 
 In such beams longitudinal cracks occur between the rods. 
 
 Stirrups are very useful and increase the strength of the 
 beam. Well designed beams reinforced with stirrups will 
 not fail as shown by Mr. Godfrey on the sketch on page 
 30 of Engineering News of July 12, though the height 
 be greater than i-io of the span, and by the by, I would 
 ask Mr. Godfrey why, in the example given by him (Eng. 
 News, March 15), he does not follow his own theory, 
 assuming for the main girder of a span of 20 ft. a depth 
 of 32 ins. instead of i-io X 240 = 24 ins. As for the 
 economy of beams designed according to the rules given 
 by Mr. Godfrey it seems to me to be very problematical. 
 A steel area of i% per cent may be, when the depth and 
 width of the beam are increased beyond certain limits, 
 too expensive for the purpose. To get a good idea about 
 the cost of reinforced beams I would suggest that the 
 211 
 
weight of the steel be given in pounds and the amount of 
 concrete in cu. ft. Very truly yours, 
 
 Michael Morssen. 
 38 West 26th St., New York City, July 15, 1906. 
 
 THE DESIGN OF REINFORCED CONCRETE BEAMS 
 
 AND THE LOCATION OF MAXIMUM 
 
 MOMENT IN A FOOTING 
 
 Sir: The writer has followed with much interest the 
 development of a theory of reinforced concrete design as 
 i presented by Mr. Edward Godfrey, and the various com- 
 I ments and criticisms thereon by other engineers. That 
 this is the writer's first participation in the discussion 
 is due to the fact that he disagrees so entirely with Mr. 
 Godfrey's fundamental assumptions that there is no pos- 
 sibility of carrying on a reasonable controversy. As 
 stated in the columns of this paper, and elsewhere, the 
 writer believes that reinforced concrete should be designed 
 for the actual loads to be carried, the factor of safety 
 being obtained by assigning allowable working stresses 
 to the concrete and steel respectively. Where the distance 
 of the neutral axis from the compression surface of a 
 beam or slab is introduced in a formula, the value used, 
 in the writer's opinion, should be that which exists under 
 the working load, when the unit stresses in concrete and 
 steel do not exceed their allowable limits. All authorities 
 seem to agree that, even for the same beam or slab, the 
 neutral axis is in an entirely different position under 
 the breaking load. Without going into the question of 
 formulas at all, there would seem to be no reason why 
 reinforced concrete should not be subjected to the same 
 rules as those which govern designing in other materials. 
 These require the stresses under actual working load to 
 be determinate, and that they shall not exceed the allow- 
 able values prescribed for each kind of material. No 
 design that has not been made on this basis can comply 
 
 216 
 
with building laws, architects' specifications, and the like, 
 which almost invariably express their requirements in the 
 form of allowable working stresses. It should be apparent 
 that no one formula, involving such variable quantities as 
 the coefficient of elasticity for concrete in compression, and 
 the distance of neutral axis from compression surface, can 
 or should be used for both ultimate and working loads. 
 Let us say, for example, that a beam has been designed 
 by such a formula to fail at four times the working load, 
 and that the maximum compression in concrete at the 
 breaking load is 2,000 Ibs. per sq. in. Does anyone sup- 
 pose that under the working load the maximum 
 compression in the concrete is necessarily one-fourth 
 of 2,000, or 500 Ibs. per sq. in.? It may be 
 more or less, according to circumstances, and yet how 
 few adherents of this method re-compute their designs 
 to ascertain the actual maximum working stresses, and to 
 make sure they do not exceed the law or the specifications. 
 Many would not know how to re-compute them, since 
 their favorite formula would have to be altered by the 
 substitution of a new, and higher, elastic coefficient for 
 concrete, and a new, and greater, distance of the neutral 
 axis from the compression surface. 
 
 In regard to the percentage of steel to be used, the writer 
 has always maintained that this is a question not only 
 of structural efficiency, but also of economy of cost and 
 architectural restrictions and requirements. We know that 
 in every member subjected to pure transverse bending, the 
 total compressive stress on one side of the neutral axis 
 must equal the total tensile stress on the other side. (Re- 
 markable as it may seem, the writer has heard this well- 
 known fact denied by men in very responsible positions.) 
 There must, therefore, be a certain ratio of steel area in 
 tension to concrete area in compression (neglecting the 
 concrete in tension) which under working loads will give 
 the maximum allowable intensities of stress in each ma- 
 terial. This is the structurally economic ratio. If a 
 greater percentage of steel be used, the maximum allowable 
 217 
 
intensity of compressive stress in the concrete becomes the 
 factor which fixes the resisting moment, and hence the 
 working load. Under this same load, the intensity of 
 tensile stress in the steel will not attain its allowable 
 maximum working value, and the design will be structur- 
 ally uneconomic. But for easily conceivable reasons the 
 price of concrete may be very high, and that of steel very 
 low, or again, architectural peculiarities may have limited 
 the size or shape of the beam or slab. Under such con- 
 ditions, the higher percentage of steel may give the great- 
 est economy of cost, and the man who clings to a hard 
 and fast percentage throughout his designing will be at a 
 serious disadvantage. 
 
 The writer believes that concrete engineers will be almost 
 unanimous in opposing Mr. Godfrey's statement that the 
 slab, for a certain width on each side of the beam at any 
 rate, should not be considered as part of the compression 
 flange of the beam, if the concrete is deposited simul- 
 taneously and shearing stresses provided for in the design. 
 The analogy, submitted by Mr. Godfrey in your issue of 
 July 12, of a buckle plate in a steel floor does not seem 
 to fit the case. If we may consider the table of a steel 
 T-beam, whose width is generally more than ten times 
 the thickness of the stem, as part of the beam, it would 
 not seem unreasonable to consider a width of slab equal 
 to ten times the width of the concrete beam, as an integral 
 part of such beam. 
 
 From the foregoing remarks, it should be evident that 
 the writer must forbear discussing Mr. Godfrey's mathe- 
 matical deductions, since there is so great a difference of 
 opinion at the very start. One point will be mentioned 
 in regard to footing design. It is the writer's belief that 
 where a cap stone or column base is superimposed on a 
 footing slab, the maximum bending moment in the slab 
 occurs at the center. To compute the slab as a cantilever 
 whose length equals the projection beyond the cap stone, 
 requires that the cap stone itself should be strong enough 
 to take at its extreme edge the entire upward pressure on 
 218 
 
the projection. As such is seldom the case, the writer be- 
 lieves in using the old reliable formula: 
 
 M=JL(l-a) 
 
 for the bending moment at the center of the footing, P 
 being the column load, / the length of footing and a the 
 length of cap stone or column base. The reinforcing bars 
 are arranged exactly as a grillage of iron beams would 
 be, the strips running perpendicular to each other. In 
 fact, a reinforced footing may be economically designed 
 in practically the same manner as an I-beam grillage, the 
 only difference being that the successive tiers are all in 
 the same plane instead of being superimposed one above 
 the other. 
 
 Before closing this letter, the writer wishes to acknowl- 
 edge the fact that it does not refute Mr. Godfrey's theories. 
 As previously stated, it is impossible to debate the matter 
 from two such entirely different points of view, and like 
 the closing addresses of two opposing lawyers before a 
 jury, these letters mean but little until the verdict is 
 rendered by the readers of Engineering News. Respect- 
 fully yours, 
 
 John Hawkesworth. 
 
 loo W. Both St., New York, July 27, 1906. 
 
 . 
 
 Sir: I beg to thank you for the opportunity to reply 
 to the letters of Mr. Michael Morssen and Mr. John 
 Hawkesworth. ? 
 
 Mr. Morssen says that the formulas and rules given 
 by me are not sanctioned by practice. My purpose in 
 writing was largely to show 1 that these rules in particular 
 are overlooked in practice. Theory and practice must go 
 hand in hand; each needs correction from the other. No 
 system of construction was ever perfected by theory alone, 
 and none was every perfected by practice alone. Practice 
 has made many test-beams with short thick rods, and 
 these rods pull out of the concrete just as theory, or the 
 219 
 
rule given by me, would predict. This kind oi practice 
 is wasting steel that cannot develop its strength. Practice, 
 of a construction in its infancy, is not a competent witness, 
 where alleged improvements on itself are concerned. . 
 
 Mr. Morssen makes an indefinite assertion to the effect 
 that the adhesion between steel and concrete decreases 
 with the diameter of the rods embedded, and he cites 
 French authority to back his statements, to which I have 
 not access. No one will deny that the adhesion decreases 
 with the diameter of the rods embedded. The tensile 
 strength of the rods decreases with the square of the 
 diameter of the rod embedded. Will Mr. Morssen assert 
 that one rod i-in. square and embedded 12^/2 ins. in con- 
 crete will hold with greater force than sixteen separate 
 rods 54-i n - square embedded the same distance? The 
 common standard of adhesion or grip of plain rods is 
 the amount of area in contact with the concrete, and a 
 simple calculation will show that rods of different 
 diameters, in order to have the area in contact in propor- 
 tion to their tensile strength will be embedded a given 
 number of diameters. While it is admitted that the unit 
 value of the adhesion is variable, as the other qualities of 
 concrete are also variable, it is generally considered that 
 a rod embedded 50 diameters in concrete will develop its 
 full strength, or at least its elastic limit, if the rod be 
 surrounded with a thickness of concrete equal to several 
 times its diameter, the concrete having set in the air. 
 
 Mr. Morssen gives an example of a "beam" of 6-ft. span. 
 If the span were only 6 ft., would not a slab be in order? 
 He says a good designer will never use 3^-in. rods in a 
 beam. As I have used 2i-in. rods in the design of a slab 
 I will refrain from answering this. 
 
 I have no apology to make for the contention that the 
 proper design of reinforced concrete demands that the 
 steel be well distributed and of comparatively small diame- 
 ter, rather than being concentrated in elements of large 
 diameter. 
 
 Mr. Morssen says that the rule given by me will induce 
 220 
 
the designer to use too large beams, and that in such 
 beams longitudinal cracks occur between the rods. Can 
 he cite any experience or results of tests to substantiate 
 this? 
 
 Another dogmatic assertion of Mr. Morssen' s is that 
 well-designed beams reinforced with stirrups will not fail 
 as shown by me though the height be greater than one- 
 tenth of the span. I made tests on quite a number of 
 beams with stirrups in a finished building. The principal 
 mode of failure was just as my sketch shows. In Pro- 
 ceedings of the American Society for Testing Materials, 
 Vol. IV, p. 498, Prof. F. E. Turneaure describes some test- 
 beams which were 6x6 ins. and 60 ins. in span, rein- 
 forced with stirrups, spaced 3 ins. apart. On page 507 
 Prof. Turneaure says: "In but a few cases was the 
 failure free from the influence of shearing stresses, the 
 rupture usually occuring outside of the load and on a 
 diagonal line." These beams were one-tenth of the span 
 in height, and they had stirrups, and they failed about as 
 my sketch shows. 
 
 The reason I did not "follow my own theory," as Mr. 
 Morssen puts it in the girder of 2O-ft. span is because it 
 would give a clumsy beam to make its depth one-tenth of 
 the span. Further, I wanted to give an example of a 
 beam reinforced partially with rods curved up and anchored 
 for their full stress at the ends, another part of the theory. 
 
 Mr. Morssen says that a steel area of i^J per cent may 
 be too expensive for the purpose. Is it too much or too 
 little? (requiring too much concrete). I have been criti- 
 cised on the ground that it is too much from alleged 
 theoretical considerations. If Mr. Morssen will look up 
 practice as it is exhibited in descriptions of reinforced 
 concrete construction in the engineering papers, I think 
 he will find that leaving out the area of the slab, as having 
 no place in the beam, 2 or 3 per cent of steel is not 
 uncommon. 
 
 It is a pleasure to reply to a letter in the tone of that 
 
of Mr. John Hawkesworth, which you have kindly sub- 
 mitted to me. This letter is from one who is manifestly 
 a fellow seeker after the truth. A letter in a very dif- 
 ferent tone came to me recently, touching on some of 
 the same points mentioned in this one, from one who 
 has not the temerity to express publicly the final judg- 
 ment which he snapped on my theory and deductions. 
 
 The question of using a certain unit stress on the steel 
 and concrete and proportioning the beam on that basis, 
 or of using certain ultimate values and then allowing 
 as a safe load some fraction of the ultimate capacity is 
 too extensive to be discussed here as a general question. 
 When confined to a single case, as reinforced concrete, it 
 is merely a question of means; identical results may be 
 obtained by either means. 
 
 In reinforced concrete design it is convenient to use a 
 certain factor of safety based on the ultimate strength 
 of the parts because of the dissimilar materials dealt with 
 and the desirability of having the same relative strength 
 in each. In choosing an ultimate value for the steel I 
 did not lose sight of the actual amount of the safe value. 
 This is made clear by my first paper on the subject (Engi- 
 neering News, March 15, 1906), for I there criticise the 
 use of high elastic limit steel, because the resultant safe 
 load on the steel when the factor of safety is applied is 
 too great. Where is the difference between using 10,000 
 Ibs. per sq. in. on the steel and 500 Ibs. per sq. in. on the 
 concrete and using 40,000 Ibs. per sq. in. on the steel 
 and 2,000 Ibs. on the concrete with a factor of safety of 
 four ? 
 
 On the location of the neutral axis of a beam or slab 
 I have said something before in these columns. The case 
 is one that has entirely too many complications to be settled 
 by theory with no other data than the relative moduli of 
 elasticity of steel and concrete. The shrinking of con- 
 crete in setting is one of the complications. The tensile 
 strength of the concrete is another. Measurements to 
 locate the neutral axis of beams under test have shown 
 222 
 
that it is close to the middle of the depth of the concrete 
 beam under safe loads. I have taken it at the middle in all 
 of my formulas. Now taking the neutral axis in the center 
 of depth of beam and assuming that the intensity of stress 
 in concrete varies uniformly from the neutral axis up, 
 there remains but one factor to fix the percentage of steel, 
 namely, the relative unit stress on concrete and steel. 
 If this is as I to 20 the percentage must be iJ4- This is 
 very simply found by the principle which Mr. Hawkes- 
 worth states and which I have given in both of my papers, 
 namely, that the amounts of stress in steel and concrete 
 must be equal. Any greater percentage of steel in a 
 rectangular beam means a greater stress, relatively, on the 
 concrete. Any less means a greater relative stress on the 
 steel. 
 
 As to the floor slab acting as a T-beam: It would of 
 course be allowable to use a part of the floor slab, pro- 
 vided it was placed at the same time as the beam, and 
 provided the owner were forbidden to cut holes in the 
 slab, as he might think he had a right to do. However, 
 the T-beam method can only show to its credit a saving 
 of concrete around the reinforcing rods, just where the 
 concrete is needed to protect and grip the steel and to 
 transfer the shear. I tested some beams in a building 
 that were 3 ins. wide and were reinforced with i^-in. 
 square rods. Is this enough concrete to protect and grip 
 a rod of this size or to take the horizontal shear? My 
 tests conclusively proved otherwise. 
 
 Mr. Hawkesworth criticises my mathematical deductions 
 on the wall footing, and states that where a cap stone or 
 a column-base is superimposed on a footing slab, the 
 maximum moment in the slab occurs at the center. A 
 reinforced concrete footing would probably be surmounted 
 by a concrete wall put in at the same time, and a column 
 base would probably have a plinth of concrete Upon which 
 it rests, instead of being placed directly on the slab. In 
 these cases the depth of beam would be augmented and 
 the tension on steel diminished toward the center. 
 
Mr. Hawkesworth gives an "old reliable" formula for 
 the bending moment at the center of a footing. It is 
 presumed that he does not mean that this formula ex- 
 presses the bending moment at the center of a column, as 
 this center is a vertical line and can have no section 
 modulus. And yet this is what his reasoning seems to 
 lead to. This is a formula for the bending moment in a 
 row of I-beams in a grillage, at the center plane of the 
 column or wall 
 
 Beams A in the accompanying sketch, at (a), could be 
 proportioned by this formula. Beams B could also be 
 proportioned by the same. If, however, the latter spread 
 out to the full width of the footing, those outside of the 
 column base would be absolutely useless. There is no 
 analogy between these steel grillage beams and the rein- 
 forcing bars as shown at (b). (I assume this is the 
 manner of reinforcing referred to by Mr. Hawkesworth. 
 My timid critic says this is the common way of placing 
 the rods.) It is not even approximately correct to use the 
 so-called old reliable formula. By that formula each set 
 of beams takes the entire reaction and transmits it to 
 the set above. If we assume that rods A in the reinforced 
 concrete footing take all of the reaction, we must also 
 assume that they give that reaction to such of rods B as 
 lie under the column base. But this puts excessive load 
 on those few rods, and leaves idle the rods B not under 
 the column base. On the assumption that both sets of 
 rods act together, necessarily more of the load must be 
 taken by the rods lying under the base, and the formula is 
 seen to be inapplicable. 
 
 224 
 
By the use of diagonal rods the upward force on the 
 footing at any part of the same is carried directly to the 
 base by the shortest route. Each part is taken care of, 
 and there is some excess of strength at the sides by 
 reason of the additional depth used in column bases over 
 wall footings. 
 
 The formula given by Mr. Hawkesworth, as applied to a 
 wall, is based on the assumption that the wall load is per- 
 fectly uniform on the slab. This would be true if the 
 wall were a fluid or yielding body that would take the 
 shape of the deflecting footing. But when the footing de- 
 flects, the tendency is to throw the load close to the edge 
 diminishing the bending moment. For all ordinary earth 
 pressures the depth of footing is a large fraction of the 
 projection beyond the wall. A considerable part of this 
 projection could be made in a plain concrete footing as- 
 suming a low modulus of transverse strength. It is legiti- 
 mate to make use of this surplus strength of the con- 
 crete to balance the small increase in the moment within 
 the edge of the wall, which an only partially correct theory 
 finds to exist. Yours very truly, 
 
 Edward Godfrey. 
 
 Monongahela Bank Bldg., Pittsburg, Pa., Aug. 10, 1906. 
 
 THE DESIGN OF REINFORCED BEAMS AND 
 SLABS 
 
 Sir : I beg once more to use the columns of your paper 
 to reply to the long and interesting letter of Mr. Godfrey, 
 published in your issue of August 23. In this letter Mr. 
 Godfrey repeats good and useful principles well known 
 by all proper designers in reinforced concrete as well as 
 by the writer. It is very old matter that theory and 
 practice must go hand in hand, that rods for reinforce- 
 ment should be embedded a given number of diameters 
 to develop their full strength and that the proper design 
 of a slab and beam demands that the steel be well dis- 
 225 
 
tributed and in small rods rather than being concentrated 
 in elements of large diameters. But repeating these prin- 
 ciples Mr. Godfrey does not say that he maintains again 
 his rules in their full conclusion as they are printed in 
 your issues and with which the writer does not agree. 
 These principles are (issue of March 15, pp. 291, 292) : 
 
 (1) The rod should be no more than 1-200 of the span. 
 
 (2) The maximum depth of a beam is 20 times the 
 diameter of the rod embedded or i-io of the span. The 
 maximum depth should be used only in extreme cases. 
 
 In your issue of July 12, p. 30, Mr. Godfrey says that 
 by his rules it becomes a simple matter to design beams 
 and slabs in this comparatively new combination of ma- 
 terial, which is to say that design will be much easier 
 than it was till now. This is not the writer's belief. The 
 examples given by the writer in his first letter (August 
 2) were only to show to what design these rules may 
 lead if the designer follow them literally. Good designers 
 who know their business will in the most cases not fol- 
 low these rules as their own author has done in his ex- 
 ample cited. For poor designers who overlook the funda- 
 mental principles stated above and who do not know much 
 about reinforced concrete, rules as these given by Mr. 
 Godfrey become a danger and make them advance from 
 bad to worse. Just because, as says Mr. Godfrey himself, 
 this kind of construction is in its infancy, the writer's 
 belief is that it will be a guess matter to give now rules 
 to govern the proper proportioning of the steel and the 
 limiting length of the span, etc. Nevertheless, papers as 
 these of Mr. Godfrey and very useful and interesting. 
 
 One point which seems to me to be overlooked by Mr. 
 Godfrey is the fact that reinforced slabs and beams are 
 in the most cases designed as continuous elements and 
 the rods of one slab or beam overlap the rods of the 
 next, and then the length of the rod embedded in con- 
 crete exceeds in many cases the length required by the 
 calculation though the diameter be larger than 1-200 of 
 the span. 
 
 226 
 
Mr. Godfrey criticises the writer's example with a beam 
 of a span of 6 ft., saying that a slab should be in order 
 for this span. I would answer that beams at a span of 
 6 ft. or less are often to be designed over openings and 
 have sometimes to carry large concentrated loads which 
 a slab would not do. 
 
 As to my so-called (by Mr. Godfrey) dogmatic asser- 
 tions about the failure of well designed beams, overlook- 
 ing laboratory tests with small elements, I would refer 
 Mr. Godfrey to the text-books of Christophe, p. 490 
 (French text) and of Prof. Morsch, "Der Betoneisenbau," 
 p. 121, etc., where the failure of beams is discussed, and 
 he will see that it is not only my own judgment. The 
 finished building test by Mr. Godfrey in which beams have 
 failed by shear under the test load (generally i l / 2 to 
 2 times the live load for which the floors are designed) 
 should be of a very poor design and for this reason can- 
 not be cited as reference. The writer has had the oppor- 
 tunity to assist in tests made in France (Paris) and in 
 Germany (Charlottenburg, near Berlin), and he himself 
 has made many tests on large elements and got other 
 results than those cited by Mr. Godfrey. The writer 
 believes that deep beams designed only for the bending 
 moment will fail by shear as well as beams of a small 
 height will do when they have to carry a concentrated load 
 near the support and the reinforcement was not designed 
 for the purpose. 
 
 To substantiate the assertion that in large beams longi- 
 tudinal cracks occur in the spaces between the rods, the 
 writer would say that an analogous fact occurs in slabs 
 reinforced in one way and to avoid these cracks additional 
 cross-rods are embedded. In some large beams the writer 
 has himself verified these cracks in cases in which special 
 arrangements, as little cross-bars or special U-shaped stir- 
 rups going under all rods were not provided. 
 
 As to the steel area to be used the writer knows that 
 sometimes beams are designed with a steel area of 2 per 
 cent or more and his idea was not so much to criticise 
 227 
 
this amount, as to give a suggestion that when speaking 
 about the cost the amount of concrete be given in cubic 
 feet and the steel in pounds per lineal foot of beam or 
 per square foot of slab. Very truly yours, 
 
 M. Morssen. 
 
 38 West 26th St., New York, N. Y., Aug. 26, 1906. 
 
 The author did not reply to the above from Mr. Morssen. 
 Of course if Mr. Morssen does not elect to accept simplified 
 assumptions, he does not come in the class to whom the 
 design of reinforced concrete beams is made a simple mat- 
 ter by those assumptions. Mr. Morssen begs the ques- 
 tion in citing continuous beams, where the rod passes 
 into the next beams. There are many beams made that 
 are not continuous, and, in any event, there must be an 
 end to a line of continuous beams. Further, a short beam 
 over a six-foot opening supporting a heavy concentration 
 would probably be isolated. If such a beam had thick 
 rods not positively anchored at the ends, it would be faulty, 
 and the rods would pull out before they received their 
 full stress, for the simple reason that they would not be 
 bedded deep enough in the concrete to have the necessary 
 grip. 
 
 It is a far cry from a slab not reinforced transversely 
 to a beam of width enough to keep the steel reinforcing 
 rods well separated. An isolated slab would not have 
 the tendency to crack longitudinally that there exists in 
 a slab built in a structure. So a beam of good width 
 would not have shrinking forces on each side of it tend- 
 ing to split it longitudinally. [AUTHOR.] 
 
 CONCERNING THE STRESSES DUE TO SHRINK- 
 AGE IN REINFORCED CONCRETE 
 
 Sir: In an article in Engineering News of March 15, 
 1906, on 'The Design of Concrete-Steel Beams and Slabs," 
 by Edward Godfrey, he says (first column, page 291) : 
 
 The fact that concrete in which steel is embedded has 
 228 
 
been stretched out in tests without cracking to elonga- 
 tions that would rupture plain concrete is evidence that 
 the concrete in setting has shrunk, thus putting the steel 
 under an initial compression which must be overcome 
 before any stretch occurs in the concrete. 
 
 Now it seems to me that when the steel is put under 
 compression by shrinking of the concrete, the latter is at 
 the same time put under tension, and any further load- 
 ing of the beam would all be carried by the concrete, 
 so that it would have to take all the tension until it has 
 stretched so far that all the initial compression has been 
 taken off the steel. 
 
 Edwin Squire. 
 
 Claremont, California, July 19, 1906. 
 
 The author did not make reply to the above. He sees 
 the force of Mr. Squire's argument. He is, however, still 
 of the opinion that the shrinking of the concrete in setting 
 has much to do with its integrity under stress. The tests 
 which have been heralded so widely in this country as 
 disproving Considered conclusion, that concrete with steel 
 embedded will withstand cracking when the calculated 
 stress in the steel is large, were made on beams that were 
 kept in water and thus prevented from shrinking. (These 
 tests were made by Prof. Turneaure. See Proc. Am. 
 Soc. for Testing Materials, Vol. IV.) It is possible that 
 the concrete, in the beam which sets in air and contracts, 
 takes more than its share of the stress, so that the tension 
 in the steel, and the consequent stretch, are not so much 
 as calculations show. It is further possible that between 
 a unit compression x in a steel rod and a unit tension y 
 the theory may not hold in its exactness that the dif- 
 ference in length is the same as that which would be pro- 
 duced by a unit tension of x plus 3; on an unstressed rod. 
 In any event practice and tests show that calculated 
 stresses in the steel in air dried beams up to 10 or 12,000 
 Ib. per sq. in. do not produce perceptible cracks. Excessive 
 shrinking is, of course, harmful. [AUTHOR.] 
 
 229 
 
ON PROPORTIONING THE REINFORCEMENT 
 OF CONCRETE COLUMNS 
 
 Sir: In your issue of July 12, 1906, Mr. Edward God- 
 frey treats at some length the question of design of rein- 
 forced concrete columns, and develops formulas for pro- 
 portioning the reinforcement based upon the theory that 
 the concrete at failure becomes a granular mass, whose 
 lateral pressure is I divided by 4.8 times that of a liquid 
 confined in a cylinder. He arrives at the conclusion that 
 in a circular column of diameter D the spiral rein- 
 forcement should be a square rod, whose side is equal to 
 1-40 D, the pitch of the coil equal to */6 D, and the longi- 
 tudinal reinforcement 8 square rods of the same dimen- 
 sions as the spiral. 
 
 It seems to the writer that your correspondent in his 
 fundamental assumptions and deductions therefrom has 
 been taking a "long shot." 
 
 The relation between the lateral and the longitudinal 
 pressure of a granular mass confined in a cylinder and 
 subjected to its own weight or to additional pressure, 
 bears very little resemblance to that of a fluid under sim- 
 ilar conditions, for the following reasons : In treating a 
 confined granular mass we are dealing with a substance 
 in which there is an appreciable friction between the 
 particles of its own mass, as well as a friction between 
 these and the walls of the confining cylinder. This is 
 obvious, for one has only to consider that a bucket full 
 of sand thrown out upon a board does not spread out to a 
 uniform depth, but remains in a more or less cone- 
 shaped pile, neither will it slide from the board until 
 the latter is tilted to a considerable angle. Owing to 
 these physical facts, when a granular mass is confined in 
 a cylinder its weight is supported partially by the bottom 
 of the cylinder and partially by the sides acting as a 
 column, while the sides are at the same time under ten- 
 sion due to the lateral pressure. 
 
 This action of granular masses confined in bins, and 
 230 
 
the relation of lateral to longitudinal pressure, have been 
 very thoroughly investigated by Mr. J. A. Jamieson, of 
 Montreal, and made the subject of a very complete paper 
 presented before the Canadian Society of Civil Engineers, 
 and later published by Engineering News (March 10, 
 1904). Mr. Jamieson found, for such granular masses 
 as wheat, corn, flaxseed, etc., that when no settlement of 
 the bin walls occurred, approximately only 20 per cent of the 
 confined mass was supported by the bottom of the bin, 
 while the remaining 80 per cent was supported by the sides 
 acting as a column; that the lateral (maximum) pressure 
 at any point was practically constant and equal to 6-10 
 of the vertical pressure when the height of the grain 
 column was equal to or exceeded about 4 times the 
 diameter of the base; also that it made little or no differ- 
 ence in these relations if the bin was round or square. 
 Among many experiments recorded by Mr. Jamieson was 
 one on dry sand, and it is interesting to note that he 
 found approximately the same results as for wheat; that 
 is, a ratio of lateral to vertical pressure of 0.65, and 
 81.5 per cent of the total weight carried by the sides of 
 the bin. 
 
 A very simple experiment in line with the above may 
 be performed by making a tube, say 10 ins. long and 2 
 ins. in diameter, from thin writing paper, placing it on 
 end and filling it with dry sand. When the sand within 
 is subjected to pressure, the first noticeable feature is a 
 buckling of the walls of the tube, generally about 1-3 the 
 height up from the bottom. Additional pressure causes 
 rupture, the resulting tear running parallel to the long 
 axis of the tube. If the length of the tube be made 20 
 ins., the diameter remaining the same, and the sand sub- 
 jected to pressure, there is a buckling of the walls of the 
 tube followed by a bending of the whole and a failure 
 near the center, the tear in this case being at right angles 
 to the long axis. In the first instance the walls acted as a 
 column until they failed (buckled), then ruptured under 
 a tensile stress such as would be caused by hydraulic 
 231 
 
pressure. In the second instance the walls failed by 
 buckling, then ruptured under the stress caused by the 
 bending moment at the center. 
 
 Sand confined in a cylinder can be made to withstand 
 enormous loads, limited only by the strength of the con- 
 fining cylinder. This is the principle of sand wedges used 
 in arch construction, and is well known. 
 
 If we are going to treat the reinforced concrete column 
 at rupture as so much disintegrated matter or as sand, 
 and from this assumption develop formulas for ascertain- 
 ing the dimension of steel spirals to withstand this dis- 
 integrating action, then there are more and different factors 
 to be considered than those used by Mr. Godfrey. In 
 view of Mr. Jamieson's experiments, quoted above, the 
 lateral pressure would be 0.60 of the longitudinal and 
 not 0.21 (i. e. I -f- 4.8) as stated by your correspondent. 
 That is, the lateral pressure is about three times as 
 great as he assumes. The matter of the walls (spirals) 
 carrying 80 per cent of the loading as a column is not taken 
 into consideration by him at all, and it seems to the writer 
 that it is radically wrong to apply to a concrete column 
 this theory of disintegration which logically demands that 
 the walls (or longitudinal reinforcement) take 80 per cent 
 of the imposed loading. To follow up this line of reason- 
 ing must induce one to dispense with the concrete alto- 
 gether and employ an all-steel column. 
 
 A mild steel rod in the form of a coil is metal not well 
 disposed to act as a column carrying loads, and experi- 
 ments on reinforced columns in which the reinforcing 
 is only spirals or hoops show a much larger degree of 
 compressibility under loading than columns in which longi- 
 tudinal rods of considerable size are employed. This is 
 well brought out in Mr. Howard's article in the issue 
 of Engineering News for July, 1906, in which he says, 
 "Hooped columns are a distinct group and decidedly more 
 compressible than the others." In the same article it is 
 clearly shown that hooping a column of 1-2-4 concrete 
 will add greatly to its ultimate strength, and sq will the 
 232 
 
addition of a fair amount of longitudinal metal (2.86 per 
 cent), while a combination of the two will further increase 
 the ultimate resistance under loading. A mixture rich in 
 cement and unreinforced (i of cement to I of sand) is 
 20 per cent stronger than a 1-2-4 concrete reinforced with 
 25 hoops and 4 angles, and considerably more rigid under 
 loading. In these tests on 1-2-4 rock concrete the hoops 
 were i l /2 ins. wide by */-in. (given as 0.12 in.) thick 
 spaced at various intervals. The smallest recorded num- 
 ber (13) increased the strength of the column 58 per cent 
 above that of the plain unreinforced piece, while the largest 
 number (47) increased the strength 274 per cent, raising it 
 to 5,289 Ibs. per sq. in. In the latter case the spacing 
 of the hoops was a trifle over 2^ ins., or the neat open- 
 ing between the hoops was 0.66 times the width of one 
 hoop. Mr. Godfrey's deductions that the diameter of the 
 square spiral rod should be 1-40 D, spaced l /% D, leaves a 
 clear opening of i-io D between the rods, which opening 
 is four times the width of the rod. This does not look 
 like metal well placed to confine a disintegrating mass. 
 
 In a reinforced beam we place the metal where it will 
 resist the tensile stresses, leaving the plain, unreinforced 
 concrete to take care of the compressive stresses of 500 
 ibs. per sq. in. or greater. It this is good practice (and 
 it is a common one) why should we design a column on a 
 basis of 550 Ibs. per sq. in. of compressive stress and 
 then reinforce it. In other words, unless we either figure 
 upon an allowable unit of compressive stress of much 
 greater amount than 550 Ibs., or assume that the longi- 
 tudinal reinforcement carries a portion of the imposed 
 load, then we have not reduced the size of the column 
 under that of one not reinforced, and have added largely 
 to its cost. It is the large size of columns (compared 
 with steel) that in actual practice makes them so objec- 
 tionable to many architects. This size can be reduced to 
 reasonable limits by using a concrete mixture rich in 
 cement, reinforced with spirals or hoops that form a close 
 enclosing mesh and longitudinals to whichjthev are firmly 
 
 233 
 
attached, assigning to the concrete a high compressive 
 unit of resistance and to the longitudinals a portion of 
 the imposed load, but not by the formulae and method 
 suggested by your correspondent. Very truly yours, 
 
 G. B. Ashcroft, 
 C. E. Assoc. M. Can. Soc. C. E. 
 
 Supt. Roman Stone Co., Ltd. 
 Toronto, Ont., Aug. 17, 1906. 
 
 THE DESIGN AND THE BEHAVIOR OF REIN- 
 FORCED CONCRETE COLUMNS 
 
 Sir: I have before me proof of Mr. G. B. Ashcroft's 
 letter in which he objects to my method of proportion- 
 ing a reinforced concrete column, and thank you for 
 the opportunity to reply to the same. The answers to 
 Mr. Ashcroft's objections are found partially in the papers 
 which he cites 'and partially in his own letter. 
 
 I have always considered the paper by Mr. J. A. 
 Jamieson on tests on grain bins as a very valuable con- 
 tribution to engineering knowledge. These tests were 
 made to determine the relation between the head of grain 
 in a bin and the horizontal and vertical pressures in the 
 grain, and were not made with a view of finding the 
 bursting pressure of a confining cylinder which has no 
 longitudinal strength. One experiment made by Mr. Jamie- 
 son on a cloth cylinder showed what one naturally would 
 suppose, namely, that if the walls can yield vertically the 
 grain itself will support all of the weight. In a steel 
 cylinder a large part of the weight would be carried by 
 the shell. A coil in a reinforced concrete column would 
 act like the cloth cylinder; that is, it would take none 
 of the load on the column. Unfortunately for column 
 investigators, Mr. Jamieson did not measure the lateral 
 pressure on the cloth cylinder. However, among his ex- 
 periments there is one which has a direct bearing on this 
 subject. The experiment referred to is one in which a 
 234 
 
bin having sides that could be raised and lowered was 
 filled. The pressures on the bottom and sides were 
 measured, and the latter was found to be about six-tenths 
 of the former, as stated by Mr. Ashcroft. Upon lowering 
 the sides all of the grain as well as the sides themselves 
 was supported on the bottom. Mr. Jamieson says (Eng. 
 News, March 10, 1904, p. 238) : 
 
 "On the bin being again lowered to its original position, 
 while no increase of lateral pressure was shown by the 
 side diaphragm, there was a very large increase of pres- 
 sure on the bottom diaphragm, or sufficient to cause the 
 water to flow out of the top of the 4-ft. gage glass tube, 
 which was not, therefore, long enough to record the pres- 
 sure; in fact, the total weight of the grain was then rest- 
 ing on the bottom diaphragm, and in addition the grain 
 was acting as a column to support the weight of the bin 
 itself." 
 
 Now the lateral pressure in this experiment at the bot- 
 tom of a bin 78 ins, high was .1894 Ib. per sq. in. This 
 is only one-twelfth of the vertical pressure instead of being 
 six-tenths. 
 
 In one of the experiments referred to by Mr. Ashcroft, 
 among those made at Watertown Arsenal, is one on a 
 column reinforced with wide bands. By my count these 
 bands comes within a half inch of each other instead of 
 ein inch. This column stood 5,289 Ibs. per sq. in. It 
 is safe to say that the concrete was in a state bordering 
 on disintegration under this load. The lateral pressure 
 on the bands could not have exceeded a force that would 
 stress the steel to its ultimate strength, and this will 
 give us a basis for determining that pressure. In the 
 2 ins. of a lo-in. column occupied by one band an equiva- 
 lent fluid pressure would be 2 X 5 X 5,289 = 52,890 Ibs. If 
 the net area of the band were an eighth of a square inch, 
 the unit tension on the basis of a liquid pressure would 
 be 423,000 Ibs. I do not know what grade of steel was 
 used, but if it were good for 80,000 Ibs. per sq. in. the 
 235 
 
lateral pressure could not have been as much as one- 
 fifth of the longitudinal pressure. 
 
 ^Mr. Ashcroft's advocacy of the closer spacing of rings 
 and of wide rings leads to the conclusion that the best 
 column is a steel tube filled with concrete. There is 
 no doubt that this would make a strong column, but it 
 is a composite column, with all that the term implies in 
 the way of uncertainty in the distribution of stress, and 
 not a reinforced concrete column. There are objections 
 to such a column for ordinary use that it is needless to 
 mention. 
 
 The objection to a flat bar in reinforced concrete is 
 that the holding power of concrete is due to its gripping 
 the steel, rather than mere adhesion. The concrete tends 
 to shrink away from the side of a broad flat bar, whereas 
 it grips firmly a small square or round bar. Further, 
 the concrete on the outside of a broad flat bar near the 
 surface may be easily knocked off. Some years ago I 
 observed some reinforced concrete beams in which the 
 reinforcement was a number of flats, which were brought 
 up and hooked over the flanges of steel beams. The con- 
 crete below the bars fell off in large chunks when the 
 forms were removed. 
 
 The objection to longitudinal steel in a column, that 
 is, to the counting upon it as taking part of the column 
 load, is that this, too, makes the column a composite 
 structure and not a reinforced concrete column. 
 
 I cannot see any objection to lack of rigidity, as it is 
 called, in a column, that is, to a column that will shorten 
 a proportionately large amount under load. Wooden 
 columns with a safe load of 1,000 Ibs. per sq. in. and E 
 = 1,000,000 will shorten three times as much as steel 
 columns at 10,000 Ibs. per sq. in. E = 30,000,000, but 
 wooden columns are not objectionable merely on this 
 account. In a beam rigidity is very essential, as the 
 deflection can be felt or readily measured; but a little 
 additional deflection in a column cannot be detected with- 
 out the most careful measurement. An explanation of 
 
 236 
 
the lack of rigidity in reinforced columns as observed 
 in the Watertown Arsenal tests is found in the tendency 
 of concrete to shrink in setting. It does not seem to me 
 to be necessary to assume that fissures occur, on this 
 theory, as suggested by Mr. Howard (in Eng. News, July 
 5, 1906). The tendency to shrink may be there and may 
 be offset partially by the steel embedded. The concrete 
 is then like a spring which is held from contracting quite 
 down to its normal length by the steel. Again the tend- 
 ency to shrink away from coils or hoops would make a 
 swelling out of the column (due to tne load) necessary 
 before the coil is brought into action. 
 
 Mr. Ashcroft says, "In a reinforced beam we place the 
 metal where it will resist the tensile stresses, leaving the 
 plain unreinforced concrete to take care of the compres- 
 sive stresses of 500 Ibs. per sq. in. or greater." This is 
 exactly what we ought to do with columns. A short 
 block one or two diameters in height could safely be 
 loaded to 500 Ibs. per sq. in., but a plain concrete column, 
 if loaded to this amount, is apt to break suddenly by 
 bulging or flexure. The coils and longitudinal rods are 
 used to overcome this weakness, just as the reinforcing 
 rods in a beam are used to overcome the weakness of the 
 beam in tension. The strength of the concrete in either 
 case is practically that of concrete in short blocks. 
 
 Confined in a cylinder, concrete (or even loose sand) 
 has a very great power for carrying loads ; but while this 
 fact is very useful in some lines it has little bearing on 
 reinforced concrete design. . 
 
 Has Mr. Ashcroft's experience with sand jacks shown 
 him that the sand issues from the gate with a pressure 
 approaching six-tenths of the unit load upon it? Would 
 he design the walls of the jack for this pressure? Yours 
 very truly, 
 
 Edward Godfrey. 
 
 Monongahela Bank Bldg., Pittsburg, Pa., Aug. 31, 1906. 
 
 [In connection with the explanation, above offered, of 
 the compressibility of concrete columns in certain cases, 
 
 237 
 
the old fallacy that two springs combined in opposition 
 are more sensitive than a single spring recurs to mind. 
 Really, the stiffness of two springs, whether in opposition 
 or in parallel, is the sum of their individual rigidities, as 
 a diagram will readily show. Now, applying this to the 
 reinforced concrete, we have the concrete in tension due 
 to shrinking, and the steel in compression to an equal 
 amount. The rigidity of the combination, that is, the 
 load required for unit compression, is just as great under 
 these circumstances as if both steel and concrete were 
 initially unstressed. The only case in which there is an 
 exception to this rule is when there is a certain range of 
 inelastic motion, or when the elastic system is changed 
 at a given period; the former is instanced by local crush- 
 ing at the bearing surfaces, the latter by loose fit of one 
 of the elements which operates to keep it free from load 
 until a certain compression is reached. Ed.] 
 
 A FURTHER NOTE ON THE ANALYSIS OF RE- 
 INFORCED CONCRETE COLUMNS 
 
 Sir: Referring to your comment on my suggested ex- 
 planation of the lack of rigidity in a reinforced concrete 
 column, in Engineering News of Sept. 6, I beg to suggest 
 further that the concrete is not in all respects like a 
 spring, but is restrained in the neighborhood of the steel 
 more than at other points. Suppose, for example, that 
 a column of concrete with a central longitudinal rod be 
 molded. In setting, the concrete will tend to shrink, and 
 near the outer edge of the column this shrinkage will 
 actually occur, in practically full amount. But near the 
 steel the shrinkage will be counteracted by the resistance 
 of the steel to compression, and only a small part of the 
 normal shrinkage will take place, resulting in longitudinal 
 tension in this zone of concrete, and longitudinal 
 compression in the steel. The end faces of the column 
 will, therefore, not be planes, but will be low at the per- 
 
 238 
 
iphery, while the end face of the steel rod will be the 
 highest point. Hence, when the column is put in the 
 testing machine for a compression test, the load on the 
 end blocks will be received by the steel and the imme- 
 diately surrounding concrete before the concrete away 
 from the steel receives its load. The concrete near the 
 steel would therefore be under greater unit stress, and 
 the apparent rigidity might be less than plain concrete. 
 The case of a spring was cited to show that it is not 
 necessary to assume that fissures exist where the concrete 
 is not shrunk down to its normal size. Yours very truly, 
 
 Edward Godfrey. 
 Pittsburg, Pa., Sept. 7, 1906. 
 
 The Designing of Reinforced Con- 
 crete Retaining Walls. 
 
 The lateral pressure of earth -is too uncertain to be 
 defined by any law, and hence a correct theory for pro- 
 portioning a retaining wall in the general sense of the 
 term is not possible. Some earths will remain vertical 
 for some time without any confining structure; some 
 will even stand tunneling without caving in. A board 
 fence will retain a considerable height of earth laid 
 against it for awhile. On the other hand, slips are liable 
 to occur in earth after it has stood for some time un- 
 supported. These often exert great force. 
 
 The lateral force of grain is, no doubt, nearly con- 
 stant for a given kind of grain under given conditions. 
 The same is probably true of sand, if one of the condi- 
 tions be a definite proportion, or the entire absence, of 
 moisture. But in the case of the substances generally 
 classed under the term earth there is, as intimated, a 
 variety of states, ranging from soft mud that will exert 
 a lateral pressure approximating a fluid pressure, to shales 
 that exert no active lateral pressure. A condition ap- 
 proximating a fluid pressure ought to be avoided in any 
 
good design by proper drainage. Two cases calling for 
 special exercise of judgment are (i) the one mentioned, 
 of shale, which is itself a sort of retaining wall of 
 little durability, and (2) a case where large slips are 
 probable, either due to an inclination of the under 
 lying rock toward the retaining wall, or to a heavy sur- 
 charge, that is, earth sloping steeply above the top of 
 the wall. 
 
 This paper treats of a wall to retain ordinary fill or 
 prevent natural earth from slipping. The most severe 
 test of a retaining wall is usually the freezing and thaw- 
 ing of the earth around it. The forces produced thereby 
 are quite indeterminate. They can, however, be largely 
 diminished by drainage. It has been found that masonry 
 walls having a base one-third the height of the earth 
 retained will resist these forces and retain any ordinary 
 earth with complete rigidity. That this relation between 
 the base and height agrees with the theory of earth pres- 
 sures commonly employed is shown by the following. 
 
 The theory referred to is based on deductions from the 
 assumed action of a granular mass having no cohesion 
 between its particles. It is found that the effect is 
 that of a wedge of the material sliding without friction 
 on a plane the slope of which bisects the angle of re- 
 pose of the material and the vertical back of the retain- 
 ing wall. It is customary in discussions on retaining 
 walls to treat the force due to this wedge as though it 
 were produced by a solid block with its center of pres- 
 sure at a distance of one-third of h from the base. The 
 calculations are simplified by treating it as a liquid pres- 
 sure, the weight of the liquid per cubic foot being a 
 certain fraction of the actual weight of the earth. This 
 fraction is equal to the square of the tangent of the 
 
 angle (Fig. i), a being the complement of the angle 
 
 of repose. 
 
 The angle of repose of ordinary earth is about 45, 
 half of its complement is 22^, and the square of the 
 
 240 
 
tangent of 22^ is .1716, or nearly one-sixth. Hence if 
 we ase the pressure of a liquid having a density one- 
 sixth that of earth we will have the effect of this lateral 
 pressure so far as horizontal forces are concerned. This 
 will neglect the vertical component of the force of this 
 sliding block. A small and uncertain amount of this 
 vertical component would act in friction on the back 
 of the wall; the remainder would be carried on the in- 
 clined surface upon which the block slides. As the 
 force of friction tends to give greater stability to the 
 wall, it is on the side of safety to neglect it. 
 
 Fig. 1. Diagram of Earth Pressure Against a Retaining 
 Wall with Vertical Face. 
 
 Now from Fig. i, if we take moments around X and 
 use as the weight of earth 100 Ibs. per cu. ft., and of 
 masonry 150 Ibs. per cu. ft., we have for stability the 
 following equation of moments: 
 
 from which we find 
 
 h = 3 b. 
 
 Hence, using only the horizontal forces and neglecting 
 adhesion or friction on the back of the wall, we find 
 that a wall having a height three times its base, which 
 is usually considered in good proportion for a retaining 
 wall, will be found to be stable against ordinary earth. 
 
 In retaining walls of reinforced concrete the earth 
 itself may be utilized to prevent the overturning of the 
 
 241 
 
wall, not by its uncertain friction or adhesion but by 
 its weight. 
 
 A form of reinforced concrete retaining wall coming 
 into use is composed of a front curtain wall and a bot- 
 tom slab, both reinforced with horizontal rods; wall and 
 slab are united by ribs at intervals. Fig. 2 is a modifi- 
 cation of that style of construction, by the addition of 
 steps at the junction of the front wall and the bottom 
 slab. The purpose of these steps will be made evident 
 further on. The ribs are spaced a fixed distance apart, 
 the same for all heights of wall. The design is to be 
 used only for walls having a base width of 5 ft. or 
 
 Pozfs"E' ' E>-fenct from Top 
 fff WaU to Toe: r 
 
 Fig. 2- Design for a Standard Re- 
 taining Wall of Reinforced Concrete, 
 for any Base not less than 5 ft. 
 
 (Dimensions of parts are given in 
 terms of width of base. Steel stress, 
 12,500 Ibs. per sq. in. Beam reinforce- 
 ment not to exceed l/ per cent.) 
 
 242 
 
more. The reason for the 5-ft. lower limit of base and 
 for the constant spacing of ribs will be shown in a later 
 paragraph. 
 
 In designs that have been illustrated in engineering 
 publications, two sets of rods are shown in the bottom 
 slab, one near the bottom of slab and the other near 
 the top, both spaced uniformly for the full width. The 
 writer believes this to be unnecessary and uneconomical. 
 The execution of the work is greatly complicated thereby, 
 and the forces are not present demanding this re- 
 inforcement. While it is true that this slab is contin- 
 uous, and while somewhat less moment is found by con- 
 sidering it as continuous, the purposes of good construc- 
 tion are better served by proportioning the slab for the 
 full moment as a simple beam and then adding some 
 short rods in the top flange running across the support 
 to relieve the concrete of tension. 
 
 The standard wall shown in Fig. 2 was evolved as a 
 result of investigation to determine the proportions of 
 a reinforced-concrete wall that would be stable against 
 earth pressure on the same basis as a solid masonry wall, 
 granting that the latter will be stable if made with a base 
 one-third of its height. Three walls were taken, having 
 bases 5, 10 and 15 ft. respectively, and heights 12, 24 
 and 36 ft. respectively, with other dimensions as given 
 in Fig. 2. The volumes per bay were found to be 96.6, 
 452.8 and 1,168.5 cu. ft. respectively. Solid masonry 
 walls of the same heights and having bases one- 
 third the height would contain 3.73, 3.39 and 3.14 
 times as much in volume of masonry respectively as the 
 concrete-steel walls; hence if reinforced concrete does 
 not cost more than three of four times as much as solid 
 masonry or plain concrete, the former is the more 
 economical in the form of retaining walls. The addi- 
 tional excavation for the wider base may enter as a fac- 
 tor in the relative costs. It is not the purpose to give 
 actual relative costs, but only to show that there is a 
 243 
 
large margin in favor of the reinforced-concrete retain- 
 ing wall. * 
 
 The centers of gravity of these three walls were found 
 to be 1.43 ft., 3.00 ft. and 4.66 ft. respectively from the 
 heel of wall. The respective volumes of earth over the 
 slab are 332.3, 1,377.2 and 3,206.3 cu. ft. The centers 
 of gravity of these volumes are located 2.96 ft, 5.97 ft. 
 and 9.01 ft. respectively from the heel of wall. The 
 moments of stability of these three walls, taken about a 
 point one-third of the base from the heel, were found 
 to be 39,599, 340,405 and 1,227,272 ft.-lbs. respectively, at 
 100 Ibs. and 150 Ibs. per cubic foot for earth and concrete 
 respectively. The earth load considered is that directly 
 over the bottom slab up to the level of the top of wall. 
 Assuming that the force of the earth back of the wall 
 is that of a liquid one-sixth of its density the weight of 
 a cubic foot of earth to balance the above moments would 
 be no, in and in Ibs. respectively. 
 
 One peculiarity respecting these three walls is that the 
 resultant center of gravity of earth and concrete is in 
 each case almost exactly in the center of the slab. This 
 makes it proper to assume that the pressure due to the 
 weight is uniformly distributed over the base, as shown 
 at a, Fig. 2, as the stiffness of the bottom slab is suffi- 
 cient to give this distribution. The reaction of the earth 
 under the slab will be uniformly varying from zero in- 
 tensity at the toe of wall to double the intensity 
 of the uniform load at the heel of the wall ? as at b 
 The difference between these sets of forces, or the forces 
 as shown at c, must be resisted by internal stresses in 
 the concrete. On the left half of the bottom slab the 
 forces are seen to be upward. If the construction were 
 a reinforced slab, it would require the principal rein- 
 forcement in the upper part. For simplicity of construc- 
 tion it is desirable to avoid this. The close proximity 
 of the vertical wall makes it possible to throw this force 
 directly into that wall by means of the steps at the junc- 
 tion of wall and slab. These steps could of course be 
 244 
 
replaced by a chamfer or slope, if the latter were found 
 to be simpler of construction. 
 
 On the right half of the bottom slab there is a vertical 
 load downward varying in intensity from zero at middle 
 to an amount at the edge of slab which may be taken as 
 the weight of superimposed earth and of the slab itself. 
 This is close to 250 X b ^ s - P er S Q- ft- Taking the effec- 
 tive span of the slab as 7^ ft. the bending moment on the 
 extreme right edge is 250 b X 7 T /^ X 7^ -^ 8 = x >75 8 b - 
 This is in foot-pounds per foot width of slab. 
 
 In order to give clearance for the angles shown in Fig. 2, 
 the steel rods are placed one-sixth of the depth of slab 
 from the bottom. Following the method employed by the 
 writer, and described in Engineering News, March 15, 
 1906, the effective depth of the slab is found to be 2/3 of 
 its depth. But as the depth of slab is 3/20 b, its effective 
 depth (that is, the distance from center of steel to center 
 of compression in concrete) is i/io b. For an area of 
 steel = A, in sq. in. per foot width of slab, and a stress 
 of 12,500 Ibs. per sq. in. we have an allowed bending 
 moment of 12,500 A X I / I ^ 1*250 A b foot-pounds. 
 
 Equating this to 1,758 b, found above, we have 
 A = 1.406. 
 
 This can be made up of four ^-in. diameter rods. It is 
 thus seen that for any size of retaining wall 5^-in. round 
 rods spaced 3 ins. apart will take the tensile stress in the 
 bottom slab at the extreme right edge. 
 
 When the area of steel does not exceed i% per cent of 
 that of the concrete in the slab (see article above referred 
 to) the stress on concrete will be within safe limits. It is 
 seen that the area A found above is \Y$ per cent of that 
 of a slab 12 ins. wide and 9.4 ins. deep. For a base of 5 ft. 
 the depth of slab is 9 ins.; hence a lower limit of about 
 5 ft. should be adhered to for this standard. For smaller 
 walls the thickness of parts for a wall of 5-ft. base could 
 be maintained and the span between ribs varied to suit 
 the bending moment found. Thus, for a wall having 
 2^-ft. base (one-half of the standard 5-ft. wall), the load 
 
 245 
 
on the slab will be approximately one-half of that on the 
 S-ft. wall. (The height of this wall would be 6 ft.) A 
 9-in. slab with the standard reinforcement will be good 
 for a span ^ "2" times the standard, or 10.6 ft, say 10 ft. 
 clear. 
 
 The span of 7 ft. in the standard wall is found as fol- 
 lows: Let s = clear span in feet. The end shear on one 
 foot of width of the slab is 250 b X Vz s := 125 b s. The 
 shearing strength of a slab 3-20 b feet deep and one foot 
 wide, at 40 Ibs. per sq. in. on the gross area is 
 3-20 b X 12 X I2 X 40 = 864 b. 
 
 Then from the equation 
 
 125 b s = 864 b, 
 we find s = 6.91 ft. 
 
 Since this remains true for all sizes of standard walls, 
 it is seen that the shear is taken care of also in walls of 
 less than 5 ft. in base, as the slabs will have a greater 
 relative depth than in the standard walls. 
 
 The reinforcement in front wall is found as follows: It 
 will be seen in the standard retaining wall that the depth 
 from top of wall to top of steps is i.gb. The intensity of 
 horizontal pressure is therefore 1.9 b X *~6 X IO ^ s - 
 per sq. ft. This gives a moment on a foot depth of wall 
 223 b ft. -Ibs. The moment of resistance of the con- 
 crete-steel slab, found as above, is 
 
 12,500 A X X =SM A b. 
 
 From 
 
 223 b = 833 A b, 
 we have A = .267 sq. in. 
 
 This would be made up by one ^-in. round rod for 
 every foot of depth of wall. This reinforcement is carried 
 up to the top of the wall and is used as indicated on the 
 lower portion of the wall and on the bottom, though theo- 
 retically less reinforcement would be required. The pur- 
 pose is to tie the wall together. 
 
 The rods in the rib act to tie together the bottom slab 
 
 246 
 
and the vertical wall, the manifest tendency being for 
 these to pull against each other. The chief use of the 
 concrete in the ribs is to protect these rods. It is essen- 
 tial that the rods have an efficient end anchorage, and 
 any other anchorage or bond can serve only a subsidiary 
 purpose. The line of cleavage in the rib may be im- 
 mediately above the bottom slab, and practically the whole 
 strength of the rod is needed at that plane. In the short 
 depth of the slab there is not length enough for even me- 
 chanical bond to take effective hold for the full strength 
 of the rods. Hooks or curves on the ends of rods have 
 not been shown by tests to be effective end anchorages. 
 Such a detail would not be accepted in structural steel work. 
 The use of plain round rods with thread and nut at end, 
 attached to a front-to-back angle in the bottom of the 
 slab, as shown in Fig. 2, seems to be the most economical 
 as well as the most effective means of meeting these con- 
 ditions. These angles may also act as anchors for the 
 horizontal rods, at ends of wall, if any such anchorage 
 is needed. 
 
 The angles serve to locate the rods properly and to hold 
 them in position against displacement during the placing 
 of the concrete. They also make it more difficult to omit 
 any rods and easy to detect any omissions. All of these 
 points are of great weight in construction where unskilled 
 labor is so commonly employed. 
 
 The rods in the rib take the downward force shown at c, 
 Fig. 2, the amount of which at the right edge is at a 
 rate per foot close to 250 b X 7 = !>75o b Ibs. On a re- 
 taining wall of 5 -ft. base the load in a foot is 8,750 Ibs. 
 At 12,500 Ibs. per sq. in. this would require four rods 
 ^-in. in diameter. For a 10-ft. base four n-i6-in. round 
 rods are required, etc. By giving these rods the same 
 horizontal spacing at bottom as those in the bottom slab 
 and varying the rate of spacing in the same manner, the 
 vertical load is taken care of. 
 
 These rods start vertical; hence the vertical load- 
 
 247 
 
measures their stress and not the component in a diagonal 
 direction. Their stress is not uniform throughout, but 
 they begin near the foot of the wall to transmit their stress 
 into the concrete to resist the upward thrust of the forces 
 on the left half of the base. Their radius of curvature 
 should not be less than about twenty times their diameter, 
 so that the unit pressure exerted by the side of rod on 
 the concrete will not exceed safe limits. (A square rod 
 curved to a radius twenty times its diameter will exert a 
 radial force on its side one-twentieth of the intensity of 
 its tension, which is the usual ratio between the allowable 
 stresses in steel and concrete. The use of sharp bends 
 in embedded rods is a structural fault often met with.) 
 
 The rods should have two nuts on the ends, so that the 
 end nut can be drawn to a tight bearing on the angle. 
 Horizontal rods should be spliced by sleeve nuts. 
 
 A modification of the design can be made in which the 
 rods in rib pass through slotted (or large sized punched) 
 holes, and have cast iron beveled washers. The rods can 
 then be straight. The inclination would be such as to 
 give about 8 per cent more stress than found in vertical 
 rods. 
 
 The gripping of concrete is sufficient to make up for 
 the difference in strength of rod at root of thread and 
 that of the full section. 
 
 Anchors that take the full stress of rods should have 
 their areas twenty times the section of the rod. This con- 
 dition would govern the size of the flange of angle to which 
 rods in the rib connect. These angles could vary from 
 about 2^ X 2 ^ X 5-i6-in. for small sized walls to 4 X 
 3 X 6- m - f r large walls. 
 
 The formulas ordinarily given for continuous beams are 
 for beams having a uniform moment of inertia. If the 
 beams have not a uniform moment of inertia, the formula 
 does not hold. If a beam be purposely designed so as 
 not to have a uniform moment of inertia, it will deflect 
 more at the section not reinforced for the full moment, 
 248 
 
and thus put greater moment on the fully reinforced 
 section. This is the basis for the somewhat arbitrary re- 
 inforcement of the upper part of bottom slabs. The bend- 
 ing moment at the middle of this slab cannot exceed that 
 for a simple span. The upper rods are added to prevent 
 cracking, and consequent weakening of the slab in shear, 
 near the ribs. 
 
 It is recommended that long walls be concreted from 
 one end to the other, and not uniformly from the ground 
 up; so that the shrinking of the concrete as it sets will 
 not act on the whole length of the wall at once. It is 
 also recommended that at expansion joints, say about 
 every 100 to 150 ft., a complete separation be made in the 
 wall, with an end rib in each portion of the wall. 
 
 THE DESIGN OF REINFORCED-CONCRETE 
 RETAINING WALLS 
 
 Sir: The article in your issue of Oct. 18, by Edward 
 Godfrey, on the "Design of Reinforced Concrete Retain- 
 ing Walls," was of especial interest to the writer^ because 
 it so closely conformed to the methods of design lately 
 developed by him in checking the computations for a 
 very high and long wall about which he was consulted. 
 
 Differences of opinion may exist as to proper methods 
 of determining the lateral pressures exerted by earths of 
 different qualities, and as to the proper design of rein- 
 forced concrete beams, etc., but certain fundamental 
 principles exist in accordance with which every proper 
 design should be prepared, and it seems to the writer 
 that Mr. Godfrey has come nearest to stating them of 
 any one with whom the writer is acquainted. 
 
 The writer's experiments on lateral earth pressures, re- 
 ported to the American Society of Civil Engineers, led him 
 to the opinion that the angle of surface repose for most 
 earths is entirely different from the angle of internal 
 friction of the same earths. Manifestly it is the latter 
 249 
 
t 
 
 k 
 
 k- 
 k- 
 
 (A) 
 
 (E) 
 
 K 
 
 (F) 
 
 (G) 
 
 
 (H) 
 
 1 
 
 ft'* 
 
 (J) 
 
 \ 
 
 I \ 
 1 \ 
 
 UH 1 i N I 
 
 H iiUH 
 ^:iii iL^ji:^:^ 
 
 250 
 
which should be used in most design work instead of the 
 former. The writer agrees with Mr. Godfrey, however, 
 that the actual active pressures may with sufficient ac- 
 curacy be considered as fluid in effect, and a certain per- 
 centage of the weight of the earth backing in amount. 
 The experiments above referred to seemed further to 
 show that for walls more than about 5 ft. high the pres- 
 sures varied practically as the depth, so that their re- 
 sultant might, with sufficient accuracy, be considered 
 as acting at the lower third point of the height of the 
 wall. For walls of less height, however, this point of ap- 
 plication rose often to a point four-tenths of the hei^nt 
 above the base. In most walls, then, the lateral pressures 
 would be represented by a triangular diagram of hori- 
 zontal arrows, having a horizontal base (sketch A). 
 
 The writer is in direct accord with Mr. Godfrey where 
 he uses a bottom slab weighted by the superimposed 
 earth, and agrees that the resultant downward pressure 
 of the earth on this slab may, for all practical purposes, 
 be considered as uniform (sketch B) unless the design 
 employs a greatly extended toe, as is often necessary 
 with high walls on soft soils. 
 
 He also agrees with Mr. Godfrey that many designs 
 are faulty in the arrangement of the reinforcement in the 
 bottom slab, probably from wrong assumptions as to the 
 distribution of the resisting earth pressures. 
 
 While some experiments lately carried. out by the writer 
 (which are now being repeated) shed some new light 
 on the distribution of resisting earth pressures under 
 walls and foundations, still for the moment a uniformly 
 varying distribution may be assumed, and, provided the 
 resultant of the two series of forces above described in- 
 tersects the base of the wall at the front edge of its 
 middle third, the variation is from zero at the back to 
 twice the average at the front (sketch C). 
 
 The diagram of resultant forces on the slab will then 
 evidently be two triangles, as described by Mr. Godfrey 
 (sketch D). 
 
 251 
 
The horizontal forces are, of course, resisted by the 
 sliding friction between the base of the wall and the earth 
 beneath, and by the pressure of the toe of the wall 
 against the earth in front of it. ' This front pressure 
 may be considered as distributed uniformly over the base 
 like the friction, for sake of convenience. 
 
 These assumptions take care of all the external forces. 
 
 If the slabs in front and base are to be tied directly 
 together by diagonal rods in the counterforts, these rods 
 must be given varying slopes (approximately as at E in 
 the sketch herewith) to correspond with the varying pres- 
 sures in front, while their bottom ends must be simi- 
 larly spaced to correspond with the resultant downward 
 earth pressure. Then, too, these rods would have quite 
 different stresses due to their varying slopes, so that the 
 proper distribution of diagonal rods of uniform diameter 
 is a very complicated affair to determine. Evidently, if 
 some satisfactory arrangement of horizontal and vertical 
 rods can be devised to produce the same effect several 
 advantages will be gained. Even the arrangement pro- 
 posed by Mr. Godfrey (the correctness of the design of 
 which the writer strongly questions) is rather costly in 
 execution, because simple horizontal and straight, approxi- 
 mately vertical rods are much more easily placed by in- 
 experienced labor. 
 
 Such horizontal^ and vertical rods in the counterforts, 
 if spaced to correspond with the assumed forces, will 
 have a uniformly varying spacing one way to correspond 
 with that which theoretically should exist on the face, 
 and a similar one in an approximately vertical position 
 the other way, the upper ends of the rods running to all 
 points along the back of the counterfort, while their 
 lower ends cover that part of the base over which the 
 resultant earth pressure is assumed as acting downward 
 (see sketch F). These rods simply carry to points within 
 and along the backs of the counterforts the active earth 
 stresses, so that the resultant diagram may be drawn 
 252 
 
as shown at G when primary stresses alone are con- 
 sidered, and as at H when the resultant earth pressures 
 and rod actions are considered. 
 
 Now the concrete in the counterforts being highly re- 
 sistant to compressive stresses, easily resists the com- 
 bined action of these loads and the whole counterfort is 
 much better tied together than in Mr. Godfrey's design. 
 The latter seems a little inconsistent in not better rein- 
 forcing the counterforts after employing more steel than 
 theory requires at several other points. A similar incon- 
 sistency crops out in the omission of any steel in the 
 steps which are supposed to carry over into the face of 
 the wall the upward pressure near the front under the 
 bottom slab. Unless the concrete is considered as taking 
 some tensile stress, reinforcement should be employed 
 in some manner in these steps, either to make them act 
 as beams of variable depth carrying the upward pressure 
 to the counterforts, or as brackets attached to the inside 
 of the front face. Under the latter assumption horizontal 
 rods perpendicular to the face should be introduced in the 
 bottom slab. These rods should also be carried through 
 the plane of the face and into the toe projection, which 
 must often be greatly extended, and the design of which 
 Mr. Godfrey does not consider even though he shows such 
 a toe in his diagrams. 
 
 If the remainder of the bottom slab outside the stepped 
 portion, besides acting as a vertical beam to take earth 
 pressures, is considered as a horizontal beam designed to 
 resist the stresses which the lateral rods might be intro- 
 duced to resist; then proper additional ties should be 
 introduced in the counterforts. Mr. Godfrey's angle iron 
 would not seem of sufficient size to cover the usual needs. 
 
 It is believed, further, that the practical construction 
 of the forms for Mr. Godfrey's stepped wall will be more 
 costly than for a wall without the steps and with steel 
 introduced instead. 
 
 Whenever the weight of a cubic foot of the earth back- 
 ing multiplied by the height of wall exceeds half the safe 
 253 
 
bearing power of the soil, an extended toe must be em- 
 ployed. In that case the diagram of vertical stresses 
 may be assumed as in sketch / and the resultant down- 
 ward effect on the bottom slab may or may not reach zero 
 behind the face. A diagram somewhat like that of sketch 
 K will result. 
 
 In this case the rods in the counterforts which are de- 
 signed to carry these vertical resultant stresses will them- 
 selves be nearly or quite vertical. The exactly vertica/ 
 condition would occur when the resultant earth pressure 
 becomes zero under the face of the wall, which condi- 
 tion would take place when the toe is extended a distance 
 outside this point approximately three-tenths of the total 
 width of base. This amount may seem rather large, but 
 is not unknown. 
 
 With such an extended toe a series of steps in the out- 
 side of the wall would be very proper because no coun- 
 terforts are available, and since the face of the wall is 
 in close proximity. Properly arranged steel would be 
 very necessary unless tension is to be allowed on con- 
 crete. 
 
 What Mr. Godfrey says wth regard to end anchorage 
 of rods, the writer believes to be eminently correct, ex- 
 cept that the writer's experiments have shown that proper 
 hooks are entirely satisfactory. The writer further agrees 
 with Mr. Godfrey in always advocating steel in beams 
 and slabs to take up reverse moments at points of support, 
 except that he feels that the design of the slabs as simple 
 beams with extra reverse reinforcement added, is erring 
 too much on the side of safety even with regard to the 
 exceedingly uncertain knowledge we now possess as to 
 earth pressures and reinforced concrete continuous beams. 
 
 The writer has been greatly interested in Mr. Godfrey's 
 design, but considers that the one briefly described above 
 is more logical and more economical of execution, espe- 
 cially as to labor. Yours truly, E. P. Goodrich. 
 
 1170 Broadway, New York, N. Y., Oct. 18, 1906. 
 254 
 
THE DESIGN OF REINFORCED CONCRETE RE- 
 TAINING WALLS 
 
 Sir : Kindly permit me space to reply briefly to Mr. 
 E. P. Goodrich in his criticism (Eng. News, Nov. 15) 
 of my article on design of reinforced concrete retaining 
 walls (Eng. News, Oct. 18, 1906). 
 
 As to the placing of straight horizontal and vertical 
 rods being simpler than the inclined rods used by 
 me, my idea would be to have the rods and angles sent 
 cut and punched and threaded to the site. The harp- 
 like arrangement in each rib or counterfort can be set up 
 on the ground and raised to position. A few braces would 
 hold all in place, whereas, with all rods separate, each 
 would have to be held individually, and liability to dis- 
 placement is multiplied. 
 
 The total pressure against the front slab is less than 
 that against the bottom, hence with the same rods, starting 
 normal, there is more than enough strength to take all 
 of the force. The occurrence of rods apparently closer 
 than necessary near the top of front slab will give an 
 extra safeguard against such pressure as that due to freez- 
 ing of the ground, which would be greatest near the sur- 
 face. Extraneous load would probably effect a lateral 
 pressure near the surface only. 
 
 In the matter of the projection in front of the wall, 
 and of the steps being without reinforcement, it is seen 
 by my sketch that the front projection is only one-third 
 as broad as its height; also the uplift under the steps 
 tapers down to nothing at the foot of the steps. There 
 is strength enough in the concrete to take the resultant 
 tension at a very low value. Spread footings are allow- 
 able even in brick or rubble masonry; they ought to be 
 so in monolithic concrete. If there were necessity for a 
 (arge projection in front of the wall, a modified design 
 ivould be required. It was my purpose to give a rational 
 analysis of the stresses and rational methods of taking 
 care of them. Yours very truly, Edward Godfrey. 
 
 Monongahela Bank Bldg., Pittsburg, Pa., Nov. IQ, 1006. 
 255 
 
A Method of Measuring- Deflections 
 in Floor Tests. 
 
 [Published in Engineering News, Aug. 25, 1904.] 
 
 By the Author 
 
 The following description of the method employed to 
 measure the deflection of a floor under test may be of in- 
 terest to any who have similar tests to make. 
 
 The floor tested was in 2O-ft. squares, and it was desired 
 to obtain the deflection at the middle of the square tested, 
 as well as at the middle of the side of the square, or half 
 way between the columns. To accomplish this, pedestals 
 or uprights were made of a single 4 x 4-in. piece of wood 
 nailed to a block about 2 x 12 ins. by 2 or 3 ft. long. These 
 were placed on the floor at points where the deflections were 
 to be measured, and blocks of pig iron were placed upon 
 them to weight them down, so as to prevent displacement 
 by the men in loading the floor. Enough pig iron was 
 placed on each pedestal to make up approximately the re- 
 quired load for the space which it occupied. 
 
 In addition to the pedestal there had been placed 2 x 10- 
 in. timbers which reached across the floor space and were 
 nailed to posts resting on the floor near the columns. These 
 were about at the level of a man's head, so as not to be in 
 the way of the men who were loading the floor. 
 
 They were vertically over the points at which deflections 
 were to be taken. The uprights were placed so that a flat 
 side of the 4x4 was against the joist or timber which 
 reached across the floor. On the back of the upright there 
 was tacked a sheet of stiff paper, upon which was ruled a 
 horizontal line. On the joist was tacked another sheet of 
 stiff paper, the edge of which had been divided accurately 
 into tenths of an inch. This was set with the zero of the 
 
scale at the horizontal line on the sheet tacked to the up- 
 right. 
 
 As the floor deflected, the amounts of the deflections 
 could be instantly read on the scale to hundredths of an 
 inch, by estimating tenths of scale divisions. The appara- 
 tus is more clearly shown in the accompanying sketch. 
 
 A number of scales were ruled at the same time by tack- 
 ing the sheets down on a drawing board with about Vz-'m. 
 
 y 2x0" Joist < 
 
 Rxper Scale 
 Tacked to Joist*. 
 
 ^~- 
 
 'I 
 
 i 
 
 < 
 
 I- 
 I 
 /W 
 
 ;^s | 
 
 PCfper h 
 
 Tacked 
 ? Upright*-' 
 
 
 EN6. NEWS. 
 
 ( 
 
 Pig j \lron } 
 
 ( 
 
 ^ I'd 
 
 C J 
 
 ( 
 
 j 
 
 
 ^ I3~l "T 
 
 ^ ^ 
 
 \ 
 
 ?"x /?" I 
 
 Apparatus for Measuring Deflections of Floor Panels 
 in Load Tests. 
 
 along the edge of each exposed. By dividing one sheet with 
 a decimal scale and ruling across the exposed edges all were 
 made alike. The tenths could be further divided into five 
 parts or fiftieths with a hard pencil, but no difficulty was 
 experienced in estimating the hundredths with a scale di- 
 vided into tenths. 
 
 257 
 
Reinforced Concrete Engineering in 
 the Making. 
 
 Concrete-steel or reinforced concrete construction is only 
 an infant as yet. The relatives have not agreed upon a 
 name. Many want the hyphenated appellation with the old 
 family name of steel retained, while others would express 
 the office of the steel rather than its presence. 
 
 To drop the figure, there is much to learn by the builders 
 of this construction, some things that only experience will 
 teach, and others that can be wrung from known facts and 
 technical knowledge in kindred lines. It is the purpose of 
 this article to point out some of the things that ought to be 
 set up as guides in the design and execution of reinforced 
 concrete constructon, if it is to have a standing in the 
 class of sound engineering. 
 
 While it is true that the manufacture of reinforced con- 
 crete can be accomplished largely with ordinary labor, it 
 is also true that this labor must have strict supervision by 
 competent foremen, who understand the importance of 
 doing the work just as the designer has planned it. A 
 laborer does not understand the importance of a small rod 
 in the concrete, and would probably see no harm in leaving 
 some rods out; or he might think that the exact location 
 of rods is a matter of no importance, so long as they are 
 present. The displacing of rods, either by accident or de- 
 sign (as to make the placing of concrete more convenient), 
 may be the result of an ignorant workman's act for which 
 he would feel no guilt because of his ignorance. Rods that 
 are intended to lie close to the bottom of a beam or slab 
 may thus be placed at the middle of its depth, resulting in a 
 great reduction in the strength, and not improbably being 
 a cause of failure. Rods bunched together, where they 
 should be separated, is a possibility that would result in a 
 loss of gripping power in the concrete. 
 
 Again a laborer may wish to save himself the handling 
 of cement and cut down on the amount used; or, with a 
 view of saving his employer expense, with the latter's con- 
 
 258 
 
sent, a bag or two of cement may be left out occasionally. 
 The time of mixing or number of turnings on the mixing 
 board, if hand mixed, should not be left to any but ex- 
 perienced and responsible persons. The uniformity of 
 the concrete depends upon the thoroughness of mixing and 
 correctness and constancy of the amounts of the ingre- 
 dients. The strength of the structure is gaged, in a large 
 measure, by the uniformity of the concrete. 
 
 An illustration of a workman's idea of the possibilities 
 of concrete is found in the following: The writer ob- 
 served some work being put in, where three or four inches 
 of plain concrete was being laid on an old wooden floor. 
 With the idea that the floor had probably been shored or 
 strengthened for the heavy load he asked the workman 
 what supported the concrete. The reply was, that "the 
 stuff didn't need any support, it supported itself." 
 
 Inspection of every part of the work as it progresses, 
 by someone not interested in the contractor's end of it, is 
 almost an absolute necessity The combination of possi- 
 bilities of skimping and scamping, through ignorance or 
 carelessness, leaves the owner with the small end in the 
 probability line, unless he adopts suitable means to correct 
 this condition. A contractor's guaranty that a structure 
 will be built according to specifications, or that it will not 
 crack or deteriorate in a given period, is scant comfort 
 when a piece of work shows defects upon its completion, 
 and the contractor's final estimate declares that the struc- 
 ture is complete and ready for use. 
 
 A guaranty that a structure will stand a specified test 
 load is another uncertainty to which owners sometimes tie. 
 A test load on a small square of a large floor of continuous 
 construction is no more a criterion of its capacity when 
 fully loaded, than the ability of a tank to hold a barrel 
 is proof that it will hold ten barrels. In the early days of 
 bridge building it was not unusual to see in specifications 
 a requirement that a bridge should be loaded for a certain 
 period with a given train load. Bridge builders have ad- 
 vanced away beyond that point. It is the man in the de- 
 
 259 
 
signing department that can tell to a nicety what the bridge 
 is fit to carry, the presumption being that all parts of the 
 fabrication of the bridge have received the necessary in- 
 spection, and the plans are carried out in every particular. 
 
 Tests on reinforced concrete construction are quite 
 proper, but they should be made on an isolated unit of the 
 floor not supported on all sides by the contiguous con- 
 struction; or else a test to be of value, should be made on 
 a large section of the floor in place, of sufficient extent not 
 to be affected by extraneous support. 
 
 One contract which came under the writer's notice called 
 for floors that had a theoretical breaking strength of three 
 times a certain load per square foot. The floors in ques- 
 tion proved to be unsafe under test with one time this load 
 per square foot, though by the designer's method of figur- 
 ing the "theoretical breaking strength" was supposed to 
 be three times. The theoretical breaking strength of 
 concrete or of a concrete-steel floor is too nebulous to have 
 any meaning in a contract. 
 
 An error that works to the detriment of reinforced con- 
 crete construction is the notion that it is the cheapest form 
 of construction. For many reasons it is economical, but 
 in no sense is it cheap. Properly built it cannot compete, 
 even at present high prices, with wooden construction in 
 the matter of first cost. It compares favorably in cost with 
 steel construction, and in many situations structures can be 
 built of reinforced concrete for less than of structural steel, 
 when the same character of design is maintained. 
 
 The necessity for using wet concrete cannot be too 
 strongly urged. Dry concrete is lacking in the essential 
 characteristics that make the combination of steel and con- 
 crete so strong and durable. Mealy concrete will be porous 
 and fail to protect the steel; wet concrete, if it contains 
 enough cement, will coat the steel with a film of cement. 
 This is one essential to the preservation of the steel ; dense 
 concrete is another. Neither of these are possible with dry 
 concrete. Dry concrete has not much adhesion; it will 
 therefore fail to take hold of the steel. It is also lacking 
 
 260 
 
in cohesion, and would therefore be weak in its gripping 
 power on the steel. Dry concrete will set in a shorter time 
 than wet concrete, and on short time tests will show greater 
 compressive strength. The wet concrete will, however, 
 attain greater strength than the dry concrete when it has 
 thoroughly set. Many erroneous notions about the strength 
 of reinforced concrete and the preservation of the imbedded 
 steel have no doubt been the result of the use of dry con- 
 crete, and the unsatisfactory conditions observed. Con- 
 crete for this class of construction should be puddled rather 
 than tamped, by means that will work out the air spaces 
 and make the concrete to run into all crevices. 
 
 In the matter of materials and the proportions of the 
 same there is not much difference of opinion. Good, hard 
 and durable broken stone or gravel is essential in stone 
 concrete for any purpose. For reinforced concrete the 
 stones should be small, say under an inch in every dimen- 
 sion for slabs, beams, columns, and small arches, and larger 
 in size for more massive work. The reason that small 
 stones should be used is that they will pack better around 
 the steel and not leave voids. Graded sizes from the largest 
 to the smallest are very essential both in the stone and in 
 the sand. Uniformity in the sizes of stone or grains of 
 sand is to be guarded against. The larger parts leave voids 
 that only the smaller parts can fill, and these leave voids 
 that still smaller parts are necessary to fill, and so on down 
 to the finest particles of cement. 
 
 In plain concrete economy can be effected by a mixture 
 that is suited to the particular broken stone or gravel used. 
 In such concrete it is only necessary to provide enough 
 sand to fill the voids in the stone and enough cement to 
 fill the voids in the sand. In reinforced concrete there 
 must be an excess of cement, so that the density of the 
 concrete will be assured, and so that the steel will be cov- 
 ered with cement. 
 
 One part of Portland cement to two parts of sand and 
 four parts of broken stone, gravel or cinders, all by volume, 
 is the generally accepted standard mixture. A leaner 
 
 261 
 
mixture than this is not recommended. Stone concrete of 
 these proportions, made of good materials, will have a 
 compressive strength in short blocks of about 2,000 pounds 
 per square inch. To have a factor of safety of four, as it 
 should have, a compressive unit stress or an extreme fibre 
 stress in beams of about 500 pounds per square inch should 
 be employed in the design. Concrete in short blocks can 
 be stressed to this amount with safety. It is therefore a 
 proper unit for reinforced concrete columns or beams. It 
 would not be safe in a plain concrete column, because a 
 plain concrete column (having a length several times its 
 diameter), will fail in other ways than in direct compres- 
 sion, such as bulging or diagonal shear. But where the 
 concrete is tied together by steel in such a way that the 
 concrete is not subject to any but compressive strains in 
 short braced elements, failures by bulging or by diagonal 
 shear are prevented. 
 
 Steel buildings are commonly built in lengths of several 
 hundred feet without expansion joints, depending upon the 
 elasticity of the steel to take up temperature stresses. Re- 
 inforced concrete builders, essaying to do the same thing 
 with the less elastic materials, are apt to have serious 
 trouble. If a long wall or building is brought up from one 
 end to the other, so that the shrinkage of the concrete does 
 not act on the whole line at once, it is believed that one or 
 two hundred feet of continuous reinforced concrete can 
 be maintained in one piece. The placing of the concrete 
 should be done from one end to the other of a long struc- 
 ture where possible. It is well to have expansion or cleav- 
 age joints and two sets of columns in very long buildings. 
 So-called expansion joints, where the two parts of the 
 building coming together are not independently self sus- 
 taining are worse than no provision whatever for expan- 
 sion. Two sets of girders on one column with an expan- 
 sion joint between them would mean the concentration of 
 all of the temperature stresses on the columns. 
 
 It is very important that, excepting at expansion joints, 
 structures be tied together continuously. A break in the 
 
 262 
 
continuity of the steel results in a weak point or section in 
 the structure under temperature stresses. 
 
 In the matter of the time allowed for the setting of con- 
 crete the practice common with plain concrete will not 
 apply in reinforced concrete. In plain concrete the forms 
 can often be removed in a day or two after the concrete 
 has been placed, and no harm results. This is because the 
 stresses in plain concrete are not of the intensity of those 
 in reinforced concrete, and because of the further fact that 
 plain concrete seldom receives its calculated load until the 
 structure it supports has been built up over it, which may 
 be months later. The dead weight of reinforced concrete 
 beams and slabs is a large part of the total load which they 
 carry, hence they should not be called upon to support their 
 own weight until the concrete has attained the greater part 
 of its calculated strength. In a current engineering periodi- 
 cal, description is given of a building in which the state- 
 ment is made that forms were removed from some very 
 large girders two days after the concrete was placed. There 
 is absolutely no warrant for such practice. The straining 
 of the steel rods before the concrete has firmly gripped 
 them is a proceeding that is fraught with great danger to 
 the safety of the structure. No wise builder would submit 
 to his structure being subjected to a test two days after 
 the concrete had been placed. It is just as absurd to re- 
 move the forms at so early a date. Two weeks of good 
 weather should be allowed before forms are removed, and 
 two weeks more should elapse before any test is made. In 
 freezing weather a longer period should be allowed, as 
 the setting of cement is retarded and sometimes almost 
 suspended in freezing temperatures. 
 
 If construction is proceeding upwards, as in buildings, 
 speed should not be too great. If too much weight is 
 placed upon the columns while the concrete is green, damage 
 will result. Forms for concrete columns should be well tied 
 together with a view of containing the semi-liquid con- 
 crete as well as resisting the bursting pressure due to the 
 load that may come upon the column. Props should be 
 
placed close to columns as well as under intermediate points 
 in the beams and girders. Column forms, as usually con- 
 structed, are not suited to taking vertical loads, but are 
 built merely as boxes to contain the concrete. The cen- 
 tering or props should be strong enough not only to sup- 
 port the concrete in the forms immediately above, without 
 sagging, but also to sustain whatever load may come upon 
 the same during construction for the time that it takes 
 the concrete to set. 
 
 The qualities that make the combination of concrete and 
 steel not only a possibility, but also a means of meeting 
 engineering problems that in many ways has no equal, are 
 these : Concrete and steel have nearly the same coefficient 
 of expansion under changes of temperature. Concrete in 
 setting in the air will shrink and grip the steel ; it will also 
 adhere firmly to clean or somewhat rusted steel, (but not 
 to oily steel). Steel imbedded in concrete will supply the 
 tensile strength that the concrete lacks, and the concrete 
 will preserve the steel against rust besides acting as a pro- 
 tection against fire. 
 
 That the coefficient of expansion of the two materials 
 is not quite the same is reason for predominance of the 
 weaker material. Large sections of steel in comparatively 
 small sections of concrete should not be used, as the ex- 
 pansion and contraction of the steel will crack the con- 
 crete. The need of mass in the concrete to grip the steel 
 to the capacity of its tensile strength is another reason why 
 the steel should occupy only a small fraction of the sec- 
 tional area of a beam or slab. 
 
 The placing of steel directly against the forms and thus 
 allowing it to be on the surface of the beam or slab is bad 
 practice. The steel is by this means exposed to fire and 
 rust, and it cannot be effectually gripped. Steel rods should 
 be several times their diameter from the surface of the 
 concrete. Beams narrow at the bottom and wide at the 
 top are irrational in shape. They lack in concrete just 
 where it is needed to protect and grip the steel. So-called 
 T beams, which are rectangular beams, including in their 
 
 264 
 
calculation a portion of the floor slab as top flange, are 
 faulty in like manner, in that they do not contain enough 
 concrete in the lower part of the beam for the amount of 
 steel used. 
 
 Floor plates in steel construction are not considered as 
 adding to the strength of floor beams, even though firmly 
 riveted thereto. It is not good engineering to consider a 
 wide expanse of floor slab as part of a narrow beam, and 
 it is not doing justice to the owner to make a floor slab 
 which he cannot cut into, for the many necessary pur- 
 poses that openings are often made in floors, without 
 weakening the primary support of his floor. 
 
 Wide flat bars bedded in concrete are not held as firmly 
 as square and round bars of the same sectional area, and 
 are not suitable shapes, for the reason that the concrete 
 tends to shrink away from the flat sides. Flat bars have 
 the further disadvantage that they make a plane of cleav- 
 age in the concrete. This is especially true if they are near 
 the surface. The writer observed some reinforced concrete 
 beams in which several flat bars were placed side by side 
 and brought up and hooked over the steel beams. When 
 the forms were removed, large chunks of concrete below 
 the flats fell off. Square and round rods should there- 
 fore be used in preference to flat bars. 
 
 The writer has no quarrel with mechanical bond, but he 
 believes th'at more is to be gained by use of plain com- 
 mercial steel and a low unit tension than by using mechani- 
 cal bond and the high unit tension advocated by those who 
 have the special material to sell. If the question of economy 
 cuts no figure, the use of deformed rods under low unit 
 stress will add an element of safety, which is more in the 
 nature of insurance against bad work in the execution than 
 a needful precaution in the design. 
 
 The proper use of the steel is to take tensile stresses. 
 Composite structures, such as the combination of wood and 
 iron in a beam, are poor makeshifts at the best. Where 
 dissimilar materials are used to perform the same office 
 jointly there is no correct way of determining just how 
 
 265 
 
much of the work each will do. A column having longitudi- 
 nal sections of steel that are intended to share in supporting 
 the load is a composite of concrete and steel and not a true 
 reinforced concrete column. Calculations to determine the 
 relative amounts taken by the steel and concrete are ren- 
 dered useless by reason of the tendency of the concrete 
 to shrink and shorten. 
 
 Segmental floor arches, that is, arches flat on top and 
 curved upward on the under surface, with steel reinforce- 
 ment near this curved surface, violate the principles of 
 good design. If these act as arches and not slabs, they 
 need tie rods where they would pierce the curved surface 
 and be unsightly in a ceiling; the steel is in compression 
 in place of tension. If they act as slabs, they are shallow 
 and weakest where they should have the greatest strength. 
 
 The steel in reinforced concrete should be in compara- 
 tively small sections, well distributed through the mass. 
 Not only should there be the steel which calculations show 
 to be required for tension, but it is very often desirable to 
 use steel rods at right angles to the primary rods in order 
 to tie the concrete together and prevent cracking. These 
 cross rods also aid greatly in the lateral distribution or 
 spreading of concentrated loads, as in arches or slabs. Wire 
 mesh, in which the wires are straight, is an excellent ma- 
 terial for floor slabs of small span; as uniform spacing of 
 the steel wires is assured, and they are not easily displaced 
 in placing the concrete. 
 
 If wires or rods are bent or kinked, the tendency of stress 
 in the same will be to straighten out the bends and kinks. 
 This means excessive stretch in the steel accompanied by 
 cracks in the concrete. The use of wire cables is irra- 
 tional. It is a well known fact that a wire cable will stretch 
 several times as much as a steel rod of the same sectional 
 area under the same load. The principal reason for using 
 wire cable must be because of the high tensile strength of 
 the steel. Now if a high unit is used in the cable, the 
 stretch will be still further augmented. 
 
 Rods imbedded in concrete should not be given angular 
 
 26G 
 
bends. If a rod under stress is bent at an angle, there 
 will be a large component of stress at the bend in a direc- 
 tion bisecting the angle between the portions of the rod. 
 There is evidently nothing at the bend to take this com- 
 ponent but a small area of concrete bearing on the rod at 
 the bend. The use of sharp bends in rods is a very com- 
 mon fault in reinforced concrete design. It is inexcusable. 
 These rods should be given gentle curves, so that the side 
 bearing will not be excessive. If we allow a side pressure 
 on the concrete one-twentieth of the tensile unit on the 
 steel, we may arrive at a safe minimum radius of curva- 
 ture of a rod as follows : Let d = diameter of a square 
 rod, and p = unit pressure allowed on the concrete. Then 
 2Op will be the unit tension on the steel, and 20 pd 2 
 stress in rod. But the stress in the rod must equal the 
 product of the width d of the rod, the radius of curvature r, 
 and the unit pressure on the concrete; or 20 pd 2 = d r p, 
 whence r = 2od. That is, the radius of curvature of a 
 square rod should not be less than 20 times the diameter of 
 the rod. The same rule may be applied to the case of 
 round rods without important error. 
 
 Hooks at the ends of rods as a means of end anchorage 
 have the same structural fault as sharp bends. They can- 
 not anchor a rod for its full tensile strength. A proper 
 anchor for a rod requires a washer plate or other bearing 
 part having a surface in bearing against the concrete about 
 twenty times the area of the rod. 
 
 No tension on the concrete should be allowed in the 
 calculation for the strength of beams or slabs. The ten- 
 sile strength of concrete is uncertain and unreliable, es- 
 pecially where it may be subject to expansion cracks due 
 to the presence of the steel. One crack in a beam may 
 destroy entirely an assumed tensile value, although the 
 same crack might not be a serious matter in a beam not 
 calculated to receive any assistance from the tensile strength 
 of the concrete. 
 
 The allowed tensile unit on the steel is a feature of de- 
 sign that has not received the attention that it merits. The 
 
 267 
 
mere integrity of the steel under a given tension per square 
 inch may be taken care of, and yet the stretching out of 
 the steel under that stress may be such as to disintegrate 
 the concrete. Cracks begin to appear in the concrete after 
 the stress in the steel has passed about ten or twelve thous- 
 and pounds per square inch. Units of about these amounts 
 should therefore be used. The use of high tension on the 
 steel is indefensible. There seems to be a prevailing opinion 
 and it is held by many men who ought to know better, that 
 high carbon steel or steel that by cold rolling or other- 
 wise is made to have a high elastic limit will elongate less 
 under stress than ordinary structural or soft steel. This 
 is entirely erroneous. For stresses below the elastic limit 
 all grades of steel have practically the same modulus of 
 elasticity, that is, they will all stretch out a given amount 
 under a given unit stress. Beyond the elastic limit the soft 
 steels will elongate more before breaking, but the proper- 
 ties of steel under stresses beyond the elastic limit have 
 nothing at all to do with the design of reinforced concrete. 
 The writer has in mind a case where an architect wished 
 to obtain rods having an elastic limit of 60,000 pounds per 
 square inch, so that he could use 20,000 pounds in his de- 
 sign ; because the building laws allowed him to use a factor 
 of safety of three on the basis of the elastic limit. In an- 
 other case a designer used 32,000 pounds per square inch 
 for dead load stress on the steel. (This information was 
 given in the defense of the design of a bridge that failed.) 
 There is absolutely no warrant for the use of such high 
 stress upon steel confined in concrete. One advocate of 
 the use of high steel, and mechanical bond, makes the de- 
 fense that the mechanical bond will distribute the cracks ; 
 thus virtually admitting that the high tension he advocates 
 will result in cracks in the concrete. Public confidence is 
 not obtained by any such admissions or practices. 
 
 Shear in steel, while it has a conspicuous place in specifi- 
 cations and building codes, has practically no meaning in 
 reinforced concrete. For a steel rod to be in shear to the 
 extent of 12,000 pounds per square inch, as sometimes 
 268 
 
allowed, there would be a pressure on the side of the rod 
 which no concrete could stand. If we imagine a bar one 
 inch square projecting normally out of a vertical concrete 
 wall, and a vertical load of 12,000 pounds resting on this 
 rod where it projects, we have the absurd proposition which 
 12,000 pounds per square inch shear on imbedded steel 
 represents. We do not measure the bearing power of a 
 nail driven in wood by the shearing strength of the metal, 
 but by the bearing power of the wood. So in reinforced 
 concrete the bearing power of the concrete must govern if 
 any steel is to be considered in shear. So-called shear bars, 
 while they may have a place in tying the concrete of a beam 
 together generally, do not perform that office by acting in 
 shear, but they are in tension tying together the parts of 
 a beam into which they extend. 
 
 Reinforced concrete will not work wonders. The ma- 
 terials are amenable to the laws of nature, including the 
 law of gravitation, as has too often been demonstrated, 
 where ignorant or careless builders have attempted its use. 
 Unscientific and misleading tests have led exploiters to 
 launch into the field of reinforced concrete with a system 
 and little or no engineering knowledge, and the recorded 
 failures are the fruit. Prospective builders are deluded 
 with the idea that some special system will accomplish 
 feats with steel and concrete that are almost magic and 
 that defy all theory. Some of these designs find their way 
 into books treating of the subject, where a learner ought 
 to expect to find only absolutely reliable information. 
 
 Designers in this new construction have the advantage 
 of access to the knowledge gained by experience and study 
 in steel construction, and as a consequence great strides 
 have been made. Arch spans of 150 feet or more and 
 buildings of sixteen stories do not astonish us because of 
 familiarity with the great achievements in steel structures. 
 In the case of steel a more or less gradual development 
 took place. The design of steel work has come to be 
 largely a matter of following certain rules embodied in 
 the specifications, and other principles known to the struc- 
 
 269 
 
tural designer; and to the extent that the personal equa- 
 tion is eliminated by these rules is the design perfected. 
 Common sense and professional judgment sound well, but 
 they are too often just another way of expressing the work- 
 ing of the process colloquially known as skinning. In light 
 steel bridges it is not uncommon to see principles of good 
 engineeering thrown to the wind. It will not do to follow 
 the same course in structures of the permanence of those 
 in reinforced concrete. A reinforced concrete structure 
 with no better provision for rigidity than the average high- 
 way bridge (put up with no disinterested engineering super- 
 vision), will very soon shake itself to pieces. The high- 
 way bridge has the advantage in this respect because of the 
 tougher material of which it is made. 
 
 The sooner reinforced concrete design is reduced to rule, 
 and the more inclusive the rules, the better for the preserva- 
 tion of life and property. 
 
 In the matter of methods of calculating the strength of 
 beams many formulas have been brought out, the great 
 part of which are very complex. Complex formulas are not 
 consistent with the nature of the materials nor with the 
 result of tests. Complex formulas lead to errors, not only 
 on account of the difficulty of applying them, but because 
 of the blind way which they are generally applied. 
 
 By assuming the neutral axis always at the center of 
 depth of the concrete beam and compression in the con- 
 crete as uniformly varying from the neutral axis up, the 
 formula for bending moment, as well as its derivation, are 
 rendered very simple. The first of these two assumptions 
 is quite rational, because of the fact that tests to locate the 
 neutral axis of beams under safe loads have shown that 
 it lies very close to the middle of beam. The second as- 
 sumption is equally sound. By the principle of the equality 
 of tensile and the compressive stresses in a beam, if 500 
 and 10,000 pounds be used as extreme compressive stress 
 in concrete and tension on steel respectively, it can be 
 shown by a simple calculation that there will be i% per 
 cent of steel area in the beam. It is not the purpose in 
 
 270 
 
this article to give formulas, but to lay down general 
 principles. 
 
 The common form of beam has one or more rods near 
 the bottom from end to end. These rods receive their 
 stress by increments from the concrete. These increments 
 come in the form of horizontal shear in the concrete, being 
 transformed from horizontal shear to stress in the rods by 
 the medium of the gripping power of the concrete. As the 
 web of a plate girder must have sufficient shearing strength 
 in any given length to take the flange increment in that 
 length, so there must be section enough in the concrete 
 beam to take the increment of the flange in a given length. 
 The shear on the concrete in a horizontal section just above 
 the rods must be provided for in section in the beam. This 
 is one of the reasons why narrow beams and beams that 
 are lacking in concrete in the lower part of the rectangle 
 are faulty. If the gripping power of the concrete is mea- 
 sured by the area of the rod in contact with the concrete, 
 and that gripping power is taxed to its safe capacity in any 
 beam, the area of the horizontal section in the beam should 
 be equal to the area of the surface of the rods. This means 
 that square rods should be placed four diameters apart and 
 round rods 3.1416 times their diameter apart. 
 
 As intimated, the holding power of concrete on a rod is 
 measured by the area of rod in contact. This cannot ex- 
 ceed, in amount per square inch, the shearing strength of 
 the concrete, for it is clear that a prism could shear out, 
 taking just the skin of concrete adhering to the rod. The 
 adhesion and shear are usually taken at about the same 
 unit value. A safe amount is 50 pounds per square inch for 
 stone concrete. It will be seen by a little calculation that, if 
 a rod is imbedded fifty diameters in concrete, at this amount 
 per square inch of its surface, it will be anchored to the 
 extent of 10,000 Ibs. per square inch. Hence, any plain rod 
 not anchored with nut and washer at the end must be im- 
 bedded fifty diameters before it is held by the concrete to 
 the amount of its safe capacity. In the case of a beam, 
 however, while the anchoring value increases uniformly to 
 
 271 
 
the center of the span the stress increases as the ordinates 
 of a parabola. Hence, in order to have the anchoring value 
 not less than the stress at any section the rod should have 
 double its safe anchoring strength at the center of span, 
 since the tangent to the parabola at the ends of beam cuts 
 a point twice as high as the middle ordinate at the center 
 of span. This would require 100 diameters up to the cen- 
 ter of span. In other words a rod not anchored at the 
 end of span, or continuous into the next span should not 
 exceed in diameter one two-hundredth of the span. 
 
 The curving of a rod up to the top flange at the ends 
 of span, without providing an end anchorage or running 
 the rod into the adjacent span for anchorage, is another 
 structural fault, and a common one. This takes the rod 
 out of the plane where flange increments are added (near 
 the bottom of the beam) and makes a suspension rod 
 of it on which the concrete rests as a saddle. It is neces- 
 sary in such a case that nearly the full stress of the rod 
 should be imparted to it at the very end, where in many 
 designs there is absolutely nothing to perform this office. 
 If a rod curved up at the end of one beam runs beyond 
 the support into an adjacent beam, it serves the double 
 purpose of anchoring the rod and taking tension in the 
 top flange of the next beam that would be caused by the 
 continuity of the beams over the support. Separate rods 
 lying near the top of beams, where two beams occur 
 end to end over the same support, are of great value in 
 resisting negative moments over supports, and should 
 be made use of in the absence of the arrangement just 
 mentioned (where the bottom rods of one span continue 
 into the next to resist tension in the top flange). These 
 separate rods should extend not less than 50 diameters 
 into each beam for anchorage, and may require to be 
 longer. Rods running from one beam into the next 
 for anchorage should extend into that beam not less 
 than 50 diameters. 
 
 In steel work beams are not usually considered as 
 continuous, unless it be necessary to take care of canfi- 
 272 
 
lever stresses, but in steel beams there is ample strength 
 in the top flange to take care of any tension that"' may 
 occur due to continuity. With reinforced concrete beams 
 the case is quite different. Where two beams in a line 
 resting on the same support are poured at once, there 
 will be sure to be some tension in the top flange; and 
 if this is not resisted by steel, a crack may be the result, 
 which would destroy the shearing strength of the con- 
 crete, and might cause the beam to fail by shear. 
 
 The end shear of a reinforced concrete beam or slab 
 with only horizontal rods must be taken by the con- 
 crete. When a beam of a given span is increased in 
 depth, the bending strength and consequently the capacity 
 for load is increased about as the square of the depth. 
 The shearing strength is, however, only increased as 
 the depth. There will therefore be a point where the 
 shearing value is overtaxed, and beyond which the depth 
 should not be increased without some provision for taking 
 the extra shear. In a subsequent article the writer hopes 
 to show that this limiting depth is one-tenth of the span. 
 When the depth of beam is more than one-tenth of the 
 span, some provision must be made for taking the shear 
 that the concrete is not capable of carrying. The mere 
 turning up of some rods and ending them short of the 
 end of span, or running them to the end of span without 
 anchorage at the end of span, will not do this. 
 
 For columns a circular coil to resist the bursting or 
 bulging pressure and longitudinal rods tied to this coil 
 at regular intervals in the circle to resist flexure, seems 
 to be the most rational means of overcoming the weak- 
 nesses of concrete as a column. 
 
 273 
 
The Design of Reinforced Concrete 
 Beams and Slabs. 
 
 Based on the principles of design laid down by the 
 writer in an article published in Concrete Engineering 
 of January I, 1907, the following is given as exemplifying 
 simplified, and at the same time rational design as ap- 
 plied to beams and slabs in reinforced concrete. 
 
 There are two ways of finding the safe strength of a 
 beam or slab, one is to use in the formula ultimate 
 values and then apply a factor of safety; the other is to 
 use in the formula safe values, thus applying the factor 
 of safety before the formula for strength is reached. 
 These two methods should not be divorced from each 
 other, but their interdependence should be recognized. 
 Stresses that would be quite safe for steel in a framed 
 structure may be unsafe in steel imbedded in concrete, 
 by reason of the excessive stretch and the consequent 
 cracking of the concrete. And again there should be 
 some approximate agreement between the ultimate strength 
 of beams as shown in the formula and the ultimate 
 strength of test beams as found by experiment. Formulae 
 to be of value, must be based upon assumption of the 
 continued elasticity of the materials up to the point of 
 failure, and for this reason exact agreement between 
 the calculated ultimate strength and that shown in tests 
 is not to be expected, In fact the variation in the strength 
 of concrete would preclude any such exact agreement. 
 
 The ultimate usefulness of steel is reached when the 
 material is stressed to its elastic limit, or say 40,000 
 pounds per square inch, which is about the elastic limit, 
 as shown by drop of beam, for the vast majority of tests 
 commercially made on structural steel. High steel is 
 not considered in this connection, for its use is neither 
 appropriate nor economical. At this value for the stress 
 in steel cracks are sure to be plainly visible and bond 
 between the concrete and steel is greatly weakened, if 
 not destroyed. Using 40,000 pounds per square inch as 
 
 1174 
 
the ultimate tensile value and a factor of safety of four 
 for rolling loads, such as those on floors where wheeling 
 is done, or in bridges, we have 10,000 pounds per square 
 inch as the safe limit on the steel. It is safe to say that 
 if the stress on the steel be kept within this limit, other 
 parts of the design being equally well proportioned, the 
 integrity of the structure will be completely safeguarded. 
 
 Unlike steel, concrete is elastic practically up to the 
 point of failure. Good stone concrete, of the proportions 
 of I volume of Portland cement to 2 of sand and 4 
 of hard broken stone, will show in short blocks an ulti- 
 mate strength of about 2,000 pounds per square inch 
 after setting several months. This may then be taken 
 as the ultimate strength of concrete in beams, and on 
 the same basis as the steel the safe value is 500 pounds 
 per square inch. The ratio then between the unit stress 
 in the steel and the extreme fibre stress in the concrete 
 is 20. 
 
 By the well-known principle of the equality of tensile 
 and compressive stresses in a beam subject to bending 
 only we know that the total tension in the steel must 
 equal the total compression in the concrete. As stated 
 in the article previously referred to, no tension will be 
 counted upon as existing in the concrete. The variation 
 of stress in the concrete will be taken as uniform from 
 the neutral axis up, and the neutral axis will be taken 
 as located in the middle of the depth of the concrete 
 beam or slab. 
 
 Let D = depth in inches of concrete beam or slab out 
 to out; B width of beam in inches; A= area of steel 
 in square inches; M ultimate bending moment in inch- 
 pounds on beam AB ; M' bending moment in foot 
 pounds on beam or slab one foot in width. 
 
 The ultimate stress in concrete is 2, oooX^ D^tyB 
 500 BD. This must equal the stress in the steel or 40,000 
 A. Hence A=i-So of BD or 1.25 per cent, of the area 
 of the concrete rectangle. 
 
 The center of gravity of the stress in the concrete is 
 
 275 
 
one-third of D above the neutral axis, and, if we place 
 the steel one-eighth of D from the bottom of concrete, 
 it will be three-eighths of D below the neutral axis. The 
 effective depth is then 17-24 D, and the ultimate bending 
 moment is 
 
 M = 17-240 X SooBD = 354BD 2 
 
 If a beam or slab 12 inches wide be considered, the 
 ultimate bending moment on the same in foot-pounds 
 will be 
 
 M' = 1-12 X 354 X I2E)2 = 354D 2 
 Allowing a factor of safety of four for rolling loads 
 and 3.5 for quiescent loads we have for safe bending 
 moment per foot width 
 
 M' for rolling loads = 88D 2 (i) 
 M' for quiescent loads = ioiD 2 (2) 
 
 By the same process we may derive the following for 
 steel placed one-sixth of the depth from bottom of 
 concrete 
 
 M' for rolling loads = SsD 2 (3) 
 M' for quiescent loads Q5D 2 (4) 
 
 For steel placed one-tenth of the depth the safe bend- 
 ing moment per foot width is 
 
 M' for rolling loads = Q2D 2 (5) 
 M' for quiescent loads = iosD 2 (6) 
 
 The foregoing considers only the bending moment in 
 the beam or slab, and deals only with the amount and 
 location of steel to reinforce a concrete beam for a given 
 bending moment. In all beams shear plays an important 
 part and must be taken care of. In steel beams this office 
 is performed by the web plate. In reinforced concrete 
 beams provision for gripping the rods must be made. 
 This corresponds in structural steel design to the spac- 
 ing of rivets in the flange to take the flange increment. 
 
 Some of the rules laid down in the writer's previous 
 article are these: 
 
 (a) The diameter of horizontal straight rods not an- 
 chored at the ends of span should not exceed 1-200 of 
 the span. 
 
 276 
 
(b) The spacing of rods in which the gripping value 
 is taxed to the safe limit (as where the diameter is 1-200 
 of the span) should be four diameters for square rods 
 and 3.1416 diameters for round rods. 
 
 Coupled with the latter rule it is to be observed that 
 the distance from center of outside rod to edge of beam 
 should be one-half of the spacing. This is so that the 
 shearing area in a plane just above the rods will be 
 equal to the superficial area of the rods. If rods of less 
 diameter than 1-200 of the span are used, the gripping 
 value is not taxed to its safe limit. In such case the 
 spacing can be closer. The area of the horizontal section 
 of the beam should be not less than the superficial area 
 of the rods in a length of 200 diameters, for beams taking 
 uniform loads. 
 
 Rods should be several times their diameter from the 
 bottom of the beam, so as to make the gripping of con- 
 crete effective. With 1.25 per cent, of steel and round 
 or square rods spaced 3.1416 and 4 times their diameters 
 apart respectively, rods % of D from the bottom of con- 
 crete, it will be found that the center of rod is 2% diame- 
 ters from the bottom of the concrete beam. This is in 
 good proportion. 
 
 By rules (a) and (b) the gripping of rods and the 
 increment to the stress in rods, as well as the horizontal 
 shearing strength of the beam, are taken care of. 
 
 For vertical shear, with only horizontal rods, the end 
 shear must be taken by the rectangle of concrete having 
 sides B and D. It is a well known principle of mechanics 
 that the intensity of shear in a rectangular beam varies 
 as the ordinates of a parabola, being a maximum at the 
 middle of the depth of rectangle, where it is three-halves 
 of the average. 
 
 Concrete in shear partakes of the weakness of concrete 
 in tension, because it depends for its value to a large 
 extent on the tenacity of the material. In simple com- 
 pression a loose hard material, such as sand, if it be 
 confined, has great strength, but it can have no shearing 
 
 277 
 
strength. Reinforcement confines concrete to a large de- 
 gree, and lessens dependence upon tenacity in the material 
 itself. Concrete in compression can therefore have a 
 much greater relative safe value than in shear. Shear 
 must be depended upon in design, but its unit value 
 should be low. If 50 pounds per square inch be taken as a 
 safe limit in shear, the average on the rectangle should 
 be two-thirds of this. The allowed end shear is then 
 shown by the following equation 
 
 W 
 
 = 12 D X 2-3 X 50, or W = 800 D 
 
 2 
 
 where W is the total load in pounds on a beam or slab 
 12 inches wide. 
 
 The bending moment in a uniformly loaded beam, car- 
 rying a total load W is W times VB of the span. If L = 
 span in feet we have, from (i) 
 
 L 
 M' 88D 2 = 8ooD x = iooDL 
 
 ^j*l 8 
 
 or 88D=:iooL, and since D is in inches and L in feet, 
 
 the actual ratio of D to L is about I to 10. Hence, when 
 the depth of a beam or slab is greater than one-tenth of 
 the span, the concrete is overtaxed in shear, and must be 
 reinforced. 
 
 This reinforcement is best effected by curving up some 
 of the rods and anchoring them at the ends or passing 
 them over into adjacent spans. 
 
 By an arrangement such as shown in Fig. i the total 
 end shear is taken by the rod, at least such of the shear 
 as is represented by the load giving the stress in the rod 
 that is curved up. If some of the rods are curved up 
 and anchored at the ends of span and others are horizontal 
 throughout, the concrete will be called upon to take only 
 the end shear represented by the part of the load taken 
 by the horizontal rods. 
 
 Continuous beams are of frequent occurrence in rein- 
 forced concrete being almost a necessary result of the 
 
 278 
 
00 
 
 rio 
 
 2 
 
 W 
 ^ 
 < 
 
 Q 
 15 
 
 W 
 J 
 
 < 
 
 s 
 
 H 
 
 K 
 
 O 
 
 
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 /> 
 
 V 
 
 l 
 
 
 
 279 
 
nature of its manufacture. The bending moment on an 
 indefinite line of continuous beams all uniformly loaded, 
 or that on a fixed ended beam, is two-thirds of that of a 
 simple beam. This moment is negative and occurs at the 
 supports; at the center of one of these beams the bend- 
 ing moment is less, but, if the adjacent beams be relieved 
 of their live load, the bending moment at the center of 
 this beam increases to an amount depending upon the 
 relation between dead and live load. For these reasons 
 some designers use two-thirds of the simple beam mo- 
 ment for reinforcement at center and ends of beams that 
 are continuous. There are several objections to this. 
 First, the formula for continuous beams is based on beams 
 having a uniform moment of inertia. This is not true of 
 reinforced concrete beams. Second, it is generally im- 
 practicable to make the last beam of a line fixed at the 
 end, and the bending moment of a beam of uniform mo- 
 ment of inertia, fixed at one end and simply supported 
 at the other, is equal to that of a beam simply supported 
 at both ends. This bending moment is, however, at the 
 fixed support and is negative. In a continuous beam the 
 moment at this support may exceed two-thirds of that 
 of a simple beam. Third, uniform load on all spans does 
 not give the maximum moment at the middle of a span. 
 Fourth, the relief moment at the supports in any beam 
 under consideration, assuming that beam to be fully 
 loaded and the side beams unloaded, is at the expense 
 of negative moments in the side beams, which may re- 
 quire reinforcement in the top of beams throughout their 
 length. Complete reinforcement at top and bottom of 
 beams throughout the span is not desirable and is not 
 economical. Fifth, some beams in the structure may not 
 be joined end to end with other beams, and some may 
 not be of the same span as those adjacent. Complications 
 would thus be introduced that no simple rule would 
 cover. Sixth, in alterations on the structure a beam 
 may be taken out upon which another depends for its 
 
 280 
 
strength. Seventh, unequal settlement of supports will 
 disturb the condition of assumed continuity. 
 
 The first reason given above is sufficient to condemn 
 the use of the purely theoretical method, not because the 
 theory itself is incorrect, but because it is not applicable. 
 Fully carried out the theory of the continuous beam 
 would greatly complicate both the design and the execu- 
 tion, and it would not possess the redeeming feature of 
 being correct. A further reason why top reinforcement 
 as a primary element of strength should be avoided 
 where practicable is this practical one. In a fire the prin- 
 cipal damage to floors is on the under side where heat is 
 greatest, and is usually, in the case of concrete, of the 
 nature of spalling at the surface. Damage to the con- 
 crete of a beam or slab on the tension side affects only 
 the grip on the steel, and would have to be extensive to 
 be serious; whereas a small amount of spalling on the 
 compression side would greatly weaken a reinforced con- 
 crete beam. 
 
 If each beam be reinforced for its full bending moment 
 as a simple span in the way outlined above, there can be 
 no question as to its safety, provided the top flange stress 
 near the support is not such as to crack the concrete and 
 thus weaken the beam in shear. There remains, then, 
 the necessity, in beams where continuity exists, of pre- 
 venting tension in the concrete "in this portion of the beam. 
 The rigidity of the beam, if fully reinforced for the 
 simple beam moment, will be greater than if reinforced 
 for only a part of that moment, and the deflection will 
 be less. Hence the tendency to produce tension in the 
 top flange near the supports is diminished. To overcome 
 this tendency it is recommended that reinforcement be 
 used to the amount of one-half of that at the center of 
 beam and that the reinforcing rods extend at least through 
 one-quarter of the span. This would be equivalent in 
 total reinforcement to three-quarters of the full rein- 
 forcement at center of span and three-quarters at sup- 
 ports, and would be distributed in a more rational manner. 
 
 281 
 
In an arrangement such as shown in Fig. 2, if the upper 
 rod is made continuous and horizontal near ends of span 
 for a portion of the span, as indicated, the tension in the 
 upper part of the beam at supports will be taken care of. 
 Tension in these rods, however, in the curves at A gives 
 a force in the direction of the arrows, causing tension in 
 the bottom of beam. In such case the bottom rod should 
 also be continuous or else anchored at supports, as there 
 is a tension under the arrows, where these rods would 
 have developed only a portion of their anchorage, if not 
 secured at the ends of span. With rods so arranged in 
 continuous beams one-half of the reinforcing rods may 
 be brought up near the top flange over supports and the 
 other half made horizontal throughout. Splicing of rods 
 should be over supports, either with sleeve nuts, which 
 is preferable, or by lapping rods fifty diameters. The 
 continuity of bottom rods, as well as top rods, adds 
 greatly to the rigidity of the building. 
 
 In the case of slabs of short span there is scarcely any 
 need of reinforcement near the top of slabs over sup- 
 ports, because of the extra concrete that is generally pres- 
 ent. The concrete supplies a rigidity that does not allow 
 of much deflection, and the danger of cracking, if the 
 slab is properly reinforced near the bottom, is small. The 
 writer made some tests on concrete slabs 3 feet 8 inches 
 in clear between the beams and 3 inches thick, in which 
 there was no reinforcement whatever. Many of these 
 were cracked through the middle parallel to beams. In 
 spite of the cracks and the absence of reinforcement the 
 slabs showed no signs of distress under 250 Ib. per square 
 foot of superimposed load. Slabs of this sort should un- 
 doubtedly be reinforced, but owing to the excess of con- 
 crete made necessary by practical considerations of thick- 
 ness, the rigidity resulting therefrom is warrant for the 
 omission of top flange reinforcement. 
 
 Continuous slabs of long span deflecting as simple 
 beams would bend at sharper angles over the support 
 than short span slabs. Hence the need of top flange rein- 
 
 282 
 
forcement in longer spans. Slabs in which there is not 
 an excess of concrete over the requirements for compres- 
 sion will not be as rigid as those in which there is an 
 excess of concrete. It is recommended that in slabs of a 
 span of 9 feet or more, and in all cases where there is 
 an area of three-quarters of one per cent or more of 
 steel, one-half of the reinforcing rods be curved up over 
 supports, as indicated in Fig. 2. 
 
 As an example of the application of the foregoing in 
 the design of the floors of a building, given a building 
 having columns 15 feet apart, to be designed for a live 
 load of 100 pounds per square foot, assumed to be quies- 
 cent. Assume girders between columns and the beams 
 supported by the same to be spaced 5 feet apart. For 
 the floor slab assume a depth of 3 inches. By equation 
 (4) the bending moment per foot of width is 855 ft-lb. 
 The dead load in this case is 40 Ib. and the live load 
 100 Ib. per sq. ft. The total moment is then 140X25-^-8 
 438 ft.-lb. The area of steel reinforcement, instead of 
 being 1^4 per cent of 12x3 sq. in. (or .45 sq. in.) will need to 
 be only 438/855 of .45 or .23 sq. in. per ft. width of slab. 
 This can be made up of J4-in. square rods spaced 3 in. apart. 
 These should be placed with centers ^ in. above the bot- 
 tom of slab. In addition there should be say two rods 
 running parallel to the beam to tie the concrete together 
 in that direction. 
 
 For the beams the span is 15 feet. The slab weighs 
 200 Ib. per ft. of beam; the assumed weight of beam in 
 addition is 130 Ib. per ft. The total load is then 830 Ib. 
 per ft. and the bending moment is 
 
 830 X i5 2 -^8 = 2340oft.lb. 
 Assuming a depth of 18 in. we have by equation (2) 
 
 M' per foot width of beam = 101 X i8 2 32700 ft.-lb. 
 The width of beam is then 23,400 -~ 32,700 = .716 ft. or 
 say 8^2 in. For reinforcement i% per cent of 18 X &/^ 
 = 1.9 sq. in. The allowed diameter of rods is 1-200 of 
 180 in., or .9 in. Three round rods of this diameter would 
 make up the exact area required. Further, the circum- 
 
ference of the three rods would just about equal the 
 width of the beam. The nearest commercial sizes to this 
 are %-in. and I5~i6-in. For the purpose of having an even 
 number of rods four round rods i3-i6-in. in diameter 
 will be used. The superficial area of these rods in 200 
 diameters, ( 162.5 in.) is 1,658 sq. in.; the area of a 
 horizontal section of the beam is SVz X 180 = 1,530; 
 but as these rods are of larger diameter than necessary, 
 the horizontal shear would be taken care of in this beam 
 if all rods were horizontal. To take the stresses due to 
 continuity two of these rods will be curved up at sup- 
 ports, as shown in Fig. 2. At center of span all rods 
 will be 2^4 -in. from bottom of beam. 
 
 For the girder assume a depth of 24 in., including the 
 depth of slab. The total dead weight of bay is about 19,000 
 lb., and the live load carried is 22,500 lb., a total of 
 41,500 lb. 
 
 When a girder carries beams equally spaced, two of 
 which are at the ends of span, the bending moment is 
 the same as though the load were uniformly distributed, 
 if one of these beams is at the center of span, that is, if 
 there is an even number of spaces. If W = the total load, 
 L= span in feet, the bending moment =WL -~ 8. If 
 there is an odd number of spaces, the bending moment 
 is less by the value of the moment that would occur in 
 a span equal to the space between beams. For example, 
 if there are five spaces, the bending moment in a span 
 L W L WL 
 
 -T- is ^~ X ""- | -^ =: ~^ ' 
 
 WL_WL 3 W L 
 
 8 200 ~~ 25 
 
 In the present case there are three spaces, and the 
 bending moment is 
 
 WL WL WL 
 
 8 ~~ 9x8 ~ 9 
 The bending moment on this girder is then 
 
 284 
 

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 I' 
 
 
 j 
 
 
 
 to 
 
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 Vj 
 
 
 
 
 ^ 
 
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 p 
 
 B 
 
 
 
 
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 5; 
 
 
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 ^Q 
 
 
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 ft 
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 2l3a 
 
 
 
 
By equation (6) M' IO5D 2 105 X 2 4 2 = 60480 
 ft.-lb. per ft. width of beam. 'The beam should then be 
 14 in. wide. The area of steel required is I 1 /* per cent 
 of 14 X 24 = 4.2 sq. in. This*may be made up of seven 
 %-in. round rods, five of which lie horizontal and two of 
 which are curved up as in Fig. i. In addition to these 
 two %-in. rods, which pass into adjacent beams to take 
 
 i the stress due to continuity, there can be two %-in. round 
 rods 8 ft. long placed near the top of girders over the 
 support, to make up the remainder of the 50 per cent 
 
 i of steel area. 
 
 The end shear of this girder is about one-third of the 
 load of a bay or 14,000 lb., as the load of one beam is 
 taken directly to the column. At a nominal ultimate of 
 200 lb. per sq. in. on concrete in shear, with a factor of 
 safety of 3^2, the allowed unit is 57 lb. per sq. in. Two- 
 thirds of this as the average on the rectangle = 38 lb. 
 per sq. in. This on a section 24 in. x 14 in. gives 12,800 
 as the shear allowed on the concrete. As the concrete 
 is called upon to take only 5-7 of the shear the shearing 
 strength is ample. At center of span all rods will be 2.4 
 in. from bottom of beam (say 2% in.). The five horizontal 
 rods a're to be equally spaced, being 2^4 in- center to 
 center, the outside ones being \Vz in. from the surface. 
 The two curved rods may lie between horizontal rods. 
 Fig. 3 illustrates this floor. 
 
 Reinforced concrete lends itself to construction in the 
 form of slabs supported on four sides, and such construc- 
 tion may in some cases be more economical than the 
 ordinary beam and slab design. Given a square slab sup- 
 ported on all four edges, the side of the square being L 
 feet, as shown in Fig. 4. Assume that this slab is to be 
 reinforced in two directions at right angles to each 
 other. It is clear that the strip A B, i ft. wide, and the 
 strip / each being similarly placed in the structure will 
 each sustain the same load. Each will then take one-half 
 of the load on the middle square foot of the slab. The 
 strips 2, 3, 4, etc., will be prevented from deflecting as much 
 
 286 
 
as strip I and hence will take less load than strip I in pro- 
 portion as their deflection is less. Strip A B will then be 
 compelled to carry more than half of the load on the 
 square at the intersection of itself and strip 2 and still 
 more at the intersection with strip 3, etc. It is sufficiently 
 accurate to assume that the deflections of strips I, 2, 3, 4, 
 etc., diminish as the ordinates of a parabola. Hence the 
 load on strip A B increases in the same relation. Fig. 
 4, at (b), illustrates the loading on strip A B. The 
 bending moment at the center of span for the uniform 
 load of intensity l /2 w, is wL 2 -f- 16. For the load in- 
 creasing from zero at middle of span to Vzw at the ends, 
 it can be shown that the bending moment at the middle 
 of span is w L 2 -~ 96. The total moment at center of span 
 
 This strip is the critical strip of the slab. Reinforce- 
 ment can be diminished towards the beams surrounding 
 the slab. This diminution is not uniform, however, but 
 as the ordinates of a parabola. At a point VL from the 
 beam the reinforcement must be not less than % of that 
 at the center. A good rule is to use the same reinforce- 
 ment for the middle half of the span and uniform varia- 
 tion from the quarter points to a minimum at supports. 
 
 For the beams supporting this slab an intensity of load 
 may be assumed equal to the reaction of strip A B, or 1-3 
 w L. Assuming a uniform load on the beams we find 
 
 Moment = 
 
 If the beam supports two equal square slabs, moment = 
 
 2^1(9) 
 12 
 
 It is to be noted that this is the same moment as 
 would be obtained by assuming that each beam on the 
 side of the square supports a load uniformly increasing 
 from ends to middle of span, being Vz wL at middle for 
 each square of slab supported. In using this formula w 
 should be taken as the weight per sq. ft of slab plus the 
 
 287 
 
uniform live load per sq. ft. The weight of the beam 
 itself below the slab is a uniform load whose moment is 
 found in the ordinary way. 
 
 Exactness is not claimed for this theory. It is based 
 on reasonable assumptions, however. 
 
 On account of the fact that the cross rods in the slab 
 cannot occupy the same position the reinforcement must 
 be proportioned accordingly. 
 
 In a rectangular slab supported on four sides and ob- 
 long in shape the amount of reinforcement needed in the 
 two directions is found as shown in Fig. 50. It will be 
 seen by trial that when there is much difference between 
 the sides of the oblong the short span will take nearly all 
 of the load. Thus when one side is 50 per cent longer than 
 the other k = I, showing that in an oblong slab of these 
 proportions reinforcement in the long direction needs to 
 be only nominal. 
 
 As an illustration of the application of the above to a 
 floor in square slabs, take the case of columns spaced 15 
 feet each way, live load 100 Ib. per sq. ft. Assuming a 
 weight of slab of 70 Ib. per sq. ft. we have by equation 
 (7) a total moment on one foot width of slab = 2,790 
 ft.-llx By equation (4) we find a depth of slab of about 
 5% in. One and one-quarter per cent of 3 in. x 5^ in. 
 would require just a little more than 7-16 in. square rods. 
 This size of rod could be used, spaced 3 in. apart and % 
 in. above the bottom of slab, but this would not leave room 
 below for the layer of rods in the other direction, with 
 sufficient concrete. To meet the difficulty we will add ^4 
 in. to the depth of slab and make the plane separating 
 the two layers of rods one inch from the bottom of slab. 
 The spacing of 3 in. will be used for the middle seven 
 feet, increasing to 12 in. towards supporting beams. To 
 take care of the continuity every alternate rod in the mid- 
 dle half of slab will be brought up near the top of slab at 
 quarter points, all other rods being straight. This will 
 make a sort of square basin in the middle of the slab. 
 
 Assume a beam supporting the slabs of a depth of 24 
 288 
 
1- 
 
 s.. 
 
 JL 
 
 ^D 
 
 K _____ 
 
 * 
 
 I* 
 
 f 
 
 < 
 
 y -j 
 
 5 
 
 Equation ofe/a>fic //ne (Orig/n c?f o) 
 
 -* z ' 
 
 96 
 
 O&f/ecfion of o - 
 
 Z&&OE1I 
 
 for equa/ def/ecf/ons 
 
 334 El 2880 El . 2>84EI 288OE/ 
 
 living H _ 75L/+-/4L? 4 
 
 Moment on sfian 
 
 289 
 
in., including slab, and a weight of 200 Ib. per ft. below 
 the slab. By equation (9) the total moment from the slab 
 is 47,800 ft.-lb. Adding 5,630 ft.-lb., due to weight of 
 beam, we have a total of 53,430 ft.-lb. By equation (6) 
 we find the width of beam to be io l /2 in. The reinforce- 
 ment can be made up of four %-in. square rods, two of 
 which curve up, as in Fig. i, and pass into adjacent spans. 
 At the middle of span all rods are 2^6 in. from bottom 
 of beam. 
 
 Comparing this floor with the one worked out above hav- 
 ing slab, beams, and girders, we find that the one having 
 beams and girders contains about 124 cu. ft. of concrete 
 per bay or square, while the other contains about 148 cu. 
 ft. The forms would be simpler in the square slab con- 
 struction, and this would tend to balance the cost. 
 
 A reinforced concrete building should be tied together 
 as a unit, just as a building having a steel frame is tied 
 together by the rivets that connect the beams to columns. 
 This can best be effected by making rods in beams and 
 slabs continuous, either by connecting them end to end 
 with turnbuckles or by lapping them over supports. It is 
 hard to see how a failure of any considerable extent could 
 take place in a building so tied together, even* under the 
 severest conditions, assuming that the columns are prop- 
 erly designed. 
 
 In the execution of plans for reinforced concrete it is 
 very essential to have steel placed just where calculations 
 show that it should be placed. This is not always easy 
 to do, especially in any complicated design. Permanent 
 templates left in the concrete may work an injury by 
 making a plane of cleavage for the starting of a crack. 
 Exactness in placing the steel may be secured in the fol- 
 lowing manner: 
 
 Given a beam having reinforcing rods placed as per Fig. 
 6, at any given section. A template of wood is made fit- 
 ting the cross section of the beam and extending up above 
 the slab 6 or 8 in. Holes are bored in this template for 
 each of the reinforcing rods. It is then sawed through 
 
 290 
 
 
these holes into pieces that can be turned and removed 
 from the box which forms the mold for the beam. It 
 could, of course, be made of several pieces fitted together. 
 When in use the parts are clamped together as in the fig- 
 ure, with the rods passing through the holes. Enough of 
 these templates should be used to hold the rods in position 
 during placing of the concrete. When the concrete has 
 been placed nearly to the template on both sides, the rods 
 will then be held by the concrete itself. The templates 
 may then be undamped and the pieces turned and drawn 
 out, and the concreting completed. 
 
 
 IB: ! 
 
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 I 
 
 < 
 
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 FIG. 6. 
 DISCUSSION OF T BEAMS AND SLABS. 
 
 Editor Concrete Engineering: 
 
 The article by Mr. Edward Godfrey in your issue of 
 Jan. I, was an excellent one, and if the many good recom- 
 mendations which it contained were generally followed 
 the number of failures in reinforced concrete constructions 
 would no doubt be greatly reduced, if not wholly elim- 
 inated. Reinforced concrete has lately received a bad rep- 
 utation, and any rules and recommendations which tend 
 to spread knowledge on the subject, and influence design- 
 ers and superintendents to exercise better judgment and 
 care in the execution of their work, are very welcome. 
 
 Referring to the clause in the article dealing with T 
 
 beams, the writer, although admitting that it is on the 
 
 side of safety, believes that it is unnecessary extravagance 
 
 to figure beams, in the .way -recommended by Mr. God- 
 
 291 
 
^ 
 
 /s-o- 
 
 32" 
 
 Live ffoor 
 A/ternafive 2 '-- Par 
 
 S /<?>:- 
 
 r? ffe foam ca/- 
 
 $. 
 - SfeeA /0% 
 
 
 s* ? 65 off"- 
 
 292 
 
G/rders - 
 
 6.0 >s# in. 
 
 ALT. II. FLOOR SLAB DISREGARDED 
 IN CALCULATING BEAMS AND GIRD- 
 ERS. 
 
 RESPECTIVE BENDING MOMENTS AND 
 DEPTHS OF FLOOR MEMBERS REMAIN 
 THE SAME AS FOR ALT. I. 
 
 SLAB: REMAINS THE SAME AS FOR 
 ALT. I. 
 
 
 
 o 
 
 
 .1 
 
 J3_* 
 
 "?! 
 
 < H 
 
 U O 
 
 -so q 
 
 i 
 
 s 
 
 -20' 
 
 ALT. II IS CONSEQUENTLY 13.9 
 CENTS MORE EXPENSIVE PER SQ. FT. 
 OF FLOOR THAN ALT. I OR ABOUT 
 50<&. 
 
 THE COST OF CENTERING WOULD 
 ALSO BE IN FAVOR OF ALT. I. 
 
 V r <^ 
 
 *J f*5 M <*5 
 
 C *? ? ^ 
 
 o q 9 q 
 
 : p w 
 
 s ii 
 
 oo O 
 
 293 
 
frey. It is safe to say that in more than 50 per cent of all 
 the reinforced concrete structures built in this country, 
 and in Europe, the beams have been treated as T beams, 
 i. e., a portion of the floor slab has been considered as 
 forming part of the beam, in calculating the strength of 
 the same. 
 
 The fact that nearly all of these structures are standing 
 today and carry the loads for which they were designed, 
 is at least partial proof that this method of calculation re- 
 sults in a sufficiently safe design. 
 
 The question of how much of the slab may be safely 
 considered as part of the beam is a matter which should 
 be determined by tests. The writer usually assumes that 
 about 1-5 of the span on either side of the beam acts as 
 top flange. This assumption is based on the condition 
 that the floor slab is built monolithic with the beams and 
 girders, and that the slab reinforcement is carried across 
 the beams continuously, and tied down into the beam re- 
 inforcement, by means of stirrups or hangers. Such a 
 slnb may be considered as a practically built-in-beam, in 
 which case the point of contra flexure occurs at a dis- 
 tance of (0.21 /) from the beam, for uniform loading. 
 (See illustration.) Within this distance the upper part 
 of the slab is in tension, and the lower part in compres- 
 sion, due to negative bending moments in the slab. In 
 addition to these stresses the bending of the beam pro- 
 duces compressive stresses in the slab at right angles to 
 the former. The latter have their maximum intensity at 
 the top and tend to increase the tensile stresses, which are 
 resisted by the slab reinforcements, and are practically nil 
 at the bottom. It is often found impracticable to raise 
 the slab reinforcement over and adjacent to the beams, 
 so as to fully resist the tensile stresses, in which case, it 
 is necessary to introduce small secondary rods of the re- 
 quired section and length near the top of the slab, as the 
 concreting proceeds. 
 
 VThat a considerable economy is effected by considering 
 the beams of T section, as compared with rectangular sec- 
 
 294 
 
tion in designing, is apparent from the example given be- 
 low, which, it is believed, represents an average case. The 
 calculations of the beams and slabs are based on the reg- 
 ulations governing the design of reinforced concrete work 
 in New York City. 
 
 Apart from the matter of economy, the beams which 
 are figured as rectangular become very clumsy, and would 
 be objected to in many buildings on-that account alone. 
 
 A. JORDAHL. 
 
 Editor Concrete Engineering: 
 
 Sir: The letter from Mr. A. Jordahl in your issue 
 of Feb. 15, in favor of the T-beam calculation of rein- 
 forced concrete, seems to me to prove something that is 
 manifest and to pass without comment the issue brought 
 up by my article in the issue of Jan. I. I do not claim 
 that it is cheaper to neglect the floor slab in calculation 
 of the beams. If the concrete is needed around the rods 
 to grip them and to take up the effect of differential ex- 
 pansion, it should be there for that purpose, and means 
 should not be sought, through some hokus pokus of 
 methods of calculation, to leave it out for the sake of 
 cheapness or supposed economy. I do not mean by this 
 to question the regularity of Mr. Jordahl's calculation. 
 I have not checked his figures, but take them to be right 
 according to some method or other of calculation. What 
 I wish to say is that any method of calculation that re- 
 quires in a girder having 426 sq. in. of concrete, 6 sq. in. 
 of steel, and in another of the same depth, having 800 
 sq. in. of concrete, 9 sq. in. of steel to perform the same 
 work, is radically wrong. 
 
 According to this method of calculation a beam of a 
 certain depth can have nearly half of its concrete shaved 
 off and 1-3 of its steel without affecting its strength; or 
 conversely, if nearly 100 per cent be added to the con- 
 crete of a beam, leaving the steel the same, it will be 
 weakened one-third on account of being shy that amount 
 in tensile strength of the steel. This difference is of 
 295 
 
course due to the shifting of position that the neutral 
 axis is supposed to undergo. The method used by Mr. 
 Jordahl to locate the neutral axis is purely theoretical, 
 and it is theoretical in a dangerous way, in that it leaves 
 out of the account the one most important consideration, 
 namely, the effect of the shrinking of the concrete in 
 setting. Furthermore, tests do not in any way substan- 
 tiate the results of this theory. 
 
 A fault in the girder preferred by Mr. Jordahl is, that 
 he has 6 sq. in. of steel in a girder only 10 in. wide. If 
 this were made up of 6 i-in. sq. rods, there would be only 
 2-3 of an inch between them. It does not seem possible 
 for the concrete to grip effectually this amount of steel 
 and to overcome the effect of differential expansion due 
 to temperature changes. I have seen beams 3 in. wide 
 with i^-in. sq. rods in them cracked up, under the dead 
 load alone, in a way that tended to prejudice one against 
 reinforced concrete construction. Under load the beams 
 resembled a string of beads. 
 
 To reiterate, my position is this : If the neutral axis 
 be taken at the center of depth of the concrete beam, 
 where tests have shown it to be, the only saving in a 
 T-beam over a rectangular beam is in concrete in the 
 lower part of the rectangle, and the concrete is needed 
 here to protect and grip the steel. The steel in each case 
 would be exactly the same in amount. 
 
 EDWARD GODFREY. 
 
 FLOOR SLAB CONTROVERSY CONTINUED. 
 Editor Concrete Engineering: 
 
 Sir: Permit me to say a few words in reply to Mr. 
 Godfrey's letter in your last issue. My letter in your 
 issue of February I5th, merely attempted to show that 
 under certain specified conditions it is entirely safe to in- 
 clude part of the floor slab in calculating the strength of 
 beams, and that such procedure is attended with consid- 
 erable economy. I did not pretend that the (T) beams in 
 the example submitted were as strong as those of rec- 
 
 
tangular sections, but I did claim that they were amply 
 strong to do the work, and that the rectangular beams 
 involved a considerable waste of materials, due to their 
 calculation being based on the extravagant assumption 
 that the floor slab did not add to their strength. 
 
 It would be interesting to have Mr. Godfrey furnish data 
 of tests on reinforced concrete T beams which uphold 
 his contention that the neutral axis is at the center of the 
 depth for any percentage of reinforcement. 
 
 The fault which Mr. Godfrey sees in my girder, in that 
 it had 6 sq. in. of steel in a width of 10 in., is not as serious 
 as he imagines. The 6 in. sq. bars would be placed in 2 
 horizontal rows, the underside of the first row i l /2 in. from 
 the bottom and with a clearance of i l /2 in. between the 
 lower and upper row. The bars in each row would be 
 placed with 2 in. clearance and i l /2 in. from the sides of 
 the girder. To insure the steel being placed in its correct 
 position in the beam box, and held there while the con- 
 creting proceeds, it is necessary to make it up into frames 
 or units, provided with saddles and spacers, and for that 
 reason it is more practicable to place the steel in 2 hori- 
 zontal rows, even if there are only 4 rods in the beam. 
 This, of course, reduces the effective depth of the beam a 
 little, but that is more than offset by the increased security 
 and ease of handling and placing the steel. 
 
 In conclusion, I have seen a large number of concrete 
 beams 6 to 10 in. wide, designed as T beams and carrying 
 test loads often several times that for which it was de- 
 signed, without showing any cracks or other evidence of 
 weakness. 
 
 A. JORDAHU. 
 
 Editor Concrete Engineering: 
 
 SIR: Replying to Mr. Jordahl's letter, in rebuttal I 
 would state briefly that if he did not pretend that the T 
 beams in his comparison were as strong as the rectangular 
 297 
 
beams, why did he compare them in cost in order to dis- 
 credit the rectangular beam? 
 
 I cannot give any data of tests on T beams that will 
 prove that the neutral axis is at the center of the depth. 
 Can Mr. Jordahl give any to prove that it is not? Mr. 
 Jordahl's theory is entirely upset in the case of rectangular 
 beams by tests which show the neutral axis close to the 
 center for safe loads. Why should it be held to be good in 
 T beams? The modulus of elasticity of concrete varies all 
 the way from one million to five million. Now if such a 
 peripatetic value as this is to have any weight in designing 
 and calculating beams, where are we at? The strength of 
 a beam would be a function of the designer's private opin- 
 ion as to what the modulus of elasticity ought to be. 
 
 EDWARD GODFREY. 
 
 The Design of Reinforced Concrete 
 Arches. 
 
 The arch is about the least promising form of reinforced 
 concrete design to standardize by reason of the apparently 
 refractory facts about an arch and its loading. In any in- 
 vestigation of the stresses or the stability of an arch as- 
 sumptions must be made, since the same degree of accuracy 
 is not possible in arches as that which obtains in steel 
 frames or even in reinforced concrete beams. The prem- 
 ises and assumptions upon which the following investiga- 
 tion is based are these: 
 
 (i) Concrete will be considered to take only compres- 
 sio" (and the shear incident to the joint action of concrete 
 and steel as a beam to resist bending). The unit com- 
 pression, or the extreme fibre stress on concrete will be 
 taken at 500 Ibs. per square inch. This would not be a 
 safe value on a plain concrete arch, but by virtue of the 
 steel reinforcement, which ties the concrete together and 
 relieves it of bending strains, the concrete thus held is 
 capable of withstanding with safety a compressive stress 
 of this intensity. 
 
 298 
 
(2) Steel will be considered to take only tension. The 
 unit tension allowed will be taken at 10,000 Ibs. per square 
 inch, because at this stress, it is believed, few if any cracks 
 will develop due to the extension of the steel under ten- 
 sion. 
 
 (3) Earth will be considered to exert only vertical 
 force. It is of course true that earth has the ability, under 
 certain conditions, to exert horizontal pressure; but it is 
 not good engineering to depend for stability upon earth 
 exerting an active horizontal pressure, unless the condi- 
 tions are such that a measurable deflection or movement 
 horizontally, is not injurious. The compressibility of earth 
 is well known. Buildings having their foundations in earth 
 will settle gradually and often continuously. If an arch is 
 made to depend for its stability upon earth against which 
 it presses horizontally, there will be the same tendency of 
 the earth to settle back in the direction of the pressure, and 
 this with a resistance but a fraction of that of a horizontal 
 surface of earth against a vertical load. An assumption of 
 horizontal pressure of the earth fill over an arch gives a 
 curve of stability for the arch that is more advantageous 
 and would give a more economical arch, but the nature of 
 the case does not warrant this assumption. 
 
 (4) An arch will be considered stable and safe if the 
 arch ring is capable of resisting the thrust and bending 
 moment due to any possible applied loading, when the 
 curve or polygon of equilibrium is drawn in such position 
 as to give a minimum bending moment, or minimum devia- 
 tion from the central line of the arch ring. In the case of 
 stone or plain concrete arches it is conceded that the arch 
 will be stable if an equilibrium polygon can be drawn, using 
 any possible applied loading, that will pass within the mid- 
 dle third of all joints. The two propositions are equally 
 sound. 
 
 (5) The arch proper will be taken as the part of the 
 structure included between two vertical planes through the 
 inner faces of the arch abutments. The rise of the arch 
 will be taken as the middle ordinate of the central line of 
 
the arch ring, considering the curve to terminate where it 
 pierces the planes above referred to. If an arch be de- 
 signed with a curve at springing joining the intrados and 
 the inner face of abutment wall, as will often be the case 
 for appearance sake, this small curve should have no 
 structural significance. The effective rise of the arch is 
 only obscured by considering the curve as having any 
 weight in determining the rise. The intrados of the arch, 
 the extrados, and the median line between these (the cen- 
 tral line of the arch ring) will in general be close approxi- 
 mations to arcs of circles, each having one radius. Embel- 
 lishments on the intrados, for grace of outline, should be 
 considered as such and omitted from the calculations. 
 
 (6) The abutments of the arch will be separately treated 
 as abutments and not as part of the arch. Their office as 
 anchoring mediums for the reinforcing rods of the arch 
 will also be recognized. 
 
 (7) It is understood that all calculations refer to a 
 foot in width of the arch ring and that the arch is one 
 having fill in the spandrel up to the floor level. For a 
 ribbed arch a modification can be made by using factors 
 that will represent the weight carried by one foot in width 
 of the rib. The arch will be taken as hinged at the abut- 
 ments. 
 
 Fig. i gives a typical form of arch. The intrados, ex- 
 trados, and median line are here shown as arcs of circles. 
 As stated these curves will approximate circular curves; 
 the actual curve to be used must be determined by the 
 calculations. Attention is called to the method of finding 
 the thickness of arch ring. If the intercepts marked 
 "equal" in the figure are so made, the thickness of arch 
 ring will be proportional to the secant of its inclination to 
 the horizontal, as should be the case where the thrust of 
 arch is constant. A constant thrust necessarily follows 
 where only vertical loads are considered. 
 
 In what follows earth will be assumed to weigh 100 Ibs. 
 per cu. ft. and concrete 150 Ibs. 
 
 For a uniform live load of W Ibs. per sq. ft. the thick- 
 
 300 
 
ness at the crown may be found in the following manner. 
 The loads to be considered are (i) the arch ring, (2) fill 
 from arch ring up to level of crown, (3) fill from level of 
 crown to floor level. (This may include paving, by mak- 
 ing proper allowance for weight in value of //), (4) live 
 load. If we find the bending moment for these several 
 loads at the center of span and divide the same by R, the 
 result will be the thrust at crown. The allowed average 
 stress on the cross section of the arch will be taken at 250 
 Ibs. per sq. in., which would be the average with the ex- 
 treme fibre stress 500 Ibs. per sq. in. and intensity diminish- 
 ing to zero at opposite edge of rectangle. A small devia- 
 tion of the curve of equilibrium will throw the same one- 
 sixth of the depth out of center, which would give the 
 conditions just named. 
 
 The bending moment due to the fill from level of crown 
 of arch down (assuming the curve of arch a parabola and 
 remembering that the area of the fill to one side of the 
 center is 1-6 5" R and its center of gravity is ^ S from the 
 center line of the arch) is 
 
 1005 Rf S 35\ S* R 
 
 Now taking the effect of the arch ring as that of a uni- 
 form load 10 per cent greater than the depth of ring at 
 crown we have for the total moment at center of span 
 
 100 H S 2 , 165 D S 2 
 
 __ 
 
 ~48~~ ~8~ T~ 8 
 
 Dividing the right side of this equation by R we have 
 the thrust, which we have assumed to equal 250 X *44 D 
 (taking all dimensions in feet.) Hence we have 
 
 From this we may derive the following value for the 
 depth of arch ring: 
 
 This formula is to be used only for a trial depth. As 
 301 
 
302 
 
will be shown later the effect of the live load covering a 
 portion of the span is to produce an extreme fibre stress 
 on the concrete greater than the unit stress from the 
 thrust of arch fully loaded with live load. 
 
 A little study of some of the curves of equilibrium will 
 be useful in the investigation of the arch. 
 
 A circular arc is the curve of equilibrium for forces 
 normal to the curve itself and of equal intensity for every 
 unit of length of the curve. This curve is useful in con- 
 nection with arches because of the ease with which it can 
 be constructed, and because the curve of equilibrium for 
 an ordinary arch will not differ much from a circular arc. 
 
 The catenary is the curve that a flexible cord will as- 
 sume from its own weight. It is the curve of equilibrium 
 for forces parallel to each other and of equal intensity 
 for every unit of length of the curve. The curve of equi- 
 librium for an arch ring of uniform thickness, supporting 
 the ring alone, is a catenary. 
 
 The common parabola is the curve of equilibrium for 
 forces parallel to each other and of equal intensity for 
 every unit along the chord of the curve. The curve of 
 equilibrium for a uniform load over the entire arch, con- 
 sidering this load alone, is a parabola. The fill over 
 the arch between floor line and a line parallel to the same 
 through the crown would demand a curve of the same 
 shape. 
 
 Another curve is one that would support a load repre- 
 sented by the distance from a horizontal line through 
 the crown of the arch and the arch ring. Such a curve 
 would be the curve of equilibrium for the fill over the 
 arch below the level of the crown. Assuming the arch 
 ring of an arch having a rise R and a span 5" to be a 
 parabola whose equation is 
 
 we have for the conditions in a curve having the same 
 rise and span, which would be in equilibrium under the 
 fill over this parabolic arch, 
 
 303 
 
dy _ihrust at {x, y) 
 llx shear at (x, y) 
 
 The thrust at any point is the same, and, as we have 
 seen above, amounts to S 2 for a load of unity per 
 unit of area of fill. 48 
 
 The shear at (x, y) is 1-3 x' y. (Note that x' is the 
 absissa of the parabola and x of the curve under dis- 
 cussion, y corresponding for both). 
 
 But *= 
 
 O 
 
 --^! X 3 5 2 = S* 
 dx 48 
 
 Integrating we have jy 4 =_ ~ 
 16/t 
 
 This is a parabola of the fourth degree. 
 
 The catenary, the common parabola, and the curve 
 whose equation has just been deduced will each have its 
 influence in determining the shape of the curve of equili- 
 brium, and hence the line of the arch ring itself, in an 
 arch having fill over the haunches and supporting a uni- 
 form live load. The curve will be a sort of composite 
 of all. 
 
 Using the circular arc and the parabola as standards by 
 which to compare the other two we find that if all four 
 curves pass through the same points at ends and crown, 
 the catenary will lie between the circular arc and the par- 
 abola. For ordinary ratios of span and length it will 
 be almost midway between these curves, being a little 
 nearer to the parabola than to the circular arc. The cir- 
 cular arc will of course be outside of the parabola. The 
 parabola of the fourth degree referred to will be outside 
 of the circular arc. It will be flatter at the crown than 
 any of the others and will rise above the circular arc over 
 the haunches of arch. 
 
 The effect of the fill in the spandrel of the arch is to 
 
 make the curve of equilibrium to rise above the circular 
 
 arc at the haunches, and that of the weight of the arch 
 
 ring and of the fill from level of crown to floor line, as 
 
 304 
 
well as the uniform live load, is to make the curve drop 
 below the circular arc. The combined effect is to make 
 the curve approach a circular arc, depending for its loca- 
 tion upon the predominence of these two influences. 
 
 In treatment of arches the graphic method is generally 
 used. This method used alone is crude and inexact. Much 
 of its inaccuracy can be overcome by combining with it the 
 analytic method to determine reactions, thrusts, etc. Thus 
 the horizontal thrust of an arch of a given rise can be 
 found by taking moments as for a simple beam at the cen- 
 ter of span: dividing the moment obtained by the rise 
 will give the thrust. This thrust laid out to scale opposite 
 the middle point of a vertical representing the consecutive 
 applied vertical loads will give the exact location of the 
 pole to make the equilibrium polygon pass through the 
 central line of the arch at crown and springing. This 
 avoids the usual cut and try method employed. The sim- 
 ple beam moment at any other section is equal to the prod- 
 uct of the thrust and the ordinate of the equilibrium poly- 
 gon. Hence dividing this moment by the thrust, already 
 found, will give the ordinate of the polygon at the section 
 under consideration, or the ordinate for the central line 
 of the arch. 
 
 Having the approximate dimensions of the arch the cal- 
 culations for the simple beam moment are readily made. 
 Of course the arch could be drawn to scale, using say a 
 circular arc for the curve, and divided into vertical strips 
 of any desired width, and the areas of these strips could 
 be used to determine the applied loads. Then treating the 
 arch as a simple beam or girder span the bending moment 
 may be found at center of span, which divided by the 
 rise will give the thrust. Then the simple beam moment 
 at any other section may likewise be computed; dividing 
 this by the thrust will give the proper ordinate for the 
 arch. 
 
 It is believed the following method will give results, in 
 any ordinary case, that are commensurate in accuracy with 
 the common assumption of the weights of concrete and 
 305 
 
earth. The uniform live load, the fill above crown, and 
 the total weight of arch ring can be taken as a uniform 
 load over the arch. To find the bending moment at any 
 section assume one-half of this total weight as concen- 
 trated at that section, treating the arch as a simple beam. 
 The moment due to weight of fill below crown level is 
 
 where y = distance from center of span to section consid- 
 ered. This is the moment for a parabolic curve for top 
 of arch ring. 
 
 Having found several points in the arch ring the curve 
 can be drawn through these points. 
 
 The effect of live load on part of the span in altering 
 the shape of the equilibrium curve is another important 
 point to consider. This can be best seen experimentally 
 by taking a cord already loaded, or a heavy cable, and 
 suspending loads upon it. The added load will cause the 
 cord to dip in the vicinity of the load. In general there 
 win be a point on each side of the load, in the new curve, 
 that will coincide with a point in the original curve, while 
 the part between these points and the end supports will 
 rise. By adjusting the length of the cord one of these 
 points could be brought to any selected position. In the 
 treatment of the arch the curve of equilibrium takes the 
 place of the cord in the suspended system and responds to 
 the shifting of the live load, rising where the other would 
 dip, and vice versa. It is plain that any number of as- 
 sumptions can be made as to the nodes or points in this 
 curve which retain their original position. In accordance 
 with the fourth of the premises given at the beginning of 
 this article the node will be taken at such position as to 
 make the curve of equilibrium to dip at one side of this 
 node by the same amount a it rises at the other side, 
 measured vertically. 
 
 By assuming that the curve of equilibrium for dead 
 and live load is the same as that for the dead load alone, 
 and that the two agree with the center line of arch ring, 
 306 
 
also that the curve is a parabola, the bending moment in 
 the arch can be determined analytically in a manner to be 
 shown presently. It is not meant that results obtained by 
 assumptions that appear to be so loose as these are to be 
 used in the final design of the arch. The assumptions af- 
 ford a means of determining the position of live loads for 
 the maximum effect on the arch, and supply a simple for- 
 mula expressing this effect, the results of which are very 
 close to the true results. The proper relation between span 
 and rise, depth of arch ring and reinforcement can be 
 studied by this means to an extent not approached by any 
 graphical or other trial method. 
 
 If the curve of equilibrium for dead load coincides with 
 the central line of arch ring, bending on the arch ring 
 is eliminated excepting for live load, and we are left free 
 to investigate the effect of a concentrated load or uniform 
 load covering part of the span with the arch as a simple 
 curved line. 
 
 In Fig. 2 A O B represents the curve of an arch shown 
 in the position in which a parabola is generally consid- 
 ered to be placed with respect to the axes of co-ordinates. 
 For a concentrated load P, the triangle A F B is an equilib- 
 rium polygon. If the distances D C and F E are equal, 
 this polygon is the one giving the minimum moment on 
 the arch. The amount of this moment is v times the 
 thrust in the polygon. The various relations shown in 
 Fig. 2 may be deduced from the properties of a parabola. 
 The moment on the arch may then be expressed in the 
 following equation: 
 
 -2.4142*') 
 
 
 For the position of P, to give the maximum value to 
 this moment, we equate the first differential coefficient of 
 this expression to zero. The value of z thus found is 
 .3305*. A concentrated load would then be placed two- 
 tenths of the span length from one end of the span in 
 order to give the maximum bending moment on the arch 
 ring. 
 
 307 
 
Reaction- -| (S- 2.4142 Z-.S 
 
 2.4142 Z- 
 
 (a) 
 
 
 Load W per, ff. 
 
 
 308 
 
Substituting the above value of z in (4) we have 
 
 For two concentrations, as at (a) Fig. 3, the equation 
 for the bending moment in the arch ring is 
 
 For the maximum value of M 2 we find by differentiating 
 and equating to zero 
 
 19.312* 18.49 S/ + 4S 2 2 = 2 Q (Ss ^) 
 
 The value of z is seen by this to depend upon that of Q. 
 The following have been worked out: 
 
 If Q i/io S, z .3085, M 2 = .osiPS. 
 
 If Q = 2/10 S 1 , * = .2875, M 2 .040PS. 
 
 HQ = 3/io 5> = .267^, M 2 .osiPS. 
 
 If Q = 4/10 5> = .2485, M 2 = .025PS. (7) 
 
 If Q be made zero, we find that z = .33o5", which agrees 
 with the value for a single load as previously found. If Q 
 be made = S 2.4142 z, the largest value of Q that would 
 bring both loads on the span, we find that z .248 S. 
 Hence a greater value of Q need not be considered than 
 this, which is four-tenths of S. 
 
 For uniform load, as at (&), Fig. 3, the equation for the 
 bending moment in the arch ring is 
 
 Differentiating this and equating to zero we obtain for 
 the position to give the maximum moment on the arch 
 z .248 S. Substituting in (8) we have 
 
 This agrees with the last equation of (7), if P be made 
 .4W, as it should. 
 
 We thus see that the maximum effect of any live load 
 in producing bending is obtained when the load covers 
 four-tenths of the arch. 
 
 The foregoing considers only the bending moment on 
 the arch produced by the live load, and not the varying 
 thrust due to the shifting position of the load. It is there- 
 309 
 
fore applicable to the steel reinforcement only, as the 
 steel is assumed to be stressed only by bending on the 
 arch ring and not by direct load or thrust. For the posi- 
 tion of live load to give the maximum effect on the con- 
 crete we should derive an expression that will combine the 
 extreme fiber stress due to bending and the unit load due 
 to the thrust or direct compression. Taking the differ- 
 ential coefficient of such expression and equating it to 
 zero we would find the position of live load that will give 
 the maximum effect on the concrete. The writer worked 
 out the problem along these lines and found that the re- 
 sulting equations involved R and D as well as 5" and Q. 
 However, by assuming ratios between R and D both these 
 terms could be eliminated. Using wide variations in the 
 ratios of R to D it was found that the values of z that 
 satisfied the equations were practically equal to those found 
 by considering the bending moment alone. This is be- 
 cause of the relatively greater effect of the bending mo- 
 ment as compared with the thrust in producing stress. The 
 equations expressing the maximum bending moments on 
 the arch, as already given, will then be used both in dis- 
 cussing the proportions of the arch ring and the reinforcing 
 steel. 
 
 This treatment of the reinforced concrete arch demands 
 practically constant reinforcement near both top and bot- 
 tom surfaces of the arch ring from end to end, with rods 
 running into the abutment for anchorage. The reason for 
 this uniform reinforcement is seen by an inspection of 
 Fig. 4. In this figure the center line of arch is represented 
 by the line A O B. The bending moment due to a single 
 load rolling across the span is represented by the vertical 
 distances from A O B to the curves A M N and Q R B. 
 The bending moment due to uniform load advancing across 
 the span is represented by the vertical distances from 
 A O B to curves A T U and Q V B. It is here seen that 
 the bending moment is pretty generally distributed in the 
 length of the arch, so that no part of the arch can be 
 lacking in reinforcement. The bending moment is of op- 
 310 
 
posite sign for load coming on from the right and from the 
 left, showing the need of reinforcement near the top and 
 bottom of arch ring from end to end of span. 
 
 Taking up first the steel reinforcement we will assume 
 that 1 54 per cent of steel area is to be used, ^ of i per 
 cent near the upper surface and the same amount near the 
 bottom surface of the arch placed % D from the surface. 
 Referring to the writer's article on beams and slabs, pub- 
 lished in Concrete Engineering, Jan. 15 and Feb. i, 1907, 
 it will be seen by equation (i) that for a reinforcement 
 of i }4 per cent at the bottom of a slab the allowed bending 
 moment for rolling loads is 88 <f per ft. width of slab, d 
 being in inches. For $i of i per cent, as here assumed, the 
 bending moment, to give the same stress on the steel, is 
 44 d 2 . Equating this to the value of the maximum moment 
 from uniform live load, as given in equation (9), and re- 
 ducing the depth to feet, we have 
 
 ^ 52 =6336JP a (10) 
 
 In the design of arches the following live loads will be 
 taken as standard: 
 
 loo Ib. per sq. ft. for foot traffic and light vehicles. 
 
 200 Ib. per sq. ft. for heavy driving. 
 
 500 Ib. per sq. ft. for trolley traffic. 
 
 l,ooo Ib. per sq. ft. for steam roads. 
 
 The latter is the live load found by taking an axle load 
 of 60,000 Ib. uniformly distributed over a space 5 by 12 ft. 
 The load of 500 Ib. per sq. ft. is probably greater than any 
 live load at present specified for trolley traffic, but the 
 experience of steam railroads teaches that it is wise to 
 anticipate heavier loading. It is especially so in a struc- 
 ture of the permanence of a reinforced concrete arch and 
 one which has so little possibility of being reinforced sub- 
 sequent to its construction or used again for another loca- 
 tion having lighter traffic. 
 
 Reverting to equation (10), if we let W = loo, 200, 500, 
 1,000, we find 
 
 S = So D for light traffic. 
 
 311 
 
S rr 56 D for heavy traffic. 
 
 S 36D for trolley traffic. 
 
 S 2^D for steam roads, (n) 
 
 These ratios of span to depth, while not intended for 
 final use in design, are of use in fixing upon a close ap- 
 proximation of the final proportions. The economical pro- 
 portions can readily be studied by means of equation (10). 
 If more steel be used than i% per cent, a less depth can 
 be employed than that given by equations (n), and if 
 less steel, a greater depth is needed. Steel reinforcement 
 is affected only by the live load, and, as seen, is inde- 
 pendent of the rise of the arch, except as the rise is gov- 
 erned by the depth assumed. 
 
 To take into account the effect of live load on the con- 
 crete we will consider the arch as being loaded for 4-10 of 
 the span, giving the moment as shown in equation (9). By 
 the principles of mechanics, in a rectangle having a width 
 B and depth D 
 
 66 D 
 
 where M is the bending moment, K is the extreme fiber 
 stress, and A is the area of the rectangle. But K A being 
 the product of fiber stress and area may be called an 
 equivalent direct stress, for if we divide this by the area 
 we obtain the fiber stress. Applying this in equation (9). 
 we have for an equivalent direct load L on the arch 
 
 <> 
 
 Under the same loading, from the expression for thrust 
 as given at (fc), Fig. (3), we find it to be 
 
 (13) 
 
 We can now modify the derivation of equation (i) 
 to include the effect of live load on a portion of the span 
 only. The allowed thrust, instead of being taken at 36,000 
 D to allow for a possible bending moment due to irregu- 
 larities, will be taken as 72,000 D, as we now have a definite 
 bending moment, which is a large factor in producing an 
 312 
 
equivalent direct stress as a component part of that thrust. 
 The second term on the right hand side of the equation 
 just above (i) will now be the value in equation (13), and 
 a new term will be added, namely, the value of L in 
 equation (12). 
 
 Hence we have, as an equation expressing the propor- 
 tions necessary in an arch whose central line coincides with 
 the curve of equilibrium for dead load, the maximum effect 
 of live load being considered, the following: 
 
 Both equations (i) and (14) should be made use of in 
 finding the depth of an arch, and the depth that is the 
 greater should be employed. For concentrated loads equa- 
 tion (14) may be modified by altering the second and last 
 terms on the right hand side in accordance with the par- 
 ticular loading used. 
 
 If for trial we make H D, using the ratios in equa- 
 tions (n), and solve equations (i) and (14), we find the 
 values shown in Table A. The values in columns 2, 4, 6 
 and 8 are found by equation (i), and those in columns 3, 
 5, 7 and 9 are found by equation (14). The approximate 
 agreement between these rises for each class of loading 
 suggests that the percentage of steel reinforcement used, 
 namely, i% per cent of total area, is probably close to the 
 economic and proper amount. As this is not far from the 
 amount of steel used in many arches already built, there 
 is a further suggestion in the table, namely, that the rises 
 shown for the various classes of loading and different 
 spans will probably give close to the right proportions. 
 
 It is recommended that reinforcement of an arch be 
 made with round rods running from end to end of span 
 and for a distance of 50 diameters of rod into each abut- 
 ment. They should be spliced, where they join, with turn- 
 buckles. Rods should lie */& of the depth from both top and 
 bottom surface of arch. Sharp curves should be avoided, 
 especially in rods near the surface, for stress in the steel 
 may cause the rod to tear out a portion of the concrete. 
 
 313 
 
in 
 
 W 
 
 w 
 
 ca u 
 
 < 
 HO 
 
 yJjS I oot^ot^o?p 
 
 
 -i ^ 00 CO CS CO 
 f* i i CO *1* 
 
 > oi w 
 
 
 
 "S^Q 
 
 !*"| 
 
 *S.9 
 
 c* 
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 G 
 
 w 
 (J 
 
 W ~ 
 
 P^ J 
 
 t H o 
 
 10 
 
 s s 
 
 o-Q 
 ' 
 
 
 .Swf 
 
 X) 
 
 ^ d*^^ 
 
 S >, 
 
 CO 00 t~<OOOCO 
 
 .2W ^ 
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 X) 
 
 ooMoooeoct 
 
 CU 
 (/5 
 
 314 
 
If rods are placed 2 diameters from the surface, the radius 
 of curvature should not be less than about 80 diameters 
 of rod. If rods are three diameters from surface, the 
 radius of curvature should be not less than about 50 diam- 
 eters of rod. This is to keep the shearing unit on the con- 
 crete covering the rod within safe limits. 
 
 There should be rods through the arch laid across the 
 main rods and wired to the same, to tie the concrete to- 
 gether in that direction and to distribute the load in a 
 transverse direction. These may have 1-3 to 1-5 the area 
 of the main reinforcing rods. 
 
 In the abutment it is necessary to consider (i) the load 
 per sq. ft. on the soil, (2) the stability against overturn- 
 ing* (3) the stability against sliding. 
 
 In Fig. I the principal forces acting on the abutment are 
 indicated in the parallelogram A B C D. In this parallelo- 
 gram D C represents the force supplied by the arch itself. 
 This is the resultant of the total weight of arch, including 
 the live 4oad supported, and the horizontal thrust under full 
 load. - The force B C is the weight of concrete and earth 
 lying directly above the base E F applied in the line of 
 the resultant of these combined weights. A C is the re- 
 sultant of these two. This latter line must pass within 
 the middle third of the base E F, so as to insure a con- 
 dition of zero tension at F. The maximum pressure on 
 the base will then not exceed twice the average pressure 
 from the total weight above given, considering this weight 
 as distributed on the base E F. To this, however, is to be 
 added a load per sq. ft. equal to the live load per sq. ft. 
 to allow for live load over the abutment. 
 
 To provide against sliding, the direction of A C should 
 be such that its horizontal projection is not more than 
 one-half of its vertical projection. This means that a co- 
 efficient of sliding friction of one-half is assumed. 
 
 The dimensions of the abutment are to be adjusted 
 until the above conditions are satisfied. If the resultant 
 pressure does not fall within the middle third of the base, 
 the base must be extended away from the arch. Also if 
 
 315 
 
the vertical pressure on the soil is too great, the same 
 extension should be made; or an offset may be made on 
 the inner edge of abutment, if this does not cause the line 
 of pressure to fall without the middle third of the new 
 base. If the inclination of the resultant A C is not steep 
 enough to have a tangent of two, the abutment should be 
 made deeper. 
 
 The above does not apply to a rock foundation. Where 
 the abutment rests on rock and can be built so as to have 
 a bearing against a vertical rock surface to take the hori- 
 zontal thrust, it need not have mass enough to resist over- 
 turning, for the rock surface can be relied upon to resist 
 horizontal forces. The inclination of the resultant pres- 
 sure may, of course, be less, as sliding is also prevented 
 by the rock. 
 
 As a corollary to the foregoing it may be added that the 
 same general principles apply to stone arches or plain 
 concrete arches, except as they bear on the steel rein- 
 forcement. In such an arch, where the material will not 
 take tension, the resultant pressure must not fall outside 
 of the middle third of the arch ring. 
 
 Fig. 5 shows the conditions that will hold when the 
 resultant falls at the edge of the middle third of the arch 
 ring. Taking equation (14) we find that the first, third 
 and fourth terms of the right hand side of that equation 
 equal the dead load thrust, and the second term is the live 
 load thrust when the live load covers 4-10 of the span 
 from either end. The distance % R in Fig. 5 is the maxi- 
 mum deviation from the arch ring, or v of Fig. 2, under 
 the same loading. Making this substitution in the equa- 
 tion in Fig. 5 and reducing we have (if D = H) 
 
 r>_5. 521 > 2 +. 0067 WD /1 _, 
 
 .01 ^-.3472 D 
 This expresses the relation between the rise and the 
 depth of an arch needing no steel reinforcement. In such 
 an arch we could allow an extreme fiber stress of 400 Ib. 
 per sq. in., or an average at the crown of 200 Ib. under 
 316 
 
CM 
 
 X 
 
 H 
 
 1 
 
 
 
 3 ^ 
 
 d 
 
 1 
 
 ! 
 
 
 1 E 
 
 3 
 
 1 
 
 
 o 
 J 
 
 i 
 
 8 
 
 
 
 
 o 
 
 |*k4 Q|vO 
 
 l*-orN- 
 
 J 
 
 317 
 
full load. Following the derivation of equation (i) we 
 ly then write 
 
 <"> 
 
 By trial it was found that using the ratios of S to D 
 given in Table B the approximate agreement in values of R 
 were found to exist It is interesting to note also that 
 these values of R do not differ greatly from those in 
 Table A. 
 
 It is to be observed that the arch of Table A is propor- 
 tioned ort the assumption that the steel reinforcement is 
 stressed by any eccentric load on the arch ring. In thick 
 arches especially reinforcement could rationally be dimin- 
 ished by reducing the bending moment by the amount that 
 the plain concrete would take. That is, in refining the 
 calculations the distance v of Fig. 2 can be diminished by 
 1-6 of the depth of arch ring. 
 
 For short spans of say 20 to 30 ft., arches do not seem 
 to be appropriate. Flat slabs or straight beams and slabs 
 would seem to be more suitable. Horizontal thrust is then 
 eliminated, and the abutments may be much lighter. 
 
 SHORT ARCH SPANS. 
 Editor Concrete Engineering: 
 
 Sir: In your issue of March I, Mr. Godfrey concludes 
 an article on "The Design of Reinforced Concrete Arches," 
 with the following statement: "For short spans of say 20 
 to 30 ft., arches do not seem to be appropriate. Flat slabs 
 or straight beams and slabs would seem to be more suit- 
 able. Horizontal thrust is then eliminated and the abut- 
 ments may be much lighter." 
 
 I am unable to discover any basis for such a conclusion. 
 The relations between arches and beams of short spans 
 are the same as for arches and beams of longer spans. If, 
 then, a beam of 30 ft. is more desirable than an arch of 
 that span, why is not a beam of 150 ft. span more desir- 
 able than an arch of the same span. The only reasonable 
 difference between the two is in forms and erection and 
 318 
 
this difference is maintained for the longer spans as 
 well as for the shorter. 
 
 I have frequently heard the statement by engineers, 
 similar to that given above by Mr. Godfrey, that the rea- 
 son an arch is not as efficient as a beam is because it has 
 horizontal thrust. But that is the very reason that makes 
 the arch more efficient than the beam. The banks of a 
 stream have horizontal resistance as well as vertical resist- 
 ance; why then throw away the horizontal reaction when 
 the arch offers so satisfactory a method of using it to re- 
 duce the material in the structure? If an arch and a 
 beam of same span and having the same depth are both 
 reinforced to the same extent, the beam will require heavier 
 abutments than the arch to support the same loading in- 
 stead of lighter abutments, as Mr. Godfrey's statement 
 would indicate. Such an arch would have the same strength 
 as the beam without exerting any horizontal thrust at all. 
 
 The above statements will doubtless appear strange to 
 many railway bridge engineers who do not understand 
 the arch, yet those same engineers will use knee braces in 
 their beam culverts, "to shorten the span," as they say, 
 without realizing that a logical conclusion of this form 
 of design would be an arch. 
 
 DANIEL B. LUTEN. 
 President National Bridge Co. 
 
 Editor Concrete Engineering. 
 
 Sir: I have before me a copy of a letter from Mr. 
 Daniel B. Luten criticising my statement that for short 
 spans arches do not seem to be appropriate, and beg to 
 thank you for the opportunity to reply. 
 
 Mr. Luten says he does not discover any basis for such 
 ?. conclusion. The basis is this: An arch of short span 
 and economical proportions, so far as the arch itself is 
 concerned, that is, eliminating the abutments, as my table 
 would show, would have a small rise, say I ft. or so. 
 Now the purpose of using any kind of a structure to span 
 319 
 
space is to get an opening for water or passage. With 
 so low a rise the arch would have to be on the top of high 
 abutments in order to get the opening necessary. Again 
 with so low a rise there would be a heavy thrust. High 
 abutments with a heavy thrust on top would be anything 
 but economical. 
 
 I attempted to show in the first part of my paper that 
 it is not good engineering to depend on earth as exerting 
 an active horizontal pressure. It is well known that earth 
 settles away from any pressure brought upon it. What 
 sort of conditions would result if a short arch of 20 ft. 
 span settled away at the ends to the extent of only an 
 inch at each end? It is especially true that earth fill 
 is quite unstable. This is what would be encountered in 
 the large majority of cases so near the top of an arch. 
 Such would be totally unfit to take any horizontal thrust. 
 
 Mr. Luten says that the relation between arches and 
 beams of short spans are the same as for arches and beams 
 of longer spans. I do not see how he can sustain such an 
 assertion. I do not think that he would attempt to make 
 or approve a beam of 150 ft. of span, and I do not believe 
 he would condemn a flat slab for a span of 5 ft. My 
 table shows a much greater relative and actual rise in 
 arches of long spans. These greater rises not only allow 
 the clearance and opening necessary, but they also reduce 
 the relative thrust and bring the points of its application 
 down near the base of abutment. These are very im- 
 portant differences in the relation between beams and 
 arches in long and short spans. 
 
 Answering the latter part of his third paragraph I would 
 say that the "arch" that exerts no horizontal thrust at all 
 is not an arch at all. It is simply a curved beam. A simple 
 truss span may be given any camber, even to a large frac- 
 tion of the span, and supported on rollers at one end. It 
 is still a simple span and in no sense an arch. So a steel 
 beam may be curved and given only horizontal supports. 
 It is only a curved beam. An arch must have thrust to be 
 an arch. 
 
 320 
 
There is a popular notion, born of little knowledge, that 
 an arch is the strongest form of construction. But an 
 arch without abutments to take the thrust is not an arch 
 and is not strong. Independent of the effect of curving 
 on the metal a curved I beam is not as strong, simply 
 supported, as a straight one. 
 
 EDWARD GODFREY. 
 
 CRITICISM OF MR. GODFREY'S ARTICLES ON 
 
 ARCHES. 
 Editor Concrete Engineering. 
 
 In your issue of April i, 1907, I called attention to an 
 erroneous statement in Mr. Godfrey's article, that short 
 beams were more efficient than short arches and he replied 
 with the remarkable argument that an arch proportioned 
 for efficiency without considering the abutments, would 
 require such heavy abutments that the beam would be 
 more economical. 
 
 Mr. Godfrey continues : "It is a popular notion born of 
 little knowledge that an arch is the strongest form of con- 
 struction." It is quite true that this notion is born of little 
 knowledge, for the most inexperienced stone mason learns 
 it, but it is surprising that Mr. Godfrey fails to see it. I 
 have been moved to investigate his series of articles on 
 arches and I find a most remarkable combination of unau- 
 thorized assumptions, too numerous to be mentioned in one 
 letter. I beg, however, to call your attention to a few on 
 the first page of his article in your Feb. 15 issue. In 
 (4) he states : "In the case of plain concrete arches it is 
 conceded that the arch will be stable if an equilibrium pol- 
 ygon can be drawn, using any possible applied loading that 
 will pass within the middle third of all joints." This 
 statement should be "*/ the proper equilibrium polygon for 
 each arrangement of loading can be kept within the middle 
 third." Otherwise it is unsound, and his accompanying 
 statement in which he selects the equilibrium polygon that 
 gives the minimum moment, is equally unsound. For an 
 arch hinged at the abutments this latter assumption will 
 321 
 

 hold good only when there is a shortening of the span on 
 striking centers, and every builder of a concrete arch 
 knows that the arch settles and the span increases when 
 the centers are removed. The assumption might prove 
 good if there were great expansion of the concrete in set- 
 ting, but in all other cases it is not only baseless, but is 
 actually on the side of danger. Many of Mr. Godfrey's 
 conclusions will require modification because of this error. 
 
 In (6) and (7) he states that "the office of the abut- 
 ments as anchoring mediums for the reinforcing rods in 
 the arch will be recognized," and in the next paragraph 
 adds that "the arch will be taken as hinged at the abut- 
 ments." 
 
 In (3) Mr. Godfrey says that "it is not good engineering 
 to depend for stability on earth exerting an active hori- 
 zontal pressure." It occurs to me that it is good en- 
 gineering to make the base of a retaining wall sufficiently 
 wide to resist the overturning action of this pressure. 
 Perhaps Mr. Godfrey meant to say that the passive resist- 
 ance of the earth should not be relied upon, but if so he 
 failed to conform to that idea in his arch design, for he 
 actually does neglect the active horizontal earth pressure. 
 Yet every retaining wall proves that there is such a pres- 
 sure. 'It not only must be depended upon for stability, 
 but if neglected it may cause the collapse of the arch. 
 Moreover the passive resistance of earth may be relied on 
 to a limited extent, as Mr. Godfrey himself shows, for his 
 abutment design allows varying intensities of stress. 
 
 Many of his assumptions are made to simplify his proc- 
 ess regardless of consequences, and he labors to make 
 himself and others believe that they are justifiable. 
 
 Mr. Godfrey is wrong in saying that a curved beam is 
 not as strong as a straight beam. The bending moments 
 on the two beams are the same, and the moments of resist- 
 ance are in favor of the curved beam as an analysis will 
 readily show. If he will compare beams and arches on 
 the basis of waterway area he will still find that the arch 
 is the more efficient. 
 
 322 
 
He suggests that I would not approve a beam of 150 ft. 
 span. Certainly not, but merely because of the cost. And 
 this is exactly the reason that I urged against the short 
 span beams. A beam of 150 ft. is quite feasible given 
 sufficient depth and material, but it is exceedingly ineffi- 
 cient as compared with an arch. For shorter spans the 
 difference is not so marked, but it is nevertheless in favor 
 of the arch. 
 
 I have not by any means uncovered all the erroneous 
 assumptions in Mr. Godfrey's article, and with your per- 
 mission will conclude in a subsequent issue. 
 
 DANIEL B. LUTEN. 
 
 MR. GODFREY'S REPLY TO THE FOREGOING. 
 Editor Concrete Engineering. 
 
 I beg to thank you for the opportunity to reply to Mr. 
 Daniel Luten's second letter criticising my paper on arches. 
 
 In Mr. Luten's first paragraph he tries to read into my 
 statements an absurdity that does not exist. It is per- 
 fectly rational to design a beam entirely apart from the 
 supporting walls or columns. Does Mr. Luten see any 
 absurdity in following this with a statement that this beam 
 requires walls or columns or other support? It is per- 
 fectly rational to design an arch without any reference to 
 what is going to support it and to offer the necessary hori- 
 zontal thrust to make it act as an arch. Is it absurd or 
 "remarkable" then to say that if economy in such an arch 
 demands a low rise, the supporting abutments must be very 
 heavy because the thrust is great? 
 
 Now an arch of small span could be made with a large 
 rise in order to get the necessary waterway under it, and 
 this large rise would permit of a small depth at crown be- 
 cause the thrust would be relatively small. So far, so 
 good. Theoretically such an arch would be economical be- 
 cause of the small thickness, for perfectly balanced static 
 loads. If such an arch be subjected to live load, because 
 of the fact that it is of shallow depth and that it has a 
 sharp curve, the equilibrium polygon would readily pass 
 323 
 

 away beyond the confines of the arch, and the bending mo- 
 ment would be great. An arch of shallow depth would 
 offer but little resistance to bending 'moments, and the 
 economy of the arch goes aglimmering. 
 
 I have heard men express the opinion that camber in 
 a girder or truss span is to prevent the span from dipping 
 from a true horizontal line for fear that the strength will 
 all be gone when the deflection exceeds the camber. 
 Others a little better informed still think that camber is 
 necessary to the strength of a truss span, when in fact 
 it does not affect the strength in any manner, and is sim- 
 ply to prevent a dip in the track. These notions are rudi- 
 ments of misinformation from the days when structures 
 were designed by judgment, or, in other words, guess. 
 Are we to return to those days and take our knowledge 
 from "inexperienced stone masons," or are we to continue 
 to analyze structures on the basis of principles of mechan- 
 ics? I would like to repeat my former assertion to give it 
 emphasis. An arch without abutments to take the thrust 
 is not an arch and is not strong. 
 
 I would not have Mr. Luten or anyone else imagine for 
 an instant that my treatment of an arch has anything of 
 the exactness of the common treatment of steel structures, 
 or that it is theoretically correct. The first paragraph of 
 my paper sets this forth clearly. Assumptions are abso- 
 lutely necessary, and a theoretically correct treatment of an 
 ordinary stone or concrete arch is an impossibility. To 
 say that my assumptions are unauthorized leaves me with 
 nothing to reply. One is naturally timid about announcing 
 himself as an authority. If the assumptions are declared 
 to be unsound, that is a different matter. I shall reply 
 from that standpoint. 
 
 Mr. Luten's first attack upon my assumptions is rather 
 upon the English with which one of them is clothed than 
 upon the assumption itself. It is instructive to note that 
 it is the proper equilibrium polygon that must be used, 
 that is, not one belonging to some other arch that may be 
 laid out on the board, but the polygon and loading belonging 
 
 324 
 
to the. arch under consideration. As I read literature on 
 arches, the proper equilibrium polygon is arrived at by a 
 system of cut and*try until a polygon is found that will 
 fill the bill. Of course this method is based on authorized 
 assumptions, and demands a drawing board and all of the 
 necessary accoutrements to make it a first class guessing 
 match. It would not do at all to ascertain beforehand, by 
 calculation, as could readily be done, where this proper 
 polygon will probably pass. 
 
 I cannot see how "each arrangement of loading" is any 
 more lucid than "any possible applied loading." I made no 
 attempt to go into the matter of explaining the well known 
 process of determining the stability of an arch by drawing 
 a polygon that will pass through certain points in the arch, 
 and then, if this fails to pass through the middle third of 
 all joints, drawing another, and another, etc., until one is 
 found that will pass through the middle third throughout. 
 This is known to engineers, and if any others wish to fol- 
 low that way, they can consult works on arches, where 
 this process is fully set forth and recommended. My 
 treatment of plain concrete arches is nothing more nor 
 less than a systematic method of finding, analytically, how 
 deep an arch should be in order to assure the equilibrium 
 polygon falling within the middle third. 
 
 I will not discuss the soundness of this "authorized as- 
 sumption" until Mr. Luten brings out something more un- 
 derstandable than the last part of his second paragraph. I 
 might state, however, that an arch that is designed to give 
 a horizontal thrust against a vertical wall of yielding earth 
 could not be expected to do anything else but settle and 
 increase in span. This is the very thing I stated in my 
 previous letter as the objection to an arch of low rise and 
 small span. It is objectionable in an arch of any rise or 
 span to depend upon a vertical wall of earth to take the 
 thrust, because the earth will settle away, and the arch, 
 to an unknown extent, becomes a beam. 
 
 In Mr. Luten's third paragraph he tries to read another 
 absurdity into my paper. It is because a well designed arch 
 325 
 
needs reinforcement near the top and bottom from end to 
 end of span that I would run the reinforcing rods into the 
 abutment, otherwise there would be no reinforcement until 
 a point was reached, some distance from the abutment, 
 where the rods had sufficient embedment in the concrete 
 to make them effective. It is because the abutment of an 
 arch would not be suitable anchorage for a cantilever that 
 it would not be suitable to hold the end of an arch fixed. 
 Heavy abutments could be designed that would be suitable 
 for taking the stress of a fixed ended arch, but their econ- 
 omy is very doubtful. 
 
 Down in Palos, Alabama, some years ago, I observed 
 some large piers being constructed in earth that was 
 "candy" to dig. These piers not only had vertical sides, 
 but they were chamfered out so as to have a base broader 
 than the section at the ground level. All of this excava- 
 tion was done without a stick of a shore to keep the earth 
 from caving in. Where was Mr. Luten's "active horizontal 
 earth pressure?" It is not an unusual thing to see trench- 
 ing done in earth with little or no bracing and to see earth 
 standing in a high vertical wall for some time. The prin- 
 cipal forces against a retaining wall are those due to the 
 loosening action of rains or the expanding action of frost. 
 These are wedging actions. They have no place whatever 
 on the haunches of an arch, and they would be broken 
 reeds to rely upon against the side of an abutment. I 
 meant exactly what I said, and not what Mr. Luten thinks 
 I ought to have meant. The horizontal pressure of earth 
 over the top of the arch may be neglected with perfect 
 safety. The horizontal pressure of earth behind the abut- 
 ment should be neglected for safety. 
 
 Mr. Luten acknowledges that the bending moments of a 
 curved and a straight beam are the same. It would be in- 
 teresting to see the analysis that shows that putting an 
 I-beam through a bulldozer and curving it in the plane of 
 the web, increases its section modulus. The reason why 
 a curved beam is not as strong as a straight one is because 
 the flange stresses, which tend to go in straight lines, will, 
 
in a curved flange, induce secondary stresses. These 
 stresses would tend to increase or decrease the curvature 
 of the outstanding flanges, according as the stress is com- 
 pression or tension. Curved flanges of a beam or girder 
 are just as irrational and uneconomical as bowed columns 
 or tension members (bowed in one direction.) 
 
 Mr. Luten says in this letter that the difference between 
 arches and beams is not so marked in shorter spans. In 
 his former letter he said: "The relation between arches 
 and beams of short spans are the same as for arches and 
 beams of longer spans." Mr. Luten has more confidence in 
 beams of reinforced concrete than I have. As an engineer 
 I would condemn a beam of 150 ft. span. Would Mr. Luten 
 condemn a slab of 6 ft. span? 
 
 EDWARD GODFREY. 
 
 The Design of Foundations. 
 
 The requisites of a good foundation are: (i) The pres- 
 sure per sq. ft. on the soil must not exceed a certain safe 
 limit. (2) The unit pressure on the entire foundation 
 should be as near uniform as practicable. (3) The pres- 
 sure should never be negative, that is, there should not be 
 a tendency to lift the foundation which is in excess of its 
 weight at any part. (4) The foundation must be suffi- 
 ciently deep not to have the underlying soil disturbed. (5) 
 The materials must be practically indestructible in their 
 respective places. (6) The integrity of the foundation it- 
 self must be assured; that is, it must be capable of resist- 
 ing the forces upon it. 
 
 To provide for the first requisite the safe bearing power 
 of the soil must be known. This is not determined by ex- 
 periment so much as by experience. 
 
 The pressures allowed by the New York Building Code 
 per sq. ft. on various soils are as follows : Soft clay, one 
 ton; ordinary clay and sand together, in layers, wet and 
 springy, two tons ; loam, clay or fine sand, firm and dry. 
 three tons; very firm, coarse sand, stiff gravel or hard 
 clay, four tons. The same building code allows for tests 
 327 
 
being made to determine the bearing capacity in special 
 cases. 
 
 In Baker's Masonry Construction the following are given 
 as the safe bearing power of soils in tons per sq. ft: 
 Quicksand, alluvial soils, etc., 0.5 to I ; sand, clean, dry. 
 2 to 4; sand, compact and well cemented, 4 to 6; gravel 
 and coarse sand, well cemented, 8 to 10; clay soft, I to 2; 
 clay in thick beds, moderately dry, 2 to 4; clay in thick 
 beds, always dry, 4 to 6; rock, from 5 up. This lower 
 value is for rock equal to poor brick masonry. 
 
 In the case of hard rock the area of foundation may 
 sometimes be determined by the strength of the foundation 
 rather than that of the rock. Thus, if concrete is used in 
 a pier with a bearing power of 15 tons per sq. ft., this sets 
 the limit, though the rock may be capable of carrying a 
 greater load. 
 
 Instability in a foundation, as regards the bearing power 
 of the soil, is exhibited in the sinking or settling of the su- 
 perstructure. This may be the result either of compressi- 
 bility of the soil or of lateral flow in it. The unit loads 
 above given are those that will generally give a structure 
 with little or no settlement. On soils other than rock, or 
 solid gravel, or hardpan a little settlement is usually ex- 
 pected and sometimes allowed for in fixing the level of the 
 floors. 
 
 Compressible soils may have their bearing power in- 
 creased (i) by ramming; (2) by driving in short piles to 
 compact the soil by this means; (3) by driving in piles 
 6 or 8 ft. and then withdrawing them and filling the holes 
 with sand, slag, gravel, or concrete, well rammed in, or 
 the holes may be made by driving a cast iron cone 20 or 30 
 ft. into the soil and ramming the hole full of the materials 
 named. The latter method was employed in the foundation 
 of some of the buildings of the Paris Exposition, the ram- 
 ming being done with a cast iron weight of I to i l /2 tons. 
 (See Engineering News, Sept. 27, 1000.) 
 
 The advantages of monolithic and reinforced concrete 
 over all other forms of construction in foundations are seen 
 
 328 
 
in structures resting on yielding soils. The solid mass of 
 concrete, as in a wall, tends to settle as a unit, and uni- 
 formly, even though the pressure may not be quite uniform 
 on the entire foundation. 
 
 Lateral flow in the subsoil is especially troublesome in 
 soils of a clayey nature or in sand that is saturated with 
 water. Quicksand is a saturated sand that flows very free- 
 ly, but many saturated sands that would not be classed 
 as quicksands are subject to this lateral flow; and founda- 
 tions upon such require the utmost care. A good precau- 
 tion is to drive sheet piling just outside of the foundation. 
 so as to retain the sand or other soil, if flowing is antici- 
 pated. This will greatly increase the bearing power. The 
 tower of the Hamburg water works is about 290 ft. high. 
 It is built of brickwork and rests on a circular block of 
 concrete 56 ft. in diameter and n ft. thick. This rests on 
 quicksand enclosed by sheet piling driven below the line of 
 saturation of the River Elbe. The pressure is about 2 tons 
 per sq. ft. on the quicksand. 
 
 Much trouble is caused in the city of Chicago due to the 
 flowing of the subsoil. In the down-town portions of the 
 city there is first a layer of about 13 ft. of made ground, 
 then 6 to 12 ft. of a hard clay, below which is a softer 
 clay for about 60 or 80 ft. to rock or hardpan. In some 
 places this clay becomes very hard towards the rock and 
 contains large boulders. Before the days of tall buildings 
 foundations in Chicago were generally laid on top of the 
 crust of stiff, blue clay found about 13 feet below the sur- 
 face. This was loaded with about 1 24 to 2 tons per sq. ft., 
 and in order to get the necessary area in contact spread 
 footings were employed. These are large pyramids that 
 had to rest on top of the hard clay, as it was found that 
 the bearing power was less if they penetrated into the clay. 
 Before building the Masonic Temple the soil was 
 tested by a tank having an area of 2 sq. ft. in 
 contact with the soil. This was loaded until the 
 pressure was 5,650 Ib. per sq. ft. In one test it 
 was placed on top of the hard clay for 100 hours; the 
 
settlement was I 13-16 in. In a second test it was sup- 
 ported at the bottom of a hole 2 ft. 4 in. deep in the hard 
 clay; the settlement was 4 l /& in. 
 
 Some of the taller buildings were founded on these 
 spread footings, but it was found that the entire crust 
 was depressed by the great load. The settlement was great- 
 er, though the unit pressure was the same as in smaller 
 buildings. This was especially the case where any exca- 
 vation was made below the crust in the neighborhood of 
 these buildings. Excavation for the freight tunnels, which 
 are about 40 ft. under ground, recently caused some tall 
 buildings to settle and develop bad cracks on account of 
 the flowing of the soil. 
 
 The present methods of sinking foundations in Chicago 
 will be described later. Even these cause some settlement 
 in old buildings because of unavoidable spaces left around 
 the lagging in the wells. 
 
 Sometimes retaining walls are built around the site of 
 a building below grade. This, however, is to prevent the 
 flowing in of the soil, if excavation is made for a sub- 
 basement 
 
 The bearing power of gravel or other similar material 
 may sometimes be greatly increased by the use of grout. 
 Gravel not mixed with sand may readily be consolidated 
 into a sort of concrete by forcing into the interstices cement 
 grout. This has been done also where some sand was 
 present in the gravel, by first pumping out some of the 
 sand. The first method was employed in the foundation 
 of a bridge over the Danube, near Ehingen, Wuerttemberg. 
 Pipes having loosely inserted driving points were driven 
 into the gravel at intervals of 18 or 20 in. By drawing 
 the pipe up a few inches to clear the point grout could 
 be pumped into the gravel. Then by successive withdrawals 
 and pumpings a concrete was made of the natural gravel in 
 place. The gravel was one which contained running water 
 and little sand. This would not work in sand or in gravel 
 where much sand is present. (See Eng. News, Jan. 9, 
 1902.) 
 
 330 
 
By the same means a sort of cofferdam can be made in 
 gravel by sinking the pipes around the site of the proposed 
 excavation and building up a wall inside of which ex- 
 cavation can be made. 
 
 There is a process (patented Dec. 8, 1891) for injecting 
 cement grout into quicksand in the making of a foundation 
 in the same. It consists of (i) sinking pipes into the 
 sand, (2) pumping out the sand so as to leave a chamber, 
 (3) forcing cement grout into this chamber. (See Eng. 
 News, April 28, 1892; June 28, 1894; Oct. 16, 1902.) One 
 way to get out the sand is to use two pipes near together, 
 forcing water into one while the water and sand are being 
 pumped out of the other. 
 
 In the foundation work of the Merrimac River bridge 
 at Newburyport, Mass., cylindrical piers were sunk by 
 open dredging to a level where rock was indicated by the 
 borings, and the bottom was found to consist of boulders 
 in a stratum of coarse sand and gravel. The cylinders 
 were then converted into pneumatic caissons, with air locks 
 placed on top, and were loaded with pig iron. The water 
 in them was then blown out. No rock ledge was found 
 within reach of steel probing rods 12 ft. long, and it was 
 decided to use the boulders and gravel as" the foundation. 
 A foot or more of water was allowed to rise in the cylinder, 
 and Portland cement was mixed with it and kept well 
 stirred. By increasing the air pressure this grout was 
 forced out into the surrounding gravel and boulders. The 
 mass was thus rendered stronger to receive the founda- 
 tion. (See Engineering Record, Vol. 50, page 220.) 
 
 When soil is deemed too soft to support the weight of 
 a structure, piles are sometimes driven in. These support 
 the weight either by virtue of their penetrating to hard 
 bottom or by friction on the surrounding soil. Where a 
 substratum of rock can be reached, the piles should be 
 driven to the same, and driving should cease as soon as 
 this is reached. Further hammering may broom or split 
 the pile or cause it to fail by diagonal shear and thus 
 destroy its usefulness. There are various rules for de- 
 
 331 
 
termining when sufficient hammering has been done. One 
 rule allows a penetration not over 16 in. in the last ten 
 blows of a 2,6oo-lb. hammer falling 15 ft. Another rule 
 allows a penetration not over I in. in the last blow with 
 a 2,ooo-lb. hammer falling 10 ft. Another allows a pene- 
 tration not over 3 in. under a 2,ooo-lb. hammer falling 15 ft. 
 for piles supported by friction only. One rule for piles 
 driven with a steam hammer, the hammer of which weighs 
 5,000 lb., requires that the piles will not move more than 
 J4 in. to the blow, when driving is complete. 
 
 By the New York Building Code piles intended to sustain 
 a wall, pier, or post must be spaced not more than 36 or 
 less than 29 in. in centers. They must be driven to a solid 
 bearing if practicable to do so. Piles less than 20 ft. in 
 length may be 5 in. at the small end and 10 in. at the butt. 
 Piles more than 20 ft. in length must not be less than 12 
 in. at the butt. The maximum load allowed per pile is 
 20 tons. 
 
 A rule quite general in Boston is to allow a safe load 
 of 10 tons per pile when supported by friction. Piles 
 reaching hard stratum may be loaded to 16 tons. (See 
 Eng. News, February 5, 1903). 
 
 Specifications for bridges in the city of Milwaukee allow 
 a load of 12 tons on each pile. Piles must be not less 
 than 14 in. at butt and 9 in. at small end and 55 ft. long, 
 driven to hard bottom. The minimum spacing is 2 ft. on 
 centers. Piles may be of pine, tamarack, or hemlock. 
 
 The "Engineering News Formula" for the safe load on 
 piles allows a load in tons equal to twice the weight of 
 hammer in tons times fall in feet divided by one plus 
 penetration of pile under last blow, in inches. 
 
 To prevent the splitting of the head of a pile a steel ring 
 about 3 in. wide and l /2 in. or more thick and about the 
 diameter of the head is laid on it and driven into the 
 fibers with the hammer. This is pulled off by. means of a 
 tool for the purpose when the driving is completed. Where 
 one piece of timber will not reach to the required depth, it 
 is sawed off and spliced by means of a dowel and side 
 332 
 
straps of wood or iron. Piles are usually sharpened with 
 a blunt point. Sometimes steel straps are laid across the 
 point two ways and spiked on, and sometimes cast iron 
 shoes are used to facilitate the penetration and to protect 
 the pile. 
 
 Timber piles in permanent structures should only be 
 used where always wet. The piles are usually sawed off at 
 an even level, below low water line, and the earth is ex- 
 cavated around them for 2 ft. or more. This is then filled 
 with concrete and the pier footing of concrete laid upon 
 the same. Care must be taken in laying masonry upon the 
 concrete to see that it is set first. 
 
 Cheap woods, such as spruce and hemlock, are generally 
 used for piles completely under water, as they will last 
 indefinitely if kept from contact with the air. These soft 
 woods can be obtained in lengths from 20 to 50 ft. and 
 diameters 10 to 12 in. at the head. Hard pine piles can 
 be obtained up to 75 or 80 ft. in length with diameters at 
 the head of about 16 in. 
 
 Concrete piles have recently come into extended use. 
 These may be made by filling up with concrete the hole 
 left by a pile of wood or metal. In some a sheet metal shell 
 covering a removable wooden core is driven into the ground 
 and then the core withdrawn and the shell filled with 
 concrete. These are often tapered. They are generally 
 of larger diameter than wooden piles. 
 
 The following method was employed in some concrete 
 pile work at Pittsburg in 1904. Steel tubes about 16 in, 
 in diameter, of metal about $i in. thick, having bullet 
 shaped shoes loosely inserted in the ends and with wooden 
 heads, were driven into the ground by means of pile 
 drivers. Where the ground was hard, these shoes were of 
 cast iron; and where sufficiently soft, they were of con- 
 crete previously made and allowed to harden. When 
 driven to the required depth, the tube was drawn up a 
 little; and a rammer, made of long cast iron weight sus- 
 pended on a rope, was let into the inside. The known 
 length of the line supporting this rammer served to in- 
 
dicate whether the shoe was in the proper place (not being 
 drawn up by the tube) ; or, if a concrete shoe had been 
 used, it would show whether it had remained whole and 
 had not been jammed up into the tube. Concrete buckets 
 made of old house boilers were then filled and the concrete 
 deposited into the tubes through gates in the bottom of 
 these buckets. After each bucketful had been deposited 
 and rammed the tube was drawn up a little further, the 
 distance being gauged by a mark on the line suspending 
 the rammer. The buckets were not let into the tube, but 
 were emptied at the upper end of the same. Parts of this 
 process are patented. 
 
 Piles reinforced with steel are sometimes molded at the 
 site, and after setting and hardening are driven in the same 
 manner as wooden piles. A method of protecting the head 
 of such a pile in driving is described in Eng. News, De- 
 cember 27, 1906. It consisted in a steel tube fitting over 
 the top of the pile and having a diaphragm against which 
 on one side was a long wooden block to receive the blows 
 and on the other side a short wooden block, and between 
 this and the head of the pile a cushion of rope. 
 
 The foundations of tall buildings in Chicago are now 
 generally made on what might be called concrete piles. 
 They vary from 3 to 12 ft. in diameter and are sometimes 
 100 ft. long or more, reaching down to hardpan or solid 
 rock. The excavation is done by hand in depths of 4 or 
 5 ft. at a time. This circular hole is sheathed with vertical 
 lagging made of boards 2 or 3 in. thick planed radially on 
 the edges and fitted tightly together. These are held in 
 place by flat steel bands, segmental in shape and flanged 
 on the ends, bolted together to form a complete circle. 
 Then the excavation is made another 4 or 5 ft., and this 
 is also surrounded by lagging. At the bottom, if the pile 
 is to rest on hardpan, the well is belled out to twice the 
 diameter. The piles are generally loaded to about 20 tons 
 per sq. ft., and this would give a load of 5 tons per sq. ft. 
 on the hardpan. The holes or wells are filled wth con- 
 crete, well tamped, which should preferably be let down 
 
 334 
 
in buckets, so as not to separate the ingredients and thus 
 impair the uniformity of the concrete. Sometimes the 
 lagging is left in place, and sometimes it is removed as 
 the concreting progresses. The concrete is best made of 
 a mixture of i Portland cement to 2 sand to 4 broken 
 stone or gravel. Sometimes 1 13 :5 concrete is used. Where 
 a pocket of quicksand is encountered, it is apt to flow 
 into the well and to make a change in the method of ex- 
 cavation necessary. One method of meeting the difficulty 
 is to use a steel cylinder, in segments bolted together, either 
 allowing it to sink as the excavation progresses or forcing 
 it down with jacks. This is not always successful, and 
 resort must be had to the use of sheet piling driven from 
 the surface through the stratum of quicksand. Thus a 
 sort of cofferdam is made around the well inside of which 
 excavation can be done without difficulty. When the sand 
 is penetrated, the first described method, using short lag- 
 ging, is resumed. Steel sheet piling is best for the purpose, 
 as it will penetrate further wthout injury, and it can be 
 drawn and used again. 
 
 The tops of these concrete shafts are capped with grillage 
 beams or other means of distributing the load of the 
 column uniformly over the concrete. 
 
 The load allowed on concrete piles should not exceed 
 20 tons per sq. ft. for those of large diameter. If there 
 is any possibility of their acting as columns, as in the event 
 of the surrounding earth being removed, the unit load 
 should be less. Concrete is weak in columns, unless it is 
 properly reinforced with steel. A better load on piles of 
 small diameter is about 15 tons per sq. ft. 
 
 Screw piles are sometimes made use of to distribute 
 pressure and to anchor structures such as lighthouses, sig- 
 nal towers, etc. They are made of a shaft of steel or cast 
 iron and an auger shaped blade of about one turn. They 
 are driven in by turning either by hand or other power. 
 Screw piles for supporting parts of the tunel for the Penn- 
 sylvania and Long Island R. R. under the Hudson River 
 are to be made of cast iron in 7 ft. sections, having inside 
 
 335 
 

 flanges at splice which take 4 i*A in. bolts and 12 steel 
 dowels. The piles are 27 in. outside diameter and of i^ 
 in. metal, and the diameter of the screw is 4 ft. 8 in. They 
 are spaced 15 ft. and aid in the support of a single track 
 tunnel. (See Eng. News, Oct. 12, 1903.) 
 
 The load coming upon the soil of a foundation or on a 
 system of piles consists of the total dead load carried and 
 some or all of the nominal live or superimposed load that 
 the structure may be called upon to carry. In tall build- 
 ings it is not necessary to include all of the live load, as 
 the floors are never all fully loaded with the calculated 
 capacity. The New York Building Code allows a reduc- 
 tion in column loads of 5 per cent of the live load of 2 
 floors (including the roof) ; 10 per cent of the live load of 
 3 floors; 15 per cent of 4 floors; down to 50 per cent of n 
 floors, and 50 per cent reduction for any more than n 
 floors. 
 
 In estimating the weight on a foundation part of which 
 is permanently under water ft is legitimate to deduct the 
 buoyancy of the water for the part of the foundation that 
 is below low water line. Thus in piers at Chicago and 
 Milwaukee 62.5 Ibs. per cu. ft. of masonry below water 
 level may be deducted from the weight of piers. On the 
 other hand this same deduction should be made in de- 
 termining the stability of a partly submerged pier used as 
 an anchor against uplift or horizontal forces. 
 
 A brief description of the processes used in excavating 
 for foundations will be in place here. The ordinary proc- 
 ess of excavating for foundations where water is not en- 
 countered is simple and the problems are few. Apart from 
 digging or blasting out the material and handling the 
 same there is often the question of shoring up the sides 
 against a cave-in. In a wide excavation in loose ground 
 the shores should not be merely horizontal struts, but these 
 struts should be braced together diagonally and vertically 
 to prevent displacement. Wedges or jacks should be used 
 to give a firm bearing against the earth, as it is much 
 
easier to prevent earth from sliding than to stop it when 
 it has once loosened and started to slide. 
 
 There is a process of excavating through flowing soils 
 known as the freezing process. It is expensive and not 
 used very much. It consists of forcing into the soil just 
 outside of the opening to be made refrigerating pipes 
 freezing the mass, excavating and then damming off the 
 soil or building in the stone or concrete work. 
 
 There are three methods of excavating for foundations 
 in water. One is by making a cofferdam by driving sheet 
 piling around the space to be excavated and digging out 
 the earth. The water is kept pumped out as the excava- 
 tion proceeds. Wooden sheet piling, called Wakefield pil- 
 ing, consists of boards spiked and bolted together in threes, 
 the middle one being set back to form a tongue at one 
 side and a groove at the other. Steel sheet piling has been 
 found to be very useful for cofferdam work. It has greater 
 strength than wooden piling, and there is less leakage. 
 The piles can be used repeatedly. Sometimes they rust 
 together in the ground. A blow from the pile driver on 
 the head of one pile will generally loosen the one to be 
 drawn. 
 
 A second method is called open dredging. This consists 
 in dredging out the earth in the inside of a casing, which 
 sinks as the earth is removed. The casing forms a shell 
 for the pier, being filled with concrete when sunk to the de- 
 sired depth. The shell has a uniform outside diameter and 
 is tapered from the inside to a cutting edge. The dredging 
 is done by means of steam shovels, or clam shell, orange 
 peel or other bucket dredges. 
 
 Hydraulic dredging, used in different methods of ex- 
 cavation, is done by means of pumps. Where loose ma- 
 terials are to be removed by pumping out, a jet of water 
 agitating the materials will cause them to be drawn up 
 by the pump. Jets of water may be used to advantage in 
 open dredging to loosen the soil under the cutting edge. 
 Sometimes the cutting edge encounters boulders which 
 
 337 
 
the dredge will not remove, and it is necessary to send 
 down divers to remove the same. 
 
 By use of the open dredging process in the foundation 
 of the Atchafalaya Bridge at Morgan City, La., the depth 
 of foundation bed was made about 120 ft. below high water 
 and 70 to 115 ft. below the silt or mud surface. The 
 greatest depth attained by this method in a bridge 
 foundation was reached in sinking the piers of the Hawkes- 
 bury Bridge in Australia, namely, about 170 ft. below water 
 or 126 ft. below the river bed. 
 
 Concrete deposited in deep water, as in an excavation 
 made by open dredging, is apt to have the cement washed 
 out. To overcome this it may be dropped through a tube 
 or a tremie in as large loads as practicable. If put into 
 jute bags, the cement will be retained; enough cement will 
 ooze out of the meshes to cement the pieces together. 
 Concrete mixed extra long or even retempered concrete, 
 if it has not stood too long, is preferable to concrete in 
 which the cement is too freshly mixed, where it is to be 
 deposited in water. 
 
 The other method of excavation is the pneumatic process. 
 An airtight timber crib or caisson is made, having a space 
 underneath large enough for men to work in, provided 
 with a cutting edge around the periphery and supplied with 
 air locks, etc., in the roof. This is placed in the position 
 which the pier is to occupy and allowed to rest upon the 
 ground. Men enter and leave through the air locks, and 
 the excavated earth is hauled up in buckets through locks 
 for the purpose. Air is continuously pumped in and it 
 escapes below the cutting edge. Ordinarily this air pres- 
 sure keeps the water out, but if the soil becomes dense or 
 is clayey, the air pressure can often be reduced below the 
 hydraulic head of the cutting edge, greatly to the benefit 
 of the workmen. In such case the water that leaks in may 
 be removed with an ejector. 
 
 As the crib sinks the pier is built on it, and when suit- 
 able bottom is reached the working chamber is filled with 
 concrete. 
 
In the Brooklyn pier of the new East River Bridge a 
 depth of 115 ft. below high water was reached by the 
 pneumatic process. In a bridge over the Barrow River in 
 'Ireland a depth of 127 ft. below high water was reached. 
 In this work the air pressure used was 42 to 45 Ib. at the 
 maximum depth. (See Eng. News, Vol. 53, p. 607). 
 
 In foundations for tall buildings in New York some- 
 times pneumatic caissons are required. These are sunk 
 under the individual columns or under two or more col- 
 umns in a group. (See Eng. Record, Sept. 3, 1904, for 
 description of caissons under Trinity Building.) 
 
 The second requisite of a good foundation, namely, a 
 uniform unit pressure on the entire foundation, has special 
 force in foundations on soft soil. On such soils there 
 will be some settlement, and if the unit pressure is greater 
 at one point than another, settlement will be greater at 
 that point. This condition of uniform pressure is effected 
 by making the area in bearing on the soil in proportion to 
 the load to be carried. A great part of the settlement of 
 a building takes place during erection, and it is hence due 
 to the dead weight in greater measure than to the super- 
 imposed weight. In any event, as only a part of the super- 
 imposed load is on the floors continuously, the dead load 
 must be taken as the prime factor in determining the size 
 of footings. If the footings of all of the columns of a 
 building were given areas in proportion to the total dead 
 and live load to be carried, those carrying the walls would 
 settle more than the interior columns. However, the areas 
 of the footings for the interior columns should be based 
 on the probable maximum load, so that the safe pressure 
 on the soil -is not exceeded. 
 
 Sometimes the density of the soil varies under different 
 parts of a building. In such case the foundation should 
 be proportioned so that the pressure will be in conformity 
 to the bearing power of the soil at different parts. The 
 leaning tower of Pisa seems to have acquired the lean 
 which has made it famous by uneven settling on soils of 
 different densities. 
 
 339 
 
Eccentrically loaded piers resting on piles should have 
 \he center of gravity of the system of piles coinciding with 
 that of the load as near as practicable. 
 
 The third requisite, namely the maintenance of a posi- 
 tive pressure on the soil at all parts, has special force as 
 applied to foundations for high or narrow structures where 
 the wind may cause tension or uplift on the windward side 
 at the edge of foundation, also for anchorages of cantilever 
 or suspension bridges. 
 
 In order to have no tension on the extreme edge of a 
 rectangle, the resultant of the vertical load and the hori- 
 zontal force (as the wind load or pull of anchorage) must 
 fall within the middle third of the base. In a circular sec- 
 tion the resultant should fall within the middle quarter of 
 the base. This is a condition which follows upon the 
 theory of flexure. It does not mean that there is a factor 
 fef safety of three when the resultant falls within the 
 middle third of the base. It simply means that this condi- 
 tion must hold, if there is to be no tension and no tendency 
 to rise, at any part of the base. In a material incapable 
 Sof taking any tension, or nearly so, such as a wall resting 
 bn the soil, or a wall laid in lime mortar, there should be 
 absolutely no tension or tendency to rise anywhere. Such 
 tendency would be detrimental to the safety of the struc- 
 ture, especially if it be a reversible condition, as, for ex- 
 ample, in a tower where joints may tend to open on one 
 side and then on the other, due to reversal of the wind. 
 Of course it is true that one application of the wind load 
 would not overturn the tower, if the resultant fell some- 
 where between the middle third and the outer edge, as the 
 resultant must fall without the base in order to overturn 
 a body. But the racking will loosen the joints and tend 
 ultimately to ruin the walls. In a foundation it is manifest 
 that any such disturbance in the region of the main sup- 
 porting medium of a structure would be harmful. 
 
 The condition requiring that the resultant fall within 
 the middle third of the base may be seen from another 
 standpoint, namely, that of uniformly varying pressures. 
 340 
 
Suppose the resultant pressure falls in the middle of the 
 base of a foundation as at (a), Fig. i. The reaction of 
 the soil will be uniform across the width of the base, as 
 represented by the row of short arrows. If the resultant 
 of the pressure falls 1-3 of the base from the edge of the 
 same as at (b), the reaction will be greatest in intensity 
 at the edge nearest this resultant, and it is necessary that 
 the center of gravity of this reaction be on the line of the 
 resultant. Again, if the reacting medium be yielding or 
 elastic, the pressure will vary uniformly from the maxi- 
 mum at the right edge of the base to a minimum at the left 
 edge. Only a triangle, as indicated in the figure, can 
 fulfill these conditions. Hence the pressure varies from 
 zero at the left edge to an intensity double the mean pres- 
 sure at the right edge. 
 
 If the resultant is closer to one edge than 1-3 of the 
 base, and the variation of pressure is uniform, one of two 
 things must occur; either there will be tension on the 
 farther edge, or the pressure will be zero for whatever 
 width of base remains in excess of 3* [See Fig. i, at (c)]. 
 A floating rectangular block supporting an eccentric load 
 whose resultant, or center of gravity, falls closer than 1-3 
 of the width from the edge would be out of water for the 
 width of block exceeding 3^:. 
 
 Fig. 2 shows the anchorage of a suspension bridge. The 
 force A B is the pull on the cable; A C represents the 
 weight of the anchor pier, applied at the center of gravity 
 of the pier; A D is the resultant. This latter force should 
 pass within the middle third of the base 
 
 Fig. 3 shows the pier for a trunnion bridge, such as the 
 bascule bridges of which a number are found in the city 
 of Milwaukee. The force A is the total dead load of 
 trunnion and approach girders. This will be at the center 
 of column supporting these loads, as the trunnion girders 
 are counterbalanced for dead load. The force B is the 
 dead weight of the pier, allowance being made for the 
 buoyancy of the water. C is the sum of the live load over- 
 hanging the pier. The resultant of all of these is in amount 
 341 
 
342 
 
equal to the sum of the three. Its position is found by 
 taking moments, say around the edge of the pier. It is 
 preferable that this resultant fall within the middle third 
 of the base, but if the pier is founded on piles, they may 
 be driven closer on the side of the higher pressure, thus 
 allowing the resultant to fall closer to that edge. 
 
 In the foundation of a chimney or tower the same prin- 
 ciples apply. The dead weight of the structure is one force 
 always present, and the greatest possible wind load is to 
 be combined with the same. The direction of this result- 
 ant must be such as to pass within the middle third in 
 the case of a rectangular base or within the middle quarter 
 in the case of a circular base, that is, it must fall not over 
 1-6 or 1-8 of the diameter of the bases respectively, from 
 the center. 
 
 It is legitimate to allow somewhat greater pressure at 
 the edge of a foundation than those given heretofore, 
 where the increase is due to the maximum wind load. An 
 increase of 25 per cent over the unit regularly allowed 
 would be a reasonable allowance at the edge where the 
 pressure is of maximum intensity. 
 
 The fourth requisite would demand that foundations be 
 made deep enough to be free from danger of undermining 
 by abrasion from streams or drainage water, or by ex- 
 cavation for foundations of adjacent structures. They 
 should be deep enough to rest on soil not affected by frost. 
 
 Many failures of bridges have been due to the washing 
 away of the soil beneath the piers. Gravel beds, upon 
 which piers often rest, could very often be cemented to 
 advantage into one mass by the use of grout, as herein- 
 before described. Often the scouring action of the stream 
 will carry away large stones of the piers themselves. These 
 stones lose nearly half their weight when submerged, and ; 
 are hence comparatively easy to move. This is a strong 
 argument for solid concrete piers. 
 
 A depth of 4 or 5 ft. is sufficient to reach soil not af- 
 fected by frost in temperate regions. This is deep enough 
 
for light foundations as for mill buildings, etc., where the 
 soil is not made ground or fill. 
 
 The fifth requisite of a good foundation, namely, that the 
 materials be practically indestructible in their respective 
 places, can be assured only by using materials of known 
 lasting qualities. Brick should not be used in sea water. 
 Wood should be used only where it will be always under 
 water or always exposed to air only. Cement mortar and 
 not lime mortar should be used in wet places, as lime 
 mortar requires a long time to harden if kept wet. Steel 
 placed in concrete is probably better not painted, as the 
 concrete will adhere better to the steel than to the paint 
 I and is a better medium of protection than paint. 
 
 The sixth requisite demands a foundation that is strong 
 enough to do the work that it may be called upon to do. 
 The forces to be resisted may be (i) a downward force 
 due to the weight of the structure carried, (2) an upward 
 force due to an uplift that may be exerted upon the foun- 
 idation, (3) horizontal or overturning forces, (4) the up- 
 ward reaction of the supporting soil. 
 
 The base of a steel or cast iron column or a bridge bolster 
 ;<>r shoe resting on stone or other masonry should have 
 sufficient area in contact with the stone to prevent crush- 
 iing. It should be borne in mind that generally such 
 ibases do not have an ideal bearing, so that the unit em- 
 jployed should be low, that is, a large factor of safety 
 (should be used It is true that building columns and some 
 (other bases are often set up a little above the surface of 
 [the stone or concrete and the space filled in with grout, but 
 lit is also true that bridge seats are very often placed directly 
 on the surface of the stone. The following are good units 
 of safe pressure to allow on various classes of masonry, 
 in Ib. per sq. in.: Brick masonry in lime mortar, 150; 
 brick masonry in cement mortar, 200; ordinary rubble 
 masonry, 200; good bridge masonry, 250; granite, 400. 
 
 It is of great importance that the masonry pier receiving 
 a cast column base be a rigid mass under the base. The 
 writer observed a number of cast column bases on rubble 
 344 
 
piers that were split in two by the weight of the column, j 
 The rubble appeared to sink under the center of the column j 
 leaving the cast base supported on its edges. Not being 
 suited to take such a heavy bending moment the cast base 
 broke under the weight. The cap of a pedestal or pier 
 taking a column should be a single stone, or, better, the 
 entire pier should be a monolith of concrete. 
 
 A large building in Pittsburg collapsed some years ago 
 on account of the fact that a brick wall between two build- 
 ings that were being thrown into one, was taken out for 
 one story and replaced by columns about 16 ft. apart. 
 These columns were supported on the rubble wall, which, 
 being intended only to carry a continuous brick wall, was 
 unfit to carry the concentrated weight of the columns. 
 Spreading beams under these columns would doubtless have 
 saved the building. 
 
 Suppose in Fig. 4 the load on the column is 150,000 Ib. 
 At 200 Ib. per sq. in. on the rubble wall a flange area of i 
 beams of 750 sq. in. would be required. Assuming I-beam 
 flanges 4 in. wide a length of 188 in. or 15 ft. 8 in. is 
 needed. This will be made up of 2 beams 7 ft. 10 in. long. 
 The pressure per lineal foot is 200 X 4 X 12 = 9,600 Ib., 
 and the span of the cantilever is 3 ft. 6 in. The bending 
 moment is 705,600 in. Ib. and the section modulus required 
 at 16,000 Ib. per sq. in. is 705,600 ~ 16,000 = 44.1. The 
 size of I-beam required is then a 12 in. 40 Ib. beam. As 
 the flange width is more than 4 in., a revision of the cal- 
 culations could be made using the 5^4 in. width of this 
 beam and trying again for the bending moment. 
 
 Beams and rails are often imbedded in concrete footings 
 and pedestals to distribute the pressure over a greater 
 surface, the beams being used to give the resistance to 
 bending which the concrete lacks. Rails are not economical 
 for this purpose, unless they happen to be old rails on hand 
 or purchasable at a much lower rate per Ib. than I-beams. 
 For the same weight of metal much greater rigidity can 
 be obtained in light weight I-beams than in rails. The 
 concrete, instead of being counted upon to assist the steel, 
 34C 
 
o 
 
 _ 
 
 346 
 
is merely the medium to transmit the upward pressure of 
 the soil into the beams, to hold them against buckling, and 
 to protect them from rust. 
 
 In Fig. 5 assume a load of 600,000 Ib. on the column 
 shown. Allowing 250 Ib. per sq. in. bearing on the con- 
 crete this would require a bearing area in the flanges of 
 the I-beams of 2,400 sq. in., or, assuming the flange to be 
 6 in. wide, a total length of I-beam of 400 in. or 33 ft. 4 in. 
 This will be made up of 4 beams 8 ft. 4 in. long. The 
 upward pressure on the beam is 6X250=1,500 Ib. per 
 in. or 18,000 Ib. per ft. of beam. The overhang of the 
 cantilever is 3 ft. &/2 in. and the maximum moment is 
 18,000x3.542x3.542x^2x12=1,355,000 in.-lb. Dividing this 
 by 16,000, the extreme fiber stress allowed, we have 84.7 
 as the section modulus. The beams will therefore be 18 
 in. I's 55 Ib. per ft. (S = 88.4). 
 
 A grillage of I-beams crossing at right angles to each 
 other as indicated in Fig. 6 is used to distribute the load 
 of a column over a rectangular concrete base. In calculat- 
 ing the bending moment on the beams the point of sup- 
 port of the cantilever should not be taken as the edge 
 of the flange of the beam above or the edge of the column 
 base, but as some point where a good substantial support is 
 assured, as indicated in Fig. 6, the span of the cantilever 
 being /. 
 
 It is sometimes necessary to place a column pedestal so 
 as not to project beyond the property line, where the col- 
 umn center is located but a foot or so within the property 
 line. No form of footing will give effective bearing on the 
 soil for a width more than three times the distance from 
 the outside line of the footing to the center of the column, 
 unless it be a cantilever balanced by interior loads. Can- 
 tilevers are sometimes employed which are supported on 2 
 pedestals within the property lines, and which in turn 
 support 2 columns. Figs. 7 and 8 illustrate cantilever sup- 
 ports of wall columns both for a narrow building, where 
 the 2 outside columns may rest on the same set of can- 
 tilever beams, and a building where an interior column 
 347 
 
348 
 
is utilized to take the uplift of the cantilever. The span 
 of the cantilever beams is the distance from center of col- 
 umn to the center of the group of supporting beams. The 
 depth of cantilever beam should be selected with the 
 length 5" in view, making it sufficient to prevent too great 
 deflection upward, say not shallower than 1-20 of . The 
 cantilever may be composed of rolled beams or of a box 
 girder. If below the surface of the ground or cellar floor, 
 the steel work should be protected by concrete. The box 
 girder may be riveted to the side of the column or may 
 have interior diaphragm and stiffeners equivalent in area 
 to the column, with the column resting on top. The 
 I-beams should have separators or riveted diaphragms be- 
 tween them. 
 
 The safe carrying power of masonry, according to the 
 New York Building Code, is as follows, in tons per sq. 
 ft. : Brick in lime mortar, 8 ; brick in lime and cement 
 mortar, 11.5; brick in cement mortar, 15; rubble in 
 Portland cement mortar, 10; rubble in other than Port- 
 land cement mortar, 8; rubble in lime and cement mor- 
 tar, 7; rubble in lime mortar, 5; Portland cement con- 
 crete, 15; other than Portland cement concrete, 8. 
 
 These units are less than those given a few paragraphs 
 preceding for columns, etc., resting on masonry, as they 
 should be. Those are for a load on only a portion of the 
 top of a wall or pier, while these are for the entire wall 
 or pier. 
 
 While no general rule prevails for the load on high 
 walls, diminishing the unit as the ratio of height to width 
 increases, it is true that high walls not braced should not 
 be loaded with the above limiting loads. Some such rule 
 as this would be a safe basis upon which to proportion 
 walls that are heavily loaded, namely ; for walls whose 
 height is 10 times the thickness, or less, use the units 
 above given, and for walls whose height is 25 times the 
 thickness, use 2-3 of the same, walls between 10 and 25 
 times the thickness to have proportionate units between 
 
 349 
 
these limits. Walls more than 25 times their thickness in 
 unsupported height are to be avoided. 
 
 For an upward pull, such as the anchorage of a can- 
 tilever or the uplift of the post of a railroad bent due to 
 wind load, rods or bars should go down deep enough 
 into the masonry to take a weight of the same 50 per cent 
 in excess of the calculated uplift. If the masonry is brick 
 or rubble, there should be a grillage of beams or rails so 
 arranged that they would lift the necessary weight of 
 masonry. For very heavy anchorages in concrete, grillages 
 should also be provided. For a small uplift in concrete 
 a good sized washer plate is usually sufficient. The anchor 
 bolts should have a square head, and the washer plate 
 should have a small stop plate riveted on it to keep this 
 head from turning. Cast washers may be made with a 
 recess in which the head of the bolt will fit. A split bolt 
 and wedge should not, in general, be depended upon for 
 anchorage against an uplift. The holding power of such 
 a bolt is more or less uncertain, and the chances are 
 many that the bolts will not all be properly set. 
 
 These split bolts, passing into the masonry a foot or 
 two, are commonly used for anchorage of stringers and 
 girders and trusses of bridges where no uplift is counted 
 upon. 
 
 Columns for office buildings are not usually anchored. 
 The cast steel or cast iron bases are generally left untooled 
 on the bottom, and holes are cored in the bottom plate 
 through which grout is poured after the base is leveled up. 
 
 No anchor bolts of any kind should be close to the 
 edge of a concrete wall or pier, as the driving may break 
 out the concrete 
 
 The stability of a masonry pier against horiontal or 
 overturning forces is met largely by the weight of the 
 pier. Figs. 2 and 3 illustrate piers subject to such forces, 
 and the remarks made in regard to these figures relate 
 to provision for their stability, treating the vertical pres- 
 sure on the soil only. In addition, if the forces are hori- 
 zontal or have horizontal components, there is provision 
 350 
 
against sliding to be considered. If we assume a coeffi- 
 cient of friction of the pier on the soil as ^, we should 
 have a horizontal projection l /2 of the vertical projection 
 in the line of the resultant pressure. Any earth packed 
 against the side of the pier will be an additional safe- 
 guard against sliding. It is best in the case of a constantly 
 exerted force not to depend upon earth exerting horizontal 
 pressure against a vertical surface, as the force will tend 
 to compact the earth and move the pier. 
 
 In the case of a pier for a mill building column or a 
 crane runway column the horizontal forces due to the 
 wind against the building or due to the thrust of the crane 
 are only occasionally exerted and very seldom to their 
 full extent. It is safe in such cases to allow for some 
 horizontal pressure exerted by the earth. 
 
 To arrive at a means of finding approximately the sta- 
 bility imparted by the lateral pressure of the earth, take 
 the case shown in Fig. 9. This represents a pole placed 
 in the ground and subject to a lateral force. The weight 
 here is negligible If we assume that the pole turns about 
 a point 2-3 of the depth below the ground, the resistance 
 of the earth will vary uniformly from this point down, 
 and would vary uniformly from the same point up, but 
 for the fact that this would make the maximum pressure 
 occurring at the ground level. Because the lateral pres- 
 sure in ordinary earth at the ground surface would be 
 practically nil, it is taken as varying from zero at the 
 ground to a maximum somewhere below the surface. This 
 is arbitrarily taken at 1-3 of the depth from the surface. 
 It is safe to say that well compacted soil will stand a 
 lateral force, for a short time, a few feet below the sur- 
 face, of 500 Ib. per sq. ft. and about twice this amount 
 at a depth of 5 or 6 ft. below the surface, all without ap- 
 preciable settlement. Now if P be assumed as constant, Q 
 will depend in amount upon F t as it must be the differ- 
 ence between P and F. For a small force at F and a long 
 lever arm L, Q will approach equality with P. Hence the 
 351 
 
approximate moment of stability in ft.-lb. about a section 
 at the force P will be 
 
 Thus a pole i ft. in diameter, 30 ft. above the ground 
 and 6 ft. in the ground would stand 3,350 ft.-lb. or a force 
 of 105 Ib. horizontally at the top. If the ground is hard 
 and rocky or if there is a pavement around the pole, it 
 will stand much more than this. 
 
 The moment of stability of a column and pier due to 
 their weight is equal to the product of the total weight 
 (under the condition of maximum horizontal pressure) 
 and 1-6 of the base. 
 
 To take an example, suppose a column supporting a 
 crane runway is anchored to a pier 6 ft. deep and 5 ft. 
 by 4 ft. in plan. The pier on account of its being planted 
 in the ground will have a moment of stability 2 ft. below 
 the ground line of 92 X 36 X 4 = 13,250 ft.-lb. On ac- 
 count of its weight (taking the weight of the pier as 18,000 
 Ib. and the minimum load on the column under the condi- 
 tion considered as 10,000 Ib) a moment of stability of 
 28,000X1=28,000 ft.-lb. at the base of pier. At a height 
 of 20 ft. above the ground the former moment would al- 
 low a force of 13,250 -r- 22 = 602 Ib. and the latter would 
 allow 28,000-^-26=1,080 Ib. A total thrust of 1,682 Ib. 
 could be exerted at this height. In general 2 columns of 
 a runway will be acted upon by the sudden stopping of a 
 load carried by the crane. The coefficient of sliding friction 
 is usually taken as 1-5. The load on the trolley could 
 then be 2 X 5 X 1,682 = 16,820 Ib. This pier would then 
 do for about an 8 ton crane runway. In a similar manner 
 the stability of a mill building column against wind loads 
 may be worked out. No rigid analysis has been attempted 
 of the forces in Fig. 9, but simply a rough approximation 
 of the stability imparted to a post or pier planted in earth 
 which is tamped around it. 
 
 The allowed slope on a concrete footing, such as either 
 the two forms shown in Fig. 10, may be investigated 
 352 
 
 - 
 
as follows: The bending moment under the edge of wall, 
 at tons per sq. ft. upward pressure of soil is 
 
 The resisting moment, at 40 Ib. per sq. in. safe modulus 
 of transverse strength is 40 h 2 ~ 6, both on a rectangle h 
 in. deep and I in. wide. Equating these we find the fol- 
 lowing to be very nearly true: 
 
 Sp* = h* 
 
 Thus for a pressure on the soil of 2 tons per ft. the 
 depth of the footings should be 1.4 times the projection 
 beyond the wall. For a 4 ton earth pressure the depth 
 should be 2 times the projection. 
 
 In a brick footing no reliance can be placed upon tensile 
 strength of the mortar in the vertical joints, but inde- 
 pendent of this there is a tensile strength in a brick wall 
 derived from the bonding of the bricks. The friction of 
 each brick against the upper and lower adjacent tiers re- 
 sists the tendency to draw it out of place. Assume the 
 coefficient of friction to be l /2. If the earth pressure at 
 the base of the footing is I ton per sq. ft. there will be 
 1-9 of this pressure on the top and on the bottom of the 
 half of a brick. Hence 1-9 of 2,000 Ib. will be required 
 to pull out a brick. This on 16 sq. in. (the section of a 
 brick longitudinally) is 14 Ib. per sq. in. Allowing a factor 
 of safety of 5 to cover irregular bonding we have an al- 
 lowed tension of 3 Ib. per sq. in. Using these values as 
 above for the concrete footing we find 
 
 h = 373 p. 
 
 Since the allowed tension on the brick footing is directly 
 proportional to the earth pressure, this relation will hold 
 true for any other earth pressure. It requires good bond- 
 ing of brick work to distribute the load on a spread founda- 
 tion, even with the small spread that this formula would 
 give. 
 
 From the standpoint of the allowed shear on the con- 
 crete, using Fig. 10, the amount of pressure on the projec- 
 tion for an earth pressure of I ton per sq. ft. is 2,000 />. 
 353 
 
11 
 
 VI& OJ .iVlCJ 
 
 :''4 
 
 &;: 
 
 v:$ 
 
 ";<< 
 
 .'.^:-; 
 
 354 
 
The area in shear is 144 h sq. in. Allowing 40 Ib. per sq. 
 in. we have 5,760 h = 2,000 p, or 
 h = .35 p. 
 
 Sometimes the upward pressure of the soil is resisted 
 by needle beams under a wall, of old rails or I-beams. 
 In Fig. ii assume the upward pressure of the soil as 2 
 tons per sq. ft. and the imbedded beams spaced i l / 2 ft. 
 apart. This upward pressure will be the same as a vertical 
 downward load on the beams, which will be cantilevers 
 having an overhanging of 3 ft. The middle distance of I 
 ft. 6 in. is taken less than the width of the wall, as some 
 space is required for bearing. The bending moment on 
 each beam is i l / 2 X 4>oooX 3 X ll / 2 = 27,000 ft.-lb. or 
 324,000 in.-lb. The value of the section modulus required 
 is 324,000 -f- 16,000 = 20.25. The section modulus of a 10 
 in. I-beam 25 Ib. is 24.4, hence this size of beam would be 
 used. It would take 4 55 Ib. rails or 73.3 Ib. per ft. to give 
 the same stiffness. 
 
 Reinforced concrete slabs are now much used in place 
 of the needle beams shown in Fig. n. Fig. 12 shows a 
 slab of the kind referred to. We have seen that in order 
 to have a proper shearing area we should have for every 
 ton of earth pressure a depth h equal to .35 p, or if S be 
 the pressure of the soil in tons per sq. ft., 
 
 h = -3SP$ (i) 
 
 If we use square rods for the reinforcement, and place 
 them as indicated in the figure, we should have the rod im- 
 bedded for 50 diameters, or p = 500?. Allowing 12,500 Ib. 
 per sq. in. on the steel, and remembering that the amount 
 of stress in the concrete must be the same as that on the 
 steel, we have for a section x in. wide and h in. deep. 
 
 M=12SWd 2 X~ =8S54</ 2 >* 
 
 Substituting for h its value, .35 pS, we have M = 3099 p 
 d*S in.-lb. From the soil pressure of 6* tons per sq. ft. 
 we have 
 
 355 
 
Equating these two values of M and using for P its 
 value Sod we have 
 
 x = 8.93 d, or, say, 9 d. 
 
 It is thus seen that for any upward pressure the same 
 rods would be used in a given projection p. These rods 
 would have a diameter 1-50 of this projection and be spaced 
 9 times their diameter apart. For different earth pressures 
 the height h would vary as per equation (i). 
 
 The foregoing does not take account of the stress on 
 the concrete, but it will be found by trial that the depth 
 of slab required for any earth pressure above about l /t ton 
 per sq. ft. would give concrete enough to keep the stress 
 on the same within safe limits. 
 
 In a square slab supporting a column similar reinforce- 
 ment can be used. The slab should be surmounted by a 
 plinth or block of concrete upon which the column rests. 
 The depth of the slab should be governed by the upward 
 pressure of the soil on all of the area of slab outside of 
 this plinth, allowing a unit in shear (on the section that 
 would be sheared if this plinth should sink into the soil) 
 of 40 Ib. per sq. in. Rods should all pass under this plinth ; 
 that is, there should be 4 sets, 2 parallel to the sides of the 
 slab and 2 diagonally. Rods parallel to the sides of the 
 slab lying toward the edges and not under the plinth 
 would be of little or no use. They will only serve to in- 
 tensify the stress on the rods at right angles to themselves 
 that do lie under the upper block or plinth. The use of 
 rods at right angles to each other spaced uniformly both 
 ways is a common but irrational method of reinforcement. 
 
 Shear of Concrete and Its Bearings on 
 the Design of Beams. 
 
 The unit shearing strength of concrete is between i and 
 2 times its unit tensile strength for practical purposes in 
 1 the design of beams. 
 
 In making this assertion the writer appreciates the fact 
 that it is a broad statement. He realizes that it is an as- 
 356 
 
sertion that will be contradicted. It is not for the mere 
 purpose of raising a controversy that this seeming dogma 
 is put at the head of this article. If the statement is right, 
 it should be given a very prominent place in every work on 
 the subject of reinforced or plain concrete design. If it is 
 wrong, it is the duty of anyone who can show it to be 
 wrong to give a sound reason therefor. 
 
 Recently some tests on the shearing strength of concrete 
 were made at the Engineering Experiment Station of the 
 University of Illinois, under the direction of Professor 
 Arthur N. Talbot. These tests have been given a wide 
 publicity. Rightly interpreted they are very valuable. 
 Wrongly interpreted they may lead to another crop of dis- 
 astrous failures in reinforced concrete construction. The 
 tests referred to appear to show that concrete has a shear- 
 ing strength nearly equal to, and in some cases in excess of, 
 the compressive strength per sq. in. In other words, they 
 lead to the conclusion that the strength of concrete in 
 simple shear is 8 or 10 times its strength in tension. 
 
 In making these tests special efforts were made to elim- 
 inate every other stress except simple shear. In the writ- 
 er's opinion the very means empfoyed introduced elements 
 that to a large extent diminish the value of the tests as 
 helps in design Reference will be made to these features 
 of the tests later. Professor Talbot states that the tests 
 are open to objection. It is the objectionable features 
 that the writer wishes to emphasize. 
 
 It is not questioned that the results of the tests give 
 close to the true value of shear in concrete in the strait- 
 ened conditions in which the concrete of the tests was 
 placed. An attempt will be made, however, to show that the 
 "laboratory" feature of the tests was so intensified by 
 eliminating the beam action, that the results are apt to be 
 very misleading if applied to design. The unit stress al- 
 lowed in shear on concrete by various building codes is in 
 the neighborhood of 40 or 50 Ib. per sq. in. Now if the 
 material has a shearing strength of 1,000 to 2,000 Ib. per 
 sq. in., it is a waste of material and an economic blunder 
 
 357 
 
to allow only 50 Ib. in design. It would not be surprising 
 if a class of designers should rise up and call for a raising 
 of this low unit to a fair factor of safety based on the 
 high units determined by these tests, especially in view of 
 the high authority from which they emanate. It would 
 further, not be surprising if the work turned out by these 
 same designers should lead to added work for coroners. 
 
 One feature of this discussion concerns the difference in 
 the shearing strength of concrete : ( i ) when in tension 
 at right angles with the plane of shear; (2) when under 
 no stress whatever at right angles with the plane of 
 shear, but free to move in that direction; (3) when un- 
 der no stress at right angles with the plane of shear, but 
 confined so that any motion would induce such stress; (4) 
 when under compression at right angles with the plane of 
 shear. 
 
 It is plain that under condition (i) failure would occur 
 the most readily, and under condition (4) it would be least 
 liable to occur. In fact there would be a large apparent 
 shearing strength between 2 concrete surfaces completely 
 severed, if these surfaces were forced together by a com- 
 pressive stress, due to the mere friction of the surfaces. 
 This element would be completely lacking in (i), and a 
 small tensile stress, coupled with a shearing action, would 
 cause failure. 
 
 Now the conditions in the tests referred to agree closely 
 with (3) and approach (4), while the conditions in actual 
 beams in a building agree nominally with (2) but approach 
 (i). This latter is due to the tendency of a slab to shrink 
 between beams and of a beam to shrink between columns, 
 giving an initial tension throughout the beam or slab. One 
 set of tests was made by punching out a cylindrical piece 
 from a concrete plate or slab. Now if this cylindrical 
 piece had been a separate piece cast in a hole in the plate, 
 with no bond whatever, but merely fitting snugly in the 
 hole, it would take much force to push it out. The appar- 
 ent but false shearing strength would be very considerable. 
 This would come under the head of condition (3), above, 
 
 358 
 
but the actual shearing strength would be zero. Molded 
 in one piece a concrete plate would then have an apparent 
 shearing strength which would be the sum of what actual 
 shearing strength the concrete possesses and this false 
 shearing strength that might be said to be due to the 
 crowding of the material. This would be true in- 
 dependent of shrinking in the concrete. As an illus- 
 tration of the effect of the crowding of the material, it 
 requires more force to punch a hole in a steel plate when 
 the clearance between the die and punch is small than 
 when it is larger, this in spite of the fact that steel is 
 stronger in tension than in shear. 
 
 Shrinking of the concrete block from which the piece 
 is punched adds a new element of apparent shearing 
 strength in that it grips the "punching" and adds, to the 2 
 other elements that go to make up the force necessary 
 to push it out, that of friction on its sides. That more 
 load was required to force out a punching in a block that 
 was reinforced with straight rods arranged in a square 
 around the tested portion, and still more when hoops were 
 used, is strong evidence of the effect of crowding of the 
 material or of the compression that will be induced normal 
 to the shearing surface by the mere action of the material 
 under the shearing test. It takes a strong pull, sometimes, 
 to draw the cork out of a bottle. There is no element of 
 shear in it, but if this friction were combined with a small 
 shearing strength, the sum would be an apparent shearing 
 strength of no small value. 
 
 In another set of tests constrained beams were used. 
 These beams were so short that but little in the way of 
 beam stresses could be expected, especially because the 
 edge of the load and the edge of the support were almost 
 vertically over each other. But the induced stresses of 
 (3) would be very clearly a possibility in these tests. The 
 crowding of the material would add a false element to the 
 apparent shearing strength which would be of unknown 
 value. 
 
 The features of these tests that render the application 
 
of their results to design not only questionable but dan- 
 gerous are these: (a) The test speciments do not resem- 
 ble anything in which concrete is used practically, (b) 
 The loads applied on the specimens, instead of being flexi- 
 ble and taking the shape of the deflecting part, were in 
 themselves rigid for the entire extent of their bearing on 
 the concrete, (c) There is scarcely any case in practice 
 where shear, pure and simple, is exerted on any part of a 
 structure in concrete. This last is emphasized in the futile 
 attempts to manufacture a condition where simple shear 
 occurs. In view of the fact that simple shearing action is 
 not a structural possibility, it is not clear why strenuous 
 attempts should be made to approach it in test specimens. 
 Concrete is unlike steel in that it is 5 or 10 times as 
 strong in compression as it is in tension, whereas structural 
 steel is about equally strong in either. Steel is little af- 
 fected in its shearing strength by the simultaneous occur- 
 rence of tension or compression. The principles of design 
 employed in steel beams and girders must therefore be 
 modified before they can be applied to the design of rein- 
 forced concrete beams. 
 
 Concrete is further quite different from wood, in that 
 
 i the latter, while it possesses great tensile strength in the 
 
 direction of the grain, and large compressive strength in 
 
 i the opposite direction, has very little tensile strength at 
 
 1 right angles to the grain. The shearing strength of wood 
 
 5 in a direction parallel to the grain is small, because of the 
 
 little tensile strength normal to the grain. If wood were 
 
 I tightly held together with tension bands, its apparent 
 
 j shearing strength parallel to the grain would be largely 
 
 e increased. 
 
 t ; About the only common structural material that con- 
 
 il crete resembles is cast iron. The tensile strength of the 
 
 ie latter in all directions is only a fraction of its compressive 
 
 ic strength. The practical value of cast iron in shear is 
 
 n comparatively small because of its weakness in tension. 
 
 and yet, no doubt, in a restrained beam of short span a 
 
 block of cast iron would resist a high shearing: strain, 
 
 360 
 
The term "practical shearing strength" is here used not only 
 to distinguish from the theoretical but also from ideal. 
 
 It is next to impossible to eliminate tensile stresses in 
 concrete beams and slabs, and shear failures will be ac- 
 companied in general by tension failures. They will be 
 so closely associated together that it will scarcely be pos- 
 sible to separate them. In fact shear and tension must 
 be considered as generally acting together in beams. A 
 practical working unit stress for shear in beams should 
 take into account the ever present tension. Building ordi- 
 nances rightly prescribe low units for shear. Reinforcement 
 of beams against shearing stresses, as very often practiced, 
 is not rational. 
 
 In Fig. i we have a simple beam uniformly loaded. The 
 load in this case is of course flexible and will take the 
 shape of the deflected beam The shear increases from 
 the center of beam to the support. Herein is this beann 
 essentially different from a test beam in which the load: 
 is a rigid block the length of the beam and in which the 
 shear is all confined in a narrow space between the edge 
 of the block and the edge of the support. The beam in 
 Fig. I represents actual conditions. 
 
 The load between B and F can be assumed as carried 
 on the surfaces AB and FG. CD represents l /2 of this load. 
 This may be resolved into CE and ED. ED is the shear 
 along the surface AB. CE is tension on the same surface. 
 The critical point in the strength of this beam is the ten- 
 sion on the surface AB. If this tension becomes too great 1 
 on this section the beam will fail. It is, of course, a ten- 
 sion failure, but in practice it is interpreted as a failure 
 in shear. In considering the design of a beam it is held to 
 be weak in shear in a section near the ends, because of' 
 the known tendency of beams to fail in a line approxi- 
 mating AB. 
 
 In order to find the value of the angle X to give the 
 tension on A B a maximum, assume a depth of beam i-id 
 of the clear opening, as shown in Fig. I. Assume also a 
 361 
 
/.one/ w pe 
 
 FIG. 1. SIMPLE BEAM UNIFORMLY 
 LOADED. 
 
 FIG. 2. COMPOSITE SKETCH SHOWING 
 CRACKS IN BEAMS. 
 
 3 
 
 K 
 . 
 
 .-J-g --- --- . -l. 1_ j._ i 
 
 *.^ 
 
 
 (dj 
 
 FIG. 3. SHOWING SEVERAL METHODS 
 OF REINFORCING BEAM FOR SHEAR.. 
 
 (a) 
 
 
 m 
 
 \ 
 
 i 
 
 (b) 
 
 FIG. 4. SHOWING SOCALLED HOWE & 
 PRATT TRUSSES. 
 
width of beam of I ft. From the trigonometric relations 
 we find 
 
 C E = C D cos X. 
 
 But C D wL ( l / 2 i-io cot X). 
 
 Hence C E = (y 2 i-io cot X) wL cos X. 
 
 If we divide this value of C E by the length A B (equal 
 area of section in tension), we have 
 
 Unit tension on A B = (5 sin x cos x cos 8 x) w. 
 
 Taking the differential coefficient of this expression for 
 the unit tension and equating the zero we obtain, after re- 
 ducing 
 
 5 cos 2 x = sin 2 x. 
 
 From which we have 
 
 x = 50 deg. 40 min. 
 
 This is the angle which gives a maximum tension on 
 the section A B. From this we have a unit tension of 
 2.05 w. 
 
 The end shear worked out in the ordinary way, is 5 w. 
 Thus in this case the unit strength of the beam in simple 
 shear is for practical purposes 2^2 times its tensile strength. 
 It would, in fact, be less than this, because the shear D E 
 in Fig. i is acting at the same time, and shear acting in 
 conjunction with tension will lessen the tensile value. 
 
 Using Merriman's formula for combined shear and ten- 
 sion, in which the resultant unit tension equals l /2 of 
 the direct unit tension plus the square root of the sum 
 of the square of the unit shear and ^ of the square 
 of the direct unit tension, we find for this case a result- 
 ant unit tension of 3.73 w. Comparing this with the 
 unit shear found in the ordinary way (the reaction of 
 beam -f- area of vertical section, or 5 w), we find that the 
 unit strength is for practical purposes I 1-3 times the ten- 
 sile strength. 
 
 If, instead of making the depth i-io of the span, it be 
 made 1-20 of the span, we find after a process similar to the 
 above, 10 cos 2 x sin 2 x, or x = 47 deg. 51 min. 
 The unit tension is found to be 4.53 w. The unit shear, 
 found in the ordinary way, is 10 w. Hence the unit shear- 
 
ing strength is, for practical purposes, about 2 l / times the 
 unit tensile strength, or about i% times, when reduced for 
 combined shear and tension. Most beams will be found 
 to be between i-io and 1-20 of the span in depth. It would 
 be found that in beams less than 1-20 of the span in depth 
 this apparent shearing strength approaches closer to the 
 tensile strength, but it is in deep beams where the shear- 
 ing strength plays the most important part. As pointed 
 out in an article in this journal, published Jan. 15, 1907, 
 the critical depth of beam from the standpoint of shear is 
 i-io of the span and over. The capacity of a shallow beam 
 in bending is not sufficient for it to carry load enough to 
 tax its capacity in shear. 
 
 Other forces are of course at work in the beam, and 
 these may tend to alter the line of failure, so that it would 
 not coincide with A B in the figure. Tension in the lower 
 part of the beam begins to make itself felt a little away 
 from the support. In beams where the bottom reinforcing 
 rods stop at the support, and therefore lack anchorage, the 
 combination of this flange tension and the diagonal tension 
 may reach a maximum a short distance from the support. 
 If a beam is continuous or restrained at the support, there 
 will be compression at the bottom of beam near the sup- 
 port, and this too will tend to make the line of failure or 
 weakness some distance away from the support. 
 
 Fig. 2 is a composite sketch showing the cracks in a set 
 of 10 beams tested by the writer. The diagonal cracks are 
 very plainly characteristic and show clearly the weakness 
 of reinforced concrete beams in this respect. These beams 
 were reinforced with straight horizontal rods near the 
 bottom and with rods across the support to take the con- 
 tinuous action. They were also reinforced with so-called 
 shear bars, that is, small vertical bars or rods strung along 
 the reinforcing rods 
 
 In "Proceedings of the American Society for Testing 
 Materials," Vol. IV, p. 498, Prof. F. E. Turneaure de- 
 scribes some test beams which were 6x6 in. and 60 in. in 
 span, reinforced with stirrups, spaced 3 in. apart. On 
 364 
 
page 507 Prof. Turneaure says: "In but a few cases was 
 the failure free from the influence of shearing stresses, but 
 the rupture usually occurring outside of the load and on 
 a diagonal line." The stirrups referred to are supposed 
 to reinforce the beam for shear. As will be noted, these 
 test beams were of a depth i-io of the span. They were 
 therefore of a depth where shearing stresses begin to play 
 an important part. 
 
 Another characteristic in the behavior of the beams rep- 
 resented in Fig. 2 is the horizontal crack just above the 
 reinforcing rod These beams were too narrow and were 
 consequently lacking in shearing strength, in a plane just 
 above the rods, to take the horizontal shear or the grip- 
 ping force of the rods. This corresponds to horizontal 
 shear in the web of a girder, the stress that the flange rivets 
 must convey from web to flange. The beams of which this 
 sketch is a composite were designed as T-beams, including 
 in their calculation the floor slab. Thus the lower part of 
 the beam did not have enough concrete to take care of the 
 stresses in the steel. When it is considered that the load 
 upon the beams was only that which the designer intended 
 should be the safe carrying capacity, the T-beam is seen 
 to be weak on account of a narrow stem that does not 
 contain enough concrete to take the horizontal shear above 
 the rods. Some of these beams, under the test load, showed 
 only vertical cracks starting at the bottom of the beam and 
 taking in the reinforcing rod. One beam had 16 of these 
 cracks in its length, another evidence of the weakness of a 
 T-beam. 
 
 The shearing stress just above a horizontal rod in a 
 reinforced concrete beam does not have the assistance of 
 any initial compression to relieve the effect on the concrete. 
 There is, further, not any crowding of the material to make 
 failure less liable. Reinforcement with short diagonal or 
 vertical rods either attached to the horizontal rods or 
 looped over them, could only take this shear by localizing 
 or concentrating the stress at these rods and introducing a 
 new element of weakness. 
 
 365 
 
It is a remarkable fact that if we apply Merriman's for- 
 mula for combined shear and tension and make the tension 
 zero, we find that the tensile unit stress due to shear alone 
 is equal to the shearing unit stress. It would follow, then, 
 that in the case of horizontal shear above reinforcing rods 
 the shearing strength is equal to the tensile strength of con- 
 crete. In the light of this fact a T-beam having horizontal 
 rods, with its narrow stem and large percentage of steel, 
 is a most absurd and inefficient, as well as unscientific, 
 form of construction. 
 
 Fig. 3 shows several ways of reinforceing a beam for 
 shear. That shown at (a) is faulty on account of the sharp 
 bend in the reinforcing rod (the one bent up toward the 
 support). Failure could occur on the diagonal line by 
 simply pulling a short length of rod out of the concrete. 
 At (b) and (c) failure could occur by the pulling out of a 
 short end of one of the "shear rods." Explanation of how 
 these shear rods act to reinforce a beam in shear seems to 
 be lacking in technical literature. A rod, to be effective 
 in taking stress, must either be anchored at the end by 
 a nut and washer, or some equally effective means, or must 
 be buried in concrete for some distance beyond its point 
 of usefulness. It is conceded that a mesh of overlapping 
 rods will be some aid in resisting shearing stresses. As an 
 economic proposition, however, this means of reinforce- 
 ment is a failure. 
 
 A steel rod in shear, that is, shear in the steel, stress at 
 right angles to the axis of the rod, is an absurdity. Con- 
 crete would not stand the side force of a rod against it 
 that is stressed in shear to anything like a reasonable safe 
 value in the steel. 
 
 In Bulletin No. 12 of the Illinois Engineering Experiment 
 Station the results of some tests on T-beams are given, 
 which illustrate shear reinforcement with vertical rods. In 
 the beams the tests of which are there described all of the 
 portion of the beam in shear, namely, the end third at each 
 end, is reinforced with T /2 in. U bars 6 in. apart. There is 
 about 2po in, of l /2 in. corrugated bars in the stirrups alone 
 366 
 
in a beam of 10 ft. span. This steel would weigh 14 Ib. If 
 the 4 34-in. plain round rods found in one beam were curved 
 up and run through a washer plate at ends of span, 2 nuts 
 on each end of each rod and 2 washer plates 5-16 in. thick 
 and 7 in. by 5 in. would not weigh as much as these stir- 
 rups. Further, these parts would not be of special steel. 
 Such a detail would give a positive and scientific provision 
 against shear. In a line of continuous beams rods curved 
 up add scarcely any length or cost. Commenting on these 
 tests it is significant to note that the unit shears given by 
 Professor Talbot as existing at first diagonal crack run 
 from 180 Ib. to 302 Ib. per sq. in. In the writer's opinion 
 these show where the concrete failed in shear, or tension 
 due to shearing action. After this failure of the concrete 
 the stirrups were brought into play, as it would be generally 
 necessary for some "give" to take place in the concrete be- 
 fore the U bars would have a working bearing on the hori- 
 zontal reinforcing bars. This is equivalent to reinforcing 
 a detail in steel work with a bent plate that will come into 
 action after the main detail fails or slips. Of course a 
 beam is stronger with a system of shear bars in close spac- 
 ing than it would be without The writer believes, however, 
 that shear bars are neither an economic nor a scientific 
 method of reinforcing a beam. 
 
 None of the tests in Bulletin No. 12 failed by shear, and 
 some of them stood double the load required to give the 
 first diagonal crack due to shear. It is a precarious sort 
 of construction, however, that entails a system of cracks 
 in the concrete before it can be brought into play. A load 
 that would produce the first crack in the concrete would 
 not be a safe load on a beam. If a given load causes cracks 
 in a beam it can scarcely be said to be in any better case 
 under a great number of repetitions of that load, than is 
 a member subjected repeatedly to stresses nearly equal to 
 the elastic limit. We know that the latter would eventu- 
 ally cause failure. 
 
 It is common to hear the system of horizontal bottom 
 flange rods and vertical or diagonal shear rods sooken of 
 367 
 
ka truss system and to hear comparisons made with a 
 sel Pratt truss or a wooden and steel Howe truss. Now, 
 since, as stated, the shear rod must have anchorage of some 
 sort outside of the point where it can take any stress, we 
 can represent these so-called Howe or Pratt trusses as 
 shown in Fig. 4 at (a) and (b) respectively. The heavy 
 lines represent the compression members, or in other words, 
 the concrete acting in compression. The light lines repre- 
 sent the tension members, or the shear rods. These are 
 good from the point where they are attached to the rod 
 to the point beyond which they have an efficient anchorage. 
 It does not take much imagination to see what would 
 happen to a truss on the lines of either of these. And yet 
 these are true representations of just what we find in rein- 
 forced concrete design as used in practice and as sanctioned 
 in some of the best works we have on the subject. These 
 abbreviated tension members must of necessity be aided by 
 tension in the concrete, the most unreliable factor in its 
 strength. 
 
 Fig. 3 at (rf), shows a beam reinforced for shear in a 
 manner that is rational and meets all requirements. If this 
 beam were cracked, the rod could not pull out because of 
 the anchorage. If the beam be one in a continuous line, 
 the rod could pass into the next span for anchorage, acting 
 in that span at the same time as reinforcement for the top 
 flange to take the stress due to continuity. This sort of 
 reinforcement is needed in beams less than i-io of the span 
 in depth. 
 
 To return to a discussion of the tests made at the Uni- 
 versity of Illinois. There are some features about the re- 
 sults of these tests that it is instructive to note. Average 
 values do not count for much where there is a wide range 
 of results. For example, if there is a difference of 100 per 
 cent between the lowest and the highest result, and if the 
 mean is midway between these, a design made on the basis 
 of the mean value with a factor of safety of 4 will have 
 a factor of safety of less than 3 on the basis of the lowest 
 value. Often there is a difference of several hundred per 
 
 
cent in the result of tests on such uncertainties as bending 
 and shear in wood, shear in concrete, etc. Designs on the 
 basis of mean values may thus have a factor of safety that 
 is half fictitious, for the lowest value is as apt to be found 
 in the finished structure as the highest or as the mean. 
 
 Among the punching tests on plain plates there is one 
 that shows a shearing strength, at first crack, of 142 Ib. on 
 1:3:6 concrete. One test on 1:2:4 concrete shows 213 Ib. 
 per sq. in. at first crack. One recessed block of i 13 :6 con- 
 crete shows 258 Ib. per sq. in. at first crack, and one of 
 1 :2 :4 concrete shows 332 Ib. One reinforced recessed block 
 of 1 :3 :6 concrete shows 496 Ib. per sq. in. at first crack 
 and one of 1 :2 14 concrete shows 668 Ib. One restrained 
 beam of 1 :2 14 concrete shows 783 Ib. per sq. in. at first 
 crack. These results run from *A to Y$ of the ultimate 
 shearing strength found. It may be true that all of these 
 low values were the result of tensile stresses due to beam 
 action. If this is true in a test where every effort is made 
 to eliminate beam action, how can anything else be ex- 
 pected in practice? 
 
 Turning now to the ratio between ultimate shear and 
 ultimate compression we find it to be as low as .37 for plain 
 punched plates, .39 for recessed blocks, .67 for reinforced 
 recess blocks, and .44 for restrained beams. In some tests 
 the apparent ultimate shearing strength was more than the 
 ultimate compressive strength. This wide variation shows 
 the uncertainty in shearing strength of concrete, to which 
 reference has heretofore been made. 
 
 A fair average value for tension in 1 :2 14 concrete is 
 about 200 Ib. per sq. in. Using i 1-3 times this as a basis 
 for shear 40 Ib. and 50 Ib. per sq. in. are seen to represent 
 factors of safety about 6 and 5 respectively. These factors 
 are not any too large, in view of the uncertainty exhibited 
 in concrete in shear and tension, for use in the design of 
 beams. 
 
 369 
 
The Design of Reinforced Concrete 
 Columns. 
 
 The strength of a plain concrete column is largely deter- 
 mined by the shearing strength of the concrete. In Fig. I, 
 at (a), is shown a column carrying a load P. If this be re- 
 solved into C B and C A, the latter will be compression on 
 the surface M N and the former will be shear on the same 
 surface. The angle y to make the unit shear on M N a 
 maximum will be 45 deg. and the intensity of that unit 
 shear is just half the unit compression on the column. Two 
 planes of failure may meet as at (b), forming a wedge. 
 The point of the wedge may be crushed, or the wedge may 
 act to split the column. This bulging or splitting action 
 is a common failure in wooden columns, on account of the 
 weakness of wood in shear. It is also a typical form of 
 failure in concrete columns. The wedges or cones may 
 form at the ends and split or bulge the entire column. At 
 (c) is shown the futility of reinforcement with longitudinal 
 rods of small diameter. These will bend if the column 
 bulges, and will be of little use. In cubes under test the 
 cones will meet, either apex to apex or base to base, and 
 
 teJ fbj (c) 
 
 (FIG. 1. SHOWING BULGING ACTION IN 
 COLUMN. 
 
 only corners will be flaked or spawled off by the shear, 
 
 leaving the core in compression; hence the fallacy of re- 
 
 370 
 
lying on tests on cubes to determine the compressive 
 strength of plain concrete shafts or columns. 
 
 In laboratory tests, plain concrete columns of 5 or 10 
 diameters in length will sustain moderately high compres- 
 sive stresses. This is because of the centric application of 
 the load. The shearing strength of concrete in a plane 
 which is at the same time subject to compression is very 
 much greater than if there is tension instead of compres- 
 sion, acting on that plane ; it is also greater than if there is 
 no stress normal to the surface. The friction between the 
 surfaces due to the compressive strength adds an apparent 
 shearing strength to the actual shearing strength of the 
 concrete. It is also true that columns reinforced with lon- 
 gitudinal rods, in laboratory tests, sometimes show mod- 
 erately high compressive strength. This may also be at- 
 tributed to the fact that the load is applied exactly in the 
 center of the column. 
 
 Only a small shifting of the load on a plain concrete col- 
 umn, or one reinforced with longitudinal rods, is necessary 
 to bring into play the weakness of the concrete. When the 
 center of gravity of the applied load on a square column is 
 more than 1-6 of the diameter from the center, or when 
 that on a circular column is more than ^ of the diameter 
 from the center, there will be tension on the extreme fiber 
 of the column. The shearing strength, which is the crit- 
 ical factor in the strength of the column, is immediately 
 weakened when the compression is removed and both shear 
 and compression become of double intensity on the other 
 side of the column. The bulging action illustrated in Fig. 
 I will be augmented by eccentric loading. 
 
 Eccentric loading of columns in buildings is the rule and 
 not the exception. In tests it is the rule to apply loads 
 centrally. It is of utmost importance that reinforced con- 
 crete columns be made capable of resisting eccentric loading 
 or flexure. 
 
 Concrete columns with longitudinal rods embedded in 
 them are not efficient and are not rational design, for the 
 following reasons: 
 
 371 
 

 (1) The column is a composite of steel and concrete, 
 and not a true reinforced concrete column, as the steel must 
 be chiefly in compression. 
 
 (2) There is no way to determine, even approximately, 
 the respective amounts of the load that the steel and the 
 concrete will bear. The use of the moduli of elasticity of 
 the two materials is no aid, on account of the fact that the 
 concrete tends to shrink and shorten, leaving the steel rods 
 longer than the normal unstressed concrete. 
 
 (3) If the rods are near the surface of the concrete, 
 they can more easily break out under the bowing action of 
 direct compression or the bulging action of diagonal shear. 
 
 (4) If the rods are near the center of column, they will 
 be of no aid to resist flexural stresses due to horizontal 
 forces or to eccentric loading. 
 
 (5) Longitudinal rods offer little or no resistance to 
 longitudinal splitting or bulging of the column. 
 
 (6) The rods cannot take diagonal shear without over- 
 stressing the concrete. 
 
 The assumption that they can take shear, in amounts of 
 anywhere near the capacity of steel to carry shear, is sim- 
 ply untenable and absurd, in spite of recognition in build- 
 ing codes and regulations. If, for example, we assume a 
 shear of 12,000 Ib. in a rod I in. sq., there must, of neces- 
 sity, be a bending moment in the rod. Now the square rod, 
 at 24,000 Ib. extreme fiber stress, would take a bending 
 moment of 4,000 in.-lb. The lever arm of the 12,000 Ib. 
 would then have to be only 1-3 of an in. The force of 
 12,000 Ib. applied on the side of a square rod in a length 
 of 1-3 of an in., or on several times this length, is beyond 
 the power of concrete to withstand. 
 
 (7) A plane of cleavage, especially if it be a sloping 
 one, such as a joint left where pouring of concrete ceases 
 for a while, will leave a weak section and vitiate to a large 
 extent the factor of safety. 
 
 Comparison of a reinforced concrete column with a steel 
 column as a basis of design is misleading, because of the 
 fact that steel is very strong in tension and therefore capable 
 372 
 
of resisting bending stresses. Cast iron columns were for- 
 merly proportioned on the basis of 11,300 Ib. per sq. in. 
 (reduced for length). Full size tests imade some years ago 
 (see Eng. Record, June n, 1898) showed this unit to be 
 too high and that a proper unit is about 7,600 Ib., reduced 
 for length of column. The compressive strength of cast 
 iron in short blocks is about 100,000 Ib. per sq. in., but on 
 account of the low tensile strength, and consequent low 
 shearing strength, the safe unit in columns has but a remote 
 relation to the compressive strength in short test pieces. 
 An exactly similar condition exists in columns of plain con- 
 crete or of concrete that is not reinforced, with a view of 
 relieving it of all tensile strains and of excessive shearing 
 strains. 
 
 Practical experience has proven the inability of concrete 
 columns in which small rods are embedded to carry heavy 
 loads. The practical experience referred to is the failures 
 of buildings that have recently occurred. 
 
 When a small section of a building falls, the failure may 
 be attributed to a local cause, generally a fault or defect 
 in the beams. When a general collapse of a large section 
 of a building occurs, it is probable that the failure is due to 
 weakness in the columns. If one beaim fails, it ought not 
 to bring down with it much of the rest of the structure. 
 When a column fails, it lets down a large section of the 
 floor; and if the other columns have the same weakness 
 they will follow. The great weight falling on lower floors 
 will overload these by the shock and add to the extent of 
 the failure. 
 
 In a failure that occurred some years ago, the reinforced 
 concrete roof of a large building fell in on account of the 
 concrete not having set before the forms were removed. 
 The weather was very cold, and the concrete froze instead 
 of setting. This great weight falling did not affect the 
 floors below and did not affect the columns supporting 
 them. The columns had steel spirals and longitudinal rods 
 wired to them. The beams and girders, while not ideal in 
 design, had rods across the supports to tie them together. 
 373 
 
Recently two large buildings being constructed exhibited 
 such serious weakness that large sections of them col- 
 lapsed. The columns of these buildings were made of con- 
 crete with some longitudinal rods through them. The safe 
 strength of such columns cannot be said to be intimately 
 related to the compressive strength of concrete in cubes; 
 and yet the unit compression, in some cases, for dead load 
 alone, was in the neighborhood of % of the ultimate com- 
 pressive strength of concrete cubes. Compare the ulti- 
 mate strength of cast iron with the unit used in a properly 
 designed column. 
 
 Square concrete columns in which longitudinal rods are 
 placed near the corners, and these rods tied together by 
 straight rods or bands, are a step in the right direction. 
 These horizontal ties will resist the bursting or bulging 
 tendency of the load; but as this tendency is in all direc- 
 tions, it will act to make the square formed by these ties 
 into a circle. The outward force at the side of the square 
 is not adequately resisted. The metal is not economically 
 disposed. It is somewhat analogous to a square vessel con- 
 taining a liquid. A round or cylindrical vessel will require 
 much less metal and will be more rigid. 
 
 It follows, then, that rational design of reinforced con- 
 crete columns demands not only longitudinal reinforce- 
 ment to take flexural stresses, but circular reinforcement 
 to take the bursting or bulging forces due to diagonal 
 shear. Columns so designed have proven under test to be 
 the strongest of all known forms of reinforced concrete 
 columns. 
 
 A steel cylinder rilled with concrete would meet the re- 
 quirements most completely. Concrete will stand very 
 great pressure thus confined, even to the extent of being 
 forced out of shape and still retaining its adhesion. Col- 
 umns so designed, however, do not seem to be suitable for 
 ordinary construction. 
 
 Flat bands in hoops or in a coil, having a diameter 
 somewhat less than the column, so that they will be sur- 
 rounded by concrete, in conjunction with longitudinal rods, 
 374 
 
would seem to be a near approach to the cylinder filled with 
 concrete. Concrete, however, will not grip flat bands as 
 it will round and square rods and will not adhere as well 
 to them. There will be the tendency of the concrete to 
 break off outside of the bands, especially if the space be- 
 tween bands is small. Columns thus reinforced will take 
 very heavy loads. 
 
 A practical objection to bands for reinforcing hoops or 
 spirals is that it is more difficult to puddle the concrete 
 around them and make it fill the voids outside of the bands. 
 Another objection is the greater liability of concrete to 
 break off the flat bar under the heat of a fire and thus ex- 
 pose the steel to the heat. Bands would have to be welded, 
 and a weld in steel is more or less of an uncertainty. 
 
 A good and efficient column is made by reinforcing a 
 round or an octagonal column with a coil made of a square 
 rod and with 8 longitudinal square rods wired to the same, 
 just inside of the coil. The purpose of the longitudinal 
 rods is to take flexural stresses, that is, to relieve the con- 
 crete of longitudinal tensile stresses due to any side force 
 or any tendency to bow at the middle of the height of the 
 column. The steel thus used is rationally employed, as it 
 takes tension that would otherwise come on the concrete. 
 These steel rods should not be counted upon to take any of 
 the direct load of the column, because of the fact that tests 
 show that such rods alone in a concrete column offer little 
 or no assistance to the concrete. 
 
 When a concrete column is under compression, its length 
 is diminished and its diameter is increased somewhat. The 
 steel coils come into play by this tendency of the column 
 to increase in diameter and are therefore in tension. 
 
 In a series of tests made by M. Considere, hooped con- 
 crete prisms showed very high compressive strengths. 
 They further showed a regularity in the matter of breaking. 
 Plain concrete prisms broke suddenly, whereas hooped 
 prisms would hold together after partial failure had oc- 
 cured and would sustain great loads in this condition. The 
 immense advantage of this toughness in a column is very 
 375 
 
manifest, and it is the strongest argument for hooped col- 
 umns. It is plain that partial failure in a column with only 
 small longitudinal rods in it would be a matter of very 
 serious moment. The possibility of shrinkage cracks in 
 concrete must always be kept in mind. Longitudinal rods 
 in a column offer no safeguard whatever against such 
 cracks, whereas in columns reinforced with a spiral or 
 hoops in addition to longitudinal rods, cracks are of no 
 serious consequence. 
 
 Tests made at the Watertown Arsenal in 1906 on col- 
 umns 10 to 12 in. in diameter and 8 ft. in height, corrobo- 
 rate the results of the tests made by Considere. They show, 
 . in general, that as hoops approach each other the ultimate 
 strength of the column is very greatly increased. 
 
 A basis for determining the size of the rods in the coil 
 is found in analogy of the column to a tube containing a 
 liquid under pressure. The stress in the rod corresponds 
 to the annular tension in the walls of the tube. Under the 
 ultimate pressure the concrete would be in a disintegrated 
 state and would resemble sand. In this condition it would 
 exert a lateral pressure, but not a pressure equal to that 
 exerted by a liquid under the same force. M. Considere 
 found that the lateral pressure was 10-48 of that of the 
 longitudinal pressure in disintegrated concrete and in sand. 
 
 If, at failure, there is a lateral unit pressure correspond- 
 ing to 10-48 of the compression in the direction of the axis 
 of the column, we can assume that the same relation holds 
 true under safe loads. Whether or not it does hold true is 
 of little consequence, so long as it is certain that this as- 
 sumed stress in the steel is not exceeded, it is a sound basis 
 for finding the size of coil for the following reason: 
 
 Suppose we have a column which, under tests, has dis- 
 integrated so as to be practically like sand in the matter of 
 exerting lateral pressure. The lateral unit pressure will 
 be 10-48 of the unit compression, and this, on rods strained 
 to their ultimate usefulness (the elastic limit, as usually 
 conceded in reinforced concrete work), would give a con- 
 dition where the concrete and steel are consistently propor- 
 376 
 
tioned. Now, if a factor of safety be applied, both to the 
 stress in rods and the compression in concrete, the consis- 
 tency of the design is maintained, though the actual stress 
 in the steel is not thereby definitely determined. Suppose 
 that it were known that the rods in some construction were 
 not stressed much until 9-10 of the ultimate load were upon 
 it, and that they then suddenly received their load. We 
 would not have a consistent design unless the ultimate 
 strength of the rods corresponds with the ultimate strength 
 of the structure, in spite of the fact that the actual stress 
 in the rods under a safe load on the structure may be small 
 and indeterminate. It is conceivable that in a reinforced 
 concrete beam the concrete, in some cases, takes nearly all 
 of the tension up to its ultimate strength, and that in the 
 case of stress above its ultimate strength the stress at the 
 crack is imparted to the steel in its entirety. This may be 
 the explanation of the fact that beams sometimes show no 
 cracks on the tension side under stresses which, if con- 
 centrated in the reinforcing steel, represent elongations 
 that would overtax the integrity of the concrete. Granting 
 for the sake of argument that this is the case and that 
 under safe loads, with perfect concrete, the steel is under 
 very little stress, and that the concrete in tension is doing 
 practically all of the work; it can by no means be con- 
 strued as warrant for proportioning the steel for this ideal 
 condition. Laboratory tests, both on beams and columns, 
 lead to conclusions such as this, because of the ideal con- 
 ditions that prevail in the manufacture and testing of speci- 
 mens. 
 
 Practical design must take into account actual conditions 
 in practical construction and practical defects that are liable 
 to be incorporated in a structure. 
 
 In a hooped column or one reinforced with a spiral, a 
 condition may exist that is analogous to that just postu- 
 lated of a beam. It is therefore in reason to proportion 
 the steel in a column as though it took all of the tensile 
 stress tending to bulge or burst the column, just as we 
 proportion the steel in a reinforced concrete beam to take 
 377 
 
all of the tensile stresses that might come on the concrete. 
 
 An assumption, such as that made in a recent work on 
 reinforced concrete, namely, that a column has a compres- 
 sive strength due to the strength of the concrete alone in 
 compression, and another compressive strength due to the 
 hoops or spirals, is untenable. Both of these supposed 
 joint strengths would break down at once. They are sim- 
 ply different phases of the same thing. The plain concrete 
 alone would be weak as a column, and the hoops or spiral 
 alone would be absolutely useless as a column. The hoops 
 supply what the concrete needs to hold it together. The 
 concrete between the hoops is simply plain concrete. No 
 quality is imparted, by the reinforcement, to the concrete 
 between the coils that it does not possess in short blocks 
 or discs. Hence a proper unit load would be a safe value 
 for compression on short prisms of plain concrete. If the 
 concrete be the standard 1 :2 14 concrete generally used in 
 reinforced concrete work, a proper unit in compression 
 would be between 500 and 600 Ib. per sq. in. 
 
 It is true that in columns where the hoops are spaced 
 close together the compressive strength of columns under 
 test runs up to 5,000 and 6,000 Ib. per sq. in., just as thin 
 discs of concrete would show correspondingly high unit 
 strength. Close spacing of hoops, however, entails prac- 
 tical difficulties in puddling the concrete around the bars, 
 and the almost continuous cylinder of metal forms a cleav- 
 age surface from which the concrete is apt to break away. 
 This last might result from ordinary changes of temper- 
 ature, and would be a strong probability in the case of a 
 fire. 
 
 In the work on reinforced concrete above referred to, 
 the author, while rinding a compressive strength in a set of 
 loose hoops, or a flimsy coil, apart from that of the con- 
 crete which they are intended to reinforce, and in addition 
 to the strength of that concrete, shows his lack of confi- 
 dence in his formula by throttling his unit value with an 
 empirical constant that almost cuts it in half. 
 
 If we assume a safe load of 550 Ib. per sq. in. and a 
 
 378 
 
lateral pressure of 10-48 of this in intensity, we have a 
 basis for the determination of the tension on a coil. Let 
 the pitch of the coil be l /% of the diameter of the column 
 and let 
 
 D =. diameter of column in inches; 
 
 d = diameter of square steel rod in the coil, in inches. 
 
 Equating the equivalent fluid pressure on the rod to its 
 tension at 12,500 Ib. per sq. in., we have 
 
 650X->|X^4=12,500*> 
 Solving we find 
 
 d= ~42 
 
 If we make the diameter of the coil % of that of the 
 column, and the diameter of the square rod of which the 
 coil is made 1-40 of the diameter of the column, we shall 
 have close to 12,500 Ib. per sq. in. on the steel. 
 
 For the 8 rods which run the length of the column we 
 may assume the same lateral pressure and proportion the 
 rods to take that pressure. Assuming that they would act 
 to resist the outward pressure of the disintegrated concrete, 
 at the ultimate strength of the column, we can make the 
 rods of a diameter that they would take the stresses in 
 bending, at a safe unit, due to a lateral pressure 10-481 of 
 550 or 115 Ib. per sq. in. The outward force per inch in 
 the length of rod is 115 X ic X D -f- 8. The clear span is 
 l /% of D less 1-40 D = i-io of D. As the rods are fixed 
 ended, the bending moment is 1-12 of w f, or 
 
 Equating this to 
 
 I25ood /8 -4- 6 
 
 the resisting moment of a square rod of a diameter d' we 
 obtain 
 
 As this is close to 1-40 of the diameter of the column, we 
 
may use the same size of square rods as that used in the 
 coil. 
 
 It is recommended, therefore, that reinforced concrete 
 columns be made round or octagonal and that the entire 
 area of the circle or octagon be considered as taking the 
 load; also that the reinforcement be made of a coil of 
 square steel rods of a diameter one-fortieth that of the 
 column; also that just inside of this coil eight rods of the 
 same diameter be wired to the coil. At the end of a coil 
 the rod should lap a half a circle, as this would be about 55 
 diameters. 
 
 The unit of 550 Ib. sq. in. would be used for lengths up 
 to 10 diameters. Between 10 and 25 diameters the allowed 
 unit pressure would be found by the following formula: 
 
 where p = allowed pressure per sq. in., 
 
 / = length in inches. 
 
 D = diameter in inches. 
 
 Columns more slender than 1-25 of their length should 
 be avoided. The same reinforcement should be used in 
 all columns of a given diameter, so that flexural and ec- 
 centric stresses will be taken care of in long columns. 
 
 The 'practice of using such units as 1,000 Ib. per sq. in. 
 on concrete in columns is fraught with great danger. Lab- 
 oratory tests on carefully prepared specimens under per- 
 fectly central loading are not proper criteria for the de- 
 sign of columns that have to take eccentric loads and in 
 addition have to resist the wind loads tending to sway a 
 building. A quality in columns that is very essential, es- 
 pecially in high buildings, is toughness. High buildings 
 of 12 to 15 or more stories require very large columns in 
 the lower stories, at units that are proper for concrete; 
 hence some other kind of column may better be employed 
 for the stories where very heavy loads are carried. A 
 suitable column would be of steel latticed on two sides 
 and filled and surrounded with concrete. Such a column 
 380 
 
could be made of two channels, either rolled or built. 
 Shelves could be riveted on to support the reinforced con- 
 crete girders, and the lattice could be left out where the 
 girder passes through the column. If girders or beams 
 connect into all four sides of the column, brackets could 
 be riveted on the side of the channels and holes left in 
 the web for reinforcing rods to go through the column. 
 Another kind of steel column could be made of four an- 
 gles set back to back, but separated so that the reinforced 
 concrete beams and girders can pass between. These an- 
 gles could be connected by batten plates at intervals. Such 
 a column, while it is objectionable in a plain steel column 
 on account of having no web to transfer shear from one 
 part of the column to another, would not have this fault, 
 if it were completely surrounded with good concrete. 
 
 Steel columns such as those referred to could be merged 
 into reinforced concrete columns by allowing the coil of 
 the latter to pass down over the steel section for a dis- 
 tance. 
 
 For a unit load on a steel column surrounded and filled 
 with concrete a value much higher than for a plain steel 
 column of the same section could safely be employed. 
 Units between 14,000 and 16,000 Ib. per sq. in. would not 
 be excessive, if the diameter of the concrete shaft is not 
 less than a tenth or a twelfth of the clear height. A 
 division of the load between the concrete and the steel 
 is not to be recommended because of the impossibility 
 of determining how much each will take. 
 
 ^I Jcat , 
 
 
 381 
 

 Design of Dams and Use of Concrete 
 Therein. 
 
 Structures for the impounding of water are among the 
 oldest of engineering works. The forces acting upon dams 
 are in many ways among the simplest and most easily de- 
 termined. It is a sad commentary on modern engineering 
 to say that some of the worst calamities in which man was 
 a causal agency have been the result of the overthrow 
 of structures whose stability is a matter of the most 
 elementary calculation and the forces against which are 
 completely determinate. 
 The writer makes this preface to the present article in 
 
 i order to emphasize a factor that he believes to be the 
 cause of many failures of dams, and because in all tech- 
 
 | nical literature there is scarcely a mention made of this 
 
 i factor. The factor referred to is none other than the 
 floating or buoyant power of the impounded water. An 
 offhand answer to this would be that water will not tend 
 to float anything not submerged. It is practically im- 
 possible to seal the up-stream side of a dam against the 
 admission of water under the dam, and the thinnest sheet 
 of water, entering the finest crevice, exerts the same up- 
 lifting tendency on the under side of a dam that would 
 be exerted in a large crack. Even if this upward pressure 
 on the under side of the dam be diminished uniformly to 
 zero at the down-stream edge of the dam, where the water 
 emerges, the effect of the pressure on the stability of the 
 
 j dam is the same as though the pressure of the full head 
 
 i were maintained for the entire width of the dam. It is 
 true that this pressure can be diminished by under-drainage, 
 
 j but this would be apt to waste much water, and it is seldom 
 resorted to. 
 
 Much has been said of the suction exerted on the down 
 stream face of a dam when water is spilling over it, in 
 attempted explanation of failures. It is a dangerous theory 
 
 i that magnifies non-essentials and overlooks essentials. 
 There is a small negative pressure under the falling sheet 
 of water, probably amounting to as much as a strong wind, 
 
 
in some cases, or even, in large dams, to a foot or two of 
 water on a portion of the face. But it has never been 
 shown that this negative pressure actually equals the drop 
 of the water head from the level of the main body to a 
 point vertically over the crest of dam. Now it is this 
 head of the main body of the water that should be used 
 in proportioning the dam; and, as the hydrostatic pressure 
 on the back of the dam is measured by the head at the 
 crest, there is this margin of the difference between these 
 two heads that will be ample to cover both the negative 
 pressure on the face and the effect of the small flow in 
 the main body. The effect of the flow is to add pressure 
 on the back of the dam above that which would be pro- 
 duced by the static head just over the crest, but, as only 
 the upper strata of the water are in motion, the water has 
 a velocity head or dynamic head only to a very limited 
 degree. 
 
 Impact of water on a dam is another element whose im- 
 portance is probably overestimated. For a large body of 
 water to impinge on the back of a dam it would have to 
 advance with a front nearly vertical into an empty reser- 
 voir. This would not even be approached except by the 
 failure of a dam at a higher elevation. Floods have the 
 natural effect of increasing the head and the static pressure 
 on the back of the dam, and if the maximum level of water 
 is known and the dam designed therefor, there should be 
 no more fear of a dam failing than of a railroad bridge 
 failing when it receives its full calculated maximum load. 
 
 The foregoing is not written to show that the design of 
 dams is the simplest of operations. There are many dif- 
 ficult problems in connection with their design, especially 
 in such construction as earth dams and rubble dams. The 
 greatest problem, however, is generally to come within the 
 appropriation, and too often this is done by ignoring the 
 most potent factor opposing the stability of the dam. 
 
 In the design of dams the factor of safety, with which 
 we are familiar in other branches of designing, has scarcely 
 any meaning, at least as regards stability against over- 
 turning. With those structures where the factor of safety 
 
 383 
 

 plays an important part there can not be said to be a point 
 where a structure ceases to be safe and becomes unsafe 
 or vice versa. In stability against overturning, however, 
 there is a distinct line on one side of which a structure is 
 stable and on the other side of which it is unstable. There 
 is a popular notion, owing its existence to public school 
 "philosophy," that an object cannot be overturned until 
 the center of gravity falls without the base. This is quite 
 true of miniature objects, but a great wall of stone stood 
 upon its corner would be disintegrated by the heavy pres- 
 sure on that corner. With all possible external pressures 
 considered and the resultant of these pressures and the 
 weight of the dam falling within or at the edge of the 
 middle third of the base, the dam will be stable. If the 
 resultant pressure falls without the middle third of the 
 base, the dam will not be stable, as it will have a tensile 
 or uplifting force sufficient to overcome its own weight at 
 the upstream edge whenever the extreme condition is 
 reached. This rocking of the structure is a distinct con- 
 dition of instability. Opening of the joints on the up 
 stream side of the dam is a menace to its stability, because 
 it allows water at high pressure to get beneath the masonry. 
 This water acts as a wedge to penetrate further. If the 
 dam is not calculated to resist this lifting or buoyant pres- 
 sure, its stability is seen to depend upon the sealing of the 
 upper face against the admission of the water. Leaking 
 of reservoirs is too common an occurrence to need any 
 emphasis. That dams should be built, as they sometimes 
 are, whose stability depends upon their watertightness, 
 seems incredible, unless it is the result of ignorance. This 
 latter assumption is probably not far from the truth in 
 view of the paucity of information in technical works on 
 the subject heretofore alluded to. 
 
 Barring dams that are built in the form of arches, that 
 is, with a horizontal curve in plan, dams are usually built 
 of a few general shapes. As the weight of water is uni- 
 formly about 62.5 Ib. per cubic foot and that of masonry 
 is generally about 150 Ib. per cubic foot, it Is a simple 
 matter to determine a ratio of base to a height that will 
 384 
 
resist all possible water pressure. It is also a simple 
 matter to try any dam of known dimensions and see 
 whether this ratio obtains. 
 
 In order to judge of the stability of a dam of ordinary 
 cross section the ratio of depth to height will be de- 
 termined for a dam of rectangular cross section capable 
 of resisting only the horizontal pressure against the wetted 
 face, neglecting in this calculation the pressure on the un- 
 der side of the rectangle. 
 
 The unit pressure of water in every direction is the same 
 at a given depth, and in amount is equal to the weight of 
 a column or prism of water whose cross section is unity 
 and whose length is the depth below the free surface of the 
 water. Another principle of the pressure of fluids is that 
 it is normal to the surface against which it is exerted. 
 The determination of the stability of a dam amounts, there- 
 fore, to finding its ability to resist easily determined forces. 
 Assuming w to be the weight per cubic foot of water, the 
 horizontal pressure per square foot on a vertical wall at 
 a depth h below the surface of water is wh. The pressure 
 increase directly as the depth, so that the triangle of Fig. 
 i represents the forces acting upon the wall or dam. The 
 center of gravity of this pressure is one-third of the height 
 from the base, and the amount, for one foot of length of 
 the dam, is the area of the shaded triangle, or wh?-z-2. 
 The overturning moment about the base of dam is 
 
 2 ~3 6~~ 
 
 This moment must be resisted by the weight of the dam, 
 and in order that there be no tension on the masonry the 
 resultant of the horizontal force and the weight of the 
 dam must fall within the middle third of the base. The 
 lever arm of the weight of the wall must therefore not 
 exceed one-sixth of the base. The moment of stability 
 for one foot of length of the dam is then Wtfh -+ 6, where 
 W is the weight per cubic foot of the masonry. Equating 
 the overturning moment and the moment of stability, and 
 solving we have 
 
 385 
 
rvh 
 
 FIG 1 
 
 rfi to 
 
 FIG. 2. 
 
 FIG. 3. 
 
 FIG. 4. 
 
6 2 TV 
 
 Using ISO and 62.5 as the weights per cubic foot of 
 masonry and water respectively we find that the base should 
 be .65 times the height. 
 
 A dam just capable at any horizontal section of resisting 
 the static pressure of water whose surface is at the level 
 of the top of the dam would be triangular in section. In 
 Fig. 2 we have for the equation between the overturning 
 moment and the moment of stability the following: 
 wy 2 _ Wx'^y 
 6 6 
 
 From which we have 
 
 Hence the width of the dam at the base should be about 
 .65 times the height. This is seen to be the same as for 
 the rectangular wall, though the amount of masonry is 
 only one-half as great. The reason that the moment of 
 stability of the triangular wall is as great as that of the 
 rectangular wall is because the center of gravity of the 
 triangle that is cut away is directly over the center of 
 moments. 
 
 A dam would of course not come to a point at the top 
 but would have some width. Masonry added to increase 
 the width at the top is well placed, as it increases the mo- 
 ment of stability. A form of cross section very often 
 used has the down stream face curved, as in Fig. 3. This 
 does not waste masonry in the third of the base where 
 weight does not count for anything in stability. This toe 
 of the dam must, however, be strong enough to resist the 
 forces induced by the tendency to overturn. 
 
 Turning now to a consideration of the proportions of a 
 dam that will resist riot only the horizontal pressure of 
 the water but also the upward pressure from beneath, we 
 have a representation in Fig. 4 of the forces acting on such 
 a dam. We might assume that the pressure of the water 
 beneath the dam gradually diminishes as it works its way 
 
 387 
 
toward the toe of the dam. The lower shaded triangle 
 would represent the upward forces against the base of the 
 dam. It will be seen that the moment of a rectangle of 
 altitude wh about the center of moments is the same as that 
 of the triangle shown, hence it is immaterial whether or not 
 we assume a diminution of pressure. 
 
 The total overturning moment equated to the moment 
 of stability gives us. 
 
 Using the same weights as before for water and masonry 
 ve have 
 
 "F 7~* 
 
 The width of the dam at its base should therefore be. 
 about .85 times the height. Of course making the cross 
 section of the shape shown in Fig. 3 will increase the 
 moment of stability, and the base need not be quite so wide. 
 On the other hand if a height of water greater than the 
 trest of the dam is anticipated, as is very often the case, 
 the above relation would not be sufficient. 
 
 This ratio of height to base is derived merely to show 
 iHiat should be the approximate relation for a solid masonry 
 dam capable of resisting all of the possible forces against 
 h. There are not many dams that have a width of base 
 .85 of their altitude and there are not many that are so 
 thoroughly underdrained as to make this width unnecessary. 
 A builder may take long chances on the probability of an 
 office building or a highway bridge never receiving its 
 load and be comparatively safe. But the pressure of water 
 is something sure and determinate, and the integrity of 
 a dam is something that ought not to be trifled with. 
 
 If the slope of a solid dam be made on the upstream face, 
 'tfrhile the pressure of the water will act partially to pre- 
 |*ent overturning, the moment of stability of the masonry 
 is neutralized. As the water is of less weight than the 
 masonry, the resultant stability is greatly diminished. If 
 Ithe slope of the upstream face were made 45 deg., the 
 'resultant pressure of the water would fall at the edge of 
 ithe middle third. Such a dam, thoroughly underdrained, 
 388 
 
would not need to depend upon the weight of the masonry 
 for its stability. If the amount of masonry can be reduced 
 by arching and the use of buttresses or counterforts, an 
 economic dam may result. In case reinforced concrete 
 slabs are used the reinforcing should be with round rods 
 with nuts and washers on the ends and spliced with sleeve 
 nuts, so as to reduce to a minimum dependence upon ad- 
 hesion or bond. A good form of reinforcement is a com- 
 bination of round rods and angles with holes punched in 
 them to receive the rods and act as bearing plates or 
 washers. Rods should have two nuts, one to bear against 
 each side of the metal. Rods should also be used trans- 
 verse with the main rods of the slabs, so as to tie the con- 
 crete together in every direction. At the counterforts or 
 walls supporting the slabs there should be angles through 
 which the rods pass and to which also rods reinforcing 
 the counterforts may connect. This tying together of the 
 entire structure adds greatly to its stability and safetj 
 and lessens the probability of extended failure, if a loca. 
 weakness develops. The deep slabs that would be requirec 
 in large dams should have a set of rods near the tensior 
 side of slab similar to the horizontal rods in beams anc 
 a set of rods that curve up about at the quarter points 
 these are to take the shear and the continuous beam stresse* 
 of the slab. All of these rods should pass through angles 
 The entire system of steel reinforcement should be a; 
 rigidly braced and held in place as possible before con 
 crete is placed, so that the placing of concrete will no 
 displace the parts. 
 
 The reason that adhesion or bond should not be reliec 
 upon in a reinforced concrete dam is because water unde: 
 pressure lessens the gripping power of the concrete. 
 
 A reinforced concrete dam could be made with a vertica 
 slab against the water sustained by counterforts or but 
 tresses on the down stream side. 
 
 A dam must be stable against sliding on its foundation 
 If the foundation of the dam is in rock, notches should b 
 cut in the rock so that slipping will be prevented by th 
 rock itself. In general dependence should not be place* 
 
 389 
 
; ipon a wall of earth to prevent slipping or a notch in an 
 ! :arth foundation because of the compressibility of earth. 
 j \ssuming a coefficient of sliding friction of the masonry 
 >n the earth of l / 2 , the dam would be stable against sliding 
 f its weight were twice the horizontal pressure of the 
 vater. Using the same unit weights as before, it will be 
 ;een by a simple calculation that a rectangular dam whose 
 veight is twice the horizontal pressure of the water would 
 lave a width of .42 times its height. A triangular dam 
 vould have a width or base .83 times its altitude. If water 
 vorks its way under the dam, it will lubricate the surface 
 ipon which sliding takes place. The sliding out of large 
 :hunks of masonry in dams that have failed would indicate 
 hat this is a mode of failure to be looked for and guarded 
 igainst. That such a failure may not take place locally it 
 s important that dams be made of monolithic concrete 
 md not of blocks of stone. It is also important that some 
 ;teel reinforcement be used, even in solid dams, to tie 
 ihe concrete together. Where in the foundation of a dam 
 the principal bearing surfaces against the earth are made 
 normal to the resultant pressure, sliding is practically elim- 
 inated, and settling would cause a uniform movement of 
 the dam of a nature similar to the vertical settlement of 
 |i structure. These foundations must be deep enough not 
 o cause upheaval of the earth due to the lateral pressure. 
 In a dam with counterforts or buttresses inclined shafts 
 j:ould be made use of as foundations for the counterforts 
 ||>r buttresses to take the inclined resultant of the pressures 
 (Being separated from the curtain wall in contact with the 
 water these would not be subject to the buoyancy or the 
 rubricating action of the water under high pressure. 
 i Anchor bolts in the natural rock to tie a dam down 
 ikgainst uplift should be used with caution. A bolt dropped 
 m a drilled hole and grouted is not the best kind of anchor. 
 |'f steel bolts are to be used as anchors, it is better to ex- 
 r:avate expanding holes in the rock and fill these with con- 
 crete around bolts suspended in them. 
 | Arched dams are sometimes made, which have their 
 ibutments in the rock on each bank of the stream. Such 
 390 
 
dams are, of course, convex on the upstream side. The 
 water acts as a horizontal load on the arch. The curve 
 of the dam in any horizontal section should be the arc of 
 a circle, as this is the shape of a curve of equilibrium for 
 a uniform load normal to the extrados of an arch. The 
 pressure around the arch at any given depth h is 62.5 hR 
 per foot in the height of dam, where h = depth below sur- 
 face of water and R radius of arch in feet. The arch 
 could not be a true reinforced concrete arch, because the 
 load is a constant one, and there is no bending moment 
 to resist. It should, however, be tied together with rods 
 runing horizontal and vertical to prevent the concrete from 
 cracking. The unit compression on the concrete (which 
 should be 1:2:4 concrete of Portland cement and good 
 sand and stone) should not exceed 200 or 300 Ib. per sq. 
 in., because the concrete is in compression over the entire 
 surface, and there is no reinforcement against diagonal 
 shear. Steel should not be counted upon to take any of 
 the compression of the arch. 
 
 391 
 
The Design of Reinforced Concrete 
 Chimneys. 
 
 There are several problems that enter into the design 
 of reinforced concrete chimneys, which are not usually 
 found in text books on mechanics of materials. These 
 will be taken up as a preface to this article. 
 
 One of these problems concerns the position of the line 
 of pressure on a hollow rectangular column of elastic ma- 
 terial in order to produce only compression on the material. 
 The rectangular column will be taken as one having out- 
 side dimensions b and d and inside dimensions b f and d'. 
 A central load P on such a column will produce a unit 
 compression K as per the following equation: 
 K = P + (bd b'd') (i) 
 
 If the load P be shifted a distance x in a direction par- 
 allel to the side d, remaining central in the rectangle in 
 the other direction, it will produce bending in the column 
 in addition to the direct stress. The eccentric load P may 
 be considered as replaced by a central load P and a couple 
 -each of whose forces is P, one being located at the shifted 
 position of the load P and the other being at the center 
 of the column but opposite in direction from the other 
 central load, thus neutralizing it. The effect on the column 
 is then a couple which will produce a bending moment Px 
 and a direct central load P. The moment will give ten- 
 *sion along one edge of the rectangle and compression along 
 the other edge with uniform variation between. The sec- 
 tion modulus of the hollow rectangle is (bd 3 b'd' 3 )-z-6d. 
 .^Hence the extreme fiber stress K' due to the moment 
 Px is 
 
 K'=(6 Pxd) + (bd* b'd' s ) (2) 
 
 When K = K f , there will be a condition of no stress at 
 one edge of the rectangle and an extreme fiber stress at 
 the opposite edge equal in intensity to double the unit 
 compression due to the direct load P. 
 
 For any given rectangle the value of x may be found 
 by equating K and K' of equations (i) and (2) respec- 
 tively and solving. This value of x will give the position 
 
 392 
 
4 
 
 
 $ 
 
 
 
 X 
 
 5 
 
 4 
 y ! 
 
 i 
 
 
 X H 
 5" 
 
 if 
 
 y "^ 
 
 1 
 
 . 5-0", 
 
 
 
 
 i 
 
 
 
 
 j 
 
 
 
 
 f* 
 
 i 
 
 5--^ 
 7-'6" 
 
 ^* o 
 
 4" V 
 
 
 
 2 I 
 
 m 
 
 
 _._ z 
 
 
 
 J 
 
 
 T r 
 
 FIG. 3. 
 
 
 I5-O* 
 
 393 
 
of a load that will give the condition named in the last 
 
 paragraph. A load placed anywhere within a distance x 
 
 \ from the center of column will produce only compression 
 
 \ in the column. In a hollow square column or chimney 
 
 i whose external and internal diameters are d and d' re- 
 
 spectively we find 
 
 x=(d* + d'*)-r-6d (3) 
 
 The resultant pressure on the section of a hollow 
 i square chimney should then fall within this distance x of 
 i the center. 
 
 When d' = o, that is, when the section of the column 
 
 'is rectangular, x is one-sixth of d. This is the familiar 
 
 "proposition that the center of pressure in a rectangle must 
 
 \ fall within the middle third of the base in order not to 
 
 produce tension on the extreme fiber. When d' d t 
 
 x = 1/3 d, showing that when the thickness of the shell is 
 
 small compared with the diameter the resultant may ap- 
 
 iproach a point one-third of the diameter from the center 
 
 i without producing tension on any part of the shaft. 
 
 1 In a hollow circle whose external and internal diameters 
 
 are D and D' respectively, we find by a similar operation 
 
 -+ > 
 
 When D' = o, x=y%D, which shows that the center of 
 
 pressure must fall within the middle quarter of the diam- 
 
 eter of a solid circular shaft in order not to produce ten- 
 
 sion on the extreme fiber. When D f approaches equality 
 
 with D, x approaches *4 of D, showing that in a thin shell 
 
 the resultant may fall within y of the diameter from the 
 
 center without producing tension on any part of the section. 
 
 Another problem that has a bearing on the design of 
 
 chimneys is that by which the stress may be found in a 
 
 system of rods disposed in a circle when subject to a 
 
 bending moment acting on the circle. This will be solved 
 
 ! through the medium of a thin tube in bending, which is 
 
 I still another problem useful in the solution of stresses in 
 
 i chimneys. The moment of inertia of a tube or circular 
 
 | shell whose thickness is t, and radius R, both in inches, is 
 
 394 
 
TT /?* t, and the section modulus is therefore -TT R* t. If 
 we let K= extreme fiber stress on the tube in pounds 
 per square inch and M the moment on the same in inch- 
 pounds, we have 
 
 M = K*R*t (5) 
 
 (M may be in ft.-lbs., K in pounds per square foot, and 
 R and t in feet.) 
 
 Suppose now that the tubular shell is replaced with a 
 system of rods equally spaced and disposed in a circle. Let 
 n = number of rods. Then 2 TT R-r-n is the space from 
 rod to rod. The rod that is located at the point of max- 
 imum extreme fiber stress can be considered as taking the 
 stress that would come on the shell in an area equal to 
 the spacing of rods by thickness of shell, or 2 ?r R t-r-n. 
 The stress on this rod is then 2 w R K t-^-n. Substitut- 
 ing the value of K out of equation (5) in this we have 
 for the stress 5" on the rod receiving the maximum stress 
 S = 2M + Rn (6) 
 
 Equation (6) is remarkable. It is derived, as observed, 
 only to be a close approximation for a comparatively large 
 number of rods arranged in a circle. By trial it will be 
 found to be exactly true for 12 rods, 8 rods, 6 rods, 4 
 rods, and probably for any even number of rods above 
 these numbers. This equation could be used in finding the 
 maximum pull on the anchor bolts of a steel stack. It 
 could be used in finding the stress on the bolts of a pipe 
 coupling under bending. It could be used in finding the 
 stress on the rivets in the circular seam of a riveted pipe 
 under bending, as in the case where the pipe spans an 
 opening. 
 
 Another problem that will need to be solved concerns 
 the extreme fiber stress on a hollow circular section under 
 bending. The formula for this case is 
 
 M = .0982 (> 4 Z)' 4 ) K ~ D (7) 
 
 The calculations on a reinforced concrete chimney or 
 stack involve the determination of the compression on the 
 concrete or the dimensions necessary to keep that compres- 
 sion within certain limits, the embedded steel required to 
 
 395 
 
relieve the concrete of all tension, and the base necessary 
 to give the required stability against the wind. 
 
 In the stack shown in Fig. 2 it is desired to investigate 
 the stability and to determine the amount of steel neces- 
 sary to reinforce the concrete. The areas and weights 
 are found to be as follows: 
 Area upper section, 829 sq. in. = 5.76 sq. ft. 
 Area middle section, 1021 sq. in. 7.09 sq. ft. 
 Area outer shell, lower section, 1583 sq. in. = n.oo sq. ft. 
 Area inner shell, lower section, 1021 sq. in. = 7.09 sq. ft. 
 Weights at 150 Ib. per cu. ft. : 
 
 Upper section 25,900 
 
 Middle section 31,900 
 
 Outer shell, lower section 66,000 
 
 Inner shell, lower section 42,500 
 
 Plinth, base 33, 700 
 
 Frustum, base 78,800 
 
 Total weight of stack 278,800 
 
 The moment of stability of the stack is 278,800 times 
 one-sixth of the width of the base, or 697,000 ft.-lb. (The 
 added weight due to the thickening up at section Y Y is 
 omitted here to simplify the calculations.) 
 
 The wind loads (at 40 Ib. per sq. ft. on one-half the 
 projection of the cylinder) are as follows: 
 
 Upper section, 40 X ^ X 5.83 X 3O = 3,5oo Ib. 
 
 Middle section, 40 X *A X 5.83 X 30 = 3,500 Ib. 
 
 Lower section, 40 X V* X 7^ X 40 6,000. Ib. 
 
 The load on the upper section is applied 85 ft. above the 
 ground, that on the middle section is applied 55 ft. above 
 the ground, and that on the lower section is applied 20 ft. 
 above the ground. The wind moments at the ground 
 level are 
 
 3,500 X 85 = 297,500 
 3,5oo X 55 = 192,500 
 
 6,000 X 20 = 120,000 
 
 Total 610,000 ft.-lb. 
 
 At the base of the foundation there will be added to this 
 396 
 
moment 13,000 X 5 = 65,000, making the total 675,000 ft.-lb. 
 This is less than the moment of stability previously found. 
 Hence the stack is stable against the wind. 
 
 The area of the base is 225 sq. ft. Dividing this into 
 the total weight found above we find a pressure on the 
 soil of 1,240 Ib. per sq. ft. When the wind load is applied, 
 the pressure on the soil on the leeward edge is almost 
 double this amount. (It would be just doubled if the 
 overturning moment just equaled the moment of stability.) 
 A pressure of 2,400 Ib. per sq. ft. is very low for ordinary 
 soil. 
 
 At the section XX the weight of the stack is 25,900 Ib. 
 and the compression due to dead weight is 31 Ib. per sq. 
 in. The wind moment at this section is 3,500 X 15 = 52,500 
 ft.-lb. The concrete is able to resist a certain part of this 
 without suffering any tension on the extreme fiber. The 
 distance from the center that the resultant pressure may 
 fall to give this condition of no tension is the value of x 
 in equation (4). Solving for the section XX we find x 
 is 1.30 ft. Hence (taking moments about a point x feet 
 from the center of stack) the moment of stability of the 
 stack, without relying upon the steel, is 25,900 X J -3O 
 33,700 ft.-lb. This leaves 18,800 ft.-lb. to be taken by the 
 steel. 
 
 At section Y Y the wind moment is 3,500 X 45 + 3>5oo 
 X 15 210,000 ft.-lb. The value of x is 1.27 ft, and the 
 moment of stability of the concrete is 57,800 X 1.27 = 73,400 
 ft.-lb. This leaves 136,600 ft.-lb. to be taken by the steel. 
 
 At section ZZ the wind moment, previously found, is 
 610,000 ft.-lb. The value of x is 1.64 ft. and the moment 
 of stability of the concrete is 123,800 X 1-64 = 203,000 ft.-lb. 
 This leaves 407,000 ft.-lb. to be taken by the steel. 
 
 For the steel reinforcement we will take the neutral 
 axis in the center of the shaft in all cases and allow the 
 concrete to take whatever compression develops. The 
 critical point is then the outermost rod on the tension side. 
 The tension on this rod is found by equation (6). Or 
 assuming a size of rod the number of rods required may be 
 found by the same equation. 
 
 397 
 
Assuming that ^j-in. round rods will be used vertically. 
 12,500 Ib. per sq. in. the permissible tension on one rod 
 
 7,520 Ib. Keeping these rods 3 in. from the outer sur- 
 face of the stack, the radius of their circle is 3.5 ft. Sub- 
 stituting in equation (6) we have 7,520 = 2X407,000-7^ 
 3.5 n, from which w = 3i bars. 
 
 At section Y Y, using the same bars and 2 ft. 9 in. for 
 the radius, we have 7,520 = 2 X 136,600 -r- 2.75 n, from 
 which n = 13. 
 
 If 32 bars be used in the lower section, half of them 
 may be dropped at section Y Y. 
 
 At section X X but little steel is required. There should 
 be some rods, however, to prevent the cracking of the 
 'concrete. Eight of the 7 /s-'m. rods could be continued io 
 the top of chimney, or smaller rods could be used, say 16 
 half-inch round rods lapping those of the section below. 
 Another method would be to run four of the ^-in. rods 
 the full length and to use smaller rods between these to 
 tie the concrete together. 
 
 The %-in. rods should have anchorage in the founda- 
 tion; preferably by a circular angle punched to receive 
 them, or by anchor plates. Two nuts on the end of each 
 rod would insure a bearing on the metal. Where rods 
 join, they should be threaded and have sleeve-nut splices. 
 
 In the horizontal direction rods in circles should be 
 placed about every 20 or 30 in., their ends being lapped 
 a foot or more. These rods could be l /2 in. square. They 
 should be wired to the vertical rods. 
 
 Around openings in the side additional rods are needed 
 for reinforcement, also possibly a thickening of the con- 
 crete. 
 
 Where the diameter of the outer shell changes there is 
 a weak section. The bend in the rods induces horizontal 
 thrust, and there is shear on the concrete because of the 
 change in direction of the line of pressure. It is recom- 
 mended that the bends in rods be made in the thickened 
 portion of the shell and that curved angles be used at 
 these bends to stiffen the concrete, as shown in Fig. 4. 
 
 The inner shell needs rods both vertically and horizontally 
 
to keep the concrete from cracking. This inner shell is 
 kept separate from the outer shell, except near the bottom, 
 where the air space is sometimes filled in. The purpose 
 is to allow free expansion and contraction of the highly 
 heated part. The amount of steel used to reinforce con- 
 crete where there is no calculable stress is usually made 
 from 1-500 to i-iooo of the area of concrete. 
 
 The compressive stress on the concrete is another matter 
 for investigation. Z Z is the critical section; other sec- 
 tions will be found to have considerable less unit stress. 
 The compression from dead load is 78 Ib. per sq. in. By 
 equation (7), using 610,000 for M, we find an extreme 
 fiber stress of 33,800 Ib. per sq. ft. or 235 Ib. per sq. in. 
 This makes the maximum compression at this section 313 
 Ib. per sq. in., which is about right. Concrete in such 
 case should not be subject to the usual allowable compres- 
 sive unit of 500 Ib., because it is not confined on one side, 
 as in the case of beams and slabs. This concrete is more 
 in the nature of a column. The hoop reinforcement does 
 not have the efficiency in this case that it has in a hooped 
 column. As a check on the compressive stress on the con- 
 crete we may use the same moment in equation (5) and 
 the mean value of R, or 3.5. The result is 220 Ib. per 
 sq. in. as compared with 235 Ib. found by the more exact 
 method. 
 
 The design of the chimney would be simplified and im- 
 proved, from a structural standpoint, if the offset in the 
 outer shell could be avoided. 
 
 For the outer shell of this chimney the concfete used 
 should be a i :2 14 mixture with small sized broken stone 
 of good quality. The inner shell should be a concrete that 
 will resist a moderately high heat. No limestone should 
 be used in this part. Small gravel and sand or trap and 
 sand would be suitable. 
 
 If sand alone is used with the cement such mixtures as 
 
 i :7 or 8 should not be employed. The voids in sand are 
 
 too great to be filled with this small proportion of cement. 
 
 About 4 or 5 parts of sand to one of cement ought to be 
 
 399 
 

 the limiting ratio, and even this ratio should only be used 
 with a very coarse sand. 
 
 The spread of the footing of this chimney is not enough 
 to require much if any reinforcement in the concrete. It 
 would, however, be desirable to have some rods laid par- 
 allel to each side and some laid diagonally in both di- 
 rections. 
 
 
 
 j T 
 
 ' vfno 
 
 f 
 
 > ariT) 
 
 
 
 
 
 
 y^o! ? 
 
The Design of Domes, Vaults and 
 Conical Coverings. 
 
 While the stresses in a flat plate supported on all sides, 
 or a flat slab similarly supported, are more or less in- 
 definite, after deflection takes place, because of the fact 
 that a flat plate may actually act as a portion of a spherical 
 shell of very long radius, the stresses in a dome or conical 
 roof are capable of more exact determination. Also the 
 analysis of these stresses is comparatively simple. 
 
 The stresses in a conical covering or roof, such as that 
 on a circular tank will first be considered. Given a conical 
 covering such as that shown in Fig. I. Let the weight 
 above the line AB be represented by IV. This can be re- 
 solved into two components, namely H and T. A thin 
 cone not capable of taking any bending but only com- 
 pression and tension may resist both of these forces or sets 
 of forces. (The cone is somewhat analogous to a thin 
 tube under external pressure so that if the thickness is 
 relatively small it may be in a state of unstable equi- 
 librium.) The component T will give compression in the 
 direction of an element of the cone, and the component 
 H, being continuous around a circle whose radius is r, 
 acts like external pressure on a cylinder, producing com- 
 pression also. 
 
 The total amount of T is found by the equation 
 
 T= Wmr_ (1) 
 
 ft 
 
 The area upon which this force acts is a ring whose 
 radius is r and whose thickness is t or an area 2 TT r t . 
 Dividing this into the above value of T we have for a unit; 
 compression C in the direction of an element of the cone 
 r Wm 
 
 C =-2^T~ < 2 > 
 
 The weight W will include the dead weight of the part 
 
 of the cone above the line AB, including any structural 
 
 features outside of the cone itself, also any snow load or 
 
 live load that may come upon that part of the cone. 
 
 401 
 
The force H in Fig. i is resisted by hoop compression 
 in horizontal planes. The force T is cumulative and 
 reaches the value in equation (i) only at the foot of the 
 slope mr. The force H is resisted by rings or hoops of 
 stress distributed along the entire surface of the cone, 
 that is; these rings make up the cone. In order to arrive 
 at the amount of this hoop compression we observe that 
 each ring is in effect an element of a cylinder under ex- 
 ternal pressure. It is well known that the tension or com- 
 pression on the shell of a cylinder due to a radial pres- 
 sure, outward or inward, of any given intensity is equal 
 to the amount of that pressure on a radius. In other 
 words the tension, or compression on the ring or hoop is 
 equal to the total pressure around the circumference di- 
 vided by 2 TT . Therefore H divided by 2 - is equal to the 
 stress on an element mr of the cone. But H = Wr -f- h, 
 and the total compression along the element mr is 
 
 *-s- 
 
 This compression is not uniformly distributed along the 
 element, but varies in intensity. In order to find the value 
 of K, for the case where the weight is only that of the 
 cone itself, we will substitute for W the weight of the 
 cone above the section AB, or w m n r* t, where 
 w = weight per cu. ft. of the material of the shell other 
 dimensions being in feet. Then 
 
 K=-^fL (4) 
 
 The unit compression at any section is found by sub- 
 stituting in (3) an element of the weight of the cone and 
 dividing by an element of the area. Letting P represent 
 this unit compression we find 
 
 (5) 
 
 If in equation (2) we substitute for W the weight of a 
 conical shell whose radius is r, or TT f 9 m w t> we shall 
 have 
 
 (6) 
 
 402 
 
Fig- -I. 
 
 a V 
 
 - 
 
 2TT 
 
 (b) 5n 
 
 403 
 
We see from equations (5) and (6) that the thickness 
 of the conical shell does not enter in the determination 
 of the unit stress in a cone supporting its own weight only 
 (in a shell where the volume is sensibly equal to the area 
 of the median cone by the thickness). It may also be 
 shown by equating C and P in equations (5) and (6) 
 that when m equals the square root of 2, the intensity 
 of stress in both directions is the same. This is true 
 when the angle of the element of the cone with the hori- 
 zontal is 45 deg. 
 
 The thickness of concrete in the cone is determined 
 by other considerations than the weight of the shell itself. 
 A uniform load, such as a snow load uniformly distributed 
 would not add much stress. The weight of a man on the 
 roof of a tank or snow load on one-half only are possi- 
 bilities that must be considered. These scarcely admit 
 of calculation. Hence a simple cone without ribs would be 
 designed largely by judgment. A thickness of shell of 4 in. 
 for a tank 15 ft. in diameter and 6 in. for a tank 25 ft. in 
 diameter would probably meet the requirements. Steel 
 rods in circles around the cone and rods down the slope 
 would be valuable to insure the integrity of the roof and 
 to guard against shrinkage cracks. If any man holes are 
 to be left in the roof, the concrete around the openings 
 should be reinforced with steel rods. The circular and 
 sloping rods in the conical covering are not true reinforc- 
 ing rods, because they would not take tension. There is 
 no basis for finding their size for the same reason. 
 
 At the foot of the slope, if the cone is supported on ver- 
 i tical walls, there is a tension which is equal to the total 
 compression exerted on a vertical section from the apex 
 to the foot of the slope, that is, the sum of all of the 
 hoop compression in the horizontal rings. The amount of 
 this is found by equation (3) by substituting R for r. For 
 example, given a tank 15 ft. in diameter, with m = 1^4, 
 the concrete being 4 in. thick, and h = 5.63 ft. The weight 
 of the concrete in the conical roof is 11,000 Ibs., at 150 
 Ibs. per cu. ft. A snow load at 30 Ibs. per horizontal 
 square foot would weigh 5,300 Ibs. Using 16,300 for W 
 404 
 
in eq. (3) we find K =3,5oo Ibs. At 10,000 Ibs. per sq. in. 
 this would require a jj-in. round rod. This rod should 
 be directly over the wall of the tank. The ends should 
 be joined by a turnbuckle or else lapped 50 diameters or 
 more. 
 
 A conical bottom in a tank has the stresses reversed 
 from those of a roof, and on account of the fact that 
 a liquid exerts normal pressure against the bottom there 
 will be additional stresses in the rings. Equation (i) 
 will serve to determine the stress down the slope, which 
 will be tension instead of compression. W is to be taken 
 as the weight of the cone, the radius of whose base is r, 
 plus the weight of the liquid directly over it. The great- 
 est amount of steel is needed near the junction of bottom 
 and sides. There should be an angle at this junction bent 
 into a ring and punched to receive the rods. The rods 
 should be round and should have thread and nut on the 
 end to anchor to this angle. It is best to make all rods 
 of the same diameter. Equation (i) may be solved for 
 r=i ft, 2 ft., 3 ft, etc. Find where the value of T is 
 one-half the maximum, and let half of the rods run 50 
 times their diameter beyond this, the others to continue 
 down the slope: half of these may end 50 diameters be- 
 yond the point where the stress is again half as great, etc. 
 Some rods should run to the apex of the cone and anchor 
 to a small circular angle. For the ring stresses solve 
 equation (5) for the unit tension on the concrete at any 
 point, due to the weight of the bottom. For the liquid 
 pressure 
 
 9 _D 
 
 Where P" = unit tension on concrete, D = depth of liquid 
 over the section under consideration, w' = weight per cu. 
 ft. of liquid. The sum of these two unit tensions is to be 
 converted into tension in steel rods according to the spac- 
 ing of rods assumed. 
 
 At the junction of the shell, or side of tank, and the 
 conical bottom there will be a compression, in amount 
 equal to the value of K in equation (3), when W total 
 405 
 

 weight of bottom of tank and liquid contents. This must 
 be resisted by concrete, and there should be area enough 
 of concrete close to this corner to take the compression 
 at about 200 Ibs. per sq. in. It is of course uncertain 
 just how much of the walls and bottom may be included 
 in the ring at the junction to take this compression. A 
 fair proportion would include twice the thickness of wall 
 up the side and twice the thickness of bottom down the 
 slope. Then the concrete over the supporting wall should 
 be thickened as shown in Fig. I. 
 
 A dome may be analyzed in a manner somewhat sim- 
 ilar to a conical covering. In the dome, as in the conical 
 roof, a thin shell will support uniform load by tensile and 
 compressive stresses alone, though if the thickness is rel- 
 atively small the equilibrium will be unstable. 
 
 If the dome is segmental, as at (a) Fig. 2, and parabolic 
 in section, a portion having a base whose radius is r will 
 have stresses at the foot of the slope (in the direction of the 
 slope) corresponding to those in a cone whose altitude is 
 h, the cone being tangent to the dome. Because of the 
 fact that it is a property of a parabola the altitude of the 
 cone will be twice that of the dome, as indicated. It is to 
 be remembered that n is not a constant in this 
 case, as in the case of the cone. For the 
 weight of the dome itself the superficial area is very 
 close to the area of a circle whose radius is the chord 
 m'r. (The area of a segment of a spherical sur- 
 face is exactly equal to the area of a circle whose radius 
 is this chord of one-half of the arc.) The volume is then 
 equal to the product of this area and the thickness /. For 
 a segmental dome, as shown at (a), reinforcement is 
 needed over the supporting wall in the shape of a steel 
 hoop to take the thrust. Assuming a dome 20 ft. in diam- 
 eter and 5 in. thick, we find a weight of 22,800 Ibs. and 
 a snow load of 9,400 Ibs. If the dome has a rise of 4 ft. 
 at the center, h = S. Substituting in eq. (3) we find 
 K = 6400 Ibs. At 10,000 Ibs. per sq. in. this would re- 
 quire a yf-in. round rod. 
 
 The circular stresses (at other sections than directly 
 406 
 
over the wall) in a segmental dome do not correspond to 
 those in a tangent cone. But as these do not play a very 
 important part in proportioning a dome, unless it ap- 
 proaches a hemisphere, they will be taken up only in the 
 case of the hemispherical dome. 
 
 In the hemispherical dome such as shown at (6), Fig. 
 2, the tangential thrust T f at any section is found by the 
 following 
 
 T W cosec x (8) 
 
 where W = weight of dome and load upon the same above 
 the section considered. If the only weight supported is 
 that of a dome of uniform thickness at w Ibs. per cu. ft. 
 we may find W thus : The area of the segment of a 
 sphere is equal to the circumference of a great circle by 
 the altitude of the segment. The weight of this segment is 
 then 2 TT R 2 (i cos#) tw. The area of the ring tak- 
 ing this tangential thrust is 2 K R t sin x. Using the 
 weight just found for W in equation (8) and dividing by 
 the area just found we find for a unit compression C' due 
 to thrust T. 
 
 C>=Rvl- cosx ^<vv> (9) 
 
 sm*x r 2 
 
 The intensity of this pressure varies from R w just 
 over the supporting wall to one-half as much as the top. 
 Hence a dome designed to take a uniform unit thrust, 
 supporting its own weight only, would be thinner at the 
 crown than over the supporting wall. A snow load, add- 
 ing weight near the crown without adding to the capacity 
 of the dome to support the weight, would tend to equalize 
 the stress. 
 
 For the annular or ring stresses the sum of these from 
 the crown down to the end of radius r is 
 
 27T 
 
 Or substituting for W y for a dome of uniform thick- 
 ness, the weight of the segment, as previously found we 
 have 
 
 K' R 2 t w (i cos x) cot x (n) 
 
 407 
 
The unit intensity of this hoop compression is found by 
 differentiating the value of K f in eq. (n) and dividing 
 by R t dx, which is the differential increment to the area. 
 The result is a unit compression P' as per the following 
 equation. 
 
 P'=Rw(cos x L "\ ( 12) 
 
 V cos -r+1 ) 
 
 By examination of equation (12) it will be seen that 
 for x = o the intensity of stress is ^ R w, which is the 
 same as that of the thrust, found by equation (9), at the 
 crown of dome. As this is positive the stress is com- 
 pression. When x = 90 deg., P' ( Rw), which is also 
 the same in intensity as the thrust found by equation (9), 
 over the supporting wall. As this stress is negative it is 
 tension. When cos x = y* (j/5 i), P' o. This is 
 true when x = 51 deg.-49 min. There is thus a point where 
 the intensity of the hoop stress is zero. Above this point 
 the hoop stresses are compression and below it they are 
 tension. Where compressive stresses occur, no steel rein- 
 forcement would be demanded for these stresses alone. 
 Where tensile stresses occur, steel reinforcement would be 
 required in a concrete dome. The tension on steel rein- 
 forcement would be found by solving eq. (12) for the 
 unit stress at any point and multiplying this by the area 
 of concrete surrounding a rod. In a dome 30 ft. in diam- 
 eter and 6 in. thick at a section close to the supporting 
 wall the unit stress = 2tw or 15 X 150 = 2,250 Ibs. If we 
 assume rods one foot apart, one rod would be surrounded 
 by ^2 sq. ft. of concrete and have a stress of only 1,125 Ibs. 
 
 There is no thrust to take at the springing of this dome, 
 as in the cone or segmental dome, as the sides start vertn 
 cal. In the cone and segmental dome there is a hoop stress 
 at the base or springing which just balances the compres- 
 sive hoop stresses along the vertical section through the 
 axis. In the hemispherical dome this equality or balanc- 
 ing of horizontal forces is accomplished, as explained under 
 equation (12), by positive and negative hoop stresses along 
 the meridian. 
 
 In a segmental or hemispherical tank bottom the 
 408 
 
stresses for the weight of the bottom alone will be equal 
 in intensity to those found for the dome but reversed in 
 sign. The unit stress in the direction of the meridian is 
 found by the following equation. 
 
 C^-l (13) 
 
 where Ci = unit tension at point S, Fig. 2 at (c), w' wt. 
 per cu. ft. of liquid, D' average depth of liquid in 
 MLSQN. 
 
 The unit stress in horizontal rings may be found by the 
 following equation. 
 
 P _w'{ 
 '~ V 
 
 (14) 
 
 where Pi = unit tension at point S, and D" depth of 
 liquid to point S. 
 
 The depth D' is found by adding to the altitude of the 
 cylinder MNSL the average altitude of the spherical 
 segment N Q S. The average altitude of the segment of 
 a sphere lies between 2/3 and ^2 of the altitude; that is, 
 the volume will lie between 2/3 and l /z of the volume of a 
 cylinder of the same base and altitude. When the angle 
 x approaches zero, the coefficient is one-half, which is the 
 exact coefficient for a paraboloid, and a flat circular arc 
 approaches coincidence with a parabola. When x 30 deg., 
 the coefficient is .512; when .ar =r 45 deg., it is .529; when 
 x = 60 deg., it is .556. For x = go deg., or when the seg- 
 ment is a complete hemisphere, the coefficient is 2/3. 
 
 To reduce tension in the concrete, as found by equations 
 (13) and (14) to tension in steel reinforcing rods, multi- 
 ply the unit values there found by the assumed spacing 
 of rods times the thickness of concrete. 
 
 In a ribbed dome, that is a dome supported by a sys- 
 tem of arched ribs meeting in a circle or regular polygon 
 at the top, each rib is like the half of an arch. Between 
 the ribs the covering may be a slab of reinforced concrete. 
 This slab would be designed according to the methods of 
 design used for floor slabs. As the inclination of the slab 
 to the horizontal increases, the possibility of carrying a 
 409 
 
snow load decreases, and the effect of the weight of the 
 slab itself in producing bending diminishes. The compo- 
 nent of the dead weight that produces bending in the slab 
 is the weight times the cosine of the angle made with the 
 horizontal. For the stress in the rib lay a rib out to scale 
 and estimate the weight carried at points at intervals 
 along its length. Take moments of these several loads and 
 the reaction at the foot of rib around the upper end of the 
 rib. This moment divided by the vertical distance from 
 upper end to foot of rib will give the horizontal thrust. 
 From these forces construct the equilibrium polygon. (See 
 similar operation and construction farther on in the case 
 of filter vaults.) This equilibrium polygon will give the 
 direct stress in the rib and will give the bending moment 
 at any section. For the latter, where the equilibrium poly- 
 gon departs from the center line of the rib, the bending 
 moment is equal to the product of the force in the poly- 
 gon and the distance from the center of the rib to the 
 force, measured perpendicular to the force. 
 
 A form of vault much used for filter covers consists of 
 a system of groined arches carried by square posts or 
 piers, spaced equal distances in both directions. These 
 arches spring in four directions from the piers. At the 
 piers the arches are of course the width of the pier, and 
 at this section they are thickened vertically. Midway 
 between the piers the width of concrete arch is equal to the 
 distance center to center of piers. The concrete is usually 
 plain, and the vaults are covered with three feet or so of 
 earth. Some such vaults are described in Engineering 
 News, November 8, 1906, and Engineering Record, May 
 19, December 15, December 22, 1906, April 27, 1907. 
 
 The load to be carried consists principally of the dead 
 weight Allowance should also be made for the superim- 
 posed load of teams driving over the ground. In this in- 
 vestigation only the dead load will be calculated. The live 
 load could be considered as a uniform load of 100 or 200 
 Ibs. per sq. ft., since the deep earth fill serves to distribute 
 well the live load. 
 
 Fig. 3 shows a section of a filter vault taken through 
 410 
 
F.q.3 
 
 411 
 
a pier and the outside wall or abutment. This illustrates 
 < the various points to be considered, namely, the pier, the 
 half of one of the groined arches, the half arch springing 
 from the outer wall, and the outer wall or abutment. The 
 distance c. to c. of piers is 15 ft. The span of arch is the 
 distance from face to face of piers or from face of pier 
 to inner face of outer wall; this is 13 ft. 2 in. Half of 
 this is divided into 10 equal parts, and the weights of con- 
 crete and earth in each part are calculated. These weights 
 are shown in Fig. 3; those on the left side of the center 
 are for the half of a groined arch, and those on the right 
 side are for the half barrel arch. 
 
 By taking moments around the center of arch at crown, 
 using the applied loads to the left and the reaction 24,200 
 Ibs., and dividing the moment thus found by the rise, 
 i ft. n l /2 in., we obtain the horizontal thrust, H, or 48,500 
 Ibs. The rise of the arch is the vertical distance from 
 the center line of arch ring at springing (center point of 
 line QS) and the center of arch at crown. With this 
 thrust H and the several vertical loads the stress diagram 
 to the left is drawn. By drawing lines parallel to these 
 rays the equilibrium polygon beginning at R is constructed 
 for the left half. By calculating the horizontal thrust 
 from the bending moment at center of arch it is assured 
 that the equilibrium polygon will pass through the center 
 line of the arch ring at the crown. It is seen that this 
 polygon lies within the middle third of the arch ring 
 throughout. Hence the arch will be stable, if the unit 
 stress is not too great. 
 
 The thrust for the half arch to the right must be the 
 .same as that to the left, but, as the load is more, the rise 
 must be greater. The rise in this case was found by first 
 laying out a trial arch and estimating the weight and 
 finding the moment. Dividing this moment by the known 
 thrust gave the rise to agree with the calculated loads. 
 By another trial a rise and moment were found that agreed 
 with the thrust. The equilibrium polygon for this half 
 arch is found as for the other. It also falls inside of the 
 middle third of the arch. In all cases the curves for top 
 412 
 
and bottom of the arches were made arcs of circles. It will 
 be seen that the equilibrium polygons almost coincide with! 
 arcs of circles. The unit compression on the arch is seenp 
 to be only about 100 Ibs. per sq. in. 
 
 The thrust of the several arches against the piers must 
 balance. No part can be taken by the piers. If the arches I 
 are not loaded alike, the additional thrust must be absorbed 1 
 in the arches themselves. For this there is a surplus! 
 strength imparted by the horizontal stiffness. The pier I 
 will then be in simple compression. The load is about 100,- 
 ooo Ibs., and, as the area is 484 sq. in., the unit compression 
 is a little more than 200 Ibs. per sq. in. This is not exces- 
 sive for a pier of this length, not reinforced, if made of I 
 good 1:2:4 concrete, when the pier is not subject to any 
 side forces. If live load is to be provided for, however, 
 the pier should be made larger, so that there will be no 
 more than about 200 Ibs. per sq. in. in compression. 
 
 On the wall the forces are the 72,000 Ibs. due to the 
 arch, acting on 15 ft. of wall, the weight of 15 ft. of 
 ABDEFG in concrete, and the weight of 15 ft. of JGFLK 
 in earth. The moments of these should balance about C t 
 which is 1-3 of AB from B. If the moment of the con- 
 crete and earth is not sufficient to balance that of the 
 72,000 Ibs., the wall should be made wider at the base. 
 Wifh the dimensions shown the moments were found to 
 balance about C. Only the part of the earth load to the 
 left of CK is taken, because that to the right does not' 
 increase the stability of the wall (considering its weight 
 alone). It cannot be said to decrease the stability, hence 
 it is neglected. If water is in the filter, not balanced by< 
 saturated earth outside, its horizontal pressure should also 
 be considered as a force against the wall. 
 
 In the construction of these vaults the forms should 
 be kept under two or three rows of vaults beyond any 
 that may have the forms removed, in order to make sure 
 that the thrust will be taken and the columns relieved from 
 taking any of it. 
 
 413 
 

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 415 
 
 
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 441 
 
INDEX 
 
 Adhesion, of concrete to 
 
 steel, 127, 128, 215, 220. 
 Aggregates, 39-43. 
 Anchor bolts, 350. 
 Anchored rods, 75, 192, 247. 
 
 248. 
 Anchorage, suspension 
 
 bridge, 341. 
 Arch, 
 
 abutments, 315, 322, 323. 
 
 bridges, cost of , 153, 
 
 154. 
 
 centering, 421-429. 
 Arches, 
 
 13-16, 298-327, 410-413, 
 
 418-421, 441. 
 
 design of reinforced con- 
 crete, 298-327. 
 
 proportions of , 314. 
 
 standard loading, 311. 
 Arch spans, short, 318-321. 
 Asphaltum, cost of , 158. 
 
 Battered abutments, 145. 
 Beam, formulas, 188, 276. 
 Beams, 
 
 and girders, 144. 
 
 and slabs, design of , 
 
 182-204, 214, 216, 225, 274- 
 
 298. 
 
 Beam, test, 11. 
 Bearing, 
 
 power of soils, 328. 
 
 power of masonry, 344. 
 Blocks, concrete, 82, 83, 91, 
 
 138 
 
 Box culverts, 143, 432. 
 Brick, 
 
 cost of , 158. 
 
 stack, cost of , 157. 
 Bridges, cost per unit, 152, 
 
 155. 
 
 Briquette, form of , 178. 
 Broken stone, 40. 
 
 weight of , 42. 
 
 Bronze, cost of , 158. 
 Buildings, cost per unit, 
 
 153, 154. 
 Cast iron, 
 
 columns, 146, 373. 
 
 cost of , 158. 
 Cast members, 83. 
 Cement, 20-33. 
 
 cost of . 159. 
 
 natural, 20, 170. 
 
 nature of , 26-33. 
 
 Portland, 20, 171. 
 
 Puzzolan, 21, 26. 
 
 Slag, 20. 
 
 specific gravity, 23, 24, 
 
 173, 174. 
 
 specifications, 168-181. 
 
 soundness, 22, 25, 180. 
 
 weight of , 22. 
 Cement skin, to remove, 99- 
 
 101. 
 
 Cement tests, 47, 49, 50. 
 Chicago foundations, 334, 
 
 335. 
 Chimneys, design of , 392- 
 
 400. 
 Cinder, concrete, 78, 141, 
 
 191. 
 
 Cinders, 43. 
 Cisterns, 144. 
 Clay, cost of , 159. 
 Coefficient of expansion, 
 
 128. 
 
 Coloring surraces, 101. 
 Columns and wall footings, 
 
 209-211, 216. 
 Columns, design of, 6, 211- 
 
 214, 230-238, 273, 370-381. 
 Column, 
 
 formulas, 213, 214, 379, 
 
 380. 
 
 test, 5. 
 Compression on concrete, 6, 
 
 119-123. 
 Concrete, 57-69. 
 
 cost of 159. 
 
 consistency of, 61-66, 260, 
 
 261. 
 
 compressive strength, 119- 
 
 124. 
 
 mixing, 54, 55, 56, 60, 61. 
 
 tensile strength, 124. 
 
 weight of , 141. 
 
 blocks, 82, 83, 91, 138. 
 
 cubes, tests on , 119-123, 
 
 in freezing weather, f~ 
 
 89. 
 
 in high temperature, ! 
 
 130. 
 
 in place, 86. 
 
 in polluted water, 8b. 
 
 pavements, 86, 87, 103, 
 
 104. 
 
 piles, 84, 333, 334. 
 
 steel beams and slabs, 
 
 182-214. 
 
 under water, 84, 85, 90,' 
 
 338 
 Conical coverings, etc., de- 
 
 445 
 
sign of , 401-413. 
 Constancy of volume, 180. 
 Continuous beams, 280-282. 
 Continuous rods, 262, 272, 
 
 290. 
 Contraction and expansion, 
 
 142. 
 
 Contractor's guaranty, 259. 
 Corners of walls, 146. 
 Copper, cost of , 159. 
 Corrugated steel, cost of , 
 
 155, 156. 
 
 Cost, estimating, 148-167. 
 Crossing, 432. 
 
 Crusher dust, tests, 49, 50. 
 Culverts, 143, 433-435, 437- 
 
 440. 
 
 Curved-up rods, 192, 272. 
 Curb, 
 
 cost of , 159. 
 
 detail, 442. 
 Dams, 17, 382-391. 
 Deflection of beams, 125. 
 Depth of beams, 195, 199, 
 
 202. 
 
 Distribution of steel, 266. 
 Domes, etc.. design of , 401- 
 
 413. 
 
 Drainage, 141. 
 Dredging, 
 
 cost of , 160. 
 
 hydraulic, 337. 
 'open, 338. 
 
 Drying of concrete, 91. 
 t>ust, crusher^ 42, 49, 50. 
 tEquipment, 148. 
 Estimating cost, 148-167. 
 Excavating, 336-339. 
 Excavating, cost of , 160. 
 Expansion and contraction, 
 
 142, 262. 
 
 Factor of safety, 222, 383. 
 Pence, 
 
 cost of, 161. 
 
 posts, 147. 
 
 Filling, cost of , 161. 
 Filter covers, 410-413. 
 Fineness of cement, 174. 
 Finishing Concrete Sur- 
 faces, 93-110, 146. 
 Fireproofing tests, 130. 
 Fire resistant, 129. 
 Flag stone, cost of , 161. 
 Flat plate theories, 11, 12, 
 
 13, 286-289. 
 Flat bars, 265. 
 Floor. 
 
 support, 146. 
 
 T test, measuring deflec- 
 tions, 256, 257. 
 Footings, 
 
 reinforced concrete, 9, 209, 
 
 210, 216, 224, 225, 353- 
 
 356. 
 
 with steel beams, 345-348. 
 Forms, 
 
 cost of , 161. 
 
 for concrete work, 110- 
 
 118. 
 Foundations, design of , 
 
 327-356 
 Freezing, effect on concrete, 
 
 51, 52. 
 
 Freight, cost of , 150. 
 French drain, cost of , 161. 
 Fuel, cost of , 161. 
 Galvanizing, cost of , 156. 
 Gang for mixing, 149. 
 General notes, 141-148. 
 Gravel, 39, 42, 129, 137. 
 
 cost of , 161. 
 
 weight of , 42. 
 Grip of concrete on steel, 
 
 128, 186, 264, 271. 
 Grout, 56, 57. 
 
 Handling and placing con- 
 crete, 76-88. 
 
 Hauling, cost of , 151. 
 Heating ingredients, 53. 
 High steel in concrete, 70, 
 
 184. 
 
 Hire of plant, 151, 156. 
 Holes for pipes and wires, 
 
 145. 
 Hooping, 
 
 in chimneys, 7. 
 
 in columns, 212, 213, 273, 
 
 374-379. 
 Ice tanks, 138. 
 Inspection of work, 69, 259. 
 Insulation, with concrete, 
 
 138. 
 
 Joining to old concrete, 82. 
 Lead, cost of, 161. 
 Lime, 33-35. 
 
 cost of , 161. 
 Limiting, 
 
 depth of beams, 190, 273, 
 
 278. 
 
 size of rods, 186, 205. 
 Longitudinal reinforcement 
 
 in columns, 5, 75, 212, 213, 
 
 371-374. 
 Macadam pavement, cost of 
 
 , 151, 163. 
 Manure, action on concrete. 
 
 50. 
 Masonry, 
 
 cost of s 161. 
 
 strength of , 349. 
 Maximum, capacity of 
 
 beams, 191, 207. 
 Measuring ingredients, 67, 
 
 68. 
 
 
 446 
 
Mineral wool, cost of , 
 
 162. 
 Mixing, 
 
 cement, 178. 
 
 concrete, 54-56, 60, 61. 
 
 cost of , 149. 
 Modulus of elasticity, 71, 
 
 126, 127. 
 
 Molding cement, 179. 
 Molds for test, 178. 
 Mortar, 44-57. 
 
 finish, 96. 
 
 strength of cement 46, 47, 49, 50 
 
 strength of lime 44. 
 Natural cement, specifica- 
 tions, 170. 
 Needle beams, 355. 
 Neutral axis, 187, 198. 206, 
 
 222, 270. 
 Notes on general design and 
 
 construction, 141-148. 
 Oil, effect on concrete, 51. 
 Paint, cost of , 162. 
 Painting, cost of , 156. 
 Paper, 98. 
 
 Partitions, reinforced con- 
 crete, 133. 
 
 Pavements, 86, 87, 102-106. 
 Paving, cost of , 162-164. 
 Percentage of steel, 188, 
 
 195, 198, 200, 206. 
 Permeability of concrete. 
 
 134-137. 
 
 Piers, 350-352. 414-417. 
 Pile protection, 148. 444 
 Piles. 
 
 bearing power of, 332, 335. 
 
 concrete, 84. 333, 334. 
 
 cost of , 164. 
 
 screw, 335. 
 
 Piling, cost of . 164. 
 Pipe, 
 
 concrete, 442. 
 
 cost of , 165. 
 Plastering, 107, 108. 
 Portland cement specifica- 
 tions, 171. 
 
 Practical tests, 204, 260. 
 Preservation of steel. 128. 
 
 264. 
 Properties of concrete, 118- 
 
 141. 
 Quantities, 
 
 for concrete, 66. 
 
 for mortar, 47, 48. 
 Bailing, 
 
 cost of , 165. 
 
 detail, 441, 443, 444. 
 Railroads, cost of per mile. 
 
 158. 
 Reinforced Concrete Columns and 
 
 Footings, The Design of, 204- 
 
 214, 219, 223, 224. 
 
 Reinforced Concrete Engineering 
 
 in the Making, 258-273. 
 Retaining walls, 17, 239- 
 
 255. 
 Retempered concrete, 56. 
 
 76. 
 
 Rivets, cost of driving, 156. 
 Rods, sharp bends in , 9, 
 
 75, 248, 266, 267. 
 Roofing, cost of , 156, 165.! 
 Sand, 35-38. 
 
 blasting, cost of , 165. 
 
 cost of , 165. 
 Salt in concrete, 52. 
 Sampling cement, 173. 
 Sawdust in concrete, 108. 
 Seawater, concrete in-, 139, 
 
 140. 
 
 Seeding, cost of , 165. 
 Segmental floor arches, 266. 
 Setting and hardening of 
 
 concrete, 88-93. 
 Sewer pipe, cost of, 165. 
 Shaft hangers, 145. 
 Sharp bends in rods, 9, 75 
 
 248, 266, 267. 
 Shear failures, 205, 215, 221, 
 
 363, 364. 
 Shear in concrete, 126, 189 
 
 356-370. 
 Shearing tests, 357-360, 367 
 Shear in steel, 7, 268, 366. 
 Shrinkage of concrete, 14 
 
 185, 228, 229. 
 Shrubs, cost of . 165. 
 Slag, 43. 
 
 cement, 25, 26. 
 Slender columns, 146, 380. 
 Sodding, cost of . 165. 
 Specifications for cement 
 
 168-181. 
 Specific gravity of cement 
 
 23, 24, 173, 174. 
 Stair supports, 144. 
 Standard concrete, 183, 261 : 
 Standard sand, 177. 
 Steel columns in concrete 
 
 146, 381. 
 Steel, 
 
 cost of , 165. 
 
 for reinforced concrete 
 
 70-76. 
 
 stack, cost of , 156. 
 Stirrups, 190. 215, 366. 
 Stone, 
 
 broken, weight of , 42. 
 
 cost of , 166. 
 
 facings, 94, 95. 
 Storage of tests, 179. 
 Sulphur in pipe cement, 27 
 
 28. 
 Surface, 
 
 cracks, 90. 
 
 447 
 
finish, 93-110, 146. 
 Survey of concrete field. 4- 
 
 19. 
 
 Tanks, 143, 405, 409. 
 Tar, cost of , 166. 
 Tarred paper, cost of , 166. 
 T-beams, 8, 207, 218, 223. 
 
 265, 291-298. 
 Tensile, 
 
 strength of cement, 180. 
 
 value of concrete, 186, 
 
 367, 369. 
 Tests, interpretation of . 
 
 18. 
 
 Ties, cost of , 166. 
 Tile in construction, 133. 
 Time, 
 
 of setting, 176. 
 
 to remove forms, 92, 263. 
 Tooling, cost of , 166. 
 Transverse strength of con- 
 crete, 126. 
 
 Transporting, cost of , 166. 
 Trap rock, 40, 129, 138. 
 Treating wood, cost of , 
 
 166. 
 
 Trees, cost of , 166. 
 Trestle, 
 
 ballasted, cost of , 157. 
 
 reinforced concrete, 8. 
 
 steel, cost of , 157. 
 
 timber, cost of , 157. 
 Tunnels, 430, 431, 436. 
 Unit compression, 6, 7, 124, 
 
 125, 183, 213, 275, 301, 
 
 316, 349, 374, 378, 380, 
 
 399. 
 Unit tension in steel, 18, 70, 
 
 184, 186, 187, 209, 245, 
 
 268, 275, 355, 37&, 398. 
 Unity in steel, 10, 262. 
 Uses of concrete, 147. 
 Vaults, etc., design of , 
 
 401-413. 
 
 Vertical pipes, 145. 
 Viaduct bents in concrete, 8. 
 Voids, measuring, 59. 
 Water, 
 
 for cement, 176. 
 
 for concrete, 54, 66, 89. 
 
 for mortar, 49. 
 Waterproof, 
 
 concrete, 134-137. 
 
 plaster, 147. 
 Whitewash, 148. 
 Wire cables in concrete, 74. 
 Wood, 
 
 beams and posts of , 114. 
 
 cost of , 167. 
 
 comparison with concrete, 
 
 5, 7. 
 
 448 
 

Expedition for Contractors 
 
 9111 
 
 in the completion of important work, is made 
 possible by the promptness with which we 
 can ship from our big new warehouse 
 
 I Everything Needful 
 I in Contractors' Equipment 
 
 Particularly : 
 
 Ransome Concrete Mixing and Handling 
 Machinery ; Twisted Steel Bars for Re- 
 inforced Concrete Construction ; Hoisting 
 Engines; Conveying Machinery ; Clam Shell 
 or Orange Peel Buckets ; Hydraulic and 
 Dredging Pumps ; Locomotive Cranes ; 
 Steam Shovels ; Excavators ; Concrete 
 Hoists and Buckets ; Dump Cars ; Steel 
 Sheet Piling ; Troy Wagons ; etc., etc. 
 
 iWhat is YOUR urgent need right NOW ? Write us 
 for prices and valuable Handbook of Information. 
 TEST OUR EXPEDITION. 
 
 William B. Hough Company 
 
 MONADNOCK BUILDING CHICAGO, ILL. 
 
 i. 
 
The 
 Railroad 
 Gazette 
 
 
 Contains each week the best and latest infor- 
 mation on all branches of Railroad En- 
 gineering the best engravings, news 
 and discussions. Everyone who desires 
 to keep informed on this branch of pro- 
 fessional work should read it. 
 
 WEEKLY Subscription, $5 yearly to 
 United States and Mexico; Canada, $6; 
 Foreign, $8. Sample Copy Free. 
 
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 logue. 
 
 ADVERTISING RATES on application. 
 
 
 
 New York, 83 Fulton Street 
 Chicago, Old Colony Building 
 London, Queen Anne's Chambers 
 
 ,' r .o -. ..:, 
 
 ii. 
 
AERIAL WIRE ROPE TRAMWAYS 
 
 MANUFACTURED BY 
 
 A. Leschen & Sons Rope Co., St. Louis, Mo. 
 
 Economical transportation of material such as Ore, 
 Coal, Stone, Earth, Sand, Rock and Timber, from one 
 place to another. 
 
 I/>w cost of operation; small expense for maintenance; 
 not affedled by the elements; free from surface traffic; 
 built in a straight line; requires no cuts, fills, bridges or 
 winding detours. 
 
 Can be successfully operated over distances varying 
 from a few hundred feet to practically any length beyond. 
 The lyESCHEN CO.'S PATENT AUTOMATIC Wire 
 Rope Tramway built for the Penn-Wyoming Copper Co., 
 Encampment, Wyoming, is 16 miles long. 
 
 This may vary from a few tons to one hundred tons per 
 hour, and in excess of this amount in many cases. 
 
 If inclination is sufficient and the loads descend, the 
 tramway will operate by force due to gravity, the sur- 
 plus power being controlled by brakes. Power, when 
 necessary, is applied at either terminal station. 
 
 Double Rope Tramway Single Rope Tramway TWo- 
 Bucket Tramway. 
 
 This is most economical type both in cost of operation 
 and maintenance. Carriers travel on independent track 
 ropes, are propelled and controlled by endless tradtion 
 rope; towers support cable at intervals depending upon 
 contour of ground, average spacing being 300 feet. 
 IvESCHEN CO.'S PATENT AUTOMATIC Tramway is 
 an automatic type of the double rope system in which 
 but one operator is required. 
 
 Endless wire rope to which carriers are positively at- 
 tached; buckets loaded by Mechanical leader; towers 
 support cable at intervals, speed about 150 feet per min- 
 ute. Not recommended for heavy capacity or long 
 lengths. 
 
 Two carriers are used each traveling backward and for- 
 ward on a track rope. A light endless tradtion rope 
 used for propelling the carriers. This is simplest and 
 least expensive system when line is short and contour 
 of ground favorable. 
 
 Tramway route should be surveyed in straight line con- 
 necting terminal points. Angles in horizontal plane to 
 be avoided. If angle is absolutely necessary an extra 
 station is required at angle point. 
 
 The A. I.ESCHEN & SONS ROPE COMPANY will 
 furnish estimates of cost upon receipt of profile of line 
 and definite data as to capacity per hour, class of 
 material to be handled, weight of material per cubic 
 foot, and terminal requirements. 
 
 An Approximate Estimate can be given, if profile is not 
 procurable, upon receipt of the data mentioned. 
 
 Above data furnished by A. LESCHEN & SONS ROPE CO., St. Louis, Mo. 
 
 Adaptation. 
 Advantages. 
 
 Length. 
 
 Capacity. 
 
 Power 
 Required or 
 Developed. 
 
 Systems. 
 
 Double 
 
 Rope 
 
 Tramway. 
 
 Single 
 
 Line 
 
 Tramway. 
 
 Two-Bucket 
 Tramway. 
 
 Selection 
 of Route. 
 
 Cost. 
 
 III. 
 
PATENT FLATTENED STRAND WIRE ROPES 
 
 C 
 
 A. Leschen & Sons Rope Co., St. Louis, Mo.\ 
 
 SOLE MANUFACTURERS / 
 
 A (5x28) B-(6x25) C (5x9) D (6x8) 
 
 HOISTING ROPES HAULAGE ROPES 
 
 With the view of increasing the wearing surface of wire rope and I 
 thereby prolonging the life of the rope, A. I^eschen & Sons Rope Co. have 
 had on the market for many years a patent flattened strand wire rope of I 
 which they are sole makers. The illustrations given above show in cross I 
 sections the construction of this style of rope. These flattened strand I 
 wire ropes are made in various grades of material. The satisfaction these 
 wire ropes have given justifies the manufacturers* claim for superiority 
 over any wire rope manufactured. The accompanying illustrations show 
 the comparative wearing surface between patent flattened strand and the 
 round or ordinary construction of wire rope. 
 
 
 PATENT FLATTENED STRAND ROUND STRAND 
 
 We give herewith Table of Weights, Breaking Strains, I^ist Prices, 
 etc., commencing with the highest grade : 
 
 "HERCULES" PATENT FLATTENED STRAND. 
 
 HOISTING HAULAGE 
 
 
 
 en 
 
 
 
 en 
 
 
 
 o 
 
 <L) 
 
 
 
 
 a p 
 
 
 Diameter in 
 Inches 
 
 *Priceperfo 
 in cents 
 
 Approximat 
 breaking 
 strain in toi 
 of 2,000 Ibs. 
 
 Average 
 weight per 1 
 
 Diameter in 
 Inches 
 
 Price per foe 
 in cents 
 
 rt 5S* 
 
 1 ^.55 
 3j| 
 
 |21 
 
 ^ MO 
 
 Average 
 weight peri 
 
 % 
 
 20% 
 
 13% 
 
 .44 
 
 H 
 
 16% 
 
 13 
 
 .44 
 
 X8 
 
 28 
 
 22% 
 
 .73 
 
 H 
 
 25 
 
 21 
 
 .73 
 
 x 
 
 37V 
 
 . 32 
 
 1.00 
 
 ?4 
 
 35 
 
 80 
 
 1.00 I 
 
 YQ 
 
 49 
 
 40> 
 
 1.35 
 
 % 
 
 44 
 
 38 
 
 1.35 1 
 
 1 
 
 60 
 
 56 
 
 1.80 
 
 1 
 
 58 
 
 53 
 
 1.80 
 
 1% 
 
 71 
 
 67 
 
 2.30 
 
 1/i? 
 
 70 
 
 64 
 
 2.30 
 
 1/4 
 
 89 
 
 84 
 
 2.80 
 
 1/4 
 
 88 
 
 80 
 
 2.80 
 
 J1Z 
 
 137 
 
 124 
 
 4.00 
 
 
 
 
 
 1% 
 
 208 
 
 168 
 
 5.40 
 
 
 
 
 
 2 
 
 225 
 
 211 
 
 7.50 
 
 
 
 
 
 2^4 
 
 285 
 
 260 
 
 9.25 
 
 
 
 
 
 * The purpose of giving these list prices is to give an idea of comparative 
 value. 
 
 IV. 
 
A. LESCHEN & SONS ROPE CO. 
 
 SOLE MANUFACTURERS 
 
 PATENT FLATTENED STRAND WIRE ROPES 
 
 CRUCIBLE CAST STEEL 
 1 HOISTING ROPE 
 
 SPECIAL STEEL 
 HOISTING ROPE 
 
 Diameter in 
 Inches 
 
 I 
 
 if 
 I- 5 
 
 -1 JN 
 | 3 .g 
 
 "3 
 
 1 
 5 ^ 
 
 a 'a 
 
 111 
 
 3*a 
 
 .3 
 
 jl 
 
 S*" 4 
 
 || 
 
 !* 
 
 Ijf-sJ 
 
 PB** 
 &ai 
 
 1 
 
 !l 
 
 u 
 
 S^ 
 
 1i- a 
 III 
 
 1*5 
 pi 
 
 |4 
 
 i /8 
 
 1 
 i?l 
 
 iH 
 
 r 
 
 2M 
 
 14> 2 
 18fc 
 24 
 30 
 
 8* 
 
 S8* 
 
 86 
 96 
 121 
 144 
 182 
 
 f. 
 
 21 
 29 
 38 
 47 
 56 
 69 
 81 
 94 
 109 
 140 
 176 
 
 .44 
 .73 
 
 1.00 
 1.35 
 1.80 
 2.30 
 2.80 
 3.40 
 4.00 
 4.75 
 5.40 
 7.50 
 9.25 
 
 t y > 
 
 3 
 
 3^ 
 
 ^ 
 
 i 
 
 6^ 
 
 F 
 
 9 
 
 1 7/ * 
 1^ 
 IK 
 1^ 
 
 $ 
 
 $K 
 
 17% 
 19K 
 22>| 
 30 
 38 
 48 
 59 
 70 
 105 
 155 
 177 
 220 
 
 P 
 
 17 
 
 24^ 
 33 
 43 
 54 
 64 
 93 
 127 
 162 
 204 
 
 .44 
 .54 
 .73 
 1.00 
 1.35 
 1.80 
 2.30 
 2.80 
 4.00 
 5.40 
 7.50 
 9.25 
 
 1 K 
 1% 
 
 2 
 3 
 
 3K 
 
 fe 
 
 5^ 
 
 P 
 
 9 
 
 HAULAGE ROPE 
 
 HAULAGE ROPE 
 
 P 
 ^ 
 
 if 
 
 7 
 10 
 14 
 20J4 
 
 g* 
 
 45 
 
 54 
 
 5 
 9 
 14 
 20 
 27 
 36 
 45 
 54 
 
 .25 
 .44 
 .73 
 1.00 
 1.35 
 1.80 
 2.30 
 2.80 
 
 
 I 
 
 1 
 
 S 
 
 11 
 14 
 18 
 27 
 35 
 45 
 54 
 68 
 
 10^ 
 
 i* 
 
 31 
 40 
 50 
 62 
 
 .25 
 .44 
 .73 
 1.00 
 1.35 
 1.80 
 2.30 
 2.80 
 
 2 
 
 2^ 
 3% 
 
 4K 
 5 
 5% 
 
 g3 
 
 7^4 
 
 These ropes are made of the best 
 crucible steel wire, combining in a 
 high degree ductility and tensile 
 strength. 
 
 As the name indicates, this rope 
 is made from a special grade of 
 steel, combining high tensile 
 strength with flexibility, without a 
 tendency to brittleness. 
 
 PATENT FLATTENED STRAND SWEDES IRON 
 
 HOISTING 
 
 HAULAGE 
 
 I 
 
 1 
 
 M 
 
 Jg 
 
 l^Ss 
 
 33 a g 
 
 i,rjsf 
 
 j|<aQ 33^ 
 
 I* 
 
 1*. 
 
 8 ta^ 
 
 * .3 
 
 111 
 l" 3 ^ 
 
 .a 
 
 it 
 
 s 
 
 1 
 
 M 
 
 ^ I.M 
 
 g be e3 ' 
 
 pi? 
 
 1 
 
 h 
 P 
 
 is- 
 
 111 
 
 "T/ 
 1 /8 
 
 \Y 8 
 
 i$l 
 " i% 
 
 2 
 
 . 2K 
 
 15>| 
 21 
 26 
 34 
 43 
 52 
 
 & 
 
 82 
 104 
 120 
 
 152 
 
 4 
 6 
 9 
 13 
 17 
 21 
 28 
 34 
 40 
 45 
 54 
 66 
 75 
 
 .38 
 .57 
 .83 
 1.20 
 1.58 
 2.00 
 2.50 
 3.00 
 3.65 
 4.15 
 5.00 
 6.30 
 8.00 
 
 2 
 3 
 
 P 
 
 4% 
 5M 
 
 P 
 
 Jfvl 
 
 1 
 
 1% 
 H? 
 
 8H 
 12)1 
 17 /l 
 22 
 29 
 
 I K 
 
 5? 
 
 / 
 10 
 
 f 
 
 p^ 
 
 .38 
 .60 
 
 7 
 
 1.^0 
 1.58 
 2.00 
 2.50 
 
 ay, 
 $, 
 
 6 
 6% 
 J& 
 
 8^| 
 9K 
 
 V. 
 
GALVANIZED 
 IRON 
 
 WIRE ROPE 
 
 7 WIRES FOR SHIPS' RIGGING, GUYS 12 WIRES 
 FOR DERRICKS, ETC. 
 
 6 STRANDS. 7 WIRES 
 
 
 a 
 
 
 
 a 
 
 ~ t4H 
 
 i 
 
 
 fl 
 
 +j 
 
 g 
 
 
 
 ^ 
 
 & 
 
 2 
 
 . v- 
 w ^ 
 
 i 
 
 8 1 8-1 
 
 c fl o r 
 
 JAZ* 
 
 3 
 
 i 
 
 'S fc 
 
 K fi 
 
 o 
 
 n C o ri 
 
 .2^ 
 
 pproxima 
 diameter 
 inches 
 
 rcumfere 
 inches 
 
 PI 
 I si 
 
 i| 
 
 ircumfere 
 inches of 
 Manila R 
 equal stre 
 
 .c o 
 
 11 
 
 pproxima 
 diameter 
 inches 
 
 ircumfere 
 inches 
 
 stimated ^ 
 per foot 
 Hemp cei 
 
 rice per fo 
 cents 
 
 ircumfere 
 inches of 
 Manila R 
 equal stre 
 
 fl 
 
 < 
 
 
 
 H 
 
 s 
 
 U 
 
 n 
 
 2 
 
 U 
 
 W 
 
 M 
 
 U 
 
 pq 
 
 2 
 
 6 
 
 6.00 
 
 
 12 
 
 50 
 
 i 
 
 3 
 
 1.44 
 
 14 
 
 54 
 
 13. 
 
 If 
 
 5J 
 
 4.85 
 
 44 
 
 11 
 
 44 
 
 i 
 
 2f 
 
 1.21 
 
 12 
 
 to 
 
 11. 
 
 itt 
 
 5J 
 
 4.40 
 
 41 
 
 10i 
 
 40 
 
 it 
 
 21 
 
 1.00 
 
 10 
 
 5 
 
 9. 
 
 1.1 
 
 5 
 
 4.00 
 
 38 
 
 10 
 
 36 
 
 i 
 
 2J 
 
 0.81 
 
 9 
 
 4| 
 
 7 " 
 
 1} 
 
 4f 
 
 3.60 
 
 35 
 
 9J 
 
 32 
 
 i 
 
 2 
 
 0.64 
 
 8 
 
 4i 
 
 5.^ 
 
 *A 
 
 41 
 
 3.25 
 
 31 
 
 9 
 
 29 
 
 A 
 
 If 
 
 0.49 
 
 7 
 
 3| 
 
 4.-^ 
 
 if 
 
 4J 
 
 2.90 
 
 27 
 
 8| 
 
 26 
 
 i 
 
 1} 
 
 0.36 
 
 6 
 
 3 
 
 3.1 
 
 U 
 
 4 
 
 2.55 
 
 24 
 
 8 
 
 23 
 
 TO 
 
 1} 
 
 0.25 
 
 5 
 
 2j 
 
 2. 
 
 Hi 
 
 3i 
 
 2.25 
 
 21 
 
 7} 
 
 20 
 
 1 
 
 H 
 
 0.20 
 
 4 
 
 2f 
 
 W 
 
 U 
 
 3J 
 
 1.95 
 
 18 
 
 6J 
 
 18 
 
 A 
 
 i 
 
 0.16 
 
 31 
 
 2 
 
 1.4 
 
 1A 
 
 3} 
 
 1.70 
 
 16 
 
 6 
 
 15 
 
 
 
 
 
 
 
 5 STRANDS, 7 WIRES 
 
 T 9 y 
 
 i 
 
 0.123 
 
 3 
 
 If 
 
 1.1 
 
 ^ 
 
 1 
 
 0.063 
 
 2J 
 
 U 
 
 0.5( 
 
 i 
 
 i 
 
 0.090 
 
 2} 
 
 11 
 
 0.81 
 
 T\ 
 
 i 
 
 0.040 
 
 2 
 
 If 
 
 0.3< 
 
 6 STRANDS, 12 WIRES 
 
 2 
 
 6 ' 
 
 6.00 
 
 
 12 
 
 50 
 
 i! 
 
 4} 
 
 2.90 
 
 29 
 
 8} 
 
 26 
 
 If 
 
 51 
 
 4.85 
 
 46 
 
 11 
 
 44 
 
 n 
 
 4 
 
 2.55 
 
 25 
 
 8 
 
 23 
 
 m 
 
 51 
 
 4.40 
 
 43 
 
 10J 
 
 40 
 
 i T 3 g- 
 
 3| 
 
 2.25 
 
 22 
 
 8 
 
 20 
 
 
 5 
 
 4.00 
 
 40 
 
 10 
 
 36 
 
 a 
 
 31 
 
 1.95 
 
 19 
 
 6J 
 
 18 
 
 u 
 
 4J 
 
 3.60 
 
 37 
 
 9J 
 
 32 
 
 1A 
 
 31 
 
 1.70 
 
 17 
 
 6 
 
 15 
 
 1A 
 
 4} 
 
 3.25 
 
 33 
 
 9 
 
 29 
 
 i 
 
 3 
 
 1.44 
 
 15 
 
 5| 
 
 13 
 
 VI. 
 
TABLE SHOWING BREAKING STRAINS, WEIGHTS, 
 'RICES, ETC., OF ROUND STRAND WIRE ROPES 
 
 FOR 
 
 HOISTING AND HAULAGE 
 
 MANUFACTURED BY 
 
 A. LESCHEN & SONS ROPE CO., ST. LOUIS, Mo. 
 
 HOISTING ROPE 6 Strands, 19 Wires 
 
 1 
 
 c 
 
 u 
 
 a 
 
 Breaking Strain 
 Tons of 2,000 Ibs. 
 
 Minimum size 
 of 
 Drum in Feet 
 
 lyist Prices per Foot 
 in Cents 
 
 Inches 
 
 
 be 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .5 
 
 "L 
 
 
 1 
 
 
 
 g 
 
 
 1 
 
 
 
 3 
 
 
 1 
 
 
 
 a 
 o 
 
 a 
 
 u, 
 
 
 
 
 4J 
 
 CO 
 
 V 
 
 
 ft 
 
 8 
 
 cr> 
 
 t) 
 
 
 * 
 
 
 
 2 
 
 JW 
 
 
 M 
 
 s 
 
 1 
 
 g 
 
 8 
 
 1 
 
 s 
 
 3 
 
 be 
 o 
 
 1 
 
 1 
 
 8 
 
 8 
 
 'u 
 
 51 
 
 1 
 
 1 
 
 
 
 1 
 
 4 
 
 3 
 
 a 
 
 3 
 1 
 
 1 
 
 JD 
 
 | 
 
 a 
 
 rt 
 
 3 
 
 ! 
 
 W 
 
 CO 
 
 u 
 
 s 
 
 to S 
 
 'X 
 
 ^ 
 
 
 
 'X 
 
 w 
 
 to 
 
 
 
 R 
 
 to 
 
 3 
 
 2% 
 
 9.85 
 
 266 
 
 222 
 
 190 
 
 254 
 
 95 
 
 13* 
 
 9K 
 
 9%13i 
 
 15 
 
 262 
 
 210 
 
 175 
 
 250 
 
 140 
 
 2% 
 
 2% 
 
 8. 
 
 238 
 
 182 
 
 156 
 
 208 
 
 78 
 
 12 
 
 8% 
 
 8% 
 
 12 
 
 13 
 
 229 
 
 170 
 
 142 
 
 200 
 
 117 
 
 2% 
 
 2 
 
 6.30 
 
 191 
 
 144 
 
 124 
 
 165 
 
 62 
 
 11 
 
 D| 8 
 
 11 
 
 12 
 
 181 
 
 134 
 
 111 
 
 156 
 
 92 
 
 2 
 
 \$/ 
 
 4.85 
 
 157 
 
 112 
 
 96 
 
 128 
 
 48 
 
 
 
 7^ 
 
 9 
 
 10 
 
 166 
 
 115 
 
 93 
 
 135 
 
 80 
 
 1% 
 
 l->8 
 
 4.15 
 
 128 
 
 97 
 
 84 
 
 111 
 
 42 
 
 oi/ 
 
 /2 
 
 6^4 
 
 6^ 
 
 8% 
 
 8^ 
 
 125 
 
 91 
 
 74 
 
 108 
 
 63 
 
 iy & 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 IV 
 
 3.55 
 
 113 
 
 84 
 
 72 
 
 96 
 
 36 
 
 
 Y -- 4 
 
 5% 
 
 8 
 
 7% 
 
 109 
 
 80 
 
 66 
 
 93 
 
 57 
 
 1% 
 
 1% 
 
 3. 
 
 96 
 
 72 
 
 62 
 
 82 
 
 31 
 
 
 5K 
 
 5y 
 
 7% 
 
 7 
 
 90 
 
 67 
 
 56 
 
 77 
 
 48 
 
 l$i 
 
 p/ 
 
 2.45 
 
 76 
 
 58 
 
 50 
 
 67 
 
 25 
 
 IT; 
 
 7 
 
 6% 
 
 i 
 
 55 
 
 46 
 
 68 
 
 40 
 
 4 
 
 % 
 
 2. 
 
 60 
 
 49 
 
 42 
 
 56 
 
 21 
 
 
 1% 
 
 4 % 
 
 6 
 
 6 
 
 57% 
 
 45 
 
 38 
 
 52 
 
 33 
 
 1% 
 
 I 
 
 1.58 
 
 50 
 
 39 
 
 34 
 
 44 
 
 17 
 
 5 
 
 4 
 
 ! 
 
 55% 
 
 49 
 
 36 
 
 30 
 
 43 
 
 26 
 
 1 
 
 % 
 
 1.20 
 
 36 
 
 30 
 
 26 
 
 34 
 
 13 
 
 4% 
 
 
 3K 
 
 4 %4% ! 
 
 39 
 
 28 
 
 23 
 
 34 
 
 20 
 
 7 /8 
 
 *A 
 
 .89 
 
 29 
 
 22 
 
 
 25 
 
 tt 
 
 ! 
 
 ... 
 
 ^ 
 
 J 4, 
 
 30 
 
 22 
 
 18 
 
 26 
 
 16 
 
 % 
 
 y% 
 
 .62 
 
 2015& 
 
 iA 
 
 186^3% 
 
 ^ 
 
 2% 
 
 3% 3% 
 
 22% 
 
 16% 
 
 14 
 
 19 
 
 12 
 
 y& 
 
 I 9 c 
 
 .50 
 
 1H2A 
 
 11 
 
 1 
 
 14% 5 %| 3 
 
 1>4 
 
 4 
 
 32^: 
 
 20 
 
 14 
 
 12 
 
 16 
 
 10 
 
 A 
 
 
 
 
 
 
 !| 
 
 
 
 
 
 
 
 
 
 
 
 % 
 
 .39 
 
 12 YA 
 
 8 T 8 
 
 11A4A,2% 
 
 ^ 
 
 1%254 
 
 2%i 16% 
 
 12% 
 
 11 
 
 14 
 
 08 
 
 % 
 
 I 7 5 
 
 .30 
 
 10 7 T % 
 
 6 T % 
 
 8.853 T % 
 
 2% 
 
 ^4 
 
 1^2% 
 
 2 
 
 15 
 
 11% 
 
 10 
 
 13 
 
 07% 
 
 i r e 
 
 3 /8 
 
 .22 
 
 75fl{, 
 
 5 
 
 6.552^ 
 
 ^ 
 
 1 
 
 i 
 
 2 
 
 
 14% 
 
 11 
 
 09% 
 
 12% 
 
 07 
 
 % 
 
 A 
 
 .15 
 .10 
 
 
 
 ^ 
 
 SA 
 
 2A 
 
 IS 
 
 g 
 
 % 
 
 7al% 
 %j 1 
 
 1 
 
 
 
 !^ 
 
 09% 
 09 
 
 12 
 
 06% 
 06% 
 
 fk 
 
 J "HERCULES" made from 
 which is made exclusively for A. 
 
 a specially drawn and patented steel, 
 I^eschen & Sons Rope Co., Sole Makers. 
 
 VII. 
 
TABLE CONTINUED 
 
 SHOWING BREAKING STRAINS, WEIGHTS, PRICES, 
 ETC., OF ROUND STRAND WIRE ROPES 
 
 FOR 
 
 HOISTING AND HAULAGE 
 
 MANUFACTURED BY 
 A. LESCHEN 6. SONS ROPE CO., ST. LOUIS, Mo. 
 
 HAULAGE ROPE 6 Strands, 7 Wires 
 
 1 
 
 & 
 
 ,c 
 
 Breaking Strain 
 in 
 Tons of 2,000 Ibs. 
 
 Minimum size 
 of 
 Drum in Feet 
 
 tr. 
 
 lyist Prices per *i 
 Foot in Cents o 
 
 
 bo 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 "53 
 
 -M 
 
 
 
 
 
 
 1 
 
 
 
 2 
 
 
 1 
 
 
 
 a 
 
 .S 
 
 h 
 
 si 
 
 1 
 
 2 
 
 3 
 
 & 
 
 8 
 
 1 
 
 'T. 
 
 3 
 
 A 
 
 M 
 
 S 
 
 to 
 
 CO 
 
 JU 
 
 3 
 
 - 
 
 S 3 
 
 i 
 
 | r v 
 
 ft 
 C 
 
 1 
 
 "o 
 
 B 
 
 M 
 
 | 
 
 1 
 
 1 
 
 1 
 
 2 
 
 3 
 
 
 "8 
 
 1 
 
 1 
 
 
 bo 
 
 'O 
 
 1; 
 
 Q 
 
 < 
 
 w 
 
 Cfi 
 
 
 
 ? 
 
 CO 
 
 K 
 
 cc* 
 
 g 
 
 S 
 
 CO 
 
 w 
 
 co 
 
 o 
 
 fe 
 
 co i G] 
 
 1% 
 
 3.55 
 
 
 79 
 
 68. 
 
 91. 
 
 34. 
 
 10 
 
 S% 
 
 8% 
 
 10 
 
 13 
 
 
 
 75 
 
 60 
 
 90 
 
 51 
 
 1 51 
 
 1* 
 
 3. 
 
 
 68 
 
 58. 
 
 78. 
 
 29. 
 
 
 8 
 
 8 
 
 9% 
 
 12 
 
 
 
 64 
 
 51 
 
 75 
 
 43 
 
 1^ 
 
 1% 
 
 2.45 
 
 74 
 
 56 
 
 48. 
 
 64. 
 
 24. 
 
 wMt 
 
 '/4 
 
 9^ 
 
 LO/^ 
 
 70% 
 
 53 
 
 43 
 
 61 
 
 36 
 
 li. 
 
 1% 
 
 2. 
 
 58 
 
 46 
 
 40. 
 
 53. 
 
 20. 
 
 s te* 
 
 *7^ 
 
 8 
 
 9% 
 
 56 
 
 44 
 
 36 
 
 51 
 
 29 
 
 U 
 
 1 
 
 1.58 
 
 47 
 
 87 
 
 32. 
 
 42. 
 
 16. 
 
 *M 
 
 5% 
 
 6% 
 
 8% 
 
 46 
 
 34 
 
 28 
 
 41 
 
 23 
 
 1 
 
 % 
 
 1.20 
 
 33% 
 
 28 
 
 24. 
 
 32. 
 
 12. 
 
 6 
 
 5 
 
 5 
 
 6 
 
 7% 
 
 35 
 
 26 
 
 22 
 
 32 
 
 17% 
 
 ? 
 
 fc 
 
 .89 
 
 25% 
 
 21 
 
 186 
 
 24. 
 
 9.3 
 
 5^ 
 
 4% 
 
 4% 
 
 5J4 
 
 6% 
 
 28 
 
 20 
 
 16 
 
 25 
 
 14 
 
 d 
 
 H 
 
 .75 
 
 
 
 18.4 
 
 15.8 
 
 21. 
 
 7.9 
 
 i 
 
 4 
 
 4 
 
 5 
 
 6 
 
 
 17 
 
 13% 
 
 20 
 
 12 
 
 i! 
 
 % 
 
 .62 
 
 18% 
 
 15.1 
 
 13.2 
 
 17. 
 
 6.6 
 
 4% 
 
 o% 
 
 3% 
 
 4% 
 
 
 20 
 
 14 
 
 11 
 
 17 
 
 10 
 
 ^ ; 
 
 A 
 
 .50 
 
 
 
 12.3 
 
 10.6 
 
 14. 
 
 5.3 
 
 4 
 
 3 
 
 3 
 
 4 
 
 4% 
 
 
 UK 
 
 9 
 
 14 
 
 8 
 
 ^ 
 
 % 
 
 .39 
 
 11% 
 
 9.70 
 
 8.4 
 
 11. 
 
 4.2 
 
 3% 
 
 2^ 
 
 2% 
 
 3% 
 
 4 
 
 13 
 
 9% 7K 
 
 11 
 
 6% 
 
 i , 
 
 
 
 
 
 
 
 
 
 i 1 i 
 
 
 
 1 
 
 
 7 
 
 .30 
 
 
 7.50 
 
 6.6 
 
 8.55 
 
 3.3 
 
 3%2^ 
 
 
 334 
 
 
 7/4' 6% 8 
 
 5% T ' 
 
 Ys 
 
 .22 
 
 
 5.58 
 
 4.8 
 
 6.35 
 
 2.4 
 
 3%l2 
 
 kC 
 
 2*J 
 
 6 
 
 5%' 6% 
 
 4H 
 
 3 
 
 ft 
 
 .15 
 
 
 3.88 
 
 3.4 
 
 4.35 
 
 1.7 
 
 3 1% 
 
 15ffl3 
 
 2% 
 
 5% 
 
 4% 6 
 
 3/4 
 
 
 A 
 
 .125 
 
 
 3.22 
 
 2.8 
 
 3.65 
 
 1.4 
 
 
 2 J 
 
 5 
 
 * Ux 
 
 * 
 
 j 
 
 
 | 
 
 
 
 
 
 I 1 
 
 
 
 
 
 1 "HERCULES" made from a specially drawn and patented steel, 
 which is made exclusively for A. I^eschen & Sons Rope Co., Sole Makers. 
 
 VIII. 
 
JNO. J. CONE 
 
 A. W. FIERO 
 
 ROBERT W. HUNT JAS. C. HALLSTEt 
 
 D. w. MCNAUGHER 
 
 ROBERT W. HUNT 4 CO, 
 
 ENGINEERS 
 
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 AND CONSULTATION 
 
 Thoroughly equipped Chemical and Physical 
 Laboratories maintained at 
 
 Chicago, New York, San Francisco 4 London 
 
 Inspection and tests of Rails and Fastenings 
 Locomotives, Cars, Pipe, Bridges, Buildings 
 Machinery and 2nd hand equipment. 
 
 Examination and reports on existing structures. 
 Reviews of metal and concrete-steel construction! 
 
 CHICAGO : 1121 The Rookery 
 
 NEW YORK: PITTSBURG : 
 
 90 West Street Monongaheia Bank Building 
 
 LONDON : Norfolk House, Cannon Street, . C. 
 
 MONTREAL: SAN FRANCISCO : 
 
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 X. 
 
Godfrey's Tables 
 
 [Structural Engineering, Book One] 
 
 This book is a compilation of tables and data for 
 use in structural designing. About one-third of it is 
 collected from manufacturer's hand-books and includes 
 such data as the properties of rolled sections, standards 
 for bolts and rivets, eyebar tables, fractions to decimals, 
 and other tables common to many books and indespen- 
 sable to the designer. Besides the foregoing there is 
 more new matter in the book than in any other simi- 
 lar book published. There is scarcely a problem in struc- 
 tural designing or detailing in which this book will not 
 be found useful. 
 
 The book contains more than 200 pages. Following 
 is a list of the contents: Decimals of a foot and inch. 
 Properties and useful dimensions of beams, channels, 
 angles, zees, tees, rails. Information on eyebars, 
 clevises, sleevenuts, separators, nuts, rivets, bolts, cir- 
 cular and rectangular plates, corrugated and buckled 
 plates. Standard beam connections. Bending moments 
 on beams for concentrated and uniform loads. Deflec- 
 tion formulas in terms of fibre stress, new. Working 
 unit stresses on columns. Ultimate strength of tank 
 plates, new. Weights of substances. Conversion table 
 for French units. Moments of inertia of rectangles 
 varying by eights, new. Weights and areas of rods, 
 bars, and plates. Mensuration, lengths of curves and 
 areas if segments, new. Miscellaneous formulas in 
 usable shape (brake bands, hoops, cylinders, springs, 
 flat plates, R. R. curves, etc.) Skewdetails, hip and val- 
 ley details, no angles used, new. Stresses in eight 
 styles of roof trusses, four pitches each. Moments, 
 shears, etc., Cooper E 50 loading Tables of built girders, 
 new. Over 2000 built sections with their properties. 
 Functions of angles. Typical details, 38 pages. Tables 
 of roots and circular areas. Tables of squares of num- 
 bers to 2736. Tables of squares of feet, inches, and 
 fractions for finding hypothenuse, lengths to 57 feet, 
 new. Gears, chain, rope. Electric cranes, clearances, 
 loads, etc. 
 
 All of this in a small pocktbook. Could anything be 
 more useful to a structural designer, draftsman or stu- 
 dent? 
 
 Book published by the Author 
 
 EDWARD GODFREY 
 
 flonongahela Bank Building Pittsburg, Pa. 
 
 Price $2.50; to clubs of 5, $2.00. 
 XI. 
 
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 XII. 
 
 I! .?"- ,1 
 

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 XIII. 
 
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