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LONGMANS, GREEN AND CO. 39 PATERNOSTER ROW, LONDON NEW YORK, BOMBAY AND CALCUTTA 1911 PREFACE. ALTHOUGH the word theory is used in the title the Authors have intentionally avoided all pure theory, and have included only those theoretical principles which are needed to enable the necessary calculations in the practical designing of such work to be understood. The formuke have been reduced to the simplest condi- tions, and worked examples are given so that the merest tyro in mathematics will have no difficulty in utilising them. The illustrations, which are very numerous, are grouped under the various branches of construction so that anyone interested in a particular subject can study a variety of typical forms. Many of the illustra- tions are published for the first time, and the Authors have to thank several kind friends for permission to publish others, and for the loan of blocks. Although there are other books dealing with both the theory and practice of reinforced concrete construc- tion, there is none that takes it quite in the same way, and the Authors trust that the facility this offers for practical use will be found one of its chief recommenda- tions. 241306 CONTENTS. CHAPTER I. PAGE History of " Reinforced Concrete " 1 Use and advantages of the material 2 Properties of Reinforced Concrete 3 Property of Concrete : Cement 3 Storage of Cement 3 Time of Setting 3 Broken Stone and Gravel . . 3 Sand 4 Proportions 4 Weight of cubic foot of cement . . . . . . . 4 Weight of cubic foot of concrete 4 Mixing Hand mixing 5 Machine mixing 5 Laying 5 Consistency . 5 Crushing Strength 6 Tensile Strength 7 Shearing Strength 9 Contraction and Expansion 9 Striking of Centres . . . 10 Properties of Reinforcing Steel 10 Plain and Deformed bars 10 Relation between Concrete and Steel 12 Adhesion of Concrete to Steel 12 Position of Reinforcement 16 Preservation of Steel in Concrete 16 CHAPTER II. General Principles of Stress 20 Nature of compression, tension and shear 20 Lines of stress in rectangular beam 21 viii CONTENTS PAGE Lengthening and shortening under stress 21 Vertical and horizontal shear 21 Bending moments 21 Bending Moments and Shear Diagrams for Beams variously loaded and supported 23-36 Reinforced Concrete Beams . 37 Reinforced Concrete Floor Slabs 37 CHAPTER III. Moments of Resistance, Loads and Reinforcement ..... 39 Moment of resistance of rectangular beam . ... . . .39 Moment of inertia and neutral axis ....... 39 Extreme fibre stress ........... 40 Section modulus ......... . . 40 Modulus of rupture for transverse strength ..... .41 Co-efficient of transverse strength ........ 41 Relation of Bending Moment to Moment of Resistance .... 41 Distribution of Shear ........... 42 Loads on Structures ........... 43 Superimposed loads on floors ......... 43 Load from wind ....... .... 44 Loads on walls, pillars and foundations ....... 44 Working Stresses on Concrete and Steel . ..... 45 Tee beams ............ 48 Reinforced concrete pillars ......... 48 Reinforced concrete walls ......... 50 CHAPTER IV. Notation, Formulae and Examples ........ 51 Standard notation for formulae . . ...... 51 Resistance moments for rectangular beams ...... 53 Example of designing a Beam ......... 53 Example of working when dimensions are given ..... 55 Shear stress in beams .......... 57 Rectangular beams with double reinforcement ..... 58 Example of Stress in Floor Slab ......... 59 Resistance moment for tee beams ........ 59 Tee beams with double reinforcement ..... 60 Example of Calculation of Tee Beam ..... ... 62 Formulae for Reinforced Pillars ...... 64 Example of calculation of pillar axially loaded . . . . .65 Stress on eccentrically loaded pillar . . . . . . .66 Example of calculation of eccentrically loaded pillar .... 67 CONTENTS ix CHAPTER V. PAGE Special Constructions 69 Retaining walls of various forms 69 Bins, bunkers, hoppers, pockets, silos, etc 76 Reinforced concrete arches 79 Reinforced concrete chimneys 83 Wind Pressures and Velocities ....... 84 CHAPTER VI. Effects of excessive heat on Concrete and Reinforced Concrete ... 92 General notes on the subject 92 International Fire Service Congress, Milan 92 British Fire Prevention Committee's tests 93 Paper by Professor Ira Woolson, M.E 93 Paper by Mr. Frank B. Gilbreth 94 National Board of Fire Underwriters ....... 94 Tests carried out by Mr. E. R. Matthews 95 Notes on these tests 103 Reinforced Concrete Tall Chimney Construction 104 General notes on the subject 104 Advantages of using this material 105 Theory of Chimney Construction . 105 Typical Examples in America and England 105 Effects of frost on Concrete 107 Tests of Professor H. Burchartz 109 Tests of Messrs. E. R. Matthews and J. Watson 110 CHAPTER VII. Reciprocation, Duality, Abridged Notation, and Projection .... 118 Reservoir and Tank Construction 118 Suitability of the material 118 Comparison with American practice 118 Cost of Reinforced Concrete covering 119 Dundee Reservoir 119 Water Softening Tank 120 Underground Tank, Dublin 122 Liquor Tank 123 Effects of Hydrochloric Acid and Ammonia Liquors on Concrete . . 125 Covered Service Reservoir, Ipswich 129 Covered Tank, Milnsbridge 129 Tank in Cheshire 129 Tank at Trafford Park, Manchester 129 Circular Reservoir, Albion, Mich., U.S.A 129 Reservoir, Annapolis, Mo., U.S.A 129 x CONTENTS PAGE Reservoir, Fort Biley, Kansas, U.S.A 132 Eeservoir, Pudsey, Yorkshire ..... ... . 132 Water Tank, Trafalgar Mills, Huddersfield 134 Rhyl Water Tower 137 Tower at Cleethorpes 137 Tower at Immingham 140 Dudley Tower 142 Covered Water Storage Tank 142 Water Tower, Newby Hall, nr. Ripon ....... 144 Water Tower, Barmby Moor, nr. Pocklington 145 Water Tower, Milford Junction, Yorkshire 145 Tower at Gascoigne Wood for N.E.R. Co 145 Tower at Londesborough, nr. York 146 Tower at Downpatrick 146 Culvert and Conduit Construction 147 Culvert at Bromboro' Port 150 Blaenavon Culvert 152 Kilton Culvert, N.E.R 154 Concrete Pipes 154 Rising Main on Bonna System, Norwich 154 Concrete Pipes on Wabash Railroad, U.S.A 154 Wilmington Sewer, Delaware, U.S.A 154 Reinforced Concrete Pipes, American Manufacture .... 164 Reinforced Concrete Pipes, English Manufacture ..... 164 Sewage Tanks 164 Tank at Ripponden 164 Reinforced Concrete Sewage Disposal Works 167 Swimming Baths 167 Salford Corporation Public Baths 167 South Shields Public Baths . 167 Other forms of Municipal Engineering Work 171 Cantilever Platform at Bridlington 171 Public Shelters at Bridlington 171 Underground Lavatories at Bridlington 175 Other Municipal Engineering Works 176 CHAPTER VIII. Reinforced Concrete in Railway Engineering 181 Introduction 181 American Examples : Reinforced Concrete on the Vandalia Railroad, U.S.A 181 The Eagle Creek Arch Bridge . . 181 Double-box Culvert at Station 3343 182 Bridge at Seelyville . * : . .185 Reinforced Concrete on the Wabash Railroad, U.S.A. . . , . .185 The Sangamon River Bridge ... 186 CONTENTS xi PAGE Forest Park Bridge, St. Louis . . 189 Standard R. C. Box Culverts 192 Prices of Materials on the Wabash Railroad 194 Vermillion River Bridge 195 Indian Creek Culvert 196 Reinforced Concrete Roundhouses in America 198 Stations and Platforms .......... 198 Tunnel Construction . 198 Railway Sleepers 201 Concrete Road-bed 201 English and Continental Examples : Bridge on G.E.R 201 Bridge at Chateau Thierry 201 Bridge at Immingham Dock 204 Luggage Subway at Middlesborough ....... 204 Railway Bridge at Avranches 204 Skew Bridge near Paris 204 Railway Viaduct at Gennevilliers 205 Bridge at Luxemburg 205 Conclusion 205 CHAPTER IX. Reinforced Concrete in Wharves, Jetties, Groynes, Sea Walls, Bins, Factories, and other Engineering Works 209 General Notes 209 Piling 209 Extension of Quay, Prince's Dock, Liverpool 209 Waterford North Viaduct 209 Underpinning of Pier, Newhaven 212 Manchester Ship Canal 212 New York Harbour . 212 Works at Southampton, and in Italy, Belgium, and Holland . . 212 Reinforced Concrete Groynes 212 Jetty Head, Thames Haven 215 Factories, Silos, Coal Bunkers 215 Factory at Noisiel 215 Silos at Hull 216 Coal Bunker at Walkmill Colliery 217 American Examples : L. & N. Ry. Co.'s Terminal Warehouse, Atlanta 218 Machine Shop at McKee's Rocks, Penn 223 Building at Rockville, Conn 223 Building at Dayton, Ohio 223 Buildings of the Atlas Portland Cement Co 225 English Examples : Grain Silos at Silvertown . , 225 xii CONTENTS PAGE Raw Meal Silos near Rugby 227 Typical example of Grain Silos 230 Coal Pocket, London 230 Coke Hoppers 230 Retaining Walls and Boundary Walls 239 American Examples : Walls on the Atlanta, Birmingham, and Atlantic Railroad . . . 239 English Examples : Boundary Wall, West Hartlepool Cemetery 243 Retaining Wall at Birkenhead Gasworks 245 Retaining Wall at Guildford 245 Retaining Wall at Hereford Gas Works 245 Retaining Wall in Piccadilly 246 Reinforced Concrete Stands 246 Stand at York Race Course 246 Reinforced Concrete Stadium 249 Reinforced Concrete Football Stand at Bradford 249 Stadium at Syracuse, U.S.A 249 Sea Wall Construction 254 Hornsea Sea Wall , 254 CHAPTER X. Reinforced Concrete in Building Construction 255 General Notes 255 Piles Coignet System 255 Piling at Tobacco Warehouse, Bristol 255 Advantages of using R. C. Piles ........ 256 Paragon System 258 Considere System 259 Hennebique Piles 262 Simplex and Raymond Piles 263 Columns, Beams, and Floors 264 Coignet System 264 Leslie's System 264 The Chain Concrete Syndicate's System . . 267 Mr. E. P. Wells' System 268 Expanded Metal Co.'s System of Floor Construction .... 268 British Reinforced Concrete Engineering Co.'s System .... 269 Kahn System 269 Hennebique System 277 Patent Indented Bar Co.'s System 277 Foundations 277 Foundations at Bridlington Electricity Works 281 Foundations at Sprecles Building, San Francisco ..... 281 CONTENTS xiii PAGE Foundations at Stoke-upon-Trent Town Hall 281 Patent Indented Bar Co.'s System 282 Expanded Metal Co.'s System 282 Walls and Partitions 285 City of Buffalo Building Regulations 285 Space gained by building R. C. Walls . . . . . . 285 Roof Construction 286 Flat Roofs 286 Mansard and Flat combined 286 Domed and Arched Roofs 287 Cathedral at Poti, Russia 287 Dome of New Wesleyan Methodist Hall 287 Roofs of Sawtooth shape 288 Expanded Metal in Arched Roof Construction 288 Stair Construction 288 Description of various types 288 Balconies and Cantilever Platforms 291 Tallest Reinforced Concrete Building in the World 291 CHAPTER XI. General Notes 299 Experienced Designer 299 Skilled Workmen 299 Erection and Removal of Forms 299 Waterproofing of Concrete 301 Expansion Joints 303 Concrete Mixers 303 Finishing of Concrete Surfaces 303 Colouring Matter 304 Pebble-dash Finish 305 Breeze Concrete 305 Avoidance of Stone Dust 305 Roughening a Concrete Surface 306 Materials in a cubic yard of Concrete 306 Acetic Acid and Concrete 306 Action of Alkali on Portland Cement 307 Action of Sewage and Sewage Gases on Concrete 307 Bonding of Old and New Concrete 307 Effects of Sea- water on Concrete 308 The Prevention of Failures '. 310 Test Loads , 311 INDEX . 313 CHAPTEK I. HISTORY OF REINFORCED CONCRETE. ALTHOUGH this material has only been extensively used during the past few years, its first use goes back to the time of the Bomans. They undoubtedly understood its principles, for we find them using reinforced concrete a hundred years B.C., in the construction of the roof of a tomb. They inserted into the concrete bronze rods crossing each other lattice wise. Their concrete was, however, very poor in quality compared with our Portland cement concrete, the aggregate used by them was very coarse, and the cementing. material consisted of rich lime with the addition of volcanic scoria. The Romans used reinforced concrete in many other ways, sometimes inserting tiles and timber to reinforce the concrete. In Loudon's " Encyclopaedia of Cottage, Farm and Villa Architecture" published in 1830, he suggests that it is quite feasible to strengthen concrete flat roofs by inserting a lattice- work of iron rods, while in 1840 M. Louis Leconte took out a patent for a reinforcing ceiling slab. At this time there were two systems of reinforced concrete floor construction employed in Paris, these were known as the Vaux and Thuasne systems. The reinforcement in the former case consisted of round rods hooked over wrought iron flat bars, and in the latter case of rods suspended by means of stirrups from small iron joists. Portland cement, which had only been invented in 1824, and of which very little had been manufactured, was not used in either of these floors, but plaster of Paris which was altogether unsuit- able, the result being that rusting of the metal occurred, and the system was looked upon as being unsatisfactory. It is unnecessary to enumerate the many patents that have been taken out since that time, (there being over seventy systems 2 EEINFOECED CONCEETE CONSTEUCTION in use to-day, that is in Europe and America) or to refer to the scores of papers on the subject which have been read, or articles dealing with it which have appeared ; it should, however, be ex- plained that the first two real inventors of reinforced concrete were Wilkinson and Coignet. Wilkinson was a plasterer resid- ing at Newcastle who took out a patent in 1855 for the rein- forcing of concrete slabs by the insertion of a network of flat iron rods placed on edge, or as an alternative wire ropes (second hand). His object seems primarily to have been to produce a floor that would resist fire. His floors were constructed either in the arch form or flat, and from the placing of the reinforce- ment it is evident that he quite understood modern principles of reinforced concrete construction. Coignet was a Frenchman a contractor of Paris, who took out an English patent in the same year (1855) as well as patents in France. His system consisted in the reinforcing of a slab by placing iron rods crosswise, lattice fashion. He constructed twenty-eight large arches in the aqueduct of the Eiver Vanne for the Paris water supply, reinforcing his concrete by the in- sertion of iron rods, but upon what method is unknown. This aqueduct is still in excellent condition. In 1861 Monier, a Parisian gardener, constructed tanks and tubs of reinforced concrete, and at the Paris Exposition of 1867 both he and Coignet exhibited specimens of their work in this material. Since then, a large number of systems have been placed on the market, including the well-known Hennebique, Kahn, Indented bar, Thacher bar, Eansome bar, Considere, Expanded Metal, and Lock-woven Mesh Systems. Use and Advantages of the Material. Eeinforced concrete has been extensively used in America, on the Continent of Europe, and also very largely in this country ; it is a material which is eminently suitable for use in engineering and archi- tectural structures. It has been used very considerably in the construction of bridges, culverts, retaining walls, dams, reser- voirs, aqueducts, conduits, sewer pipes, water mains, wharves, jetties, lighthouses, warehouses, silos, bins, and a score of other engineering works ; it has also been used very largely in building construction, being most suitable for all heavier struc- HISTOEY OF EEINFOKCED CONCKETE 3 tures such as warehouses, factories, hotels, public buildings, etc. In the construction of beams, floor slabs, columns, piles, canti- levers, stairs, flat roofs, arches, etc., it is an ideal material to use. Why is this material so serviceable? It is because its strength, rigidity, durability, lightness, ability to resist vibra- tion, and fire-resisting properties are unsurpassed by any other material ; it also incurs no cost in maintenance. Added to these advantages are two others, namely, that it is an economical material to use as regards initial cost, and that works can be executed very rapidly where it is employed. Properties of Reinforced Concrete. Properties of Concrete. (a) Cement. Only the very best Portland cement should be used in reinforced concrete, and this should meet the require- ments set out in the " 1910 Amended British Standard Speci- fication for Portland Cement " or those of the American Society for Testing Materials. In America, natural cement has been used very considerably, but this is unsatisfactory, an artificial cement being far pre- ferable. The percentage of lime in good Portland cement should not exceed 62, and it is of the utmost importance that the cement should be finely ground, as the finer it is, the greater the strength. (6) Storage of Cement. It is very desirable that cement should be stored in the original packages in a dry shed, having a wooden floor, and proper ventilation. (c) Time of Setting. Generally speaking a slow-setting cement should be chosen in preference to a quick-setting cement. Broken Stone and Gravel. The choice of the aggregate both as regards its hardness and size is a matter of the greatest importance. Broken stone (granite, trap, or other hard rock) or gravel are suitable, provided the utmost care is taken in the choice of either. Coke breeze and furnace clinker are not satisfactory, and some object to broken brick, although this is far superior to the two former. If the work is to be water- tight, gravel concrete has an advantage over broken stone owing to the fact that when gravel is used a lesser proportion of voids occurs, as the rounded shape of the particles allow of a closer association, and it is specially suitable for foundation work 4 KEINFOBCED CONCEETE CONSTKUCTION and mass concrete. It has been estimated that gravel concrete averages 7^ per cent less in voids than crushed stone. 1 Limestone should not be used where the finished work may have to resist fire, as this stone suffers severely by calcination ; gravel, broken sandstone, and broken brick are the best aggre- gates to use for work of this class. The size of the aggregate should be variable, but such that the whole of it will pass through a f in. ring. If broken stone is used it should be well screened before use so as to remove dust. If gravel is used it is desirable that it should vary in size from say J 'in. to f in. ; material passing through a J in. sieve should be considered as sand. Sand. It is preferable that this should be of fairly coarse grain ; 75 per cent of it, however, should be capable of passing through a J in. square mesh. 2 It is very important that it should be absolutely clean and free from any clay, chalk, lime, or earth. Sea sand, or coarse gritty river sand are suitable. A very fine sand is undesirable. Proportions. The materials should be measured separately in gauge boxes. The proportions generally used vary from 1 : 1^ : 2 to 1:2:4 and 1:3:6, these representing cement, sand, and gravel or broken stone respectively. The nature of the work will largely govern the proportions of ingredients to be used. For example, a reservoir floor or bottom, and walls, should be of concrete of the proportions of 1 : 1-J : 2 or 1 : 2 : 3, while if the concrete is for the roof of a covered service reservoir 1:2:4 will do admirably. Weight of a Cubic Foot of Cement. For the purpose of pro- portioning the amount of cement to be added, this may be taken at 90 Ib. Weight of a Cubic Foot of Concrete. 145 Ib. may be taken as the approximate weight of a cubic foot of concrete, and 150 Ib. to 156 Ib. the weight of a cubic foot of concrete includ- ing the reinforcement. 150 Ib. will undoubtedly be sufficient in most cases; it will seldom occur that more than 5 Ib. of re- 1 Paper by Hewson, Architects' Business Association of Chicago. 2 "Provisional Report on Reinforced Concrete," B.I.B.A. HISTOEY OF KEINFOKCED CONCKETE 5 inforcing steel is added per cubic foot of concrete : but in certain rare cases where heavy reinforcement is necessary the weight may equal 156 Ib. Mixing. Concrete should be mixed in small batches, the proportions having been accurately measured. It should be laid as soon as mixed, and rammed or tamped vigorously till mois- ture appears at the surface, and all air bubbles are excluded and voids filled. Hand Mixing. When concrete is mixed by hand the materials should be turned over at least twice dry or until the colour is uniform, and twice wet on a wooden platform. Machine Mixing. This is preferable to hand mixing. There are many excellent concrete mixing machines in use to-day in this country and in America ; some of these are briefly described in Chapter XI. Laying. The thickness of loose concrete that is to be punned should not exceed 3 in. before punning. Special care should be taken to ensure perfect contact between the concrete and the reinforcement ; the punning should be continued until the concrete is thoroughly consolidated without disturbing the position of the reinforcement. Each section of concreting should as far as possible be completed in one operation ; when this is impracticable, and work has to be recommenced on a recently-made surface it is necessary to wet the surface, and where it has hardened it must be hacked over, swept clean and covered with cement grout. The concrete when laid should be protected from the action of frost, and shielded against too rapid drying from exposure to the sun's rays or winds, and kept well wetted. All shaking and jarring must be avoided. The effi- ciency of the structure depends chiefly on the care with which the laying is done. 2 Consistency. No- definite rule can be laid down as to the proportion of water which should be added in mixing concrete, but the concrete should always be sufficiently plastic to thoroughly fill the mould, and to fit very compactly around the reinforce- 1 " Preliminary and Interim Report of the Committee on Reinforced Concrete, Inst. C.E.," p. 61. 2 "Provisional Report on Reinforced Concrete," R.I.B.A. 6 REINFORCED CONCRETE CONSTRUCTION ment. The temperature at the time of mixing will also govern the amount of water to be added. In America what is known as a " wet mixture " is invariably used. It was thought at one time that the greater the quantity of water added, the less the strength of the concrete, but ex- haustive experiments carried out in 1896 by Mr. Geo. W. Rafter, M.Am.Soc.C.E., for the State Engineer's office of New York, indicate that a " wet mixture " is not materially weaker than a "plastic mixture," whilst it fills the moulds more easily. The average results obtained by Mr. Rafter were as follows : Compressive Strength. Dry mixture . . 2470 lb., per sq. in. Plastic mixture . 2294 ,, ,, ,, Wet mixture . . 2180 ,, The number of blocks tested in the first case was 156 ; in the second 144; and in the case of the "wet mixture" 148; each block consisted of a 12 in. cube ; the age of the blocks varied from eighteen to twenty-four months. English engineers and architects do not look with favour upon a "wet mixture," but as a rule advocate a "plastic mix- ture," and less often a " dry mixture ". The authors favour a "plastic mixture" which will quake under a moderate amount of punning, but in reservoir work, or any work which is to be watertight, a " wet mixture " may be used. In fact wetter mix- tures are now more used than formerly. In work which is to be fireproof, as in the case of tall chimneys, a " dry mixture " should be used. Sea water should not be used except for mass concrete on marine works. Crushing Strength. In the British Standard Specification there is no compression test included ; this, in the authors' opinion is an unwise omission, as concrete is so largely used for foundations, columns, etc., where it is subject to severe com- pression. The recommendations of the R.I.B.A. Joint Committee are that the crushing strength of concrete of a mixture of 1 : 2 : 4 (cement, sand, and hard stone) should be not less than 2400 lb. to 3000 lb. per square inch after twenty-eight days ; this appears HISTOKY OF BEINFOKCED CONCKETE 7 to be reasonable, for exhaustive tests made by Mr. Geo. A. Kimball, chief engineer of the Boston Elevated Railway Com- pany, 1 show that concrete blocks of a mixture of 1 : 2 : 4 at a period of one month after mixing crushed at an average of 2399 Ib. per square inch. At three months similar blocks crushed at 2896 Ib., and at six months at 3826 Ib. The Building Kegulations of 'New York, Buffalo, San Fran- cisco, and Cleveland specify that the safe working stress on concrete in compression shall be taken as 500 Ib. per square inch. It is certainly desirable, before commencing the carrying out of concrete work of any importance, that test blocks should be made, say 4 in. cubes. They should be carefully prepared in moulds, and tested twenty-eight days after moulding, the load being slowly and uniformly applied. The average of the results should be taken as the strength of the concrete. Tensile Strength. The " British Standard Specification for Portland Cement" 2 specifies that the average breaking stress of briquettes made of neat Portland cement shall be as follows : At 7 days after gauging not less than 400 Ib. per square inch of section. At 28 days the briquettes must show an increase on the breaking stress at 7 days after gauging of not less than : 25 per cent when the 7 day test is above 400 Ib., and not above 450 Ib. 20 per cent when the 7 day test is above 450 Ib., and not above 500 Ib. 15 per cent when the 7 day test is above 500 Ib., and not above 550 Ib. 10 per cent when the 7 day test is above 550 Ib., and not above 600 Ib. 5 per cent when the 7 day test is above 600 Ib. The test for tensile strength (cement and sand, 3 to 1) is specified to be not less than : 7 days' test. 28 days' test. 150 Ib. per sq. in. of section. 250 Ib. per sq. in. of section. 1 " Tests of Metals," U.S.A., 1899, p. 717. 2 " British Standard Specification for Portland Cement " (No. 12, Revised August, 1910), pp. 8 and 9. 8 REINFORCED CONCRETE CONSTRUCTION The increase in the breaking stress from 7 to 28 days must be not less than : 25 per cent when the 7 day test is above 200 Ib. and not above 250 Ib. 15 per cent when the 7 day test is above 250 Ib. and not above 300 Ib. 10 per cent when the 7 day test is above 300 Ib. and not above 350 Ib. 5 per cent when the 7 day test is above 350 Ib. The American Standard Specification for cement l demands a higher tensile strength as follows : NEAT CEMENT. Age. Strength. 24 hours in moist air 150-200 Ib. 7 days (1 day in moist air, 6 days in water) 450-550 ,, 28 days (1 day in moist air, 27 days in water) 550-650 One part cement, three parts sand/ 7 days (1 day in moist air, 6 days in water) 150-200 28 days (1 day in moist air, 27 days in water) 200-300 The tensile strength of concrete may be roughly taken as one-tenth the compressive strength. The well-known tests of Prof. W. K. Hatt 2 would seem to substantiate this ; these tests were as follows : Mixture. Age. Compressive Strength in Ib. per sq. in. Tensile Strength in Ib. per sq. in. 1:2:5 (broken stone) 1:2:5 1 : 5 (gravel) 1:5 28 90 28 90 2290 2413 2400 2804 237 359 253 290 1 ' ' Standard Specification for Cement American Society for Testing Materials," pp. 7 and 8. 2 "Journal of Assoc. Eng. Societies," Sept. 1900. HISTOEY OF BEINFOBCED CONCBETE Shearing Strength. A series of tests made at the University of Illinois in order to ascertain the shearing strength of concrete gave the following results : Mixture. Compressive Strength in Ib. per sq. in. Shearing Strength in Ib. per sq. in. Ratio of Shearing to Compressive Strength. 1:2:4 1:3:6 3210 2290 1418 1250 44 57 Keinforced concrete beams rarely fail through shearing of the concrete, but when the shearing force exceeds 100 Ib. per square inch of section, the beam often fails by " diagonal tension " in a curved crack which crosses the neutral axis at an angle of 45 degrees. 1 Diagonal reinforcement often doubles the resistance of a beam to shearing. Modulus of Elasticity. This may be taken as varying from 2,500,000 to 3,500,000 Ib. per square inch for working loads for ordinary concrete ; it will depend upon the mixture and age of the concrete. It has been suggested 2 that it is safer to take 2,000,000 Ib. for most calculations. Contraction and Expansion. Considered experiments indi- cate that a 3 to 1 mortar will shrink from '05 per cent to '15 per cent if the hardening takes place in air, and extends over a period of from two to four months, and that neat cement shrinks nearly three times as much. He also discovered that by reinforcing his mortar the shrinkage was reduced to '01 per cent. The coefficient of expansion of concrete is about '000006 per 1 F. change of temperature, while that of steel is '0000064 to 0000068, practically the same, showing that there is no danger of unequal expansion causing a separation between the con- crete and the steel. Centering or Casing. This should be so constructed that it will remain rigid and unyielding during the placing and punning 1 Memorandum " E," p. 101, " Report of Committee on Reinforced Con- crete, Inst. C. Engineers ". 2 " Reinforced Concrete Construction," by Turneaure & Maurer, p. 25. 10 EEINFOECED CONCEETE CONSTEUCTION of the concrete. It should also be so fixed that it will admit of easy removal, and should be well greased with soft soap or oil before the concrete is laid. Striking of Centres. The centres should be removed most carefully to avoid vibration ; on no account should they be knocked down, falling with a crash. No definite time can be fixed for their removal unless the concrete has been laid by specialists, it may vary from ten to thirty days, and it should never be less than ten days. When the concrete has been laid by skilled men under strict supervision the centering should remain until the expiry of the following periods from the placing of the concrete in position ; walls and chimneys, two days ; sides of beams, three days ; pillars, floor slabs, and roof slabs, seven days ; underside of beams, fourteen days ; arches and domes, one day for each foot of span, but not less than seven days nor more than twenty-eight; for all other portions of a building not less than fourteen days. Days in which the temperature falls below freezing-point are not to be counted in the above periods. Properties of Reinforcing Steel. The steel used in reinforced concrete structures should answer the following requirements : Its ultimate strength should not be less than 60,000 Ib. per square inch. Elastic limit 50 to 60 per cent of the ultimate strength. Modulus of elasticity, 30,000,000 Ib. per square inch. Working stress, factor of 4^ according to the nature of the 5/ structure. The steel should afford an elongation of not less than 22 per cent in round bars less than one inch in diameter on a gauge- length of 8 diameters, and should stand bending cold 180 degrees to a diameter of the thickness of the pieces tested without frac- ture on the outside of the bent portion. All rods, plates, bars, and other reinforcement should be of mild steel, manufactured on the open hearth basic or acid Siemens process. Plain and Deformed Bars. In Europe plain bars have been chiefly used, but in America deformed bars are looked upon with much favour, it being contended that the deformation in the bar tends to increase the mechanical bond. With this in view HISTOKY OF REINFOBCED CONCEETE 11 many devices have been introduced, such as twisting square rods, making round bars of alternate round and flat sections but with the same sectional area at every point. Some engineers have preferred I joists of light section, others flat bars. In the illustrations here given : FIG. 1. FIG. 2. KAHN TRUSSED BAR. FIG. 3. FIG. 4. Pig. 1. Represents the Indented Steel Bar Co.'s patent bars. Fig. 2. Ransome bar (both of these have been largely used in America). Fig. 3. Kahn bar (Trussed Concrete Steel Co., Ltd.). This bar is formed by shearing and turning up the side wings of the bar. Fig. 4. Havemeyer bars. 12 BE1NFOKCED CONCBETE CONSTKUCTION Fig. 5. Cumming's bar. Fig. 6. Lug bars. Fig. GA. Another variation in twisted bars. Other methods of reinforcing concrete consist of the inser- tion of Figs. 7 and 8, expanded metal ; Fig. 9, lock-woven wire fabric ; Fig. 10, Messrs. Win. Moss and Sons' patent. The Thacher bar, invented by Mr. Edwin Thacher, M.Am.Soc.C.E. has been largely used in America. Relation Between Concrete and Steel. Adhesion of Concrete to Steel. A great many tests have been made in order to deter- mine the adhesion of the concrete to the reinforcement. Among the most recent of such tests were those carried out a short time ago at the Gewerbe Museum, Vienna. The test blocks consisted of 8 in. cubes, and the reinforcing steel of f in. steel bars (round). In order that the tests should* be varied, four different mixtures of concrete were used, namely : 1:4; 1:6; 1:8; 1 : 12, and the bars were drawn out after a period of six weeks from the time of moulding. The mean adhesive strength for the four mixtures was as follows : Proportions. Adhesive strength. 1 : 4 656 Ib. per square inch. 1:6 646 1:8 601 1 : 12 448 The ultimate compressive strength of the concrete at a period of seven months from time of moulding was : Proportions. Adhesive strength. 1 : 4 2176 Ib. per square inch. 1 : 6 1834 1:8 1450 1 : 12 1052 These results indicate that ordinary plain bars are quite satisfactory for reinforced concrete work. It will be noted from the result of the above experiments that the adhesive strength depends largely on the quality of the concrete. Other interest- ing tests include those carried out by Mr. Withey in 1907 at HISTOKY OF EEINFOKCED CONCKETE 13 FIG. 5. FIG. 6. FIG. GA. FIG. 7. 14 EEINFOECED CONCEETE CONSTEUCTION the University of Wisconsin. 1 The concrete mixture in this case was 1:2:4; plain steel rods were used varying from ^ to FIG. 8. | in. in diameter. The rods were embedded to a depth of 6 and 8 in. respectively, and the average adhesive strength was 1 " Bull. Univ. of Wisconsin," 1907. HISTOEY OF KEINFOKCED CONCEETE 15 found to be 400 and 310 Ib. per square inch respectively. These results are not so high as those obtained at Vienna. A reasonable objection has been taken to all these tests on the ground that when the steel is put under tension the pro- FIG. 9. PIG. 10. jecting part is elongated by the stress and that a progressive separation is caused between the steel and the concrete, but it is difficult to devise any method of testing that would be entirely 16 EEINFOKCED CONCKETE CONSTKUCTION free from objection. It would be safe to assume that with or- dinary round rods, not too smooth, embedded in good concrete, the bond strength may be taken at 250 to 300 Ib. per square inch. The safe working adhesion is usually taken at 60 to 100 Ib. per square inch, and it is always advisable that the ends of the rods should be split or bent as a precaution against sliding. The working stresses allowed by the regulations of various Governments are as follows : Austria 1 : 3 concrete 78 Ib. per square inch. J. ^r ,, /O ,, ,, ,, ,, 1:5 64 Germany .... 64 United States . . . 50 Position of Reinforcement. On no account should the rein- forcement be placed nearer the face of the concrete than -J in. in slabs, 1 in. in cross beams, and 1^ in. in main beams and pillars, and not less than 2 in. in structures exposed to the action of sea water. Preservation of Steel in Concrete. There are still a few engineers and architects who look with disfavour upon reinforced concrete on the grounds that corrosion of the steel is likely to take place, and that being encased in the concrete that corrosion cannot be detected as it might be in an open steel structure. The authors would emphatically state that, in their opinion, where good concrete surrounds the reinforcing steel, no such fears need be entertained. Many experiments have been carried out in connection with this important matter, and what is even a more reliable test of fitness, the condition of steel wherever found to be embedded in concrete in buildings or other struc- tures which have been demolished, has been carefully noted. One of the authors, for example, had occasion recently (1910) to pull down a partially underground public convenience at Bridlington, which was erected fifteen years ago ; the roof was reinforced by steel joists and iron rods, and these were found to be in excellent condition, there being no sign of corrosion, except where the end of one of the joists projected 4 in. beyond the face of the concrete; this exposed part was greatly corroded, HISTOKY OF KEINFOKCED CONCKETE 17 but the corrosion ended flush with the face of the concrete. He also had occasion two years ago (1908) to strip the face off a concrete-in-situ sea wall at Bridlington. This wall had been erected twenty-five years previously, and was reinforced by iron chains. These chains carne as near as 1 in. in places to the surface of the sea wall, and, in spite of the fact that the lower half of the wall was covered by the sea at each tide, the chains were quite bright, and no signs of corrosion were detected. In August, 1907, a concrete pier was constructed at some works at Newark, N.J. ; part of this was removed in October, 1910, and the reinforcement was found to be perfectly clean and bright, regardless of the fact that the concrete was practically under water. The mixture was a sloppy or wet one, and of the following proportions, one of cement, two of sand, and four of | in. stone. Prof. C. L. Norton of the Massachusetts Institute of Technology has carried out some exhaustive experiments in connection with this matter, and his conclusions are as follows : 1. " That neat Portland Cement, even in thin layers, is an effective preventative of rusting. 2. Concrete, to be effective in preventing rusting, must be dense and without voids and cracks. It should be mixed quite wet when applied to the metal. 3. The corrosion found in cinder concrete is mainly due to the iron oxide, or rust, in the cinders, and not to the sulphur. 4. It is of the utmost importance that the steel be clean when embedded in concrete. Scraping, pickling, a sand-blast, and lime should be used, if necessary, to have the metal clean when built into the wall." Note. The authors do not recommend the use of breeze or cinder concrete. The tests of German engineers l might be referred to as being particularly interesting, for they show that cracks occur- ring in the concrete do not result in the reinforcement becoming corroded at these points, and that only those beams that were 1 Paper on " The Corrosion of Steel Reinforcement in Concrete," by E. R. Matthews. Trans. Soc. of Engineers. 2 18 EEINFOECED CONCEETE CONSTRUCTION stressed to more than 35^000 Ib. to .the square inch showed any corrosion. The method of testing was briefly as follows : Beams were prepared which were reinforced by the steel which is generally used in reinforced concrete structures, this steel being placed 1J in. above the bottom of the beams. The concrete was mixed in the following proportions : 1:2:4, 101 per cent of water being added. The forms were removed after a set of twenty-four hours ; the beams were then stored for three months, some in wet sand, others in the open air, water being poured over them daily. For the next three months the beams were subjected to load tests, and of fifty-eight beams made, twenty-six were broken under these tests. The thirty-two beams which had not been broken were then sub- jected to a rusting test under a load, sheet-iron casing being fixed around the middle third of the beam, through which a mixture of carbon dioxide, oxygen and water vapour passed. The beams were kept in this rusting atmosphere for three days from 7 a.m. to 4 p.m. The steel was then examined with the following results : In twenty-seven out of the thirty-two cases no rusting had occurred. These twenty-seven beams had been subjected to a load causing stresses of 18,000 Ib. to 35,000 Ib. per square inch in the steel, and the five remaining beams had been subjected to a greater stress, viz. : 35,000 Ib. to 44,000 Ib. per square inch. Other experiments might be referred to as follows : In 1908 Sir H. Tanner had three blocks of concrete with steel inside put in the lake at St. James' Park, and left there for about a year ; when one was broken the steel was found to be quite unaffected. In 1884 when the Eddystone Lighthouse (originally con- structed in 1757) was pulled down, a bundle of rods which had been accidentally left in the concrete in the centre of the light- house was found to be in perfect condition. In views of the tests and observations before-named, we may safely conclude that steel does not corrode in good Portland cement concrete, where the load applied does not exceed the elastic limit of the material. HISTOKY OF EEINFOECED CONCKETE 19 A thin surface coating of rust on the reinforcing bars has proved to be no detriment when the concrete is so made as to be in perfect contact with the bars. Paint or oil should under no circumstances be permitted on the bars, but they may be coated with cement grout immediately before depositing the concrete. CHAPTEK II. GENERAL PRINCIPLES OF STRESS. THE principal stresses in structures are those of compression, tension, and shear. The first two are so generally known that no explanation of their nature is needed, but with regard to shear, although it may be known to be a tendency to cut the material transversely, its mode of action and amount are not as commonly understood and will involve a detailed description in the proper place. Eeinforced concrete is cement concrete strengthened by steel rods in such a manner that the compressive stress will be taken by the concrete and the tensile stress by the steel, with some slight modifications of the rule to suit special circum- stances which will be dealt with hereafter. The shear stress is taken partly by the concrete and partly by the steel. The stresses above named are produced in the material by the weight of the material itself, by the action of external loads, and by the force of the wind. They are common to all struc- tures of whatever material they may be formed, and may there- fore be studied in the abstract before considering their special applications. Direct compression is concerned with a total force P and a total sectional area A to resist it, the intensity of p the compression being given by j- =p Ib. per square inch, or tons per square foot, as the case may be. Where the length exceeds about six times the least breadth this intensity of pressure will be modified by the tendency to bend, which will increase it on the hollow side of the bend and reduce it on the rounding side. p Direct tension follows the same law as regards intensity -r=p, A. but when the weight of a horizontal piece causes any tendency 20 GENEKAL PKINCIPLES OF STRESS 21 to sag, the tension will be increased on the rounding side and reduced on the hollow side. A homogeneous rectangular beam of any given material, loaded on top and supported at the ends, is put in a state of stress as indicated by Fig. 11, the beam being drawn abnormally deep in proportion to the span to exaggerate the peculiarities. The forces there shown may, by the rules of elementary me- chanics, be resolved into others acting vertically and horizontally. The compression acting on the upper half and tension on the lower half produce a shortening and lengthening respectively which may be indicated by drawing parallel transverse lines on the side of the unloaded beam and showing how these would vary in distance when the beam is bent as in Fig. 12. The variation from the original distance between the lines indicates precisely what is happening ; the compression, greatest at top, reduces gradually down to zero at the centre of the depth, and the tension, greatest at the bottom, also reduces to zero at the centre of the depth where the spacing is unaltered. This line of no stress is called the neutral layer, or in cross-sections the neutral axis. That the beam is not only undergoing these simple stresses may be understood by considering the result of bending if the beam were made up of independent layers like boards. It is evident that there would be a slipping between the surfaces in contact as shown in Fig. 13, and this tendency exists in the solid beam although it cannot actually be seen. This endeavour to slip is known as horizontal shear. If again the beam were composed of blocks slightly attached to each other to make up the length, a vertical slipping would take place as shown in Fig. 14. This is known as vertical shear, and the two shears being compounded with the direct tension and com- pression make up the stresses shown by the curves of thrust in Fig. 11. Besides varying throughout the depth of a beam, the tension and compression vary also throughout the length, and, as these stresses are set up by bending, the measure of their value at any point of the length is known as a bending moment and the whole series is usually plotted as a bending moment diagram. A bending moment is like all other moments in being the product of a force into a leverage, and in the case of a 22 REINFORCED CONCRETE CONSTRUCTION beam, whatever cross-section be considered, the forces whether loads or reactions, tend to turn the end of the beam clockwise or anti-clockwise round the given section. The bending moment N FIG 12 FIG 13 FIG. 11. Lines of stress in a rectangular beam. FIG. 12. Lines showing alter- ation in length of beam under stress. FIG. 13. Diagram showing effect of horizontal shear. FIG. 14. Diagram showing effect of vertical shear. at the section is the algebraic sum of the clockwise and anti- clockwise moments and is given in lb.-in., or other unit compounded of the units of the force and leverage. It is only GENEEAL PRINCIPLES OF STRESS 23 necessary to divide the bending moment at any section by the effective depth of the beam to obtain the total stress of tension or compression at that section, and that again divided by the effective area above or below the neutral axis gives the intensity of the stress. By Newton's third law of motion " Action and reaction are equal," and a bending moment can only exist when there is a moment of resistance to balance it. Bending moment diagrams may be constructed to suit any condition of loading or supporting, but moments of resistance are dependent upon the material used, its strength, the sectional area and the way it is disposed round the neutral axis, and can only be determined by the exact conditions of the piece. To put it another way, the bending moment may be said to be the theoretical effort and the moment of resistance the practical opposition. A simple cantilever loaded at the free end and built firmly into a wall at the other end may be taken for the purpose of showing how bending moments are calculated. Fig. 15 shows such a beam with a concentrated load W at the outer end, and a clear span or length I. The bending moment at any point x will be W (I- x\ that is, the load' multiplied by its leverage to the given point. A series of such points may be taken and the results drawn to any convenient scale, and finally the whole length giving the maximum bending moment as W/ at the face of the wall. All the intermediate points being joined up will give the outline of a triangle, therefore, working graphic- ally there will be no need to do more than calculate the maximum moment and draw in the full outline as in Fig. 16. The vertical shear at any point depends upon, and is equal to, the amount of load passing through that point to the support. In this case the whole load passes equally through each point, and the shear diagram will be shown by a rectangle with a depth = W, as in Fig. 17. The formulae for determining the bending moments and shear stresses and also the deflection have been added to the diagrams to make them more complete. In the deflection formulae A = the maximum deflection in inches, W = the total load in lb., Z = span in inches, E = 24 REINFOKCED CONCKETE CONSTKUCTION modulus of elasticity of the material in lb., I = the moment of inertia of the section in inch units, sometimes called the " second moment ". When more than one concentrated load is carried, as in Fig. 18, the same method will be adopted to find the bending moment and shear diagrams. Take first the outer load W, then Wl will give the maximum bending moment, the triangle occupying the i /f\ v\ I 1 FIG . 15 -< - H ' FIG 18 I T \\w i I w^ yr*~~j;~. \\)S ~~ *"r nf jj^ moments 3 i ^FG. 3* - ->U-x) WL* * = JTT T * Shear d/aaram FIG. 17 FIG .19 JL K When (t,-3c) or (Ij-x) AS ncqct->ve it is to bet omitted FIG . 2O FIG. 15. Cantilever loaded at the end. FIG. 16. Bending moment diagram for cantilever loaded at the end. FIG. 17. Shear diagram for cantilever loaded at the end. FIG. 18. Cantilever with three concentrated loads. FIG. 19. Bending moment diagram for cantilever with three concentrated loads. FIG. 20. Shear diagram for cantilever with three concentrated loads. whole length of cantilever as in Fig. 19. Next take the load Wi with a leverage Z x and add the maximum bending moment W 1 l l at the face of wall below the previous one, then complete the triangle up to the point where the load Wx is applied. Pro- ceed in the same way with load W 2 having the leverage Z 2 , and the full bending moment at any point will then be obtained by measuring the depth of the diagram at that point, It is best GENEEAL PEINCIPLES OF STKESS 25 to commence the shear diagram at the support and then to reduce its depth as each load is passed, leaving a depth equal to the amount of load passing through the point, and giving the whole diagram as in Fig. 20. When the load is uniformly distributed and continuous over the span, as in Fig. 21, the same principles may be adopted, and the points found for the bending moments will give the out- ur per ft r*ur> _ _ _ i _ _ - -H FIG . 21 FIG 23 FIG 2 FIG. 21. Cantilever with uniformly distributed load. FIG. 22. Bending moment diagram for cantilever with uniformly distributed load. FIG. 23. Shear diagram for cantilever with uniformly distributed load. FIG. 24. Cantilever with uniformly distributed load, and concentrated load at end. FIG. 25. Bending moment diagram for cantilever with uniformly distri- buted load and concentrated load at end. FIG. 26. Shear diagram for can- tilever with distributed load and concentrated load at end. line of a semi-parabola with the vertex at the outer end, as in Fig. 22. This fact being known, the parabola may be set off with only the one calculation for maximum bending moment. A simple method for drawing a parabola by the intersection of lines is shown by dotted lines upon the same diagram. Divide the base line into any number of equal parts and draw vertical 26 REINFORCED CONCRETE CONSTRUCTION lines. Divide the height into the same number of equal parts and from each draw lines to the vertex, the intersections give points in the curve required. For the shear diagram, the same rule of starting at the support with the whole load carried there and diminishing the depth by the amount of load passed, will give the outline of a triangle as in Fig. 23. It will be useful to collect together all the usual modes of loading and supporting and indicate the required calculations by the algebraic method of letters so that they can be readily applied to any given case. With a distributed load and also a concentrated load upon a cantilever as in Fig. 24, the diagrams from each may be com- bined as in Figs. 25 and 26. With a distributed load over a portion of the length only, as Fig. 27, the bending moment and shear diagrams will be as Figs. 28 and 29. In a beam supported at the ends and carrying a concentrated load in the centre as Fig. 30, the bending moment diagram will be a& Fig. 31 and the shear diagram as Fig. 32. The question is often asked in the latter case " what is the shear stress at the centre of the beam, from the appearance of the diagram it might be nil or double". The answer is that it is uniform throughout, the change at the centre is due to the subtraction of the whole load as it is passed, and the measurement of depth changes from above the datum line to below. Sometimes the two portions are marked plus and minus, then + -J W on the left - W at the centre = - ^ W on the right. In the bending moment diagram Fig. 21, the maximum occurs immediately under the load and is arrived at thus : reaction at support = -JW, leverage to centre = \l, therefore bending moment . When the load is out of the centre, dividing the span I into the portions a and b, as in Fig. 33, the reactions at the supports must first be calculated. W x -- y will give the reaction at A and therefore the shear at that point, while W x -- - will give the Q/ -f GENERAL PRINCIPLES OF STRESS 27 reaction and shear at B. The maximum bending moment will be immediately under the load = W x 7 as in Fig. 34, and the shear diagram will be as Fig. 35. With two concentrated loads as in Fig. 36 there are two alternative methods of drawing the bending moment diagram. I I K - B x when x (1- z) J uf per fc run FIG. 27 .--- t - - - FIG 3O FIG za FIG 31 jc being measured from the s>earer pier 7 S .1 ^ J *-48Z7 1 \ FIG . 32 FIG. as FIG. 27. Cantilever with load uniformly distributed over a portion of its length. FIG. 28. Bending moment diagram for cantilever with load uniformly dis- tributed over a portion of its length. FIG. 29. Shear diagram for a canti- lever with load uniformly distributed over a portion of its length. FIG. 30. Beam supported at the ends with load concentrated in centre. FIG. 31. Bending moment diagram for beam supported at the ends with load concen- trated in centre. FIG. 32. Shear diagram for beam supported at the ends with load concentrated in centre. Fig. 37 shows the two triangles set out on opposite sides of the datum line, the measurements for the bending moment at any point being taken right through. Or the triangles may be set out on the same side of the datum line as in Fig. 38, and the overlapping parts added on to the outline. By calculation the reactions will be, at A = x - 7 - + -= , V ( 28 KEINFOECED CONCEETE CONSTRUCTION and at B = T mi , + ~. The bending moments will then be, Wc\ ^- h -, and under W under W 1 = aj- The shear diagram will be constructed as before, the result be- ing shown in Fig. 39. A 3 i <-----/-- * FIG. 33 1 1 'VlG. 36 11 FIG. 34 Between A anal W , Between W and & , B f ~ .BfS, being nrteasureat from pie on Carrie side of W FIG. 35 FJG 39 FIG. 33. Beam with concentrated load out of centre. FIG. 34. Bending moment diagram for beam with concentrated load out of centre. FIG. 35. Shear diagram for beam with concentrated load out of centre. FIG. 36. Beam with two concentrated loads. FIG. 37. Bending moment diagram for beam with two concentrated loads. FIG. 38. Alternative bending moment dia- gram for beam with two concentrated loads. FIG. 39. Shear diagram for beam with two concentrated loads. With two equal concentrated loads symmetrically placed on each side of the centre of span, it will be found that the bending moment will be uniform between the loads and the shear stress will be reduced to zero. With more than two concentrated loads on a beam the graphic method of finding the bending moments will be as shown in Fig. 38 ? but they may also be calculated. The reaction at A GENEBAL PEINCIPLES OF STKESS 29 multiplied by the distance to the first load, will give the bending moment under the load, and the reaction at B multiplied by the distance from it to the third load will give the bending moment under this load. The bending moment under the second load will be found by multiplying the reaction at A by the distance to the second load and subtracting the product of the first load into its distance from the second load, that is, obtaining the algebraic sum of the moments clockwise and anti-clockwise. The same procedure will be followed with any additional loads. When the load is continuous as in Fig. 40 the calculated bending moment will be fyvl for the reaction, multiplied by \l for the leverage to centre, minus $wl for load on one half, mul- tiplied by the distance of its centre of gravity from the centre, for the opposing moment ; or %wl x \l - %wl x \l = ^wl 2 - ^wl 2 = . o The outline of the bending moment diagram will be a parabola as in Fig. 41, and the shear diagram will be a double triangle as in Fig. 42. It should be noted, in this and other cases of loaded beams, that the maximum bending moment and minimum shear occur at the same point, and that the bending moment at any section is equal to the area of the shear diagram up to that point mea- sured on the length-load scale adopted, due attention being given to the plus and minus values of the shear diagram. The formula B^ gives the maximum bending moment and B x the bending moment at any point x measured from the left-hand support. With a uniformly distributed load over the whole span and a concentrated load in the centre, as Fig. 43, the bending mo- ment diagram will be as Fig. 44, and the shear diagram as Fig. 45. With a load distributed uniformly from one end over a por- tion of the span as in Fig. 46, the bending moment diagram will be as Fig. 47. Here it will be observed that there is first drawn a triangle, as if the load were all concentrated at its centre of gravity, and then, cutting off from the triangle a piece whose extremities correspond with the position of the load, upon the 30 REINFOKCED CONCRETE CONSTEUCTION line so drawn across the triangle a parabola is raised with a central depth equal to what it would be if the distance z were the whole length of a girder under a uniformly distributed load, 7/2 y viz. -- . The shear diagram, Fig. 48, is constructed as previously described, and it will be seen that the minimum shear occurs immediately under the maximum bending moment and indicates the position where the measurement of the latter should be taken. ur per ft. FIG. 40 us /oer FIG 43 FIG. rrti FIG. 4-4 FIG . 42 FIG. 40. Beam supported at the ends with a uniformly distributed load. FIG. 41. Bending moment diagram for beam supported at the ends with a uniformly distributed load. FIG. 42. Shear diagram for beam supported at the ends with a uniformly distributed load. FIG. 43. Beam supported at the ends with a uniformly distributed load and load concentrated in centre. FIG. 44. Bending moment diagram for beam supported at the ends with a uniformly distributed load and load concentrated in centre. FIG. 45. Shear diagram for beam supported at the ends with uniformly distributed load and load concentrated in centre. Fig. 49 shows a girder with a concentrated load and a parti- ally distributed load as before. The two loads shown are equal and their centres of gravity equidistant from the supports. The bending moment diagram, Fig. 50, is a combination of previous GENEKAL PRINCIPLES OF STRESS 31 diagrams, and the shear diagram, Fig. 51, is set out as before. If the loads have been given exactly as in Fig. 49 the stress diagrams will be as shown, but if loads of other magnitudes or position are given, although of the same character, there will be a corresponding alteration produced in the diagrams, the shear diagram being more especially affected in appearance. With a load uniformly distributed over a part of the span, away from the ends, as in Fig. 52, the bending moment and shear diagrams will be as shown in Figs. 53 and 54. us per ft. run FIG 46 or per ft run \^^S^^SSSSS$SS^ 1 1 1 - =r H FIG .49 I FIG 4*7 1 1 1 1 1 1 1 1 FIG 48 FIG. 51 FIG. 46. Beam supported at the ends with a uniformly distributed load over a portion of its length. FIG. 47. Bending moment diagram for beam sup- ported at the ends with a uniformly distributed load over a portion of its length. FIG. 48. Shear diagram for a beam supported at the ends with a uniformly distributed load over a portion of its length. FIG. 49. Beam with concentrated load and partial distributed load. FIG. 50. Bending moment diagram for beam with concentrated load and partial distributed load. FIG. 51. Shear diagram for beam with concentrated load and partial dis- tributed load. Beams with rigidly fixed ends, or beams continued over one or more intermediate supports, are known as continuous beams, and the stresses are much more difficult to determine than in the cases previously considered. 32 REINFORCED CONCRETE CONSTRUCTION Fig. 55 shows a beam built into a wall at each end and loaded in the centre. Generally speaking a length of not less than four times the depth must be built in, or it must be rendered sufficiently rigid by other means, in order that the full strength may be obtained. The load will cause a concave curvature on the top of the beam in the central portion for half the span the same as occurs throughout in a beam simply supported at the ends, but the building-in of the wall ends causes a convex curvature for one-quarter of the span at each w per ft. run i C v ^>^^^sS^^sS^^^ I ! 1 * - - - I - FIG 52 - - 1 T ^-i-^r-l M \ ? 5 f"s^ r ~ L _ & FIG. 55 ^tfEBHt Tn>>^ FIG. 53 FIG. 5G FIG 54. FIG. 57 FIG. 52. Beam supported at the ends with load distributed over a portion of its length. FIG. 53. Bending moment diagram for beam with load distributed over a portion of its length. FIG. 54. Shear diagram for beam with load distributed over a portion of its length. FIG. 55. Fixed beam with load concentrated at centre. FIG. 56. Bending moment diagram for fixed beam with load concentrated at centre. FIG. 57. Shear diagram for fixed beam with load concentrated at centre. end, the junctions being called the points of contra-flexure. This indicates that the upper part of the beam will be in com- pression for the length of the concave portion, and in tension throughout the convex portions, the stresses in the lower half of the beam being reversed. The compression is shown in Fig. 55 by thickened lines. The bending moment diagram, Fig. 56, GENEEAL PEINCIPLES OF STKESS 33 is produced by first forming a triangle as if the beam were simply supported at the ends, and then cutting off the top by a rectangle equal in height to the maximum bending moment at the supports. The positive bending moments are shown by the wide spacing of the ordinates and the negative bending moments by the narrow spacing. The shear diagram, Fig. 57, is the same as for an ordinary beam. In the case of a continuous beam with a uniformly distri- buted load, as Fig. 58, there are two bending moment values, according to whether the beam is of uniform section or of uni- 1 r ft. run FIG. 58 Uniform sgction ft _L w % T * i 1- - FIG. ei FIG. 59 FIG. 60 FIG 62 FIG 63 FIG. 58. Fixed beam with uniformly distributed load. FIG. 59. Bending moment diagram for fixed beam with uniformly distributed load. FIG. 60. Shear diagram for fixed beam with uniformly distributed load. FIG. 61. Beam fixed one end and supported the other with concentrated load. FIG. 62. Bending moment diagram for beam fixed one end and supported the other with concentrated load. FIG. 63. Shear diagram for beam fixed one end and supported the other with concentrated load. form strength, as shown on the two sides of Fig. 59. The fundamental parabola is first drawn and then the top cut off by a rectangle according to the circumstances. Uniform section occurs in rolled joists and practically in reinforced concrete beams ; uniform strength occurs in built-up girders where the 3 34 EEINFOECED CONCRETE CONSTRUCTION sectional area is proportional to the stresses. The shear dia- gram is shown in Fig. 60. It should be specially noted that in the case of reinforced concrete beams loaded and fixed in this manner the bending moment in the centre should be taken as -=-~- instead of ^j-, to allow for possible defect in the fixing of the ends. Floor slabs will be dealt with presently, as there are several variations from pure theory, to allow for the practical conditions arising in reinforced concrete construction. Vs i * - - t - - * FIG 64- i ttr per- ft. run Uniform secdon ^ FIG FIG 68 FIG FIG 69 FIG. 64. Beam fixed one end, supported the other with uniformly distributed load. FIG. 65. Bending moment diagram for beam fixed one end, supported the other with uniformly distributed load. FIG. 66. Shear diagram for beam fixed one end, supported the other with uniformly distributed load. FIG. 67. Continuous beam over three equal spans with uniformly distributed load. FIG. 68. Bending moment diagram for continuous beam over three equal spans with uniformly distributed load. FIG. 69. Shear diagram for continuous beam over three equal spans with uniformly distributed load. When a beam is fixed at one end and merely supported at the other, with a concentrated load in the centre, as in Fig. 61, the bending moment diagram is formed from the fundamental triangle cut off by another triangle, having a height at the fixed end of yV W/, as shown in Fig. 62. The distribution of the GENEKAL PKINCIPLES OF STKESS 35 compression is as shown by the thickened lines in the elevation. The shear diagram will be as Fig. 63. With a beam similarly supported and carrying a uniformly distributed load, as Fig. 64, the bending moment diagram will depend upon whether the beam has uniform section or uniform strength, as shown in Fig. 65. The shear diagram will also depend upon the same conditions, as shown in Fig. 66. A modification is adopted in the case of reinforced concrete beams supported in this manner, the negative bending moment at the ', per fc run - a - FIG 7O T FIG 73 FIG 71 FIG. 72 FIG. 75 FIG. 70. Cantilever with column support and uniformly distributed load. FIG. 71. Bending moment diagram for cantilever with column support and uniformly distributed load. FIG. 72. Shear diagram for cantilever with column support and uniformly distributed load. FIG. 73. Beam with con- centrated rolling load. FIG. 74. Bending moment diagram for beam with concentrated rolling load. FIG. 75. Shear diagram for beam with concen- trated rolling load. fixed end being taken as ^wl 2 and the maximum positive bend- ing moment beyond the centre as T V^ 2 at f/ from the sup- ported end. A beam carrying a distributed load, supported at the ends and with a central support also, will have bending moment and 3* 36 EEINFOKCED CONCEETE CONSTKUCTION shear diagrams for the right-hand span like Fig. 65, and the left hand span like Fig. 65 reversed. The shear diagram will be found in the same way from Fig. 66. When a beam with a distributed load is continuous over three equal spans, as in Fig. 67, the bending moment diagram will be as Fig. 68 and the shear diagram as Fig. 69. The reactions, or loads on the supports, will be as marked in the shear diagram, the maximum shear always occurring at the supports. There are many other cases that might be taken of irregular loading or unequal spans, but the foregoing will show the genera} principles upon which the diagrams should be con- structed. Fig. 70 shows a beam in the condition of a gallery cantilever one end fixed and the other projecting over a column or other support. The bending moment diagram will be as Fig. 71 and the shear diagram as Fig. 72. All the previous examples of beams with concentrated loads might have diagrams given for the same loads rolling from end to end, but one illustration of the effect of this form of loading must suffice. Fig. 73 shows a beam supported at the ends with a concen- trated load W rolling along it from end to end. The stresses for any given position of the load may be determined by Figs. 23, 74, and 75, but it will be seen that the maximum effect of a stationary concentrated load, which occurs when it is in the centre, is a series of bending moments as ordinates to a triangle WZ of a height = -j-, while the ordinates must be taken to a parabola of the same height to cover the whole effect of a similar rolling load, as shown in Fig. 74. The shear stress will be increased to double the amount = W at the supports, but at the centre it remains -JW as shown in Fig. 75. When the load is carried on two wheels the effect will be somewhat less, but no great error will be introduced by assuming the whole load to be concentrated at its centre of gravity. With a continuous beam similar altera- tions of stress will occur, but the details are rather complicated, and with beams of uniform section, such as rolled joists and GENEBAL PBINCIPLES OF STBESS 37 reinforced concrete beams, only the additional shear need be considered. In all beams the span I should be the effective span, that is, from centre to centre of the bearing surfaces, although in the case of rolled joists architects usually take I as the clear span between supports. In reinforced concrete beams the effective span must be taken, which should not exceed twenty-four times the effective depth ; and the end spans of continuous beams or slabs must not be considered as fixed at the extreme ends. For floor slabs in reinforced concrete, supported at the edges, the span is to be taken as the clear span plus thickness of slab, and when continuous over more than one span the distance from centre to centre of the beams. The bending moment across the centre of a square slab supported on four edges and rein- forced in two directions at right angles to each other with load W/ uniformly distributed is to be taken = yp The bending moment along the edge of a square slab fixed along four edges, and reinforced in two directions at right angles to each other, with reinforcements bent up over the supports, the load being uni- WZ formly distributed, is to be taken = ^j. For any other ratios of length to breadth, the bending moment on floor slabs should be taken as follows : Bending moments on floor slabs, edges supported only, I = length, b = breadth, W = weight of and on slab. For shorter span Tt - Wb l ^ c "^ x :"T 4 For longer span Wl 1 ~r x P Bending moment on slabs continuous or with fixed edges. 1 24 12 38 RBINFOBCED CONCRETE CONSTEUCTION Bending moments on outer bays of floor slabs. One supported edge, three fixed edges I in direction of supported edge Wl 1 at fixed edge i e ~ 8 " i 6 4 Z in direction of fixed edges, same as fixed all round. Bending moments at corner bays same as last equations above. When the length of a slab exceeds twice the breadth no calculation is required in the direction of the length. CHAPTER III. MOMENTS OF RESISTANCE. LOADS AND REINFORCEMENT. THE moment of resistance of a beam will depend upon the nature and strength of the material, and the form of cross-section or the disposition of the material with regard to the centre of gravity of the section. A rectangular beam of timber will be the simplest case that can be taken to illustrate the principles, see Fig. 76. Draw two diagonals by joining the opposite corners and put shading lines across the middle triangles. Then remem- bering that the longitudinal stress is greatest at the top and bottom surfaces, and reduces to nothing at the neutral axis, the shaded portion may be looked upon as giving, by its horizontal width at each part, the comparative intensity of stress ; or it may be looked upon as giving the amount of material in use if it were all equally stressed ; with this in view it is sometimes called the inertia area, or the area of effective resistance. The 1 'moment of inertia" is the summation of the areas of all the individual fibres or parts in the cross-section of a beam multi- plied by the squares of their distances from the neutral axis, I = 2ay 2 . In Fig. 76, the moment of inertia of the section is DAG + dag, where D and d are the depth above and below the neutral axis, A and a the area of each shaded portion, G and g the distance of the centre of gravity of each from the neutral axis. It will be seen that DAG + dag = 2DAG, and using b and d for the breadth and depth of the beam, the moment of inertia may be given in terms of the dimensions, then 2DAG = 2 x d x &d x f (|cZ), and multiplying this out and cancelling it will be found that bd z I = r-p, which is the moment of inertia for any homogeneous solid rectangular section. If the moment of inertia of such a 39 40 BEINFOECED CONCEETE CONSTEUCTION section be divided by the depth from the neutral axis to the top or bottom, which measurement is generally known as y, it will give the " section modulus " Z, or - = Z. But y = ^d, therefore x 1 . = %bd 2 . The section modulus may be described as the resistance-value of the section depending upon the area and disposition of its parts. The maximum stress at the upper and lower surfaces is known as "the extreme fibre stress". When a beam is tested to destruction this extreme fibre stress is theoretically the ultimate stress in tension, or compression but it does not cor- -4- FIG 76 FIG. 77 FIG. 76. Distribution of longitudinal stress in cross-section of rectangular beam. FIG. 77. Distribution of shear stress in cross-section of rectangular beam. respond with either, as is easily shown by calculation of the stress, and its value is found to vary with the form of cross- section of the material. Several theories have been propounded in explanation of this peculiarity. Professor Eankine suggested one cause to be the fact that the resistance of a material to direct stress is increased by preventing or diminishing the alteration of its transverse dimensions ; he also suggested that when a bar of metal is torn asunder the strength indicated is that of the centre part, which is the weakest, whilst when it is broken transversely the strength indicated is that of the outer part which is the strongest. In the case of timber it is suggested that the lateral adhesion of the fibres prevents the outer ones from moving freely, and hence in all cases the actual extreme MOMENTS OF KESISTANCE 41 stress is considerably less than it appears by calculation. This also holds good when the beam is merely subjected to its work- ing load. In any event, the difference really exists, and instead of determining the modulus of rupture from the tensile and compressive strength, it can only be found accurately by experiments on cross-breaking. The extreme fibre stress, cal- culated from the load required to break any beam, may be stated as so much in excess of the tensile strength, e.g. in plain cement concrete beams the apparent increase in strength under transverse load is such that the extreme fibre stress, or strength modulus, is about 1J times the tensile strength. The "modulus of rupture for transverse strength," or " strength modulus " is C in the formula -j- = ZC (W being in Ib. and I in in. ; while 7 jn c in the formula W = -y ( W being in cwts., b and d in in., and L in ft.) may be called "the coefficient of transverse strength ". In general C = 18c x 112 ; C is the so-called extreme fibre stress = K of Molesworth, k of Tredgold, and / of other writers, and c is the weight in cwts. in centre required to fracture a bar 1 in. square and 1 ft. between the supports. The relationship of the bending moment to the moment of resistance in a rectangular beam is shown by the following equations : Bending moment = Moment of resistance = 4 y or = If the principle of leverage be considered, the relationship of bending moment and moment of resistance can be shown more clearly in diagrammatic form. The two sets of forces, as shown in Fig. 78, form two " couples," a couple consisting always of two equal parallel forces, and the value of a couple in mechanics is the product of one of the forces-into the distance between the pair. The reaction at the support, and the half load in centre 42 KEINFOKCED CONCRETE CONSTRUCTION transmitted through the beam to that support, form the bending moment couple, and the resistance to tension and compression acting at the centre of gravity of each of the inertia areas form the moment of resistance couple. Thus Wl whence r- = as previously shown. The shaded portion of the section, pre- viously called the inertia area, is sometimes known as "the modulus figure," as it is the graphic representation of the section modulus Z. - - -feL- FIG 78 FIG. 78. Diagram showing the principle of leverage applied to the bending moment and moment of resistance of a beam. The shear diagrams already shown, give, by their ordinates, the whole shear across any section, but the shear stress is not distributed equally throughout the section. Fig. 77 shows the actual distribution throughout a rectangular section. If the horizontal lines in Fig. 76 be looked upon as dividing up the shaded portion into individual parts, then the shear ordinate in Fig. 77 opposite the bottom of the first part, will be equal to the area of that part ; the next shear ordinate will be equal to the combined areas of the first and second part, and so on to the neutral axis. Below the neutral axis the area of each part will be deducted, so that the shear stress is zero at top and bottom of the section, giving a parabola for the complete outline. It can be proved mathematically that the maximum shear at the centre of the section is 1^ times the mean shear, that is, the LOADS AND BEINFOBCEMENT 43 total shear across the section being 5, the mean shear will be s HS j-j, and the maximum shear per square inch will be j^=- . It will thus be seen that the longitudinal stresses are at a maximum at the top and bottom surfaces, where the shear is zero, and that the longitudinal stresses gradually reduce to zero at the neutral axis, while the shear increases to its maximum, at that layer, and that the whole of the fibres are thus doing approximately uniform work. These matters have been gone into fully for a homogeneous rectangular beam, as a knowledge so gained will bs useful in understanding the more complex problem of a reinforced concrete beam. Loads on Structures. The first preliminary in finding the actual stresses is to determine the weight of the parts and the loads to be carried, or as they are sometimes called, the struct- ural loads and the superimposed loads, the latter being subdivided into dead loads and live loads. It frequently happens that the structural load cannot be accurately determined until the design is somewhat advanced ; in that case reinforced concrete is as- sumed to weigh 150 Ib. per cubic foot, calculated upon an approx- imate design. Asphalte covering to concrete floor = 12*6 Ib. per foot super per inch thick. The weight of wood coverings will depend upon the arrangement, but will average about 5 Ib. per foot super. SUPERIMPOSED LOADS ON FLOORS. Ib. per sq. ft. Warehouse (minimum) ..... 224 Book store at library 224 Drillroom or ballroom 150 Public assembly or concert-room, theatre, read- ing-room at library, workshop or retail shop 112 School or college classroom, office or counting house ....... 100 Hospital ward, lodging-house or hotel bedroom, workhouse, or dwelling-house ... 70 44 REINFORCED CONCRETE CONSTRUCTION But in any case, if the actual load to be carried exceeds any of the above, such load must be provided for. In order that the calculated loads may not be exceeded, every building of the warehouse class must permanently exhibit in a conspicuous position upon each storey a notice stating the maxi- mum superimposed load which may be carried upon the floor of such storey or any part thereof. A suddenly applied load will produce double the bending mo- ment of a dead load or one gradually applied, while if a load is dropped on to a beam there will be additional energy to be re- sisted, due to the falling load. In ordinary structures a moving load is not considered to give any increase of stress unless the application of it is rhythmical, as in the case of a drill hall or ballroom, and the higher figures given in the table are for the pur- pose of making the required allowance for safety. A dense crowd of persons will not generally exceed a load of 84 Ib. = f cwt. per foot super, and they will then be packed too closely to permit of any movement. Load from Wind. For a roof of more than 20 degrees pitch the external load including wind must be estimated at 28 Ib. per square foot of sloping surface perpendicular to that surface. For all other roofs the external load must be estimated at 56 Ib. per square foot measured on a horizontal plane, but for a flat roof liable to be used as a store, or otherwise, such additional load as may be probable must be allowed for. All buildings must be designed to resist safely a wind pressure in any horizontal direction of not less than 30 Ib. per square foot of the upper two-thirds of the surface of such building ex- posed to wind pressure. In exposed positions it may be neces- sary to allow as much as 56 Ib. per square foot. Loads on Walls, Pillars, and Foundations. In buildings of more than two storeys in height, except in buildings of the ware- house class, the superimposed loads for the roof and topmost storey must be calculated in full, but for the lower storeys a re- duction may be allowed as follows. For the storey next below the topmost storey a reduction of 10 per cent, and for each suc- ceeding storey below a further reduction of 10 per cent, pro- LOADS AND KEINFOKCEMENT 45 vided that the maximum reduction for any storey shall not exceed 50 per cent of the full load for that storey. The modulus of elasticity for stone or gravel concrete in cement, not weaker than 1:2:4 (that is, 1 part by measure of standard Portland cement, 90 Ib. being taken as equivalent to a cubic foot, 2 parts clean sand, and 4 parts broken aggregate varying in size from J in. to f in.) may be treated as constant and taken at one-fifteenth of the modulus of elasticity of mild steel. The actual figures are, in tension or compression : Ib. per sq. in. For concrete, E c = 2,000,000 mild steel, E.= 30,000,000 Modular ratio B. ,, IT 15 whence it follows that at any given distance from the neutral axis, the stress per square inch on steel will be fifteen times as great as on concrete. The resistance of concrete to tension is neglected, and the steel reinforcement is assumed to carry all the tension. The stress on the steel reinforcement is taken as uniform on a cross-section, and that on the concrete as uni- formly varying. The ultimate compressive strength of the concrete should not be less than is given in the following table : Uses. Proportion by volume. Ultimate Compressive Re- sistance in Ib. per sq. in. Cement. Sand. Coarse Material. 28 days after Mixing. 90 days after Mixing. For beams and pillars . 1 1 1 2 1* 1 4 3 2 1800 2100 2700 2400 2800 3600 pillars only . Working Stresses. If the concrete is of such a quality that its crushing strength is 2400 to 3000 Ib. per square inch after twenty-eight days, and the steel has a tenacity of not less than 46 REINFORCED CONCEETE CONSTRUCTION 60,000 Ib. per square inch, the following stresses may be allowed : Concrete in compression in beams subjected to bending ....... Concrete in columns under simple compression Concrete in shear in beams .... Adhesion of concrete to metal . Ib. per sq. in. 600 500 60 100 Steel in tension 15,000 to 17,000 When the proportions of the concrete differ from those stated above the stress in compression allowed in beams may be taken at one-fourth, and that in columns at one-fifth of the crushing strength of cubes of the concrete of sufficient size at twenty-eight days after gauging. If stronger steel is used than stated above, the allowable tensile stress may be taken at one- half the stress at the yield point of the steel. The working stresses may be tabulated as follows : Except as provided for in pillars, the safe working stresses on concrete should not exceed the following : Proportions by volume. - Cement. Sand. 1 2 Coarse Material. 4 Cement. Sand. 1 Coarse Material. 3 Stresses on Concrete. Stress in Ib. per sq. in. Stress in Ib. per sq. in. Direct compressive stress 600 700 Extreme fibre stress 600 700 Frictional stress between concrete and steel 60 60 Shearing stress 60 60 Tensile stress . nil nil and the safe working stresses on mild steel should not exceed the following : LOADS AND EEINFOECEMENT 47 Stresses on Mild Steel. Ib. per sq. in. Direct compression stress = me, where m = modular ratio and c = compres- sive stress on concrete surrounding the steel Tensile stress on mild steel . Shearing me, or 16,000 whichever is the lesser. 16,000 12,000 In calculating the steel reinforcement to provide for the shear stresses, only the balance after allowing 60 Ib. per square inch on the section of concrete need be provided for. In order that a reinforcing rod may take the direct stress at any point for which it is calculated, the "grip" length in inches of a bar embedded in concrete, measured along the bar from any given cross-section to the end of the bar, must not be 10 x sectional area x t ,. , less than which gives for rounds and perimeter squares 2500&Z, and for flats -r -v- where t = the tensile or o ~i~ d compressive stress at the given cross-section, and d = the dia- meter of the bar in inches. In designing the reinforcement the following rules must be observed. The least diameter or thickness of the main reinforc- ing bars in beams or slabs must not be less than \ in., but wiring may be used solely for holding the bars in position during the process of placing the concrete. All other reinforcements must be at least J in. diameter or other section of equal area. The reinforcement must not be placed nearer the face of the concrete than -J in. in slabs, 1 in. in cross beams, and 1^ in. in main beams and pillars. A distance of at least 1 in. must be left horizontally between the bars and in. vertically except at points where the bars are in direct contact and transverse to one another. The maximum distance between the main tensile reinforcement of slabs must not be greater than 12 in. Mesh reinforcement must be of such dimensions as will enable the coarse material in the concrete to pass easily through the meshes of such reinforcement. Where compressive rein- 48 KEINFOKCED CONCEETE CONSTKUCTION forcement is provided in beams and calculated to take part of the compression it must be anchored by bars extending down to the bottom of the middle third of the effective depth of the beam. The anchors must not be further apart, centre to centre, than the effective depth of the beam. All beams must be provided with shear members throughout the length of the beam. All shear members must be spaced according to the actual shear stress or at a distance apart not exceeding the effective depth of the beams, and extend from the centre of the tensile reinforcement to the centre of pressure of the concrete under compression, be passed under, or round, or secured to, the tensile reinforcement, and have a mechanical anchorage with the concrete at the free ends or throughout their length. The brackets or splays at the ends of beams and fillets in the angles between floor slabs and beams are necessary for securing efficiency and stiffness of the work, but are not to be taken into account as reducing the span. The effective depth of a beam or slab is measured from the compressional edge of the concrete to the centre of the tensional reinforcement. Tee Beams. There is a modification sometimes permitted in calculating the strength of secondary beams. A portion of the floor slab not exceeding twelve times the thickness of the slab plus the width of the rib may be taken as part of the beam in computing the bending moment of the beam, which is then known as a tee beam. In that case the tensile reinforcement of the slab must be continuous across the full width of the portion of the slab forming the flange of the tee beam, and shear rein- forcement is required in the plane of junction of the rib and the flange. Reinforced Concrete Pillars. In reinforced concrete pillars the maximum value of the ratio of length to effective diameter must be taken between the lateral supports, irrespective of any bracketing. The effective diameter will be the measurement to the outside of the vertical reinforcement. Pillars are deemed to have fixed ends when the ends are sufficiently secured to other parts of the construction having such rigidity as will maintain LOADS AND KEINFOKCEMENT 49 the axis of the pillar at the ends in its original vertical position under all loads less than the crippling load. When both ends are fixed the following stresses may be allowed : Length Stress Allowed. Effective Diam. 18 Full stress 22 8 of 24 6 27 *4 ,, 30 " 55 >5 If P = the maximum pressure on pillars and compression members having fixed ends, compression members not having both ends fixed may have working loads as follows : One end fixed and one hinged = 4 P Both ends hinged . . . . . . . = J P One end fixed, the other free or not supported in all directions = T V P Each pillar with straight laterals (hooping) must have at least four lines, and with curved laterals six lines, of vertical reinforcement throughout its entire length. The least diameter of straight laterals must be not less than Y\ in., and curved laterals in. The pitch of the laterals must not exceed -$ of the effective diameter of the pillars, joints in the vertical reinforcement may only be made at a floor level or other point of lateral support. At all joints in the vertical rein- forcement, the bars should overlap a distance equal to required grip length, or have flitch bars of double that length, or have butt ends and a close fitting sleeve. In the case of rectangular pillars in which the ratio between the greater and lesser diameter exceeds 1, the cross-section of the pillar must be subdivided by cross ties, and the number of vertical rods must be such that the distance between the rods along the longer side of the rectangle shall not exceed the dis- tance between the rods along the shorter side of the rectangle. The total cross-sectional area of the vertical reinforcement in 50 REINFORCED CONCRETE CONSTRUCTION any pillar must not be less than 0'8 per cent of the area of the hooped core, and the volume of the lateral reinforcement must not be less then 0'5 per cent of the volume of the hooped core. Reinforced Concrete Walls. Reinforced concrete enclosure walls, where the main loads of the structure are carried by pillars to the foundations, may be not less than 6 in. thick pro- vided they are designed and reinforced under similar rules to the remainder of the structure for the loads and pressures they may have to carry. When portions of the external walls between the reinforced concrete pillars and beams are constructed of other materials than reinforced concrete, they must be not less than 8-J- in. thick for the top 20 feet of their height, and 13 in. for the remainder of their height. All walls must be securely connected to the continuous part of the reinforced concrete con- struction. Party walls of reinforced concrete must nowhere be less than 8 in. thick. Openings may be made in external walls provided that in any storey above the ground storey the aggregate area of such openings will not exceed three-fourths of the whole area, or the aggregate widths nine-tenths of the whole length of such storey. [The above notes are based upon the probable conclusions which will be put forward by the London County Council to regulate the construction of reinforced concrete buildings, but as the matter is still sub judice no authoritative statements can be made.] CHAPTEE IV. NOTATION, FORMULAE, AND EXAMPLES. Resistance Moments for Rectangular Beams. Notation. b = breadth of beam in inches. d = the effective depth of the beam in inches, i.e. the distance from the top of the beam to the common centre of gravity of the tensile reinforcement. n = the distance of the neutral axis from the compressed edge of the beam in inches. k = the fraction of the depth given by the distance of the 77 neutral axis from the compressive edge = -5. A c = area of concrete in square inches = bd. A, = area of tensile reinforcement (in square inches). E,= elastic modulus of steel in tension. E c = elastic modulus for concrete in compression. Tjl m = ^ = 15 = Modular ratio. J^c B = bending moment of the external loads and forces in Ib.-in. E = resistance moment of the internal stresses in the beam in Ib.-in. c = compressive safe working stress on extreme edge of the concrete in compression, i.e. the strength modulus for concrete in compression (in pounds per square inch). t = tensile working stress on steel in tensile reinforcement (in pounds per square inch of cross-section). A r = ratio of A, to bd, i.e. r = T^> p = the percentage of tensile reinforcement = 100?*. 51 4* 52 EEINFOECED CONCEETE CONSTEUCTION a = the arm of the couple formed by the compressive and tensile forces in the beam. W = the total weight to be carried by a beam. 1= the length of the effective span of a beam. Fig. 79 shows the cross-section of a reinforced concrete beam and Fig. 80 a diagram illustrating the use of the terms given above. Neutral Axis. In a homogeneous beam the stresses are pro- portional to the distances from the neutral axis, but in a dis- crete beam, such as a beam of concrete reinforced with steel, on - -b- - k c -H T J FIG 79 FIG. SO FIG. 79. Cross-section of a reinforced concrete beam. FIG. 80. Diagram show- ing neutral axis and resistance areas of a reinforced concrete beam. account of the greater rigidity of the steel, at a given distance from the neutral axis the stress in the steel will be m times as great as in the concrete. Calculations for locating the neutral axis are based on the equation n _. and n = L v(/ ^ 2 + 2rw) - rm]d. Mean compressive stress on the concrete = ^, n Arm of resistance moment a = d - r . NOTATION, FOEMUL^E, AND EXAMPLES 53 (n\ d- o)- o/ C ( fl\ Compressive resistance moment E c = ^bni d - ). A \ o/ Maximum bending moment under distributed load ends W supported B c . = -^-. -r> Maximum tensile stress t = ,,.,,.. rbd 2 (l - i&) Maximum compressive stress c = kbd*(l - Jfc)' Example of designing a Reinforced Concrete Beam. A reinforced concrete beam is required to carry a uniformly distributed load of 8 tons in addition to its own weight over an effective span of 16 ft. The stress on the steel not to exceed 16,000 Ib. per sq. in. and on the concrete 600 Ib. per sq. in. Assume width of beam in inches to be f of span in feet, jx!6 = 12 in. and total depth to be twice width = 24 in. Approximate weight of beam = Total load 8 x 2240 + 300 = 18220 Ib. Maximum bending moment = = 1822 X Q 16 X 12 = 437280 o 8 Ib.-in. but ck = 2rt, or 600 x '36 = 2r x 16000. 600 x -36 16000^2 B 437280 = -00675 = 16000 rbd*(l - P) '00675 x 12 x d* x (1 - J x -36) . , / 437280~ V '00675 x 12 x -88 x 16000 " m> 54 EEINFOECED CONCKETB CONSTKUCTION Sectional area of metal = rbd = -00675 x 12 x 19-5 = 1'58 sq. in. say four f in. rods. B 437280 t = T, 9/1 17N = AApryE :r~ -, n K9 ^H = 16133 Ib. per sq. m. rbd 2 (l - J&) '00675 x 12 x 19'5 2 x '88 _ 2B 2 x 437280 " kbd\l - P) ~ '5625 x 12 x 19'5 2 (-88) " Obtaining depth by c = 600 2x437280 5625 x 12 x tf x -88 2x437280 _-,** ~600x-5625xl2x-88 It therefore appears to be impossible to stress both materials to their maximum value, but the most economical percentage of reinforcement = 0'675 per cent. With a fixed ratio between the working stresses of steel and concrete, say 17000 Ib. per square inch and 600 Ib. per square inch, and a given percentage of reinforcement, beams may be calculated approximately by the formula where for '5 per cent. C = 76 ,, ,, '75 ,, ,, =98 ,, I'O =108 ,, ,, 1 25 ,, ,, = 115 ,, 1-5 =122 Thus for a reinforced concrete beam as above 12 in. by 19' 5 in. with '75 per cent reinforcement cbd? = 98 x 12 x 19'5 2 = 447174 lb.-in., which is rather higher than the bending moment required because a higher percentage of reinforcement has been taken. By the authors' empirical formula for safe distributed load = (-37 x -675 + - = 132cwt. = 6'6 tons NOTATION, FORMULA, AND EXAMPLES 55 as against 8 tons for which the beam has been designed, but an approximate formula should always be on the safe side. Example of Working when the Dimensions are given : say 6 = 10, d = 20, Z>d = A c say 1 per cent reinforcement _. __ A C ~200 100 n = [ V(-01 2 x 15* + 2 x -01 x 15) - '01 x 15]20 = [ V00225 + -3) - -15J20 = (-5679 - -15)20 = 4179x20 = 8-358 in. , = 16000x2(20-^) = 32000x17-213 = 550827 Ib.-in. E c = ~ x 10 x 8-358 (17-213) a = 25074x17-213 = 431607 Ib.-in. If the span be 20 ft. the total load distributed based upon the resistance moment of the concrete will be .. Now by E.IB.A. Journal, 1907, p. 533, Keport of Joint Committee on Reinforced Concrete n 8-358 =;r-2o- -1- Jx -4179 = '8607 2 x 431607 C - -4179x10x20^-8607 56 EEINFOECED CONCEETE CONSTEUCTION It is evident then that the steel is in excess for the maximum economy. Try a reduced percentage of reinforcement. Say b = 10,d = 20, U = K C = 200, say f per cent (*75) reinforcement. l'5s. in. = 15 n = [ V(-0075 2 x 15 2 + 1-5 x '0075 x 15) - '0075 x 15J20 = [ VC01265625 + 16875) - '1125]20 = (-4259 - 1125)20 = 6'268 in. , = 16000x1-5(20-^?) = 24000 x 17-91 = 429840 Ib.-in. = x 10x6-268 (17-91) & = 18804 x 17-91 = 336779 Ib.-in. 8E 8x336779 j n_ 6-268 ~d~ 20 1-P='8955 336779 -0075 x 10 x20*x -8955 2 x 336779 C = -3134x10x20^-8955 = 5 " Therefore when the reinforcement is decreased the total safe load is less, the neutral axis is higher, and the steel is stressed nearer to its full value. Try a further reduction in the percent- age of reinforcement. Say 6 = 10, d = 20, 6d = say "5 per cent reinforcement A e = r-r^r x 200 = 1 so. in. JLUU NOTATION, FORMULA, AND EXAMPLES 57 m = 15 n = [ V('005 2 x 15' 2 4- 1 x -005 x 15) - '005 x 15] 20 = [ V0005625 + -075) - '075] 20 = (2839 -'075)20 = 4178 B, = 16000 x = 16000 x 18-607 = 297712 Ib.-in. E c = x 10 x 4-178 (18-607) & = 12534 x 18-607 = 233220 Ib.-in. w 8R 8 x 233220 W = -=- = 7^7: ZTTJ = 7774 Ib. I 20 x 12 20 233220 005 x 10 x 20 2 x -9304 2 x 233220 ' m ' Shear Stress in Beams. a, = total sectional area of shear reinforcement (diagonal tension) on each side of centre. bd "' = 48 placed approximately from centre at, "25, '4, "57, '72, "84, "93, "98, 1*0 of semi-span. For example, take the beam 12 in. by 19'5 in. as first above bd 12x19-5 a ' = 48 = -48" say 8 stirrups in length of -J span 4-875 o = '61 sq. m. each. .'. section for 2 stirrup-bars = f sq. in. each. ) > j > = T6" > > 6 4 j> 8 85 j> = TF n 58 BEINFOBCED CONCBETE CONSTBUCTION Owing to the reduction of the bending moment towards the supports of a beam under a uniformly distributed load the tensile reinforcement may be bent up to take part in the shear stress as follows : one-third at a distance of '212 from the centre of bearing or one-half at a distance of '15Z. Generally it will depend upon the number of rods which figure is adopted. With three rods one could be turned up at '21 1 and with four rods two could be turned up at 15Z. The beam as designed will now be in section and elevation as Figs. 81 and 82 which may be looked upon as typical. V* shear * stirrups >/ K- ~~ -------- - /6'.O' effective FIG. 81. Cross-section of reinforced concrete beam. FIG. 82. Part elevation of beam showing the reinforcement. FIG. 83. Section of reinforced con- crete floor slab. Rectangular Beams with Double Reinforcement. In addition to the symbols already given, let x = distance from the top of the beam, to the centre of gravity of the top reinforcement. A = area of compressive reinforcement in square inches. c, = compressive working stress on steel in compressive reinforcement. d- n t = cm n n- x c t = cm n NOTATION, FOKMUL^E, AND EXAMPLES 59 Example of Stresses in a Floor Slab. Say a reinforced concrete floor slab 7 ft. 6 in. span, supported at the ends, 5 in. effective thickness, reinforced with T 7 ^ in. bars, 4 in. centre to centre, carrying a superimposed load of 2 cwt. per foot super, as in Fig. 83. Structural load (5 12 x 150= 75 Ib. per sq. ft. Wood floor, etc. ... 5 ,, Superimposed load . . =224 304 Taking a 12 in. breadth of slab, the span 1= (12x7-5)+ 6 = 96 in. and the bending moment in centre WZ 2 304 96 2 on B c = -g- = -jg- x -g- = 29,184 Ib.-m. The effective depth = 5 in., in 12 in. wide there are -\ 2 - = bars*, each y^ = 0*15 sq. in. area. Then r = ^ = ^^ = '0075, m = 15 A. c JLZ x o k ^J(f i m L + 2rm) - rm = V00075 2 x 15 2 + 2 x -0075 x 15) - '0075 x 15 = '3750 Stress in steel B c 29184 rbd\l - P) '0075 x 12 x 5 2 ('875) = 14,822 Ib. per sq. in. Stress in concrete 2B C 2 x 29184 '3750 x 12 x 5 2 ('875) = 593 Ib. per sq. in. which is satisfactory as being reasonably within the allowable limits of maximum stress. Resistance Moment for Tee Beams. A, = area of tensile re- inforcement. 60 EEINFOECED CONCEETE CONSTEUCTION b = breadth of compression flange of tee beam. d = effective depth of the beam, measured from the top of the beam (surface of floor) to the centre of gravity of the tensile reinforcement. d t = Total depth of slab. p = percentage of reinforcement in the equation A L= p bd s 100 ^' = the ratio of d to d t , i.e. n = the neutral axis depth, i.e. the distance from the com- pressed edge to the neutral axis. & = the ratio of n to d, i.e. the fraction of depth from the compressed edge to the neutral axis. If n ri ~z d c = the compressive stress on the compressed edge of the concrete. z = distance from upper surface to centre of pressure in con- crete, ~3 2n-d. a = the arm of the compressive and tensile forces. Tee Beams with Double Reinforcement. When the neutral axis is above or coincides with the under side of the floor slab the formulae for doubly reinforced rectangular beams may be used, but b will equal the breadth of compression flange of tee beam instead of breadth of rectangular beam. When the neutral axis is greater than the depth of floor slab bd s + m(K t + A) a = d- z. s 1 = the slab depth ratio = djd. Fig. 84 shows the section of a reinforced tee beam and Fig. 85 a diagram illustrating the use of the terms given above. NOTATION, FORMULA, AND EXAMPLES 61 The position of the neutral axis must be obtained from the equation Q'5s' + Q'l5p 1 + 0'15p The mean compressive stress must not be taken at more than c c - or or c 1 - H- C H FIG FIG. 84. Cross-section of reinforced concrete tee beam. FIG. 85. Diagram of neutral axis and resistance areas. The compressive resistance moment = B r where - - a or Stress on the concrete = c where The tensile resistance moment = B T where B T = tA. t d. Stress on the steel reinforcement = t where B 62 KEINFOBCED CONCEETE CONSTKUCTION Shearing force at ends of beam o Wl = ~2~' Shearing stress on section of beam The floor slab to the extent of not more than twelve times the thickness of slab may be taken as the width of compression flange. Example of Calculation of Tee Beam.- Say the floor is 20 ft. span, the floor slab 4-J in. total thickness, the external load f in. asphalte and 140 Ib. per foot super uniformly distributed. Beams 12 in. wide and 18 in. deep below concrete to centre of reinforcement, which consists of six f in. rods; beams 6 ft. centre to centre, as in Figs. 86 and 87. - - - - - - - - - 2O'. O" effect/re FIG. 86. Cross-section of reinforced concrete beam and floor slab from calcula- tions. FIG. 87. Part elevation of the same. Assume twelve times thickness of slab as width of flange of tee beam. 12x4-5 = 54 in. Weight of floor : NOTATION, FOKMUL^, AND EXAMPLES 63 lb. per ft. run. Slab 6x^x150 . . =337-5 LA (18+2-5)12x150 _. or Beam - - ... =256'25 144 Asphalte 6 x "75 x 12'6 . . = 56'7 Superimposed load 6 x 140 . . = 840 '0 1490-45 say total load 1490 lb. Maximum bending moment, ends supported, wli ^0(20x12)' ? = -L2 _ - 894000 Ib.-in. 8 8 The sectional area of six j rods = 6 x '442 = 2'652. Width of slab forming flange of tee beam = twelve times thickness, 12x4-5 = 54 in. Position of neutral axis , + 0-15^ 4-5 2-652 0'15 X (18 + 4-5) 54 x 4-5 54 x 4'5 = 0-226 71 = ^ = 0-266(4-5 + 18) = 5-09. Distance from upper surface to centre of pressure in concrete x = ^5 3x5-09-2x4-5 3 > 2x5-.09-4'5 = 1-656 in. Stress on the steel reinforcement B 89400 *) 2-652(22-5-1-656) = 16172 lb. per sq. in. 64 BEINFOBCED CONCBETE CONSTBUCTION Stress on the concrete c- ,(2n - d g ) (d - z) = _ 2x89400x5-09 _ ~~ 54 x 4-5(2 x 5'09 - 4'5) (22'5 - T656) = 316 ib. per sq. in. Maximum shearing force at ends of beam Shearing stress on section of beam S 14904-5 = 7 f , v- = ^ 0/on g i-p-F7^ = 59'6 Ib. per sq. in. l>(d-z) 12(22-5-l'656) This is within the allowable limit of 60 Ib. per square inch, but it is usual to bend up the upper row of steel rods at the ends, so that there will be ample margin. The perimeter (o) of a f in. rod is '75 x 31416 = 2'36 in. The adhesion stress of the lower rods near the ends will be gtf-12) ^(240-12) 2o(d - z) 2 x 3 x 2-36(22-5 - T656) = 96 Ib. per sq. in. which is within the allowable limit of 100 Ib. per square inch. Formulae for Reinforced Pillars. C = the ultimate crushing resistance of concrete at 3 months. Sp = the safety factor = say 4. k = the reciprocal of the safety factor = ^-. Op /= form factor, depending upon the form or type of laterals, (see table). s = spacing factor, depending upon the spacing or pitch of the laterals (see table) r = ratio of the volume of lateral reinforcement to the volume of the hooped core in any given length of pillar. The stress on the concrete in the area bounded by the lateral reinforcement must not exceed The value of/ and s are given in the following table : NOTATION, FOKMUL.E, AND EXAMPLES 65 Form of Lateral Reinforcement. Form Factor =/ Spacing of Laterals in terms of Diameter of Hooped Core. Spacing Factor = s. Helical 1-0 0'2d 32 ? J * 1-0 0'3d 24 1-0 0'4d 16 Circular Hoops 075 0-2d 32 55 55 075 0'3d 24 075 0'4d 16 Rectilinear . 0-5 0'2d 32 55 * 0-5 0'3d 24 55 0-5 0'4d 16 55 0-5 0-5d 8 55 * 0-5 0'6rf The safe load on pillars should be obtained from the equa- tion P = c[A + (m- 1)AJ where P = Total permissible pressure in Ib. c = working compressive stress Ib. per sq. in. on the concrete of the hooped core. W = actual load on pillar in Ib. A = effective area of the pillar insq. in., i.e. the area bounded by the lateral reinforcement measured to the inside of the hoop- ing. A D = Area of the vertical reinforcement in sq. in. m = Modular ratio = E./E C = 15. The following limits of stress should be observed in pillars : (a) The stress on the steel must not exceed one-fourth of the ultimate tensile strength of the metal, or 0'5 of the elastic limit, or the value of me. (b) Whatever the percentage of lateral reinforcement the working stress on the concrete of pillars must not exceed 0*5 C with rectilinear laterals, 0'58 C with independent circular hoops, 0'66 C with helical reinforcement. Example of Calculation of Pillar Axially Loaded. A reinforced concrete pillar 10 in. square, 15 ft. high, is rein- forced with four f in. rods, bound together spirally at intervals of 3 in. with ^ in. diameter wires, and carries an axial lo^d of 66 REINFORCED CONCRETE CONSTRUCTION 20 tons, as in Fig. 88. Find the stresses on the steel and the concrete. 15 x 12 Ratio of length to least diameter = ^Q = 18, therefore the full stress may be allowed on the pillar. Total area of steel 4x -75 2 x -7854 = 1-76 sq. in. -1)~ 49 + 1-76(15-1) Maximum permissible stress in concrete = &C(1 +/r) = i x 2400(1 + 1 x 16 x "005) = 648 Ib. per sq. in. Stress in steel, mW 15x20x2240 -l) 49 + 1-76(16-1) the maximum permissible for pillars being 12,000 Ib. per sq. in. The maximum stress on an eccentrically loaded pillar will be given by the formula, , W Wx f =-K ~7T where /= maximum stress in Ib. per square inch at edge of sec- tion, NOTATION, FOBMUL.E, AND EXAMPLES 67 W = total load from all sources in Ib. A = equivalent area in square inches = A + (ra-l) A, W = eccentric load in Ib. x = eccentricity or distance in inches from neutral axis of pillar to centre wf application. Z = section modulus of pillar. The section modulus of a rectangular reinforced concrete pillar h is the whole diameter of the pillar at right angles to the neutral axis, h, is the diameter from centre to centre of rein- forcement. The section modulus of a circular reinforced pillar with four bars, The section modulus of a circular reinforced pillar with bars arranged in a circle, Example of Calculation of Eccentrically Loaded Pillar. A rectangular reinforced concrete pillar 18 in. square, with four 2 in. rods, 13 in. centre to centre, 16 ft. high, with straight laterals in. diameter, 4 in. centres, has an axial load of 50 tons, and a load of 20 tons applied at the side, as in Fig. 89. Find the stresses on the two faces. Area of steel = 2 2 x -7854 x 4 = 12*5664 Area of pillar = 15x15 = 225 Equivalent area = A + (m - 1)A. = 225+14x12-5664 = 400. Section modulus Z = JA C A + |(w - l)A,-j-, 1Q2 = x 324 x 18 + 1 x 14 x 12'5664 x ^ =1798. io 5* 68 EEINFOBCED CONCEETE CONSTEUCTION The stresses on the two faces are, W Wo; /= r^ (50 + 20)2240 20x2240x9 ~~ ~ = 616 Ib. per sq. in. compression under eccentric load = 168 ,, ,, on opposite face. The allowable stress = kC(l +fsr) = i x 2240(1 + 0'5 x 24 x -003) = 621 Ib. per sq. in. and the pillar is therefore safe. CHAPTER V. SPECIAL CONSTRUCTIONS. Retaining Walls. Retaining walls of reinforced concrete are built upon principles quite contrary to those of ordinary retain- ing walls. The latter depend for their stability upon their mass and weight, and the line of thrust, compounded of their weight acting through the centre of gravity and the thrust of the earth which they support acting at one-third of their height, must fall sufficiently within the face of the wall to leave the maximum stress of compression at the outer edge and tension at the inner edge within safe working limits. It is generally assumed that this line of thrust must fall within the middle third of the base, but this is not essential unless it be desired that there shall be a complete absence of tension. Reinforced concrete retaining walls rely chiefly upon their strength, and when they are pro- perly designed they only require to be about as many inches in thickness as the old-fashioned walls require to be feet. There are only a few principal types but many modifications. Fig. 90 shows an L-shaped wall, where the foot is held down by the weight of the earth and the thrust is resisted by the upright cantilever. In Fig. 91 the wall is placed in the centre of the base, and in Fig. 92 the wall is placed at the inner edge of the base. In these two cases the wall has a tendency to lift, rotat- ing on the outer edge of base. In Fig. 93 the same type is strengthened by counterforts every 10 ft. on the inside ; there is also a cleat, or projection, on the underside to prevent the wall from being pushed out. In Fig. 94 the wall takes the form of two cantilevers, the upper one being loaded by the weight of footpath and the lower one by the reaction of the earth under foundation. The weight and natural slope of various soils required in 69 70 KEINFOECED CONCKETE CONSTRUCTION calculating retaining walls are given in the following table. They must be taken as approximate only, as no two writers L ; . s /a shrinkage roo/s 18' cencres r -^S'/ve/s S'cenfres * FIG 91 Zt'rocts 'cencres \ ^SRf ,^^m -: FIG 9Z -ff.'ff- FIGS. 90 TO 94. Sections of reinforced concrete retaining walls. agree, and considerable variation will arise under different climatic conditions. SPECIAL CONSTKUCTIONS 71 Soil. Ib. per cub. ft. (w). Angle of Repose (6). Vegetable earth 90 30 Sandy loam 100 34 Loamy clay 110 36 Firm gravel 120 40 Loose gravel 110 36 Stiff clay .... 128 45 Wet clay .... 120 16 Fig. 95 shows a graphic diagram of the pressures on the vertical and horizontal portions of a retaining wall like Fig. 90. The bending moment at the foot of the wall per foot run is The moment of resistance of cantilever (at foot of wall) as shown in last chapter is E ( = A,(d - g), or R. - |6n(d - J), whichever is the lesser. To balance the horizontal thrust the theoretical length of base is For stability the actual length of base should be not less than say To find the pressure on the foundation an\actual case must be taken, Fig. 96, say wall 20 ft. high, earth 90, Ib. per cubic foot., natural slope 35, then the horizontal thrust at J the height is = x90x20 2 x-52 2 = 4867 Ib. The theoretical length of base is tan 2 (45- that is, equal to or greater than, 72 KEINFOKCED CONCKETE CONSTEUCTION but for stability L = 1-^ = 1^x6 = 9 ft. Then, assuming the wall to be 9 in. thick (average) the weight will be 75x20x150 = 22501k The weight of earth on the base will be whlj = 90 x 20 x 9 = 16200.1b. The mean centre of gravity of loads will be 16200x|_ 2250 + 16200 from inner edge of base. The resultant of the thrust and loads will then cut the base at x 20x4867 2250 + 16200 90 Ltos per cub ft FIG 96 h - -L-9'.O'- - FIG. 95. Diagram of horizontal and vertical pressures on reinforced concrete retaining wall like Fig. 90. FIG. 96. Horizontal pressure against given wall. FIG. 97. Vertical pressure on foundation of given wall. beyond the centre of gravity line, or 5'04 + l-76 = 6'8 ft. from inner edge of base. As this is outside the middle third of base it is evident that there would be tension at the inside edge which is not permissible. The base must therefore be extended, SPECIAL CONSTRUCTIONS 73 the simplest and best method being to make the distance from the point where the resultant cuts the base to the front edge C.Q half the distance from resultant to inner edge, thus, - = 3*4, LJ and 6'8 + 3'4 = 10'2 ft. total width of base, projecting 10-2 -9- 1-2 ft. in front of wall as in Fig. 97. The maximum pressure on found- ation will then be - -- x2 = 36181b. or TGI tons per square foot. An example may now be taken for calculations like Fig. 93. In this case, instead of 1 ft. run, the whole length of one bay must be considered. Assume the same general dimensions and external conditions as before, and the counterforts 10 ft. centre to centre. The wall will not now be a cantilever but equivalent to a piece of floor slab with one free edge, and the counterfort will be a cantilever in the form of a tee beam. Total pressure at \ height of wall = i x 90 x 20* x 10 x -52* = 48,670 Ib. Weight of wall = (^ x 20 x 10)150 = 17,500 Ib. Weight of counterfort = (\- x 9 x A)150 = 10,125 Ib. Weight of earth = 90x20x9x10 = 162,000 Ib. Mean e.g. of loads = (17500 x 9) + (10125 x x 9) + (162000 x |) 17500 + 10125 + 162000 = 5 ft. from inner edge of base. The resultant of thrust and loads will then cut the base at t x 20 x 48670 17500 + 10125 + 162000 = ft bey nd the C ^ lme or 5 + 1'7 = 6*7 ft. from inner edge of base as in Fig. 98. The base should therefore be extended to 6' 7 + -~- = 10 ft. The maximum & pressure on foundation will then be 17500+10125 + 162000 10x10 or 1'69 tons per sq. ft., as in Fig. 99. 74 REINFORCED CONCKETE CONSTRUCTION Bending moment on cantilever tee beam = 48670 x x 12 = 3,893,600 Ib.-in. Assuming three 1 in. rods as reinforcement 100 x 2-3562 *>= 84x7 - =Q ' 4 3 x 9'45 - 2 x 7 = 2-81 in. 2x9-45-7 2 x 3,893,600 x 9'45 84 x 7(2 x 9-45 - 7) (105 - 2'81) 3,893,600 2-3562(105-2-81) 103 ' m Counterforts ^ 9" Chick \\ /O'.O 'centres >\ Three I'roa/s FIG 98 FIG. 98. Horizontal pressures against given retaining wall like Fig. 93. FIG. 99. Vertical pressures on foundation of given retaining wall like Fig. 93. FIG. 100. Completed design of retaining wall with reinforcement. It will be sufficiently near in most cases to take the bending moments on the base between counterforts as ^r, w being the weight of earth per foot super on base and / the width of base. SPECIAL CONSTKUCTIONS 75 For the vertical wall W the total load will be the thrust and I will be the height, and the bending moment at the bottom will \V7 be -^p If the top of wall is stiffened sufficiently to form a girder carrying full stress it will be designed as described in the section on bins. The maximum bending moment on base wl 1 (20 x 90) (9 x 12) 2 16" 12x16 =109>3501b,m. The effective depth of base slab = 8 in. and the reinforcement 0'9 per foot wide = 3 x 0'3 = 0'9 sq. in., then r = n - -5- = *01, ra = 15. LA X o k = v/001 2 x 15* + 2 x -01 x 15) - -01 x 15 = '42 ,^-f-o.e. / 109350 lAKrcn" = -01xl2x8*(-86) =L6 '^ 2 x 109350 -42xl2x8x(-86) but this is making no allowance for the projection on inner edge of base. The maximum bending moment on vertical wall WZ 48670 x (20 x 12) = 24= 10x24 = 48670 lb,m. The effective depth (thickness) at bottom of wall = 6 in. and the reinforcement per foot, width = 3 x 0'3 = 0'9 sq. in. then k = V00125 2 x 15 2 + 2 x -0125 x 15) - '0125 x 15 = 0-453 = 10>62 2 x 48670 586 -453xl2xffl(-849) 76 BEINFOKCED CONCEETE CONSTKUCTION The wall slab must also be calculated in the other direction in order to obtain the horizontal reinforcement. The maximum WZ bending moment will be B e = ^ where W = earth pressure on a(J wall varying from maximum at bottom to nil at top of wall, and I = span or centre distance of the counterforts. In the present , . . 4623+4867 . , case taking the bottom foot of wall w=- ~ = 4745 Ib. a and B e = 4745x 2 Q xl2 = 28470 Ib.-in. The effective depth of wall = 6 in. and the reinforcement may be ^ in. rods, 6 in. centres or 2 x 0'2 = 0*4 sq. in. in the bottom foot of wall. Then r = = '006, m = 15 k = v /(-006 2 x 15 2 + 2 x -006 x 15) - '006 x 15 = 0'34. 28470 -006 x 12xffl 2 x 28470 C = -34xl2x6(-89) Similarly the spacing may be found at any point in the wall. The complete design may now be drawn out as in Fig. 100. Bins. Bins, bunkers, hoppers, pockets, silos or cells, as they are variously called, are modified retaining walls, they are boxes, circular or rectangular, generally of considerable height in pro- portion to their diameter, built to contain grain, coal, cement, ore, or similar material. When the width is not less that half the depth the pressure at any point of the depth will be found exactly in the same way as against a retaining wall ; with less width in proportion to the depth the friction against the vertical sides will become appre- ciable and require to be allowed for. To enable the necessary calculations to be made, the weight of the material per cubic foot and the natural slope or angle of repose, are required. SPECIAL CONSTEUCTIONS 77 Material. (w) Ib. per cub. ft. (6) Angle of Repose. Ore . 100-150 35-45 Slag (small) 100-112 45 Coal (house) 50-55 36-40 (gas) . 56-58 36-40 (Welsh) 70-75 36-40 Coke 25-35 35-45 Shingle 88 39 Sand (river) 110 30 (pit) 110 30 Cement (Portland) 85-95 25-35 Wheat 50 25 Barley 39 26 Oats . 28 24 Malt . 33 22 Fig. 101 is the vertical-section of a coal bunker to carry heavy coal say 75 Ib. per cubic foot with provision for surcharge, which should always be made. It is assumed that the length in the other direction is such that the centre is unaffected by the tying in of the ends. The pressure per square foot at the top will be nil, increasing downwards until at the bottom of the vertical side it is equal to wh cos 2 0. Upon the sloping sides of the bottom, lying at an angle of 45, the pressure per square foot at the upper edge will be wh cos 6 and at the lower edge wH cos 6. The pressure per square foot on the flat bottom will be If the top edge of bunker is stiffened by a flange or girder so that the pressures are transmitted to the ends, then one-third of the total thrust will be taken by the top edge and two-thirds by the bottom edge, the upright portion being subject to a maximum bending moment of B = ^wh 3 cos' 2 6 occurring at a height of $h from the bottom. Mr. E. F. Etchells has given a simple series of formulae for coal hoppers as follows : Horizontal thrust at J height, in tons per foot run, coal level .,, ,, Height in feet 2 with the top = - . 240 If surcharged to the full angle, thrust = 78 EEINFOECED CONCEETE CONSTEUCTION If the sides are tied in, horizontal thrust at top J of above, and at bottom f of above. tvh cos FIG FIG. 101. Vertical section of coal bunker with diagrams of pressure. FIG. 102. Diagram of pressures on high bin or bunker of same horizontal measurements as Fig. 101. FIG IO2 Maximum bending moment on upright = Thrust x i Height. When the width of bin is less than half the depth the greatest SPECIAL CONSTRUCTIONS 79 pressure per square foot against the side will be given by the formula Aw where p = maximum pressure against side in Ib. per square foot. w = weight of material in Ib. per cubic foot. P = perimeter of bin in feet. A = area of bin in square feet. tan = coefficient of friction of material against wall = say from to J and the depth (d) in feet from the surface to point of maximum pressure is A d = P tan tan 2 (46 - | the pressure at the top will be zero increasing gradually to maximum at this depth, then remaining constant to the bottom. On the horizontal base the maximum pressure (q) per square foot will be q = wd. If the bottom slopes at angle 6 the pressure per square foot on it will be q sin 0. As an example, a square bin may be taken of the same hori- zontal measurement as Fig. 101 but a height (h) of 30 ft. with coal as before. mi_ 7x7x75 on/< ,i , Then p = is r = -= r = 394 Ib. per sq. ft. P tan 7 x 4 x j __ A __ 1*1 _1Q-*Jff ,/,- W'TttTftW- P tan tan 2 (45 - = 1 q = wd = 75 x 19-5 = 1462'5 Ib. per sq. ft. On the sloping bottom p = q cos 45 = 1462*5 x '7 = 1023'75 Ib. per square foot. On the horizontal bottom ^ 2 = g = 1462'5 Ib. per square foot. These pressures are shown graphically on Fig. 102. Arches. Arches in reinforced concrete are subject to the 80 KEINFOECED CONCEETE CONSTEUCTION same principle of stress as when built of other material, 1 but as their construction admits of a greater intensity of stress in tension this point must receive special attention. If the abut- ments of an arch are not rigid the arch becomes a beam with the minimum depth where the greatest bending moment occurs, and it is therefore essential that a reinforced concrete arch should have rigid abutments although the material can be designed to resist tension. The curve of thrust must be drawn upon the elevation of the arch, as with other materials, and the maximum stresses in tension and compression must be provided for in the design. Fig. 103 shows an arch formed of two circular arcs, - 12 - -H FIG IO4- FIG. 103. Curve of thrust on arch. FIG. 104. Section at crown of arch showing reinforcement. under a load distributed uniformly over the horizontal span, and Fig. 104 a section at the crown of arch. Under this condition we know that the curve of thrust will be a parabola and it may therefore be drawn in without any preliminaries ; but there are various possible lines of thrust according to the points taken for them to pass through at the crown and skewbacks. Nature chooses that line of thrust which will, on the whole, give the l See Paper on "The Stability of Arches," by Henry Adams. "Trans, 0. & M.E.S.," 4 Feb. 1909. SPECIAL CONSTKUCTIONS 81 minimum stresses, and although we may endeavour to find it by trial we cannot always succeed, particularly when moving loads have to be taken into account. In the present case we may assume it to pass through the neutral axis at the crown wl* and at the skewbacks. The thrust at the crown will be O7* where w = load per foot run, / = span of line of thrust, r = rise of ?7?/** line of thrust, equivalent to the -^ of a flanged beam. The curve of thrust should pass through the neutral axis of the rib and the maximum thrust on the concrete will then be W -r- where W = total thrust at each point of the curve and A = the A. area of concrete above the reinforcement + 14 times the area of the steel. In nearly all practical cases a reinforced concrete arch has to be designed for a rolling load in addition to the dead load of the structure. It is usual also to provide for an external distributed load of say 1^ cwt. per foot super. A rolling load, say a traction engine, may bring a load of 10 tons on one point, and the position where it will cause a maximum distortion of the line of thrust may be taken as about one-fourth of the span, but both these loads will not occur at the same time. The loads are often transmitted from the surface of the roadway to the arch ring by means of vertical pillars, and the arch ring will consist of a thin shell with deep ribs at intervals. Consider one of the arch ribs as in Fig. 105 loaded as shown. Then by calcula- 19*25 10*25 tion the sum of the loads at A = - + 10 x - = 12*065 tons - r_ 1 Q'95 ^1 "7^ and at B - + 10 x ^p=17'186 tons. Set down the load ^j 42! line 1 to 8 in Fig. 106, and mark off the calculated reactions, giving point 9. Select any point horizontally from 9 and draw vectors to the points on the load line, and parallel with these vectors, across their respective spaces, draw the funicular polygon ACB in Fig. 105, producing the lines across spaces 1 and 8 to intersect in a point on the mean centre of gravity line. Bisect the depth of arch ring on this line at E, then in Fig. 107 6 82 KEINFOKCED CONCEETE CONSTKUCTION set up FG = DE and at any convenient distance from it set up HJ = DC. Produce G J and EH to meet in K. Then mark off on HJ the heights of the funicular polygon ACB, join to K and produce to cut FG, thus obtaining magnified ordinates to the curve of thrust AEB which passes through centre of depth of arch on the mean centre of gravity line. The maximum stresses will Roadway ; 2c#e. per ft j sup x sty centres \ of r/(>s < ; FIG ' Section a-a FIG IO8 FIG. 105. Reinforced concrete arch with ribs and pillow supporting roadway for rolling load. FIG. 106. Vector diagram for Fig. 105. FIG. 107. Diagram for raising line of thrust to required height. FIG. 108. Section of arch rib showing reinforcement. occur across space 7 where the thrust is 33*2 tons with an eccentricity of 1 ft. \\ in., hut the thrust may be taken as 35 tons, as the weight of rib has not been allowed for in the pre- vious working. The arch may be treated as a column with a section as shown in Fig. 108. SPECIAL CONSTRUCTIONS 83 Then area of steel = 1 2 x '7854 x 6 = 10'6 sq. in. Area of section = 22 x 10 = '220 sq. in. Equivalent area (A) = 220 + 14 x 10'6 = 368 sq. in. Section modulus (Z) = (J- x 27 x 12 x 27) + ( x 14 x 10'6 x f i 2 ) = 2770. The stresses on the two faces are , W Wx f ^^ ~Z~ (35 x 2240) 35 x 2240 x 13*5 368 2770 = 213 382 = 595 Ib. per sq. in. compression on the loaded side and 169 Ib. per sq. in. tension on opposite face, but as tension is pro- duced it is advisable to work by the formula for doubly rein- forced beams, as the formula -r-^r does not appear to be suitable A. Li for reinforced concrete when tension occurs. The equivalent area of the section = (12 x 27) + 14(5'3 + 5'3) = 472'4 sq. in. 35 x 2240 Therefore thrust = VWOTT- = 166 Ib. per sq. in. The maximum allowable compression on the concrete to resist the bending moment = 600 - 166 = 434 Ib. per sq. in., and the maximum allowable tension on the steel = 16000 + 15 x 166 = 18,490 Ib. per sq. in. The bending moment B = 35 x 2240 x 13*5 = 1,058,400 Ib.-in. Then by the formulae for doubly reinforced beams i* /e.o K oxf /i 2x12(3x5*3 + 24x5-3) _"] * = (5-3 + 5-3)^1 + - i 5(5 . 8 + 6 . 8y = 10 in. 10 x 1058400 i x 10* x 12 + 15{5'3(10 - 3)* + 5'3(24 - 10) >2 [ = 450 Ib. per sq. in. 94. - 10 = 450 x 15 ^JQ^ =9450 Ib. per sq. in. 10 3 c, = 450x 15 =4725 Ib. per sq. in., so that the design will be suitable. Chimney Shafts. Chimneys in reinforced concrete were at 84 KEINFOECED CONCEETE CONSTBUCTION first made with so little taper as to be practically in the form of cylindrical pipes and were most unsightly. There have been some more recent examples with a considerable amount of taper, to their manifest advantage from an aesthetic point of view. There are two points connected with their design in which they differ from other structures in reinforced concrete. The first has to do with the question of wind pressure and difficulties arise first from the great height making it important to determine accurately the normal pressure to be allowed for and next from the form making the effective pressure uncertain. Those who have studied the subject of wind pressure are aware that within certain limits it varies as the square of the velocity, so that until the wind reaches the velocity of a gale the pressures are only trifling. The following table shows the various de- scriptions of wind with the velocities and corresponding pressures against a plane surface perpendicular to its direction. Description. Velocity in Miles per hour. Approximate i Corresponding Pressure Ib. per sq. ft. Barely perceptible wind 2* h Light breeze . 5 * Pleasant breeze 7* 1 Good breeze 10 I Strong breeze 15 u High wind 20 2 Half gale 30 4* Strong gale 40 8 Whole gale 50 m Great storm 60 18 Hurricane 80 32 Violent hurricane 100 50 In the discussion on a paper upon " The Stability of Chimney Shafts" read before the Society of Engineers in 1887, the writer called attention to the variation of wind pressure at different heights caused by the resistance offered to its motion by buildings, etc., upon the ground. The experiments of Sir B. Baker also showed that the pressure of the wind at one time was not equally diffused over a large area, and that it might be SPECIAL CONSTKUCTIONS 85 as much as 40 Ib. per square foot over a small portion of a structure while at the same time the average pressure over the whole did not exceed 24 Ib. per square foot. These two con- siderations show that a working formula for wind pressure should combine the elements of width and height. An empirical formula designed by the writer for this purpose is log p = 1-125 + 0*32 log h - 012 log w where p = ultimate wind pressure in Ib. per square foot necessary to be allowed for against a plane surface normal to the wind. h = height of centre of gravity of surface considered above ground level in feet. w = width in feet of part to be taken as one surface. The following table shows the figures given by this formula for various widths and heights ; Fig. 109 shows the curves of pressure given by the formula. Width in ft. Height in ft. 5 10 20 50 100 200 500 150 54-6 50-3 46-3 41-4 38-1 35-1 31-4 100 48-0 44-2 407 36-4 33-5 30-8 27-6 50 38'4 35-4 32-5 29-1 26-8 247 22-1 20 287 26-4 24-3 217 20-0 18-4 16-5 10 23-0 21-1 19-5 17-4 16-0 14-8 13-2 2 18-4 17-0 15-6 13-9 12-8 11-8 10-6 MULTIPLIERS FOR ANGLE. 10 20 30 40 50 60 70 80 90 sin 174 342 500 643 766 866 940 985 1 sin 2 0303 117 250 413 587 750 884 970 1 When the exposed surface is not perpendicular to the direc- tion of the wind, allowance must be made for what may be 86 BEINFOECED CONCEETE CONSTEUCTION termed " slipping off," the effective pressure being reduced by the multipliers given in the above table according to the angle. The sin is used for obtaining the normal pressure on an inclined surface and the sin* for obtaining the effective pressure in the same direction as the wind. The additional curves marked Rogers Field and Thos. Stevenson are based upon formulae by those engineers which take account of variation in height of object but not width. They appear to be about a mean of those given by preceding formula. Mr. E. Fiander Etchells of the London County Council Architect's Department, has recently given a formula for 20 40 6 Lfos per sq ft. to be allowed for /n calculat/oris FIG IO9 FIG. HO FIG. 109. Diagram showing variation of wind pressure according to height and width. FIG. 110. Effective pressure on circular chimney. variation of wind pressure to be allowed according to the width and height of the object, as follows : where p = equivalent uniform wind pressure acting over whole surface, exposed, in Ib. per square foot. h = height of top of structure above level of ground in feet. l> = breadth of part exposed to wind pressure in feet. SPECIAL CONSTEUCTIONS 87 The curve produced by this formula for a width of 50 feet has been plotted upon Fig. 109 for comparison with the others. A circular chimney stack will not come under the last table owing to the surface being curved and therefore presenting all the angles at one time. The multiplier or coefficient for a cylindrical surface is variously given by different authors as follows : Kankine = '5 Prof. Hutton = *66 Wilson ='55 Gaudard ='666 Borda ='57 Bresse ='78 Sir B. Baker = '57 Adams = '7854 The principle involved in obtaining this latter constant is shown in Fig. 110. Then the average pressure on the wind- ward side will be the pressure of the wind per square foot on a normal plane multiplied by the summation of the squares of the sines of all the angles from O c to 90. or 2(psin 2 . . . 90)='5p or total result against the diametrical plane = * '5p = *7854p. a It should be noted that the square of the mean of several figures is not the same as the mean of the squares : for example, the square of the mean of 2, 4 and 6 is 16 ; while the mean of the squares of 2, 4 and 6 is 18f. In the present case the mean of the sines is 0'627, the square of the mean 0*3931 and the mean of the square 0'5. The opposite extreme of coefficient for wind pressure on circular chimneys appears to be that given in Lamb's " Hydro- dynamics," p. 87, where the resistance is given as zero "in the absence of friction and under the critical velocity at which dis- continuity takes place ". As a reinforced concrete chimney shaft has little weight it is necessary to tie it well into the foundation by hooking the vertical rods under the horizontal rods of the base, which should be well extended on all sides so that it will not overturn. The height of the centre of pressure of the exposed surface of a circular tapered chimney shaft will be h= -oWr ~^\~' where tJ^iJ + Cij 88 EEINFOECED CONCEETE CONSTEUCTION h = height of centre of pressure of wind, H = total height, D = outside diameter of base, d = outside diameter of top all in feet. When the allowable stresses are 600 Ib. per sq. in. on the concrete in compression and 16,000 Ib. per sq. in. on the steel in tension the thickness of chimney may be found by the formula 0'24M 0'4W , ,, , -065M '"055W , I > an d the total area of steel ---- ~ where o n > ~ O 2 O Cr G W = the weight of chimney above the section under considera- tion in Ib. M = the bending moment due to wind about this section. C = the compressive stress in the concrete in Ib. per sq. in. r = the inside radius of the shell in inches. As the bending moment reduces in proportion to the distance from the base the reinforcement would be reduced as the chim- ney rises. Calculations by the above formula would be made at say 20 ft. intervals to ascertain the proper allowance. An example may be taken for calculation, say chimney stack 120 ft. high, 6 ft. outside diameter at the top, and 8 ft. 6 in. outside diameter at the base. Foundation base 20 ft. square, bottom of foundation 12 ft. below surface of ground. 120(8-5 + 2x6) KaKKf . ' 3(8-5 + 6) - and log p = 1-125 + 0'32 log 56'55 - 012 log ^^ = 1-125 + 0-561 - 0-103 = 1-583 or p = 38-28 Ib. per sq. ft. or the total pressure on windward side of chimney = 120 x *^? x 0-7854 x 38'28 & = 26,160 Ib. and M = 26160x56-55x12 = 17750000 Ib.-in. Weight of chimney with average thickness of 6 in. = 1586-5 x 150 = 237975 Ib. Then thickness of chimney = 0'24 x ^ .^ + 0'4 x = 3-51 + 3-52 = 7-03 in, or say 7 in. thickness at base, SPECIAL CONSTEUCTIONS 89 . 17750000 237975 Area of steel = '065 x - '055 x --- = 42-73 -21-81 = 20-92 sq. in. or say f in. rods at 6 in. centres. The strength of this construction may be calculated as follows. The equivalent area of section shown in Fig. 111 = FIG. 111. Cross-section of circular reinforced concrete chimney showing neutral axis. (102* - 88 2 ) + 14 x 22 = 2397 sq. in. 237975 Therefore thrust (c) = 9007 = 99 Ib. per sq. in. The maximum allowable compression on the concrete to resist the bending moment (C) = 600 - 99 = 501 Ib. per sq. in., and the maximum allowable tension on the steel = 16000 + 15 x 99 = 17485 Ib. per sq. in. The distance from centre of section to neutral axis by the for- mula in Marsh and Dunn's manual of Keinforced Concrete, R ~ * 1067+c y= - = - -; - = 21 in. 1067 + c 1067 + 99 90 BEINFOKCED CONCKETE CONSTEUCTION and n = 51 -21 = 30 in. 6 = 0%59, d = 0-59x100 = 59 in. x = 2 in. A = 18 x -4417 = 7-9 A, = 32 x -4417 = 141 Then by the formula for doubly reinforced beams _ 30 x 17750000 " i x 30 s x 59 + 15 { 7-9 (30 - 2) 2 + 14'1 (100 - 30) 2 } = 321 Ib. per sq. in. *-*/-- ~t ** JLvyw Ov/ ^ x-v^*. ^ t 1 = 321x15 OQ = 11235 Ib. per sq. in. SO 2 c s = 321 x 15 '^^ = 4494 Ib. per sq. in. oU and the design therefore appears to be suitable. The upper stages of the shaft would be calculated in a similar manner. It would appear that the strength of the chimney shaft might have been calculated by taking it as a column under direct load and bending moment, and deducting the value of the central core. The method would be as follows : Equivalent area of concrete and steel to edge of reinforce- ment = ?(102 2 - 88 2 ) + 14 x 22 = 2397 sq. in. Total area of base = x 102 2 = 8171 sq. in. Section modulus - {(J x 8171 x 102) + i(15 - 1)23 x - x 88 = 104180 + 7580-66903 = 44857 in. units. W M 237975 17750000 44857 = 495 Ib. per sq. in. compression 297 ,, tension. SPECIAL CONSTKUCTIONS 91 The tension given is that upon the concrete and the concrete equivalent of the steel. It would represent a tension on the steel of 297 x 15 = 4455 Ib. per square inch, but this differs so considerably from the previous calculations that the method does not appear to be applicable. CHAPTEK VI. EFFECTS OF EXCESSIVE HEAT ON CONCRETE AND REINFORCED CONCRETE. TALL CHIMNEY CONSTRUCTION. EFFECTS OF FROST ON CONCRETE. Effects of Excessive Heat on Concrete and Reinforced Concrete. The subject of the fire resistance of reinforced concrete has from time to time been fully discussed, and the general conclu- sion arrived at is that the material is an excellent fire resistant. This was brought into evidence most forcibly during the great San Francisco fire, for while there were in that city on the Pacific seaboard no buildings which were entirely of reinforced concrete, there were many in which the floors and beams were of that material, and these stood both the earthquake shocks and fire admirably. At the International Fire Service Congress at Milan in 1906 the fire resistance of reinforced concrete was fully discussed, and the following important resolutions were passed : " That the Congress considers that no reinforced concrete construction should be permissible in buildings intended to be fire resisting, unless the aggregate be most carefully selected and applied in such a manner as to give substantial protection to all metal parts." " That it is advisable where reinforced concrete is intended to be fire resisting, that every portion of the metal rods or bars contained therein be covered by not less than 2 in. of concrete, the aggregate of which must be able to pass through a sieve having a mesh of no more than 1 in. in diameter, and that Portland cement of great fineness only be used." "That where feasible all external angles should be rounded." " That any angle-iron needed for mechanical protection should be held in position independently of the concrete, ' ' 92 EFFECTS OF EXCESSIVE HEAT ON CONCKETE 93 These resolutions are interesting coming as they do from a conference of men who are chiefly interested in the protection of life and property, and including the chiefs of the Fire Brigades of all the principal cities of Europe. The British Fire Prevention Committee have carried out a series of important tests with reinforced concrete floors, beams, etc., with most satisfactory results, it being found that no appre- ciable effect occurred by the combined application of fire, in some cases up to 2000 F., followed by water for five minutes from a steam fire engine. Prof. Ira Woolson, M.E., in a paper read in 1906 before the American Society for Testing Materials, describes a series of interesting tests which he made with a view to finding out the thermal conductivity of concrete, and the effect of heat upon its strength and elastic properties. Some points from his paper are as follows : Composition of Specimens. Prof. Woolson' s test specimens were composed of a 1 : 2 : 4 mixture of Portland cement, sharp sand, and f in. clean broken stone, both trap rock and lime- stone being employed. In addition to these, other specimens were made in the same proportions, using clean | in. quartz gravel instead of the broken stone, and, in another set, clean boiler cinders. Slow Setting Cement. The cement used was a very slow- setting cement, taking seven hours forty minutes for initial set, and fourteen hours ten minutes for hard set. Tensile Strength of Cement Used. Tensile strength for neat cement at 7 days = 710 Ib. ,, 3 to 1 concrete ,,7 ,, = 160 ,, ,,28 =286 The concrete was mixed moderately wet. Age of Specimens. The specimens varied in age from two months to two years. The Two Months Blocks. These were left in moulds thirty- six hours, then submerged in water for seven days, then allowed to stand in air for seven weeks, being occasionally sprinkled. 1500 F. Heat Test for Two to Five Hours. The heat test was as follows : Three and five hours were chosen for the times of heating 94 KEINFOKCED CONCEETE CONSTRUCTION the large specimens, and two and three hours for the 4 in. cubes, and the temperature in the furnace in which these speci- mens were placed was raised to 1500 F. (average) ; the furnace was raised to this temperature (after the blocks had been inserted) in forty to sixty minutes. After heating, the specimens were allowed to cool slowly. Conductivity (interior Heat Recorded) Results. The gravel specimens were the only ones that attained an interior tempera- ture equal to the furnace temperature. It is surprising to note that cinder came next to gravel in the amount of interior heat recorded, .for cinder concrete is supposed to be an effective fire resistant. Prof. Wool son says : " These tests prove that 2 or 3 in. of concrete properly mixed, tamped and set, will resist a fierce conflagration for hours without permitting a serious temperature rise upon the opposite side." Effect of Heating on one Side only. The strength of the 6 in. by 6 in. by 14 in. specimens heated on one face is in marked contrast to those heated on all sides, and shows that under that condition the concrete retains a large part of its strength even after five hours of exposure to a temperature of 1500 F. Loss in Strength due to Excessive Heat. The limestone lost about 50 per cent of its strength when heated two hours, and the trap about 55 per cent. The difference was probably accidental, for it is generally supposed that trap is superior to limestone in resisting heat. They both lost 68 per cent of their strength in five hours, when heated on all sides with no radia- tion permissible. In a paper read by Mr. Frank B. Gilbreth before the American Society of Mechanical Engineers (1910), entitled " Fires and their Prevention " the author urged the use wher- ever possible of concrete and reinforced concrete in order to afford fire protection. The National Board of Fire Under- writers in Chicago have been carrying out some severe tests on various building materials, including reinforced concrete, and have subjected this material to a very high temperature for a period of two hours, after which water was applied. The tests were carried out by Mr. Kichard L. Humphrey, who says : EFFECTS OF EXCESSIVE HEAT ON CONCEETE 95 " The fact brought out most clearly by these tests is the low rate of heat transmission of Portland cement concretes and mortars. This is one of the desirable qualities in buildings in- tended for ' fireproofing purposes '. One of the authors, in a paper read before the Concrete Institute, 1 described a series of tests carried out by him in order to ascertain 'the effect of excessive heat upon concrete and steel reinforcement. A few extracts from this paper are here given : Effect of High Temperature upon Concrete. " In order to obtain some reliable data regarding this important matter the author determined to carry out two series of tests, one dealing with concrete that had only had a short set, the other with concrete that had had at least two months' set. Twenty-four briquettes were made and placed in a boiler flue where the temperature averaged 850 to 900 degrees F. The briquettes were as follows : 3 neat briquettes, placed in flue for 14 days. 3 _ 28 ,; 3 sand and cement (3 to 1) briquettes in flue for 14 days. 3 ,, ,, ,, ,, 28 3-2f in. cubes, placed in flue for 14 days. 3-2} 28 3-2} ,, (3 to 1) sand and cement, in flue for 14 days. 3-2} 28 At the same time that the above briquettes were placed in the boiler flue a similar number were placed in water. The experi- ments were carried out for the author by Messrs. G. & T. Earle, Ltd., cement manufacturers, Hull. The results were as follows : Tests of Cements Used in Experiments. Cubes and bri- quettes in water for 7 and 28 days, after being in air for 14 days. " l Reinforced Concrete Chimney Construction," paper by E. R, Matthews, Concrete Institute, January, 1910. 96 KEINFOKCED CONCKETE CONSTRUCTION 7 days Ib. 28 days Ib. Neat tensile strain, 1 in. section, moulds filled by thumb pressure 620 740 Neat tensile strain, 1 in. section, moulds filled by brass rammer ....... 720 850 Sand tensile strain, 1 in. section, moulds filled by brass rammer 310 460 tons. tons. Neat compression strain, 2f in. cube, moulds filled by brass rammer 26-5 33-6 Sand compression strain, 2f in. section, moulds filled by Klebb hammer 11-5 141 Tons. Average. 3 neat cubes in air, 14 days ; in flue, 14 days j 50-0 1 49 '4 tons, on 2| in. cube (4.q.^ 3 neat cubes in air, 14 days ; in flue, 28 days & u i 547/ 52-6 3 sand cubes in air, 14 days ; in Jii-nl 1Q.Q flue, 14 days 114-6/ 77 ?7 ?J 7? ,1Q.fJ>. 3 sand cubes in air, 14 days ; in flue, 28 days f 10 OA (l3-8[ U47J 14-0 Ib. 3 neat briquettes, in air 14 days ; in flue, 14 days r880^ 1900/ 890 Ib. on 1 inch section 3 neat briquettes, in air 14 days ; in flue, 28 days r 955^ \ 990^ U,080J 1,008 3 sand briquettes, in air 14 days ; in flue, 14 days f 110 ) w 113 3 sand briquettes, in air 14 days ; in flue, 28 days f 85 1 ]ioo[ U30J 105 Temperature, 850 to 900 F. Fire-box Test : The author then had a fire-box made of concrete composed of 3 parts of ironworks clinkers (screened EFFECTS OF EXCESSIVE HEAT ON CONCKETE 97 and broken to pass through a 1 in. ring), 2 parts pit sand, and 1 part cement. After a set of thirty days this fire-box was used, the result being that three or four very fine cracks appeared, which were undoubtedly caused by the sudden extraction of the moisture in the concrete. Apart from these cracks, the concrete remained in good condition for two months, in spite of the fire- box being used daily. The face of the concrete which came in actual contact with the fire daily was just as good at the ex- piration of two months as on the day the fire-box was first used. The cement used in this and the block tests described later was supplied by Messrs. Robson & Sons, of Hull, particulars of which are as follows ; April 15. April 23. April 29. Neat cement at 7 days . 550 Ib. 647 Ib. 631 Ib. 5 M 28 ,, . 752 821 805 3 sand ; 1 cement at 7 days . 191 207 215 3 1 28 . 269 286 250 Le Chatelier test, 2*5 mm. 0'75 mm. 3*0 mm. Residue on 76 x 76 sieve 0'6 per cent 0'5 per cent 0'4 per cent 180 x 180 sieve . 17-0 16-0 ., 15-0 ANALYSIS OF CEMENT. Loss on ignition Insoluble residue Silica Alumina . Oxide of iron . Lime Magnesia . Sulphuric anhydride Alkalies . 1'36 per cent. 0-52 21-17 7'68 3-64 62-92 1-21 1-18 0-32 The quantity of water used in the mixing of the concrete was 10 per cent. The fire-box, was made on 4 June, and left in the open until it was used on 3 July. Its construction is shown in Fig. 112, and it may be briefly described as follows : It consists of reinforced concrete bottom and three sides, with J-in. iron plate top supported by three J in. diameter round bars. The slab forming the bottom of the fire-box is 4 ft. 6 in. sq., 6 in. thick, and reinforced on the underside by ^ 7 98 KEINFOBCED CONCEETE CONSTRUCTION in. diameter round bars and clips ; these have a covering of concrete on the underside of 1^ in. Upon this slab the three sides of the box are erected ; these are each 6 in. thick and 2 ft. 8 in. in height, and are reinforced in the centre with T 7 ^ in. diameter bar's. At the back of the box is a 4 in. flue. The 6 * 1 I B * |< ----- Section. Plan. FIG. 112. fire is supported by | in. diameter loose bars, which have spaces of 2 in. between them, and which rest on three f in. diameter round bars. It should be observed that this test is a most severe one, as the actual fire came daily in direct contact with the concrete. Block Tests. The author next determined to test concrete that had had two months' set and upwards, and for this purpose he had three blocks of concrete made, each being reinforced ; the sizes and aggregates of the blocks were as follows : Sizes of blocks. 12 in. x 12 in. x 4 in. thick, 12 x!2 x4 12 x 12 x 6 Aggregates. The first two blocks were composed of 3 parts of ironworks clinkers (screened and broken to pass though a 1 in. ring), 2 parts of pit sand, and 1 part Portland cement. The 6 in. block was composed of 3 parts of broken stone (broken to pass through a 1 in. ring), 2 parts of pit sand, and ] part Port- land cement. EFFECTS OF EXCESSIVE HEAT ON CONCEETE 99 Reinforcement. The blocks were reinforced with T 7 F in. bars and clips, and each block was an exact reproduction of a portion of a floor panel. Ten per cent of water was used in mixing the concrete ; the blocks were kept in air for two months and one day, and were then placed in boiler flues on 31 July. 1909, the temperature (average) being about 1250 F. during the whole of each day ex- cept Sundays, and falling at night and on Sundays to 260 F. at lowest. They were kept in these temperatures for twenty-one days, and when taken out of the flues and carefully examined the blocks were found to be quite unaffected by this great heat, except that one of the blocks, which was 4 in. thick, showed a slight hair crack on the face. No sign whatever of damage or cracking occurred on the other blocks, and they were in as good condition as when placed in the flues. The reinforcement in the blocks was also quite unaffected. In addition to these blocks, the author had other pieces of concrete 5 to 1, and of the same composition, but which in one case had had an eighteen months' set and in the other a six months' set placed at the back of the fire-box before referred to, and resting on the fire-grate just below the flue-opening. These blocks came daily into contact with the actual fire in fact, they were in the fire and on being taken out at the expiration of fourteen days the condition of the concrete was not satisfactory ; the blocks were not reinforced. The concrete fell to pieces on handling, and it is scarcely to ba expected that it would do otherwise under such a terrific test. The flue tests are, in the author's opinion, more satisfactory and reliable, as the actual flames did not reach the concrete. These block and fire-box tests were carried out for the author by Mr. A. Mitchell, one of the partners in the firm known as The Chain Concrete Syndicate, of Leeds. They were carried out at the works of this firm at Pudsey. Further Tests and Examinations. The author then deter- mined to obtain some information regarding the condition of the concrete and reinforcement in an existing reinforced-concrete chimney, and he is greatly indebted to Mr. H. K. G. Bamber, F.I.C., of the Associated Portland Cement Manufacturers, who 7* 100 KEINFOKCED CON0KETE CONSTKUCTION kindly supplied him with some most useful information on this subject. Mr. Bamber informed the author that in order to ascertain if concrete deteriorated through the effects of heat, he inspected on several occasions the face of the concrete shell inside the re- inforced-concrete chimney at the works of his firm at Northfleet, and he failed to observe any signs of deterioration. Not con- tenting himself with this, he subjected the ash in this chimney on various dates, to an analysis, and compared this with an analysis of the ash taken from the base of a brick Custodis shaft, also at his firm's works at Northfleet. The comparison is most interesting ; it will be noticed that there is very little difference in the percentage of insoluble residue present, which residue would, of course, include any portions of sand that might, from deterioration, be coming away from the inside of the inner shell of the concrete chimney. The result of Mr. Bamber' s analyses is set forth in the table on page 101. Sevan's Works Chimneys, samples of flue dust taken from the Custodis (brick) and Weber (reinforced concrete) shafts : These residues are also periodically examined microscopically, and no perceptible difference has as yet been found. Again, Messrs. G. & T. Earle, Ltd., inform the author that in order to ascertain the effect of heat upon concrete they placed a block of concrete (which had had several months' set) in one of their boiler flues for some months, the temperature in the flue being about 700 F. The block came out quite un- affected. Effect of High Temperatures upon Steel Reinforcement. The reinforcement in the blocks which the author has previously re- ferred to was, as already stated, none the worse for being placed in a temperature of 1250 F. for twenty-one days ; it was in precisely the same condition after the test as before. Then Mr. Bamber very kindly had a small hole cut for the author in the base of the inner and outer shells of the rein- forced-concrete chimney at Northfleet (see Figs. 113 and 114) for the purpose of exposing a portion of the reinforcement. These were made just over the flue opening where the heat would be most likely to affect the concrete. The result was most satis- EFFECTS OF EXCESSIVE HEAT OF CONCKETE 101 factory, the steel being in as good condition as when first in- serted in the concrete. Date, 1908. Weber Shaft. Custodis Shaft. Remarks. October 17 13-00 19 14-10 20 14-60 17-90 21 16-30 22 16-70 23 17-06 17-20 24 13-68 2G 15-90 Examined residue 27 16-40 both shafts exactly 28 16-10 18-62 the same. 29 16-84 30 16-90 18-44 31 1770 November 3 16-66 1708 4 15-40 5 12-60 7 13-60 9 16-90 10 16-90 18-50 11 13-80 12 14-80 13 16-80 13-80 16 15-30 17 14-80 12-30 18 12-46 19 12-26 20 13-60 12-90 21 18-00 23 16-20 24 16-20 16-68 . 25 19-80 * 2o 16-90 27 15-64 16-70 28 16-04 30 19-40 Decc nber 1 19-66 17-14 Examined residue 2 2148 from both shafts 3 16 -Oo fine silica as from 4 14-66 16-36 slurry. 5 1620 7 1886 8 17-20 17-30 Mr. Bamber describes his experiment thus : " I enclose you two photographs which will illustrate the experiments. The 102 BE1NFOKCED CONCRETE CONSTEUCTION one with the square opening showing the hole at the back re- presents a photograph taken of the outside surface of the chimney, and the wall in which the smaller hole appears re- FIG. lie FIG. 114. presents a 4| in. concrete lining inside the chimney, there be- ing a 4 in. air space between the outer shell and this inner lining. A hole was cut through the inner lining for convenience during inspection, and in doing so we came across a portion of the steel reinforcement in this concrete. This has been in place for EFFECTS OF EXCESSIVE HEAT ON CONCKETE 103 nearly two years, and has been subjected to a temperature inside the chimney of 500 to 600 F., and about 200 to 300 F. on the outside of the lining, i.e. in the air space. The concrete was carefully chipped away from the reinforcement, and upon care- ful examination, personally, I found that the concrete was ad- hering tightly to the reinforcement, which was in splendid condition. I marked the reinforcement lightly with the chisel, exposing the clean metal, and the white spots on the photograph are the reflection of light upon this metal. This second photo- graph was taken with a magnesium light close up to the inner opening. This seems to be an excellent example of the use of reinforced concrete under very trying conditions, and I would add that the internal examination of the chimney, which was done by means of a powerful searchlight thrown upon the in- terior surface from the bottom, showed this surface to be in as perfect condition as the outside." Author's Conclusions. The author's experiments led him to the following conclusions : 1. That neat cement behaves better under great heat than out of it. The average compressive strength of 2f in. cubes placed in flue for twenty-eight days, after having remained in air for fourteen days, was 52*6 tons on the cube compared with 33'6 tons when placed in water for a similar period ; the tensile strength per square inch of the briquettes being 1008 Ib. com- pared with 850 Ib. in the water test. 2. That concrete (3 parts standard sand to 1 part Portland cement) if not well set behaves very badly under heat. The average tensile strength of briquettes 1 in. section (3 to 1) placed in flue for twenty-eight days, after being in air for fourteen days, was 105 Ib. compared with 310 Ib. at seven days, and 460 Ib. at twenty-eight days in water. 3. That if the concrete has had at least a two months' set before heat is applied a temperature of 900 F. will not affect it in the least. This might be taken as the safe temperature in reinforced-concrete chimneys. 4. That the 3 to 1 specimens in these tests giving such poor results point to the necessity of having no voids whatever in any concrete work, it being well known that 3 to 1 briquettes 104 BEINFOECED CONCEETE CONSTEUCTION made of standard sand contain a considerable quantity of air spaces. 5. That only allowing the specimens fourteen days before subjecting them to the heat is far too short a period in actual work. The greatest advantage is obtained by letting the heat get at the concrete after the longest possible time has been given for the cement to set. 6. Concrete mixed with 10 per cent of water (which should be the maximum in work of this class) would contain only about 1 per cent of free water after a two-months' set. Heat should not be applied to concrete until the latter has had a two-months' set ; a longer set, say three months, would be preferable. The block tests carried out by the author were a most reli- able guide as to the behaviour of concrete under conditions similar to that existing in a reinforced-concrete shaft. They were even subjected to a much more severe test than the inner or outer shell of a reinforced-concrete chimney would ever be subjected to, and in spite of that they came out unaffected. They were exposed to the heat on all sides, while the concrete in a chimney would only be attacked on one side. The tempera- ture varied from 1250 F. during the day, to 260 F. during the night, and they were kept in these temperatures for twenty-one days. If concrete will successfully withstand the severe test here indicated, it will much more easily withstand the conditions to which it would be subjected if forming the lining of a reinforced- concrete shaft. 2. Reinforced- concrete Tall Chimney Construction. In the United States, over 1000 reinforced-concrete chimneys have been erected during the past eight years by one firm alone the Weber Company of Chicago. In the British Isles not more than a dozen examples are to be found. The authors intend to give a brief description of two typical American chimneys, and two British. Before doing so, however they would enumerate the advantages of using this material in chimney construction, which are as follows : TALL CHIMNEY CONSTKUCTION 105 (a) Economy in cost (there being a saving of 25 to 30 per cent as compared with brick shafts). (6) Saving of space. (c) Less weight than brick shaft. (d) Greater stability. (e~) Freedom from repairs. (/) Kapidity of execution of work. a FIG. 115. These advantages were set out in a paper read before the Concrete Institute in January 1910. l Typical Examples : The typical examples which the authors propose to refer to are : 1 " Reinforced-concrete Chimney Construction," by E. R. Matthews, Concrete Institute, January, 1910. 106 KEINFOBCED CONCRETE CONSTKUCTION 1. Chimney at Tacoma, Wash., U.S.A. 2. Chimney at Butte, Mont., U.S.A. FIG. 116. 3. Chimney at Messrs. Lyle & Sons' Works, London, E., 4. Large chimney at Northfleet, Kent. The latter is illustrated in Figs. 115 and 116. TALL CHIMNEY CONSTRUCTION 107 Illustrations are also given of a re- inforced - concrete chimney at In- dianapolis, Ind., U.S.A., and of one at New Bedford, Mass., U.S.A., the former being 200 ft. high and 12 ft. internal diameter, the latter 200 ft. high by 8 ft. 6 in. in diameter. 3. Effects of Frost on Concrete. Many experi- ments have been made in order to ascertain the ex- tent to which excessive frost in- jures freshly mixed concrete, and with a view of discovering if concrete frozen and again thawed before setting, is permanently re- duced in strength, and if so, to what extent. With regard to the latter point, it may be stated that until recently it was generally be- ios BEINFOKCED CONCBETE CONSTEUCTION FIG. 118. FIG. 119. TALL CHIMNEY CONSTRUCTION Particulars Relating to Four Typical Chimneys. 109 O> 1 |<- - 7.' 6" IN EARTN Scale; I Inch -8 Feet FOOT Ifr? . . . . ? Jf FEET FIG. 150. Culvert at Bromboro' Port. Fig. 153 represents a large cul- vert erected by the British Reinforced Concrete Engineering Co., at Bromboro' Port. It is a good illustration of what can CONCKETE IN ENGINEEKING WORKS 151 152 EEINFOKCED CONCKETE CONSTKUCTION be done in this material. Messrs. William and Segar Owen were the engineers. " Concrete and Constructional Engineering. FIG. 152. FIG. 153. Blaenavon Culvert. This is shown in Fig. 154. It has been CONCRETE IN ENGINEEEING WORKS 153 ~\ I I T- 1 I I I I 1- FIG, 154. 154 KEINFOKCED CONCKETE CONSTRUCTION constructed by the same firm for the Blaenavon Urban District Council, South Wales ; it is 4 ft. 9 in. in diameter, and the thick- ness varies from 6 to 3 in. It has a square base, and is rein- forced in the manner shown. Kilton Culvert for N.E.R. Co. This is an important culvert constructed on the Kahn system by the Trussed Concrete Steel Co., and designed by the late Mr. W. J. Cudworth, M.Inst.C.E. It is 446 ft. in length, and of the section shown in Fig. 155. The photos Figs. 156 and 157 also illustrate the culvert. The work was completed in 1908. Fig. 158 shows the timbering, and Fig. 157 the test load being applied. The aggregate used consisted of 3 parts of a mixture of gravel and crushed whin stone, f in. gauge, with sufficient sand to fill interstices, to 1 of cement. Expanded metal has been used very considerably in conduit construction, Figs. 159 to 163 representing its use in a variety of such ways. The Lock Woven Mesh System has also been adopted in many cases, Fig. 164 representing an 8 ft. Penstock 4600 ft. long, which is carried out on this system. CONCRETE PIPES. In America these are used very considerably, sometimes plain, but generally reinforced. For water mains the Bonna pipe is chiefly used : this is too well known to need description. Bonna pipes have recently been used for the construction of a rising main for the Norwich City Council, Mr. A. E. Collins, M.Inst.C.E., being the engineer. This new sewage pumping main is 36 in. internal diameter, and about 4500 yards in length. The work has been executed by the Columbian Fireproofing Co., the cost of the pipes including specials being upwards of 9000. Each pipe weighs about 1^ tons ; the work has been well tested, and is in every way satisfactory 1 (see Fig. 166). On the Wabash Eailroad, U.S.A., reinforced concrete pipes have been made of sections varying from 2 to 4 ft. 2 1 " Reinforced Concrete Rising Main on the Bonna System at Norwich," by E. R. Matthews, " Concrete and Constructional Engineering," December, 1910. 2 " Reinforced Concrete on the Wabash Railroad, U.S.A.," by Matthews and Cunningham (1909-1910). CONCEETE IN ENGINEEKING WOKKS 155 FIG. 155. 156 KEINFOKCED CONCBETE CONSTBUCTION CONCEETE IN ENGINEERING WORKS 157 m 158 REINFORCED CONCRETE CONSTRUCTION FTG. 158. CONOKETE IN ENGINEEKING WORKS 159 FIG. 160. EXPANDED STEEL & CONCRETE SEWER FOR THE CALICO PRINTERS ASSOCIATION LT? at Reddish Ya/e, near Stock port. 7 -/V' '61 Expanded Stcet in Baof Ground. FIG. 161. 160 REINFORCED CONCRETE CONSTRUCTION FIG. 163. CONCEETE IN ENGINEEBING WOEKS 161 11 162 REINFOKCED CONCRETE CONSTEUCTION FIG. 165. CONCKETE IN ENGINEEEING WOBKS 163 " Concrete and Constructional Engineering. FIG. 166. 11 164 KEINFOECED CONCEETE CONSTEUCTION Fig. 167 illustrates a 4 ft. type. The reinforcement consists of woven-wire fencing. FIG. 167. The quantity of material required to make a 4 ft. pipe, 3 ft. in length is : Portland cement . . . . 1 barrel = 376 Ib. = 3'8 cub. ft. Sand . . . . . .0-3 cub. yd. Stone or gravel (capable of passing through ^ in. ring) . . .0*61 cub. yd. Wire fencing 34 in. wide . . 28 lin. ffc. \ in. corrugated steel bars (3 ft. long) 22 lin. ft. A number of English firms now manufacture reinforced concrete pipes, one of the best-known firms being Messrs. Ellis & Sons. Figs. 168 and 169 illustrate some of the pipes manufac- tured by this firm. SEWAGE TANKS. Tank at Ripponden. The material has also been used very largely in the construction of sewage disposal works. Fig. 170 represents a sewage tank at Eipponden, designed by Mr. F. Gordon, engineer to the Soyland Urban District Council. The work has been executed by the Yorkshire Hennebique Contract- ing Co. Reinforced Concrete Sewage Disposal Works. Sewage disposal works constructed by the British Eeinforced Concrete CONCKETE IN ENGINEERING WORKS 165 Fia. 163. 166 EEINFOECED CONCEETE CONSTEUCTION CONCRETE IN ENGINEERING WORKS 167 Engineering Co. are shown in Fig. 171. It will be noticed that there is a pair of liquefying tanks and filters, the former being covered. Fia. 170. SWIMMING BATHS. Many excellent works of this class might be referred to ; the authors will draw the attention of the reader however to two only, which may be taken as typical examples. Salford Corporation Public Baths. These -are represented in Fig. 172. They were designed by Messrs. Mangnall & Littlewoods, architects, Manchester, the work being carried out by the Fram Fireproof Construction Co. The reinforcement is expanded metal, arranged as shown in the section. The dimensions of these baths are : length 75 ft., width 30 ft., depth 4 ft. 4 in. to 7 ft. 4 in. The ladies baths, also of reinforced concrete, are somewhat smaller, being 50 ft. by 25 ft. The walls in both baths are buttressed. South Shields Public Baths. These are shown in Fig. 173. They are constructed throughout of reinforced concrete, and 168 REINFOKCED CONCBETE CONSTBUCTION CONCKETE IN ENGINEEKING WOEKS 169 FIG. 172. 170 BEINFOBCED CONCKETE CONSTEUCTION CONCEETE IN ENGINEEBING WORKS 171 were designed by Mr. J. H. Morton, F.R.I.B.A., architect of South Shields. The swimming pond is 101 ft. long by 30 ft. wide, it is 7 ft. at the deep end, and 4 ft. at the shallow end, with gallery, steps, and a subway, all of concrete reinforced by expanded metal and steel rods. The pond bottom was made 1 ft. 6 in. thick on account of the bad ground met with. The walls are 9 in. thick with 1 ft. 9 in. buttresses placed at 10 ft. centres ; the buttresses are continued to form beams to support the gallery steps. The treads of the latter are 4 in. thick, and the risers 3 in. reinforced by expanded metal. The inside of the pond is lined with 3 in. of fine concrete and Calender's bitumen sheeting, and finished with interlocking tiles. OTHER FORMS OF MUNICIPAL ENGINEERING WORK. Cantilever Platform. The Bridlington Corporation have recently erected a reinforced concrete platform as illustrated in Figs. 174 and 175. This was designed by the borough engineer (one of the authors) and is being used as a fish stand. It is 50 ft. in length, and 9 ft. 6 in. in width, over all measurement. It is carried by reinforced concrete brackets which are 5 in. in thick- ness, of 4 to 1 concrete, and are spaced 6 ft. 2 in. centres. The platform diminishes from 8 to 4 in. in thickness, and is connected to a concrete wall which has been built at the back of the masonry wall of the harbour. The platform and wall are of 6 to 1 concrete. The reinforcement consists of f in., T 7 F in., and in. rods, together with special clips and stirrups, and the work has been executed by the Chain Concrete Syndicate of Leeds upon their system. The aggregate consisted of sand and fine sea-gravel or ballast capable of passing through a -f in. ring, and the contract price was 114 12s. 6d. (this was exclusive of excavation, and cost of iron railings). On the completion of the work in December, 1910, a test load of 2 cwt. per square foot was applied. Public Shelters. Eeinforced concrete lends itself admirably to work of this description. One of the authors has designed for the Bridlington Corporation two reinforced shelters ; these 172 REINFORCED CONCEETE CONSTRUCTION " Concrete and Constructional Engineering. FIG. 174. CONCEETE IN ENGINEEEING WOEKS 173 are shown in Figs. 176 and 177, and are fully described in a paper read by him and which appeared in the " Transactions of the Society of Engineers " for August 1910. The shelters have each " Concrete and Constructional Engineering." FIG. 175. an open front, reinforced concrete retaining walls at the back and ends, and reinforced concrete roof supported by reinforced concrete beams. Structures of this type can be erected 25 per cent cheaper than when the retaining walls are of brick or mass 174 REINFORCED CONCEETE CONSTRUCTION CONCKETE IN ENGINEEEING WORKS 175 concrete, and the roof is of the old-fashioned steel joists and concrete type. Underground Lavatories. The material also lends itself to this class of work. One of the authors has erected an under- 176 EEINFOECED CONCEETE CONSTEUCTION ground lavatory at Bridlington, 1 where reinforced concrete has been used in the construction of the retaining walls and roof (see Fig. 178) and a considerable saving has been effected thereby. The work was carried out by the Chain Concrete Syndicate. He is now erecting two other public lavatories on the south side of the harbour. The material has been used with great advantage for various other classes of municipal en- gineering work in this country, such as for highway bridges, retaining walls, boundary walls, sea defences, piles, dams, etc. Its use for some of these pur- poses is here illustrated. The authors are of the opinion that reinforced concrete will be extensively used in muni- cipal engineering work in the future seeing that the advan- tages of using this material are becoming so much better known. " Trans. Soc. of Engineers," Aug- ust, 1910. Paper by E. R. Matthews, on " Reinforced Concrete Retaining Walls". CONCKETE IN ENGINEEEING WORKS 177 ftoad Lere/ BOROUGH OF GUILDFORD. E.S.& CONCRETE RETAINING WALL G.H Mason Esq. A.MI.C.E., Guildford. Engineer Ground Level W 10 Expanded Steel ff i^ap^iraS- l^/WJO Expanded Steel .Piles under Buttresses FIG. 179. FIG. 180. 12 178 EEINFOECED CONCBETE CONSTBUCTION FIG. 181. W8 Expanded Stee/ \ PP- m I* -i $r 1 Surfa.ce of Water N 62 Expanded Steel 8'-0" [_ '1 f .' *A Tie Rod \ j | /,V; * | fjt^ J-i ji^^^ fM^ -^ =i=^^ ^;^fL^i^4'^^ fr '! ..* LOCH LEVEN WATER POWER. TYPE SECTION OF CONDUIT. FIG. 182. CONCRETE IN ENGINEERING WORKS 179 BlRKENHEAD CORPORATION GAS WORKS RIB EXPANDED STEEL & CONCRETE RETAINING WALL T. 0. Pater son Esq. MICE. Birkenhead. Engineer. N4 Rib Expanded Steel N?2Rib Expanded Steel ELEVATION. PLAN. I00'~- CROSS SECTION. FIG. 183. FIG. 184. 12* 180 EEINFOECED CONCEETE CONSTBUCTION H.M.LAND COMMISSION OFFICES. DUBLIN. EXPANDED STEEL-CONCRETE RETAINING WALL. /i :-.! 'I A J Howard Pent land Esq F.R IB A. Dublin, Architect. . : l JLJ '^ \ 1 v| /^ t- - / / 1 '1 i / ^ M S H 9'-o" "-nH'XlMHHMStal *' 1 .''l \ 1 -f^~. _ %: i 1 1 i ; : | V i Vjg^W!!^SJ ^ 1 w*** ' ; 'iilu;::jij *.^ -t-i^-r gg3j^25* TTr** 1 v|. v: .r^ >.:; ' FT PLAN. 'vS--!:v:M CROSS SECTION. FIG. 185. EXPANDED STEEL & CONCRETE RETAINING WALLS. AT PONSBOURNE PARK. POTTERS BAR. P.K.^LLEN ESQ -Architect. lOrnamertt*/ Stonework \ ty Mess" Pu//>am 12 N 3 /4dia r Rods to each Bin U? 6? Expanded Steel ^ GRAIN SILOS,- ENLARGED SECTION OF ONE BIN FIG. 245. ENGLISH EXAMPLES 233 GRAIN SILOS. FIG. 246. 234 KEINFOBCED CONCEETE CONSTKUCTIOtf hoppers, when full, carrying about 90 tons of coke, the capacity of the water tank being about 100 tons. The centre columns vary in size from 20 in. by 20 in. to Expanded Stee/ ' 4*- J-e" >L- FIG. 247. in. square ; the side columns being 15 in. square. The bases for the columns vary in size from 5 ft. square to 8 ft. 3 in. square. ENGLISH EXAMPLES 235 o LU i LU UJ a CO 85 Q. Q. O o LU O CO LU O o LU CL O O o UJ O O Lu 1 236 REINFORCED CONCRETE CONSTRUCTION FIG. 249. FIG. 250. ENGLISH EXAMPLES 237 II -0 FIG. 252. 238 KEINFOECED CONCEETE CONSTEUCTION 't AMEEICAN EXAMPLES 239 Retaining Walls and Boundary Walls. The material has been used very extensively for this purpose both in this country and in America. American Examples. In a paper which appeared in the August, 1910, " Transactions of the Society of Engineers," l the author describes briefly one or two important reinforced con- C ROUND L/A 14-11/2. FIG. 255. crete retaining walls, American examples. Two of these are illustrated in Figs. 257, 258. They represent very large hollow retaining walls constructed l " Reinforced Concrete Retaining Walls," by E. R. Matthews. " Jour. Soc. of Engineers," August, '1910. 240 KEINFORCED CONCRETE CONSTKUCTION in reinforced concrete on the Atlanta, Birmingham and Atlantic Kailroad. These walls were designed by Mr. Alex. Bonnyman, chief engineer, who writes regarding them : " By the contract prices for plain concrete and reinforced concrete, we figure that there is a saving in the reinforced walls of about 25 per cent." FIG. 256. The wall shown in Fig. 257 is 61 ft. in height. English Examples. Some examples have already been given by the authors in the chapter on Municipal Engineering. Others will now be given. AMEKICAN EXAMPLES 241 242 REINFORCED CONCRETE CONSTRUCTION Fia. 258. ENGLISH EXAMPLES 243 Boundary Wall, West Hartlepool Cemetery. This is con- structed in reinforced concrete. It was designed by the Borough CEMETERY AT HARTLEPOOL. EXPANDED STEEL & CONCRETE WALL. H. C. Crummack. Esq AM/C.E., Engineer. < - fO'-O" /yo/ots^fSS?. ->! 1 J8'i irrm\- ' WNX ELEVATION PLAN. FIG. 259. CEMETERY. WEST HARTLEPOOL. CROSS SECTION T EXPANDED STEEL - CONCRETE WALL Nelson F.Dennis Esq MICE.. Engineer. f --- /2-0 ___ ELEVATION. N 9 Expanded Steel --12 0" J PLAN AT A A. - -j'-o- - J CROSS SECTION. FIG. 260. Engineer, Mr. Nelson F. Dennis, A.M.I.C.E., and is illustrated in Figs. 259-262. 16* 244 EEINFOKCED CONCRETE CONSTKUCTION FIG. 261. ENGLISH EXAMPLES 245 Cross-sections through the wall are shown in Figs. 259 and 260. The reinforcement used was expanded metal. Retaining Wall at Birkenhead Gas Works. This wall was designed by the engineer, Mr. T. O. Paterson, M.Inst.C.E., and expanded metal was used as the reinforcement. The wall is 159 ft. in length, and 23 ft. in height above ground level. This is an interesting piece of reinforced concrete work. Retaining Wall at Guildford. This wall is carried on piles and is reinforced with expanded metal and plain bars. Buttresses FIG. 263. are built at 5 ft. 6 in. centres, these are 9 in. in thickness. The wall tapers from 9 to 6 in. in thickness, and was designed by the Borough Engineer, Mr. G. H. Mason, A.M.I.C.E. The Patent Indented Steel Bar Co. have done some excel- lent work of this class, a few examples of which are now given : Wall for Coal Store at Hereford Gas Works This wall acts 3,8 a cantilever attached to a horizontal slab, without the assist- 246 REINFORCED CONCRETE CONSTRUCTION ance of counterforts. The wall was designed by the Indented Steel Bar Co., Ltd., and encloses a coal store. It is 10 ft. 6 in. high and 150 ft. in length, and is illustrated in Fig. 263, which shows the arrangement of the reinforcement. The roof princi- pals are carried by buttresses spaced at regular intervals. Wall at Royal Insurance Offices, Piccadilly. This wall was designed by the Indented Bar Co., and built under the supervision of Mr Alex. Drew, M.I.Mech.E. The additional area gained by building a reinforced con- crete wall in a case of this kind may be gathered by glancing at the section shown in Fig. 264. If this wall had been of mass concrete it would have been about 9 ft. thick at the base, whereas it is only 2 ft. 6 in. This wall was con- structed in 1908, it is 24 ft. 6 in. in height, 9 in. in thick- FIG. 264. ness at the top, and supports the heavy traffic of Piccadilly. Other illustrations might have been given, but space will not permit. REINFOECED CONCEETE STANDS. Stand at York Racecourse. This is an interesting piece of reinforced work ; it has been carried out on the Kahn system, and is illustrated by the accompanying drawings, and two photos. The structure consists of an approach, bridge, and stand. The approach road is carried by reinforced columns 10 in. by 10 in. reinforced by four f in. bars running from base to top of parapet. The bases for the columns are 2 ft. 6 in. by 2 ft. 6 in. by 6 in. thick, and are reinforced by six f in. bars, KEINFOECED CONCKETE STANDS 247 The parapet walls are 5 in. in thickness ; one parapet is 5 ft. 6 in. high, the other 4 ft. ; these walls are reinforced by f in. FIG. 265. FIG. 265 A. bars. The roadway is formed of reinforced concrete, 4 in. in thickness, the reinforcement consisting of ^ in. and f in. bars- 248 KEINFOKCED CONCEETE CONSTEUCTION GROUND LEVEL FIG. 266. FIG, 267, KEINFOKCED CONCKETE STANDS 249 The approach road is 15 ft. 2 in. in width between parapets. The bridge has a clear span of 74 ft. 9 in., with a 13 ft. 2-J in. headway. The height of the top of the bridge above ground level is 21 ft. 2-j- in. The whole structure is of reinforced con- crete. The stand is an interesting piece of work, the beams, deck- ing, ties, and supports being shown in Figs. 265 and 266. Reinforced Concrete Stadium. The reinforced concrete stadium at the Franco-British Exhibition is another excellent example of work of this class ; this was described in " Concrete FIG. 268. and Constructional Engineering," May, 1908. The structure is illustrated in Fig. 269. Reinforced Concrete Football Stand at Bradford. This is another good example of the use of this material in the con- struction of stands. The structure is illustrated in Fig. 270. The architect for this work was Mr. Archibald Leitch, M.LMech.E., and the contractors were Messrs. John Ellis and Sons, Ltd. ; the design of the structural members of the rein- forced concrete work and of the steel reinforcement were pre- pared by Messrs. F. A. Macdonald and Partners of Glasgow. Reinforced Concrete Stadium at Syracuse, U.S.A. This stadium has recently been built at the Syracuse University. It 250 KEINFOKCED CONCKETE CONSTKUCTION KEINFOKCED CONCEETE STANDS 251 252 EEINFOECED CONCEETE CONSTEUCTION *^K / ^ m sr ci *- t & CM SEA WALL CONSTKUCTION 253 is 670 ft. in length, and covers an area of 6J acres. It has a normal seating capacity for 20,000 with a possible seating capacity of nearly double this. CO The superstructure is supported by concrete columns, and main girders which are 2 ft. in depth by 1 ft. wide. 254 KEINFOBCED CONCKETE CONSTRUCTION The stairs, approaches, towers in fact, the whole structure is built in reinforced concrete, and is illustrated in Fig. 271. Sea-wall Construction. One illustration only will be given of the use of this material in the construction of sea-walls. The new sea-wall at Hornsea, Yorkshire, designed by Mr. W. T. Douglas, M.Inst.C.E., of Westminster, is a very good example. This is illustrated in Figs. 272, 273. The reinforcement used was expanded metal, 3 in. mesh. FIG. 273. The cliff wall averages 13 ft. 6 in. high, the foundation platform is 14 in. thick at the back tapering to 9 in. at the front. The counterforts are at 7 ft. 9 in. centres, and are 9 in. thick ; the face wall is 9 in. thick at the toe and tapers to 4-J- in. thick at top, where it returns to form a coping 1 ft. 6 in. in width, and 6 in. in thickness. Reinforced concrete has been used for a score of other useful engineering purposes, but space does not permit of the authors describing or illustrating these. CHAPTEK X. REINFORCED CONCRETE IN BUILDING CONSTRUCTION. NOT only is this material eminently suitable for use in the con- struction of engineering works, but it may be used with equal advantage in building construction, and has been used very ex- tensively for this purpose. The authors propose in this chapter to give typical examples of its use in all classes of buildings, and for a variety of purposes, including piles, foundations, columns, floors, roofs, beams, stairs, balconies, walls, partitions, retaining walls, etc. PILES. Coignet System. Reinforced concrete piles are a valuable substitute for the ordinary timber piles which are subject to deterioration. One of the first to recognize this advantage was Mr. Edmond Coignet, who made two reinforced piles in 1894 ; these were driven in connection with the foundations of the Generating Station of the Champs Ely sees, Levallois Perret, Paris. Their length was about 16 ft., and diameter 10 in., they were examined some time after having been driven, and were found to be in excellent condition. Many piles have since been driven on this system. The piles are concreted in a horizontal mould instead of a vertical one as in the case of some systems. Coignet piles are generally of a circular section, varying between 10 and 16 in. in diameter. Piling at Tobacco Warehouses, Bristol. The arrangement of the reinforcement is shown in Figs. 274, 275, which represent piling used in the foundations for a tobacco warehouse at Bristol, where 650 piles were driven. It was necessary that the piles should be of considerable 255 256 REINFORCED CONCEETE CONSTRUCTION length in order to reach a stratum of gravel situated at a depth of about 45 ft. below the surface. It should perhaps be mentioned that circular piles are easier to drive than square ones, and that as they have no sharp edges they are not likely to be broken by coming into contact with boulders. The area of the foundations which were required to carry the warehouse the authors are referring to, was approximately 215 ft. by 102 ft. ; the piles were calculated for a safe load of 56 tons each ; some of them were tested to 90 tons before being driven, without show- ing any sign of failure. The piles were 14 to 15 in. in diameter, with two flat surfaces of about 5 in. wide for guiding pur- poses in driving. The reinforce- ment consisted of a number of longitudinal bars of small diameter bound by a spiral wire, and the spiral was bound to the bars with annealed wire. Each pile was shod with a cast- iron shoe which was first placed inside the mould. The concrete was machine mixed, the aggregate consisting of sand and granite chippings. The piles were moulded on a flat sill, to which were bolted the two semi-circular detachable sides. The concreting operation was car- ried out horizontally, the frame- work being suspended inside the mould by the upper bolts. =., BUILDING CONSTRUCTION 257 The sides were removed as soon as the concrete had beun FIG. 275. FIG. 276. to set, the pile being allowed to season for a fortnight before re moving it from the sill. Each pile weighed about 5 tons. 17 258 KEINFORCED CONCRETE CONSTRUCTION Six weeks were required for the proper seasoning of the piles before the driving operation. Method of Driving. The piles were driven in the following manner : They were pitched by firmly securing them at about one-third of their length and gradually lifting them to their proper posi- tion ; the head of the pile was then fitted with a wooden dolly in order to prevent the ram from 1 injuring the concrete. The weight of the ram was 2 tons, with a drop of about 4 ft. The enormous strength of these piles is shown by the fact that some of them received over 2000 blows without injury. Two driving machines was used, and the work, when nearing completion, was also carried on at night ; in this manner it was possible to drive about 12 piles per twenty-four hours. The piles were driven in groups of six, and a reinforced con- crete cap was provided in order to evenly spread the load of the pillars supporting the floors. The weight on each cap is about 300 tons, and the caps are connected by reinforced concrete beams. The advantages of using reinforced concrete piles are that a pile of this description will carry about twice as heavy a load as that of a timber pile ; it can be driven to a much greater depth, and is practically indestructible. A timber pile of similar sec- tion may be less expensive, but considering the advantages of the reinforced concrete pile it is in the end most economical. The foundations for the Dundee Generating Station, and of many other important buildings, are on the Coignet system. The piling at Bristol above referred to was executed by Messrs. W. Cowlin & Son, contractors, Bristol, licensees of the Coignet system, the work, executed for the Bristol Corporation, being designed by, and carried out under the supervision of, the Docks Engineer, Mr. W. W. Squire, M.Inst.C.E. Paragon System. The British Reinforced Concrete Engin- eering Co., of Manchester, make a similar pile, except that it is octagonal in section, and sometimes square. These piles are made from 30 to 45 ft. in length, and are each capable of carry- ing a safe load of 50 tons. Fig. 277 represents one of such piles, the special feature of which is the helical reinforcement, BUILDING CONSTRUCTION 259 which is so arranged that a pile may be built up in sections, the heli- cals being sectionized. At certain distances are fixed frame hoops for keeping the longitudinal bars in place. Considere System. -The method of in- creasing the strength of concrete in compression whether in piles or columns by the intro- duction of helical rein- forcement was really invented by M. Con- sidere, and after re- peated independent tests has been officially recog- nized in the Regula- tions of France, Ger- many, and Austria ; detailed accounts of these tests on spiralled concrete may be found in the Report of the French Commission on the subject, as well as in the writings of Prof. Bach, Von Thullie, Morsch, and others. It has been conclu- sively proved that spiral reinforcement, in addi- tion to giving a much greater safeguard against the effects of bad workmanship, is, weight for weight, 21 260 KEINFOKCED CONCEETE CONSTKUCTION to 2'4 times more efficient than longitudinal rods and links, or ties of the usual type. A special feature of the Considere piles FIG. 278. is that in driving them it is not necessary to protect the pile with a sawdust-filled cap over the head, and a timber dolly. BUILDING CONSTRUCTION 261 M. Considere points out that driving them in the manner adopted FIG. 279. by him is more economical and efficient. The system is illus- trated in Figs. 278 to 281. 262 KElNFOKCED CONCRETE CONSTBUCTlON Hennebique Piles. These have been used chiefly in the construction of wharves and jetties, and have been referred to FIG. 280. in a previous chapter. They are square in section, the angles being splayed and the top of the pile is of a round section to admit of the application of a driving-cap. The reinforcement BUILDING CONSTKUCTION 263 consists of a longitudinal rod at each corner, wired together at intervals. PIG. 281. Simplex and Raymond Piles. These are the two piles used chiefly in America. The first is built in place, and is reinforced 264 BEINFOKCED CONCKETE CONSTKUCTION by a cylinder of expanded metal, the latter is reinforced by a round rod about 1 in. diameter which passes along its axis, and three f in. bars placed around the circumference. The " Simplex " pile is the patent of the Simplex Concrete Piling Co., of Philadelphia, Pa., the " Raymond " pile is the patent of the Eaymond Concrete Pile Co., of Chicago, 111. Columns, Beams, and Floors. These three portions of con- structional work are taken together, and the illustrations which are given show the connection which is made between the column, beam, and floor. The various systems previously described of reinforcement for piles, are also suitable for the construction of columns, and are largely used for that purpose. Columns, Beams, and Floors on the Coi^net System. A good example of the construction of columns, beams, and floors on this System may be found in the Tobacco Warehouse at Bristol previously referred to. Fig. 282 represents a view of the ground floor of this building. The doors are all fire-proof, and the walls of lifts are built in reinforced concrete. The stairs and landings are also built in this material, and the columns, beams, and floors. The floors are calculated for a superimposed load of 1^ cwts. per square foot. Another excellent example of the use of this System in building construction may be seen in the new Money Order Department for H.M. General Post Office, which is fully de- scribed in " Concrete and Constructional Engineering," 1910. The building was designed by Sir Hy. Tanner; the Con- tractors being Messrs. W. King & Son. Leslie's System. The system of reinforcement for columns invented by Messrs. Leslie & Company, Ltd., of London is clearly seen in Fig. 283. Leslie's system of beam and floor construction is also shown in Fig. 283. This system includes reinforcement with vertical hangers rigidly attached by links or rings to the main reinforcement. The whole of the steelwork is framed up completely as a unit, so as to be capable of inspection before concreting, and so that f BUILDING CONSTBUCTION 265 it may not be displaced when the concrete is put in place, There is complete truss action in beams constructed on this system. 266 EEINFOKCED CONCKETE CONSTEUCTION BUILDING CONSTKUCTION 267 Figs. 283, 284 represent the interior of a portion of a new factory at Messrs. Bryant & May's, Ltd., Bow, London, E., con- structed on this system, the architects being Messrs. Holman & Goodrham. The Chain Concrete Syndicate's System This has already been described and illustrated in the chapter dealing with Muni- cipal Engineering. The authors would, however, here insert a 268 KEINFOKCED CONCRETE CONSTRUCTION view of the inside of a factory at Cleckheaton, where the columns, beams, and floors have been constructed on this system, the architects being Messrs. Howarth & Howarth of Cleck- heaton. FIG. 285. Mr. E. P. Wells' System. Stuart's Granolithic Co., Ltd., have carried out a great deal of similar work on Mr. Wells' system ; some of the most interesting being the factory erected at Portobello, N.B., for Messrs. Schulze & Co., manufacturers of chocolate confectionery, and a factory at Hayes, Middlesex, for the London Orchestrelle Co., the Architect of which was Mr-. Walter Cave. The Eoyal School of Electricity at Chatham for the War Office, and a large factory near Edinburgh, are also examples of work on this system. Fig. 286 illustrates the Portobello building, and Fig. 287 the factory at Hayes. Expanded Metal Co.'s System of Floor Construction. Various methods of floor and beam construction are suggested by this firm, the reinforcement being Expanded Metal, with the addition of rods in the case of beams. Fig. 288 represents a floor slab carried by an offset in the wall. BUILDING CONSTKUCTION 269 Fig. 289 shows a slab carried by a corbel. Fig. 290 shows one carried by a chase. Fig. 291 illustrates various methods of inserting the rein- forcement in floor and beam construction. Figs. 292 and 292a represent the use of expanded metal in the construction of sea defences. British Reinforced Concrete Engineering Co.'s System. The accompanying drawings illustrate the method of placing the reinforcement in columns, beams, and floors on this system (see Figs. 244, 245, and 246). FIG. 286. Kahn System. The Trussed Concrete-Steel Co.'s system known as the Kahn System is well illustrated in the important work now being executed at the Wesleyan Methodist Hall, Westminster, S.W. Drawing No. 297 illustrates one of the main arched beams. The placing of the reinforcement is clearly shown. 270 EEINFOECED CONCKETE CONSTRUCTION FIG. 287. BUILDING CONSTKUCTION 271 ^-Expanded Metal Lath mo Tension Strip - I fa" mesh Expanded Steel Floor finish may be earned on Breeze Concrete Filling or on nailing strips as shorn Expanded Metal Lathing ''.- - .-.: v - Reinforced Concrete Beam Reinforced Concrete Beam -Expanded Metal Lathing ik'mcsh Expanded Sf.ee/ to be fixed when Plasterirx* is required for Concrete Encasing FIG. 291. Fia. 292. 272 KEINFOECED CONCKETE CONSTKUCTION BUILDING CONSTBUCT10N 273 __!' -J--JL II II ll d^U- T -r ={j-=. -.t -=*.-. Hi i 1 ! li I _U LL FIG. 293. 18 274 KEINFOKCED CONCEETE CONSTRUCTION FIG. 295. BUILDING CONSTEUCTION 275 n . . FIG. 265. 18 276 EEINFOECED CONCEETE CONSTEUCTION :t=^&~^= ti K Ei^fC^^t BUILDING CONSTRUCTION 277 Drawing No. 298 shows the beams carrying floor over Tea Room in the same building. The Architects for this important work were Messrs. Lan- chester and Rickards, London. Drawings Nos. 299 and 300 show the reinforced concrete columns, beams, and floors on the Kahn System supporting and forming the gallery of the Stoke-upon-Trent Town Hall, which has recently been extended. Hennebique System. The general arrangement of the rein- forcement in this system is shown in the diagram, Fig. 302a, which represents a reinforced column supporting a beam, details of a column, etc. The special feature in this system is the patent stirrups used. A great many excellent examples of work carried out on this system might be described ; illustrations of three, however, only will be given. Fig. 301 illustrates the R.C. arched beams and flooring at the building of the Yorkshire Mutual Garage Co., Ltd., Leeds. The beams have a span of 41 ft. Fig. 302 shows the columns and underside of ground floor in the new Almond Block, at Messrs. J. Rowntree & Co.'s Works, York. Fig. 303 represents the columns and underside of floor in the New Warehouse of the Carron grove Paper Co., Ltd., at Denny, N.B. The beams have a span of 34 ft. Patent Indented Bar Co.'s System. A good illustration of work carried out on this system may be seen in the case of the erection of Rawson's Factory, Leicester, where the footings, columns, beams, floors, and roof were built in reinforced con- crete. Mr. J. H. Simpson was the Architect. Foundations. The authors have already dealt with piled foundations, they will now briefly describe the use of this material in the ordinary foundations of buildings, and they will give several examples of the use of reinforced concrete for pur- poses of this kind. The material is employed in a variety of ways in foundation 278 KEINFOKCED CONCKETE CONSTEUCTION BUILDING CONSTKUCTION 279 280 KEINFOKCED CONCEETE CONSTEUCTION work. Where piling has to be resorted to, the tops of the piles are usually run into a reinforced beam, which connects the whole of them, and upon which the structure is erected. Some- times a beam of this description connects the tops of timber FIG. 300. FIG. 301. piles, but such an arrangement is never so satisfactory, for in time the heads of the piles rot, and the beam is therefore con- siderably reduced in strength. It is also occasionally necessary, on a doubtful foundation, BUILDING CONSTKUCTION 281 to construct a reinforced concrete raft or platform. One of the authors found it necessary to construct such a raft in con- nection with the foundations of a tall chimney at Bridlington. The concrete in this case consisted of a 5 to 1 mixture (5 of gravel to 1 of cement), and the reinforcement of 9 in. by 6 in. rolled steel joists, bolted together by means of cross joists 9 in. by 6 in. being secured to them. The chimney, which is situated at the Bridlington Electricity Works, is about 150 ft. in height above foundations, and is 9 ft. internal diameter, and built in brick. Foundations similar to this have been frequently put in in connection with the construction of tall buildings in Amercia, and the result has been found to be very satisfactory. The foundations of Sprecles Building, San Francisco (a nineteen storey building) is of this type. FIG. 302. A good example of a reinforced concrete raft to form the foundations of an important building in England, is seen in connection with the foundations of the Stoke-upon-Trent Town Hall Extensions, 282 BEINFOBCED CONCEETE CONSTKUCTION This is carried out on the Kahn System. The Patent Indented Steel Bar Co.'s method of reinforcing foundations for columns or walls is seen in Fig. 304. FIG. 302a. Fia. 303. The Expanded Metal Co. recommends the use of expanded metal in foundations on any of the lines indicated in the dia- grams on pages 284, 285. BUILDING CONSTEUCTION 283 f er 1 \ G-ff =4=i=4=l -I-I-4H- i ii i ii i i _J_.|~|.-H_|-j. =I=44+H= = r=ir = HrHH == T = -|-4-44-l-4-f M-Mr44H+f H-M- -4-1-4 -M-4 =1=1=4=1 -hH- -H44-J-44 -H4-H-K -l44^H-hf44HH-t -H-44H-I-*- =M 44=1=4=*= =h444=H=|= =144= HM-4H H-HH hH H-44=f tH- H= =j= i n =H44^J= f4=H=h<= f44H+l- =444H+fc =1,44=4=4=^ 284 KEINFOKCED CONCKETE CONSTEUCTION EXPANDED STEEL- CONCRETE WALL FOOTINGS SOME EXAMPLES. * i i _ _ _ *VT9>X ^ Steel N k -2'3"- 4 RESIDENCE OF SHYNES Eso Architect. Cork. ^ _ _ . _ 6-0 J, MESS'-FELTHAM & Go's FACTORY. TOWER BRIDGE ROAD S.E. GHCnckmay Esq. Architec. L. 46"- - - ~ STORE, BELFAST. H Keith Esq, Contractor \M62Exp d Stee/-:. : r<\> bQ _N30_Expanded_ Steef^A \ N 6?E*p* Steel I ; 5-0' *^ k-- - : "- - --H k- - 5 : | 5-0- FIG. 306. Walls and Partitions. A very great saving is effected by the use of reinforced concrete in the construction of walls and foundations ; a reduction in cost occurs, and also a saving of valuable space. The latter has been set out by one of the authors in a paper read before the Koyal Society of Arts, 1 in which he says : "The regulations (1906) of the City of Buffalo specify that the thickness of the reinforced concrete walls of a building shall be as follows : Where there is a basement : If one storey, 8 in. ; if two storeys, 10 in. ; if three storeys, 12 in. Where there is no basement : If one storey, 6 in. ; if two storeys, G and 6 in. ; if three storeys, 8, 6 and 6 in. What an improvement is, therefore, effected in respect to additional space obtained by using reinforced concrete. Assum- ing, for example, that a warehouse is 70 ft. in length, 33 ft. in width, and has three storeys, each of which is 12 ft. in height. 1 " Reinforced Concrete in Engineering and Architectural Construction in America," by E. R. Matthews, read before Roy. Soc. of Aits, March, 1908. 286 BEINFOECED CONCKETE CONSTBUCTION It has no basement. The thickness of the walls, if of reinforced concrete, would be, first storey 8 in., second 6 in., third 6 in. ; but if the walls were built of brick, then, taking say the city of Birmingham regulations as being a fair example of our British regulations, these being up-to-date, the thickness of the longi- tudinal walls of the warehouse under consideration would be as follows : First storey 22-J- in. thick, second storey 18 in. ; third storey 13^ in. ; the thickness of end walls would be : first storey 18 in. thick, second storey 18 in., third storey 13^ in. By using reinforced concrete, under the American building regulations, there would be an increase of floor area on the ground floor of 227 '48 sup. ft. made up as follows : Floor area with reinforced concrete walls, 71 ft. 8 in. by 35 ft. 5 in. = 2537*48. Floor area with brick walls, 70 ft. by 33 ft. = 2310*00. Increase of floor area on ground floor, 227*48 sup. ft. An increase of floor area would occur on the first floor of 211*5 sup. ft., as follows: Floor area with reinforced concrete walls, 72 ft. by 35 ft. 9 in. = 257 4*00. Floor area with brick walls, 70 ft. by 33 ft. 9 in. = 2362-50. Increase of floor area on first floor, 211*50 sup. ft. On the second floor there would be a saving in floor area of 133*13 sup. ft. Foor area with reinforced concrete walls 72 ft. by 35 ft. 9 in. = 2574*00. Floor area with brick walls 70 ft. 9 in. by 34 ft. 6 in. = 2440*87, a difference of 133*13. So that the total floor area saved by building the walls of reinforced con- crete instead of brick would be 572 sup. ft." Roof Construction. Most of the systems of reinforced con- crete floor construction already referred to are also suitable for roof construction, the bars or other reinforcement being usually of lighter section owing to the lesser weight that will come upon a roof than that which a floor would have to carry. It some- times happens, of course, that a flat roof will be required to carry quite as heavy a load as a floor, in which case it will be designed as a floor. A mansard and flat reinforced concrete roof are sometimes combined ; several good examples of this are to be found in New York residences. The Hennebique system has been introduced in several con- structions of this kind. BUILDING CONSTKUCTION 287 Then domes and arched roofs are occasionally constructed in this material. Two notable examples may be referred to, namely, the dome of a cathedral at Poti, Kussia, and that of the New Wesleyan Methodist Hall, Westminster. Illustrations of one, and a brief description of both of these are given. FIQ. 307. Reinforced Concrete Cathedral at Poti, Russia. The dome of this cathedral has been built on the Hennebique system. The whole building is in reinforced concrete, and has been fully de- scribed in ''Concrete Engineering" for August, 1910, published in Cleveland, U.S.A. A few particulars will be given regarding the construction of the dome only. The reinforcement of this consisted of tension and compression bars, and of stirrups in the ribs, the slabs between these ribs being reinforced by wire mesh reinforce- ment ; these slabs were 4 in. in thickness, and the ribs 10 in. deep on the outside. The space between the ribs was filled in with an insulating material, and the surface of the dome was covered with sheet iron. Dome of New Wesleyan Methodist Hall. This is illustrated 288 BEINFOKCED CONCRETE CONSTRUCTION by the drawing, Fig. 307 and is a good example of what can be done in reinforced concrete. The work is being carried out on the Kahn system, the reinforcement consisting of Kahn bars of various sections, but chiefly 1J in. T.'s, with angle irons, and metal plates of circular shape. This important work was designed by Messrs. Lanchester and Kickards, Architects, London. Roofs of Sawtooth Shape. A number of roofs of this class have been erected in reinforced concrete, and the material is eminently suitable for their construction. Expanded Metal in Arched Roof Construction. A good ex- ample of the use of expanded metal in arched-roof construction, occurs in the roof of St. Barnabas Church, Dalston, London. The views show the nave roofing in progress, and also the temporary timbering to dome. The architect for this work was Prof. C. H. Keilly, M.A., A.K.I.B.A., of Liverpool. Illustrations of reinforced concrete flat roofs have already been given. Stair Construction. Stairs are constructed in this material in a variety of ways. One of the authors is now constructing at Bridlington two flights of steps, each flight 8 ft. in width, and these are rein- forced in the manner shown on the accompanying section. A 1 : 2 : 3 mixture is being used, namely, 3 of gravel, capable of passing through a 1 in. ring, and 2 of clean sharp sand, to 1 of cement. The reinforcement consists of f in., % in., and f in. bars and patent clips. The steps have moulded treads, and are finished in non-slip carborundum concrete. The authors have described in the Chapter on General Engineering, the Stand at the York Race Course, where the various flights of steps, in fact the whole structure has been built in reinforced concrete, and should prove of interest to the reader. At the Stoke-upon-Trent Town Hall Extensions the rises in the gallery are formed in reinforced concrete (see Fig. 311). BUILDING CONSTEUCTION 289 FIG. 308. Fia. 309. 19 290 KEINFOKCED CONCEETE CONSTKUCTION The illustrations are self-explanatory. Many staircases have also been constructed on the Lock FIG. 310. FIG. 311. Woven Mesh System, the two methods usually adopted being shown in Figs. 312. BUILDING CONSTKUCTION 291 Balconies and Cantilever Platforms. These are often constructed in this material. The authors have already de- scribed in the chapter on Municipal Engineering, the canti- lever platform forming the Fish Stand recently con- structed at Bridlington. A good many other examples might have been given, particularly of works on the Hennebique System. A balcony recently con- structed at the Girls' High School, Bridlington, is shown in Fig. 313. It is an interesting piece of work, and was well tested before use. It was built on the " Wells' System of rein- forcement by Stuart's Granolithic Co., Ltd., the Architects being Messrs. Botterill, Son & Bilson of Hull. The Tallest Reinforced Concrete Building in the World This is illustrated in Figs. 314 to 320 and is known as Ingall's Building at Cincinnati, Ohio, U.S.A. The building is a sixteen- storey one, and has been fully described in "En- gineering News," 30 July, 1903, in which some of the illustrations here given have ap- peared. It is a remarkable structure, and the views show the building at various stages of its erection. 19 * 292 KEINFOKCED CONCKETE CONSTKUCTION BUILDING CONSTKUCTION Fig. 314 shows the lower six storeys in course of erection. Fig. 315 shows the construction of one of the floors. FIG. 314. Fig. 316 shows the construction of another floor. Fig. 317 shows some of the beams and columns. 294 EEINFOKCED CONCRETE CONSTRUCTION FIG. 315. FIG. 316. BUILDING CONSTKUCTION FIG. 317. Fia. 318. EEINFOECED CONCEETE CONSTEUCTION Fig. 318 shows other beams and columns. Fig. 319 shows the building nearing completion. Fig. 320 shows the completed structure. The engineers and contractors for this interesting building were the Ferro-Concrete Construction Co., of Cincinnati. The building is situated at the corner of Vine and Fourth Streets, and is owned by the Ingall's Eealty Co. The first floor is occupied by railway ticket and telegraph offices, stores, and entrance hall ; the second by a bank ; the whole of the top floors being in the occupation of the Western Union Telegraph Co. The Architects were Messrs. Elzner & Anderson of 18 E. Fourth Street, Cincinnati. The reinforcement is on the Eansome System, and consists of rods, stirrups, and hoops of twisted steel. Plain bars were used in the columns. The general contractors were Messrs. W. H. Ellis & Co., Cincinnati. The work was commenced in October 1902 and completed by the end of 1903. The building occupies a site, the dimensions of which are approximately 100 ft. by 50| ft., and the natural foundation consists of gravel and sand. The building has four hydraulic passenger elevators. The exterior face- work to a height of three storeys is of 4-J in. marble ; above this it is of glazed light-grey brick with terra- cotta trimmings. The columns are 16 to 33 ft. apart, centre to centre, and vary in size from 34 by 38 in. at the bottom to 12 by 12 in. at the top. CONSTEUCTION 297 FIG. 819. 298 KEINFOKCED CONCKETE CONSTEUCTION FIG. 320. CHAPTER XI. GENERAL NOTES. THE authors propose in this concluding chapter to deal with many matters which occur in the actual carrying out of rein- forced concrete work. Such points will be dealt with as, the finishing of concrete surfaces, the waterproofing of concrete, bonding of old and new concrete, effects of sewer gases on con- crete, choice of concretemixers, expansion joints, breeze concrete, action of alkali on Portland cement, the prevention of failures, erection and removal of forms, and other important matters. 1. Experienced Designer. They would first emphatically state that as reinforced concrete work is a speciality, the designing of structures to be erected in this material should be entrusted to those who have had experience with the material ; it is not suffi- cient for an engineer or architect to insert into his concrete slab or beam a certain amount of reinforcement, the amount being often a matter of guess-work, a thorough knowledge of what the slab or beam which has been designed is capable of doing is ab- solutely necessary. 2. Skilled Workmen. And not only should the designer be a man who thoroughly understands his work, but it is equally important that the placing in position of the reinforcement, and the supervision generally of the work, shall be entrusted to a competent foreman who has had experience in this class of work, and should not be left in the hands of an ordinary con- creter or bricklayer, as is so often the case. 3. Erection and removal of Forms. There are matters that require the greatest care. In connection with all reinforced concrete work the erection of the centres and forms is a large item compared with the total cost of the works. The center- ing should be of such dimensions, and so constructed, as to 299 BOO EEINFOECED CONCEETE CONSTRUCTION remain rigid during the laying and punning of the concrete. It should be so arranged as to permit of its easy removal. Pro- vision should also be made wherever practicable for splaying or rounding the angles of the concrete. It is advisable to lime- wash the centering before the concrete is filled in. The authors give several illustrations of how forms should be constructed. Fig. 321 represents the method of building forms for a 2 ft. sq. column. The angles are not splayed in this case. FIG. 321. Figs. 322, 323 show the centering for the reinforced concrete bridge near Teufen, Switzerland. Fig. 324 shows the timbering for the new retaining wall for the Kensington Borough Council designed and carried out by Leslie & Co., London. GENEEAL NOTES 301 Concrete and Conttntctwnal Engineering, FIG. 322. The removal of the forms should be done in a very careful manner. On no account should they fall with a crash, but should be taken down timber by timber. The main supports should always be left to the last. 4. Waterproofing of con- crete. Large numbers of experiments have been made from time to time to determine if possible the best means of rendering concrete watertight, that is, when the concrete is under water pressure on one side. In America the follow- ing method is often adopted. Concrete and Constructional Engineering. FIG. 323. 302 EEINFOKCED CONCKETE CONSTKUCTION Liquid asphalt is mopped on to the concrete, this forms a coat upon the surface of the unset concrete, the thickness of the asphalt varying from J to - in. This method is open to the objection that asphalt when exposed to the action of water has a very short life, and the authors do not recommend it. FIG. 324. Some engineers in America adopt the following practice : They have the face of the reservoir wall or dam rendered over with a semi-liquid mortar, composed of : 1 part Portland cement. 3 parts sand. -J part thoroughly slaked lime. When this is set, the face of the wall receives a coat of cement grout. The method recommended by Prof. Ira. 0. Baker l consists of the application to the concrete of a compound of alum and soap. This may give satisfactory results in a laboratory, but the authors do not think it can be relied upon in actual work. 1 " The Technograph and Contractors' Record," 23 Feb. 1910, p. 480. GENEKAL NOTES 303 "Watertight" concrete in their opinion can be obtained where a most careful selection is made of the aggregate, the latter being small, able to pass through a J in. ring ; where the greatest care is taken in mixing and placing the concrete, and where a fairly " wet " mixture is put in. On no account should a " dry " mixture be made if intended to be watertight. 5. Expansion joints. These are very necessary in walls of large sectional area and considerable length. Several examples of the insertion of expansion joints have been given by the authors, notably the illustrations of the Angel Road Railway Bridge, and the Bridge at Thierry. Undoubtedly many of the cracks which one observes in long walls of concrete would not have occurred had there been a care- ful distribution of expansion joints, which really locate the cracks to predetermined positions. 6. Concrete Mixers. Wherever works of any magnitude are to be carried out, a concrete mixer should be used, and in selecting a machine one should be chosen into which the materials, including the water, can be accurately proportioned, and which will produce a mixture of uniform consistency. There are many good machines in the market, 1 some of the best known being, the, Owens Gravity Mixer, Koehring Mixer, Pansy Mixer, Kent Precision Mixer, Taylor Mixer, Coltrin Mixer, Empress Mixer, Trump Mixer, Universal Drum Mixer, Smith Mixer, Ransome Mixer. A " batch" mixer is preferable to a "continuous" mixer, as the proportions are more likely to be correctly maintained. 7. Finishing of Concrete Surfaces. The finishing of a concrete surface may at first seem a matter of little consequence, but it is really one of great importance, and requires the most careful consideration. Many English engineers favour the rendering with cement mortar (1 of cement to 2 of sand) of the surface of the concrete to about an inch in thickness. American engineers on the other hand deprecate this practice, believing that it is impossible to get cement rendering to per- 1 Vide " Concrete and Constructional Engineering," Jan. 1909 and May, 1910, 304 EEINFOECED CONCEETE CONSTKUCTION manently adhere to a concrete face, and the authors admit that there is a great deal to be said for such a contention. A method which the authors advise is as follows : Assum- ing that the moulds are well constructed (planed boards being used) and perfectly clean ; also that the concrete has been care- fully placed ; the slight imperfections in the face of the forms, and the joints between the boards which have left their marks upon the plastic concrete, can be easily removed when the mixture has hardened by rubbing down with sand paper after taking off the projections with a chisel. Any small cavities should next be filled with cement. When this has set the whole face should be washed down with a thin grout of the consist- ency of whitewash, mixed in the proportions of 1 part of cement to 2 parts of sand, the wash being applied with a brush. This method the authors consider is far preferable to that of cement rendering. If the finished work is inside a building, and it is necessary that it should present a very neat appearance, the following is a good method to adopt : Dress down the face of the wall or underside of ceiling, or the sides of the beams, and apply a thin coat (less than -J- in.) of Parian Cement ; this makes an excellent finish. 8. Colouring Matter. This is used a good deal in the United States, but not much in this country. The cement, sand, and colouring matter are mixed together dry, and it must not be forgotten that the mortar will appear several shades darker while wet than after it has dried. By mixing five pounds of colouring-matter with a bag of cement the following colours are obtained 1 : Eaw iron oxide will give bright red. Eoasted iron oxide will give brown. Ultramarine will give bright blue. Yellow ochre will give buff to yellow. Carbon black or lamp-black will give grey to dark slate. Manganese dioxide will give black (using eleven pounds per bag of cement). It should be noted that in all cases the addition of mineral 1 " Concrete and Constructional Engineering," Dec. 1910, p. 904. GENEBAL NOTES 305 colours causes a loss of strength, but this is not important seeing that the colour is used only in the surface coat. Lighter shades may, of course, be obtained by using one-half the quantities above specified. 9. Pebble-dash Finish. This method is sometimes adopted, and the finished work presents a very pleasing appearance. The work should be screened from the sun and kept wet for three or four days. 10. Breeze Concrete. At the present time a great deal of discussion is going on regarding this. It is the authors' opinion, however, that slag, clinker, and coke-breeze are not suitable aggregrates for reinforced concrete. The compressive strength of concrete formed of such aggregates is not satisfactory, and cannot compare with concrete in which gravel or broken stone has formed the aggregate. There is also a risk of such an aggregate having a chemical effect upon the reinforcement. The sulphur in the breeze un- doubtedly has also a deleterious effect upon the concrete, and will cause such concrete to become disintegrated. Mr. E. P. Wells carried out an interesting experiment with breeze concrete some little time ago, which he describes as follows l : " The experiment was with a beam of 14 ft. span by about 4 ft. wide and 6 in. thick. Half-inch rods for reinforcing were used with about J in. of concrete covering them as a minimum. The rods were clean when put in ; but after the lapse of twelve months, when the beam was broken, the rods were badly oxidized, and deep pittings had taken place in all of them. There are many instances of this kind" (Mr. Wells goes on to say) " and I strongly advocate that in no case whatever should breeze or cinder concrete ever be used where small rods for reinforcing purposes are inserted." 11. Avoidance of Stone Dust. Stone dust should never be allowed to form part of the aggregate of concrete. The dust particles are inert and entirely without value, and if broken stone forms the aggregate, it should be well screened before it is used. lecture by E. P.Weils on "Concrete and Reinforced Concrete" (L.C.C. School of Building at Brixton), February, 1910. 306 EEINFOECED CONCEETE CONSTEUCTION 12. Roughening a Concrete Surface. It is occasionally re- quired that the finished surface of a floor shall present a roughened appearance. This is easily done by the use of what is known as a bush-hammer. This tool has a wide striking face with several rows of projecting points, by means of which the concrete is roughened. 13. The material required for one cubic yard of concrete is so often needed by engineers that a table setting it out is very useful; such a table is given in "How to use concrete," pub- lished by the Concrete Publishing Co., of Detroit, Mich., U.S.A., from which the following is taken. Concrete with gravel f in. and under. Proportions required for one cubic yard concrete. Cement. Sand. Gravel. Cement. Bushels. Sand. Cubic yards. Gravel. Cubic yards. 1 1 2 272 0-41 0-83 1 1 2* 2-41 0-37 0-92 1 1 3 2-16 0-33 0-98 1 1* 2* 2-16 049 082 1 1J 3 1-96 0-45 0-89 1 li 3* 179 0-41 0-96 1 1* 4 1-64 0-38 1-00 1 2 3 178 0-54 081 1 2 3J 1-66 0-50 0-88 1 2 1-53 0-47 0-93 1 2 *i 1-43 0-43 0-98 1 2* 3* 1-51 0-58 0-81 1 2* 1-42 0-54 0-87 1 2* 4* 1-33 0-51 0-91 1 2* 5 1-26 0-48 0-96 1 2* 5 1-18 0-44 0-99 1 3 4 1-32 0-60 0-80 1 3 *i 1-24 0-57 0-85 1 3 5 1-17 0-54 0-89 1 3 5| 1-11 0-51 0-93 1 3 6 1-06 0-48 0-97 1 3* 5 1-11 0-59 0-85 1 81 6i 1-06 0-56 0-89 1 3* 6 1-00 0-53 0-92 1 3J 6 0-96 0-51 0-95 1 3* 7 0-91 0-49 0-98 14. Acetic Acid and Concrete. Though one of the weakest GENEKAL NOTES 307 acids, acetic acid is very violent in its action on concrete. Con- crete tanks designed for containing vinegar should be lined with glass, or other material which will not be affected by the action of acetic acid. 15. Action of Alkali on Portland Cement. It has been stated that the alkalies of our soils are destructive to Portland cement, and that this harmful action, which is a chemical one, is going on most rapidly in partly submerged work such as piers or dams. The experiments of Prof. Edwin Burke and Mr. E. Tappan Tannatt l would seem to substantiate this. The authors, how- ever, do not consider that this matter has been sufficiently investigated to warrant them in expressing any opinion thereon The matter is still in its experimental stage. 16. Action of Sewage and Sewage Oases on Concrete. In an interesting paper on this subjest read in April, 1910, by Mr. Sidney H. Chambers, before the Concrete Institute, it was pointed out that under certain conditions disintegration of concrete was caused by sewage and sewage gases, and the conclusions he arrived at were as follows : " That the gases in solution in sewage, and those expelled from it, arising from its decomposition, do act injuriously upon Portland cement concrete, notwithstanding the fact that the concrete is constituted of sound and good materials, when the following conditions prevail : " (1) A high degree of putrescence of the sewage. " (2) A moistened surface, which held or absorbed the putrid " (3) The presence of a free air supply. " Further, that in the absence of one or the other of the above enumerated factors little danger from erosion need be feared." 17. Bonding of old and new Concrete. This is a matter that requires the greatest care, as shrinkage cracks almost invariably occur in concrete floors, etc., along the joints between successive layers of concrete. Even retaining walls will occasionally give evidence where one day's work ended and the next began, and frequently a crack will occur along this line. Messrs. Taylor 1 " Action of Alkali on Portland Cement," by E. Tappan Tannatt in " Con- crete Engineering," Cleveland, U.S.A., May, 1910, p. 12Q. 20* 308 REINFORCED CONCRETE CONSTRUCTION and Thompson in their "Concrete, Plain and Reinforced," page 376, cite an interesting case in the New York Subway ; they say : "Work was commenced with no provision for bonding horizontal layers, but it was soon found that more or less seep- age occurred, and in one case where a large arch was torn down the division line between two days' work was distinctly seen." How then should bonding of the old and new concrete be effected ? The authors recommend the following method : Sweep off the concrete surface thoroughly with a stiff broom, applying water, none of which must remain upon the concrete. As soon as the excess water has been taken up by the atmosphere or absorbed by the concrete, well grout the whole surface with a sand and cement (2 to 1) grout, put on -J in. in thickness. Repeat this after an interval of a few minutes ; then proceed with the next layer of concrete. 18. Effects of Sea Water on Concrete. One of the authors (Mr Matthews) has carried out a series of tests in order to as- certain the effects of using sea water in the mixing of concrete, and the result may be stated briefly to be that sea water has no immediate detrimental effect upon the tensile strength of the concrete, for at the expiration of 7 and 14 days from the mixing of the concrete, it will be quite as strong as if it had been mixed with fresh water ; at 28 days, however, it will be of considerably less tensile strength. His results are set out in the following table: Briquettes mixed with sea water and immersed (after 24 hours under damp flannel) in sea water. Mixed with sea water. Mixed with fresh water. Days. Neat. 3 to 1. Neat. 3 to 1. Remarks. 7 14 28 693 775 773 180 287 293 685 787 875 200 277 353 Same consign- ment of cement used in both cases. The initial set when mixed with fresh water was 35 minutes, when mixed with sea water 9 minutes ; permanent set, fresh GENEEAL NOTES 309 water 6 hours ; sea water 6 hours, so that we observe that when concrete is mixed with sea water its initial set occupies about one-fourth the time that it does when mixed with fresh water, the time for the permanent set being the same. The authors, as already stated in Chapter I, do not recommend the use of sea water except for mass concrete in marine works. With regard to the action of sea water on concrete per- manently immersed in same, or alternately in and out of sea water as occurs in tidal works, the most important tests which appear to have been carried out in order to ascertain this, are the Scandinavian and German Tests described in "Concrete and Constructional Engineering," January, 1910, p. 23. The conclusions arrived at were as follows : " (1) Good Portland cements, such as are now on the Euro- pean market, are very resistant to the action of sea water. A marked difference in the behaviour of cements of slightly differ- ent composition has not been found, except that a high proportion of aluminates tends to cause disintegration. " (2) In a dense mortar, the chemical action is confined to an outer layer of small depth, further action being checked by the slowness of diffusion. A porous mortar, by admitting salt- water to the interior, is apt to crack by expansion owing to chemical change. " (3) The main agency in the destruction of mortar and con- crete in marine embankments, harbour works, groynes, etc., is not chemical action, but the alternations of saturation, drying in the sun, freezing, etc., due to the alternate exposure and covering by the rise and fall of the tide. Destruction takes place sometimes by cracking, sometimes by scaling, the latter effect being produced especially by frost. " (4) The denser the mortar the better (1 cement : 3 sand is too poor). An admixture of fine sand with the ordinary sand increases the closeness of the mixture. A well-graded aggregate would be advantageous for the same reason. " (5) The addition of finely ground silica or trass to the cement before mixing is possibly advantageous in the case of weaker mortars. It is very doubtful whether anything is gained by add- ing trass to the richer rnortars, 310 EEINFOECED CONCEETE CONSTEUCTION "(6) Hydraulic lime mixed with trass, etc., whilst of some value, where a cheap material is required, in the mild climate and absence of tide of the Mediterranean, is incapable of withstanding the conditions of coast work in northern latitudes. " (7) The destructive action of the sea being mainly physical and mechanical, and not chemical, tests by mere immersion in still sea water are of very little value in determining the be- haviour of concrete in marine engineering works. A mixture which disintegrates under this test is certainly useless, but a mixture which passes the test may disintegrate under the more stringent conditions of practical use. " (8) As long a period as is practicable should be allowed for the hardening of concrete blocks before placing in the sea. The German recommendation of one year in moist sand before set- ting in place is probably impracticable in most places, but should be approached as nearly as possible. " (9) The behaviour of test specimens for the first twelve months is very irregular, and definite conclusions can only be drawn from the results of long-period tests. " Both of the reports contain very full tables of crushing and tensile tests, and a complete record of the appearance of each concrete block at stated intervals." 19. The Prevention of Failures. Failures" in reinforced con- crete structures may be divided into two classes. (1) Failures from unavoidable causes. Under this class will come earthquakes, inundations, lightning, fire, tempest, explosions; and the authors know of no material which, if properly designed, can resist any of the above so well as this material. (2) Failures from preventable causes. Among these may be included failures owing to errors in calculation, insufficient or badly arranged shuttering, mistakes in the construction of the pillars, a poor concrete mixture owing to unsuitable aggregate or cement, or both, being used, or through bad workmanship or inefficient supervision. Any of the above causes may be responsible for a reinforced concrete structure being a failure, but there is absolutely no GENERAL NOTES 311 reason, if these matters are carefully attended to, why every structure should not be a complete success. 20. Test Loads. A test load is frequently applied before a reinforced structure is used ; it is not necessary with every struc- ture, but with bridges, floors, balconies, and similar works the authors look upon it as a desirable safeguard. INDEX. A. Acetic acid and concrete, 306. Adhesion, Working stresses in, 16. Adhesive strength of concrete, 12. Aggregate, Choice of, 3. - Size of, 4. Arched roof construction, 288. Arches, Calculations for, 81. Line of thrust in, 80. Atlas Portland Cement Co.'s smiths' and boiler shop, 225. Bamber, Mr., tests by, 100. Beaconsfield Lavatory, Bridlington, Reinforced concrete work at, 176. Beam, Designing reinforced concrete, 53. Rolling load on, 35. Beams, Continuous, 32, 34. - Fixed, 32, 33, 34. - Shear stress in, 21, 40, 57. Stress in, 27. and floors, 264. Bending moments on beams, 30, 31. on cantilever, 23. on continuous beam, 32, 33, 34. on floor slabs, 37. Bevan's Works, Chimneys at, 100. Bins, 76. Block tests, 98. Bonding of old and new concrete, 307. Bonna pipes, 154. Boundary walls, 239. wall, West Hartlepool Cemetery, 243. Box culvert at station, No. 3343, 182. Breeze concrete, 305. Bridge at Seelyville, 185. - Eagle Creek Arch, 181. - Sangamon River, 186. Forest Park, 189. Vermillion River, 195. on G.E.R., 201. at Chateau Thierrv, 201. Bridge at Immingham Dock, 204. over River See at Avranches, 204. Skew, near Paris, 204. at Luxemburg, 205. Broken stone and gravel, 3. Bunkers, 76. C. Cantilevers, Stress in, 23. Cantilever platform at Bridlington, 171. Cathedral at Poti, Russia, 287. Cells, Reinforced concrete, 76. Cement, Storage of, 3. - Tensile strength of, 7. Weight of, 4. Centering for bridge near Teufen, Switzerland, 300. for concrete, 9. Chain Concrete Syndicate's system, 267. Chimney construction, 104. Advantages of use of reinforced concrete in, 105. at Butte, 106, 109. at New Bedford, 107. at Indianapolis, 107. - at Northfleet, 106, 109. at Messrs. Lyle & Sons' Works, London, 106, 109. - at Tacoma, 106, 109. shafts, Designing, 83. Coal bunker at Walkmill Colliery, 217. pocket at Tate's Sugar Works, 230. - pockets, 76. Coefficient of transverse strength, 41. Coignet's system, 2. Coke hoppers, 230. Colouring matter, 304. Columns, beams, and floors, 264. on the Coignet system, 264. on Leslie's system, 264. Compressive strength of concrete, 6, 8, 45. Concrete, Adhesive strength of, 12. Action of sewage and sewage gases on, 307. 313 314 KEINFOECED CONCKETE CONSTEUCTION Concrete, Centering for, 9. Compressive strength of, 6, 8, 45. - Consistency of, 5. Effect of heat on, 92. Effects of sea water on, 308. mixers, 303. Modulus of elasticity of, 9, 45. - pipes, 154. on Wabash Railroad, U.S.A., 154. manufactured by Messrs. Ellis & Sons, 164. - Proportions, of, 4, 45. - surface, Roughening a, 306. Shearing strength of, 9. Strength of, 6. Weight of, 4. Conduit at Jersey City, 148. Continuous beams, 32, 33, 34. Couples, 41. Culvert at Blaenavon, 152. at Bromborough Port, 150. and conduit construction, 146. Indian Creek, 196. No. 24, 193. Cumming's bar, 13. D. Designer, Experienced, 299. Dome of New Wesleyan Methodist Hall, 287. Double reinforcement, 58, 60. Dundee reservoir, 119. Eagle Creek Arch Bridge, 181. Earle, Messrs. G. & T., Tests by, 100. Elasticity, Modulus of, 9, 45. Expanded metal, 13, 14. metal in arched roof construction, 288. Expansion joints, 303. Extreme fibre stress, 40. F. Factory at Noisiel, 215. construction, American examples of, 218. Failures, Prevention of, 310. Finishing of concrete surfaces, 303. Fire-box test, 96. Fixed beams, 32, 33. Floor slabs, 37, 264. slab, Example of stresses in, 59. Force of wind, 84. Forest Park Bridge, St. Louis, 189. Forms for concrete, 9, 299. Foundations, Loads on, 44. Frost, Action on cement and cement mortar of (Paper read American Soc. C.E.), 110. Effects on concrete, 107, 109. G. Girders. See Beams. Grain silos at Silvertown, 225. silos, Typical examples of, 230. Groynes, Reinforced concrete, 212. Havemeyer bars, 11. Heat, Effects on concrete, 91. Loss of strength due to, 94. History of reinforced concrete, 1. Hydrochloric acid, Effects on concrete, 125. I. Indented steel bars, 11. Indian Creek culvert, 196. Inertia area, 40. Moment of, 39. J. Jersey City conduit, 148. Jetty head, 215. Kahn trussed bar, 11. Kilton culvert, 154. Lavatories, Underground, 175. Laying concrete, 5. Lecomte's patent, 1. Leverage in beams, Principle of, 41. Limestone, 4. Liquor tank, 123. Load from wind, 44. Loads on structure, 43. on walls, pillars, and foundations, 44. Lock-woven wire fabric, 15, 154. Louisville and Nashville Railway Co.'s Terminal Warehouse, 218. Lug bars, 13. Luggage subway, 204. M. Machine shop of Taylor Wilson Manu- facturing Co., 223 f INDEX 315 Mechanical bond, 11. Minterburn Mills Co.'s Building, Rock- ville, Conn., 223. Mixing concrete, 5. Modular ratio, 65. Modulus of elasticity of concrete, 9, 45. of steel, 45. of rupture for transverse strength, 41. of section, 40. Moment of inertia, 39. of resistance, 23, 39. Monier's system, 2. Moss & Son's Patent, 15. N. National Cash Register Co.'s Carpentry Shop, Dayton, Ohio, 223. Neutral axis, 52. Newton's third law of motion, 23. Norwich Rising Main, 154. Notation, formulae, and examples, 51. P. Pebble-dash finish, 305. Pier, Newhaven, Underpinning of, 212. Piles, 255. Simplex and Raymond, 263. Piling, 209. at tobacco warehouses, Bristol, 255. Coignet system, 255. Considere system, 259. - Hennebique system, 262. Paragon system, 258. Pillars, Example of calculation of, 65. of eccentrically loaded, 67. Loads on, 44. Reinforced concrete, 48. - Formulae for, 64. Stress allowed on, 49. Portland cement, Action of alkali on, 307. Preservation of steel in concrete, 16. Prevention of failures, 310. Prince's Dock, Liverpool, 209. Prof. Woolson's tests, 93. Public baths at Salford, 167. at South Shields, 167. shelters, 171. R. Railway sleepers, 201. Ransome steel bar, 11. Raw meal silos near Rugby, 227. Rectangular beam, Lines of stress in, 22. Shear in, 21. Rectangular beam, Stress in, 21. Reinforced concrete, Advantages of, 3. - beam, Example of designing, 53. by the Romans, 1. Coignet's system, 2. dome in Cathedral at Poti, Russia, 287. dome at New Wesleyan Methodist Hall, 287. Expanded Metal Co.'s system of floor construction, 268. E. P. Wells' system, 268. football stand at Bradford, 249. groynes, 212. Hennebique system, 136, 277. History of, 1. in building construction, 255. in harbour and dock construction, 209. - in municipal engineering, 118. - in railway engineering, 181. jetty head, 215. Kahn system, 269. - Lecomte's patent for, 1. Monier's system, 2. on Vandalia Railroad, U.S.A., 181. on Wabash Railroad, 185. Properties of, 3. Patent Indented Bar Co.'s system, 277, 282. raft, 281. sea-wall construction, 254. stadium, Syracuse, 249. stadium, 249. stands, 246. System of British Reinforced Con- crete Engineering Co., Ltd., 127, 269. System of Chain Concrete Syndi- cate, Ltd., 136, 267. wharves, jetties, groynes, sea- walls, bins, factories, 209. Uses of, 2. Vaux and Thuasne's system, 1. Wilkinson's system, 2. Reinforcement, Position of, 16. Reservoir and tank construction, 118. at Dundee, 119. at Ipswich, 129. at Albion, Mich., 129. at Annapolis, Mo., 129. at Fort Riley, Kansas, 132. at Pudsey, Yorkshire, 132. Resistance moments for rectangular beams, 51. Retaining wall at Birkenhead Gas Works, 245. at Guildford, 245. .at Hereford Gas Works, 245. 316 KEINFOECED CONCKETE CONSTBUCTION Retaining wall at Royal Insurance Offices, Piccadilly, 246. walls, 69, 239. Calculation of, 71. Roadbed, Concrete, 201. Rolling load on girder, 35, 36. Roof construction, 286. Roofs of sawtooth shape, 288. S. Safe load on floors, 43. Sand, Character of, 4. Sangamon River Bridge, 186. Section modulus, 40. Sewage Disposal Works in reinforced concrete, 164. tanks, 164. tank at Ripponden, 164. Sewers at San Francisco, 148. Shear, Distribution of, 40. in rectangular beam, 21, 40, 57. members, Provision of, 48. Shearing strength of concrete, 9. Shuttering for concrete, 9. Silos, Calculations for, 76. Examples of, 216. Stair construction, 288. Stand at York Racecourse, 246, 288. Stations and platforms, 198. Steel, Preservation of, 16. Properties of, 10. Reinforcement, Effect of high tem- peratures upon, 100. Stirrups, Position of, 58. Size of, 57. Stoke-upon-Trent Town Hall extensions, 288. Stone dust, Avoidance of, 305. Storage of cement, 3. Strength modulus, 41. of cement, 7, 8. of concrete, 6, 8, 9. Stress, General principles of, 20. in beams, 27. in cantilevers, 23. in continuous beams, 32. in fixed beams, 33. in rectangular beam, 21. Suddenly applied load, 44. Swimming baths, 167. T. Tank in Cheshire, 129. at Dublin, 122. at Manchester, 120. Tank at Milnsbridge, 129. - at Newton, 127. at Storage Warehouses, Manchester, 129. - at Trafalgar Mills, Huddersfield, 134. Tee beams, 48, 60. Calculations of, 62. Tensile strength of cement, 8. of concrete, 8. Test loads, 311. Timbering for retaining wall, 300. Trussed bars, 11. Twisted bars, 11, 13. u. Underground lavatories, 175. Uses of reinforced concrete, 2. V. Vandalia Railroad, Reinforced concrete on, 181. Vaux and Thuasne's system, 1. Vermillion River Bridge, 195. Viaduct at Genevilliers, 205. w. Walls, Loads on, 44. - and Partitions, 285. Water softening tank at Manchester, 120. storage tank constructed by the British Reinforced Concrete En- gineering Co., Ltd., 142. tower at Barmby Moor, 145. at Cleethorpes, 137. at Down District Asylum, 146. at Dudley, 142. at Gascoigne Wood, 145. at Immingham, 140. at Londesborough, 146. at Milford Junction, 145. at Newby Hall, 144. at Rhyl, 137. Waterford North Viaduct, 209. Waterproofing of concrete, 301. Wesleyan Methodist Hall, Westminster, 269. Wilkinson's system, 2. Wind, Force of, 84. Load from, 44. Pressure of, 84, 85. Working, Rules for, 50. stresses, 45, 46, 47. when dimensions are given, 55. Workmen, Skilled, 299. ABERDEEN : THE UNIVERSITY PRESS THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. 12 lW 1 NOV 44 nt JUN 11 At ouec 26.W58CSi NOV 12 1958 LU 250CT J 61RR REC O LD JAN 36 1962 21-100m-8,'34 TU 13596 THE UNIVERS,TY OF CAL.FORN.A