UC-NRLF SB Et Ebl LIBRARY UNIVERSITY OF CALIFORNIA. Deceived JAN 11 1893 .... 189 ^Accessions No. IfQOif \T~. Class No. JIITI-ESIT PRACTICAL TREATISE CONSTRUCTION IRON HIGHWAY BRIDGES USE OF TOWN COMMITTEES. TOGETHER WITH A SHORT ESSAY UPON THE APPLICATION OF THE PRINCIPLES OF THE LEVER TO A READY ANALYSIS OF THE STRAINS UPON THE MORE CUSTOMARY FORMS OF BEAMS AND TRUSSES. BY ALFRED P. ROLLER, A.M., 1 1 CIVIL ENGINEER, MEMBER OF THE AM. SOC. CIV. ENGINEERS. FOURTH EDITION. NEW YORK: JOHN WILEY AND SONS, 53 EAST TENTH STREET, Second door west of Broadway. i8c Entered, according to Act of Congress, in the year 1876, by ALFRED P. BOLLER, in the Office of the Librarian of Congress, at Washington. DEDICATION. TO TOWN COMMITTEES, SELECTMEN, COUNTY FREEHOLDERS, AND OTHER PUBLIC OFFICERS, TO WHOM IS INTRUSTED THE RESPONSIBILITY OF ERECTING "IRON BRIDGES," THIS BOOK IS RESPECTFULLY DEDICATED BY THE AUTHOR. INDEX. PART I. GENERAL AND DESCRIPTIVE. SkOX 2Ebthetical Effect w. Plain Utility 87 American and Riveted Systems Compared , 61 Angle Iron 26 Angle Irons, Section of, how Determined 64 Architecture of Bridge Building 82 Asphalt, Weight of 79 Author's Bridge Frontispiece. Beam Bridges 74 ' " PlankFloor 75 " " Wood Pavement on Buckle Plates 75 *' " Telford Pavement on Brick Arches 76 Bearings and Connections, Machine Made 47 Bolster Pieces 71 Braces, Main and Counter .... 33 " Proportions of 33 Bracing, Horizontal 67 " Sway 67 Brick Work, Weight of 79 Bridge Settings 90-96 ' Platforms '. 74 Bridges, General Rules for Selection of 43 " How Classified 32 " Kinds of 32 ' Selectionof 43 Buckle Plate for Floor 73 Cast Iron 28 Chords, Strains in 32 ' TheirOffice 32 Cincinnati Bridge Co.'s Bridge 90 Columns, Cast Iron, Formula for their Strength 57 44 Table of Breaking Strer gth for Cast and Wrought Iron 58 With Square Ends and with Round Ends 66 " Wrought Iron Formula for Strength 57 Tl INDEX. PAGE Compound Riveted Girder 64 Concrete, Weight of , . , . . 79 Construction, Methods of 44 Counter Braces, their Action 33 Corrugated Plate for Floor 73 Cross Beams 63 Decoration, Constructed 83-84 Detroit Bridge Co.'s Bridge 96 Elasticity, Limit of 12 End Struts, Method of Adding to Architectural Effect 85 Eye-Bars 51 * Their Manufacture 53 Factor of Safety. 11 Fairmount Bridge 83 Fastening Iron Stringers to Floor Beams 69 Fink Suspension Truss 41 Floor-Beams 63 " Factor of Safety for 16 " Rivetingof 65 ' Their Connection 66 Floor, General Type of, for Road Bridges 71-72 Flooring 69 " Examples of Permanent 73-74 " System 62 Floor Planks, Method of Laying 70 Floor Plates, Forms of Wrought Iron, Illustrated . . . . . 73 " Wrought Iron 73 Form of Specifications in Bridge Letting 93 Framing, American System 47 Girard Avenue Bridge 84 Girders, Apparent Stiffness of 62 " Compound Riveted 34 " Depthof .... 64 " Solid Rolled 34 Good Bridge, Elements of 11 Gordon's Formula, Modification of , 57 Gravel, Weight of 79 Guard Timbers 71 Hangers, Best Form of 65 " Factor of Safety to be Used 67 Height of Truss when Sway Bracing is Used 78 Inclined Struts, Architectural Effect 86 Invitation to Bridge Builders, Form of 93 Iron, Cast 27 " " Cold-Short 27 INDEX. vii fl PAQB Iron, Cast, Cold-Short, Distinctive Features of 27 " " Danger from Cross Strains 28 " Red-Short 27 " * " Distinctive Features of 27 " " Test by Short and Long Grooves 27 " " WhentobeUsed 28 44 Decarburizing of 19 44 Grey 18 44 Large and Small Specimens, Testing of 26 4 4 Manufacture 17 " Ordnance 29 44 Pig, Grades of 18 4 ' White 18 44 Work, Examination of 80 41 44 'Maintenance 79 4 44 Method of Avoiding Rust 76 * 4 " Painting of 80 44 44 Removal of Scale 80 44 Wrought ' 21 " " Elastic Limit of 25 4 ' " Grades of 26 Joint Box, Cast Iron, Advantages of 60 King Post Truss 85 Lattice-Truss or Double Triangular 40 Loads on Bridges. ... * .... 14 Loading, Table of, Proportioned to Span 15 Material, True Value of 12 Materials of Construction 17 Needle Beams 63 Panel, Length of 33 " Point 33 Pavement Blocks 74 Pig-Iron, Grades of 18 44 Manufacture of 19 Pins and Eyes 49 Pins, Benders' Theory 49-50 Pin Holes, Boring of 61 Plainfield Bridge, Section of 63 44 " SideViewof 63 Plank for Flooring, Method of Laying 31 " Layingof , 30 Planks protected against Sun-Cracking 72 Plate, Bar and Angle Iron 26 Plate Iron , 26 Posts, Connection.... K viii INDEX. PAGE Posts, Sections of, Illustrated 65 " Strength of ? 56 " Their Resisting Power. 55 Queen Post Truss 36 Rail Base, when to be Used 71 Riveted Work 45 " System, how to Use it *. 61 Rivets, their Pitch 65 Riveting, Hand and Power 46-47 Sap Wood 30 Screw Ends. 54 Shoes or Bases 55 Sidewalks, Drainage of 71 " Method of Laying 71 Specifications for Bridges 93 Strains, Kinds of 82 Strength of Cast and Wrought Iron Columns, Table of 58 Stringer Beams 67 Stringers, Factor of Safety for 16 u Iron 68 " Tables of, Proportioned to Wheel-Loads 69 " Timber to be Used 68 " Wooden 68 Struts 33 " andTies 33 Strut Tie 33 Testing of Bridges 88-90 Thin Webs, Precautions if Used 65 Ties 33 Timber for Stringers, Inspection of 31 " Kindsof 31 " Merchantable 29 " Preservation of 31 " Quality of 29 Timber, Season Cracks, Heart Cracks 30 Top Chord Section, Kinds of Joints 59 Top Chord Sections, \ Riveted S ^ stem nitrated, , ^ ( For Pin Connections ) Truss Bridge, its Architectural Effect 84-85 Truss Bridges 34 Trusses in Tension and Compression 34-43 Unit of Area 13 " of Strain 13 Upper Chord Section 58 Warren Truss or Single Triangular 3tJ INDEX. iZ f PAOH Web, Strains to '. 82 " System 83 Weights of Material 78 " " Plate Iron 79 " Timber, Table of 79 Whipple Truss, Single Canceled 88 " " Double " 89 Width of Roadway and Sidewalks 77 Wrought Iron, Characteristics of 21 ". " Cold-Bend Test 24 ** " Fracture of 23 ' " ItsRupture 26 " ' Manufacture of 20 ' Testing of 25 Zore or French Section for Floor . ,73 PART II. SOLUTION OP STRAINS IN GIRDERS AND TRUSSES. PAGE Action of Forces on a Beam 101 Angle and Plate Iron, Elastic Limits 118 Beams under Different Conditions of Loading 105 Bowstring Truss, Illustrative Example of Strains Solved 140-144 " 4 Longitudinal Thrust 139 " * Strains in 138 Breaking Load 106 Compound Girders. 113 " Center of Gravity, how Found 113 " " Horizontal Increment in Web 115 " " " Strains in Flanges 115 " " Rivetingof 115 Composition and Resolution of Forces 120 Compressive and Tensile Strains 102 Coup'es 103 Factor of Safety 107 Fink Suspension Truss, Solution of Example 138 " " Strainsin. 137 " " on Suspension Rods 137 Flange Beams. 109 " Moment of Resistance of Ill Forces Represented by Lines 121 X INDEX. PAOI Formula, Practical Application of 107 King Post Truss, Strains in. 122 Law of the Lever, Example. 97 Lever Arm 100 Loading, Different Conditions of 109 Modulus of Rupture 104 Moment of Resistance 104 44 ofRupture 104 Neutral Axis 101 Plate Girders .* 116 44 ** Allowance for Rivet Holes 114 Principle of Moments 99 Queen Post Truss, Counter Diagonal 125 " " Example Solved 126 44 4t " Reactions on Abutments 127 44 " " Strainsin 124 Reactions on the Abutments 98 Rivets, Duty of 115 44 Number to be Used 116 44 Table of Sizes Proportioned to Thickness of Web Plate 118 44 Value of 116 Shearing Tendency 109 Strains 121 Strength of Rectangular Beams 103 4 ' of Stringers for Working Load 108 Table of Moment of Resistance of American Beams 1 12 44 of Safe Center Load for Depths of Stringers. 107 * 4 of Size of Stringers for Various Spans 109 44 of Web Strains Due to Movable and Fixed Loads 136 Triangle of Forces 121 Trusses, Strains in 119 Value of a Rivet Determined 117 Warren Girder, Chord Strains 133 4 ' 44 Web Strains, Dead Load. 134 44 . 44 " Variable Load 135 44 4t Table of Strains on Diagonals 135 4 " ofWeb Strains 136 WebStiffners 117 Whipple Truss 127 " ' 4 ChordStrains 128 " " 44 " Example Solved 129 " " WebStrains 130 41 4 ' 4< Example Solved 131 Working Value of Rivets, Tables of 118 Wrought Iron Beams, Co-efficient of Safety .. Ill 'UNIVERSITY; PREFACE. IT will be the effort of the writer in the following pages to point out the peculiarities of material and con- struction involved in the designing and building of " Iron Highway Bridges," in the hope that a dissemination of their scientific principles in a popular form, will bear fruit in a more thorough appreciation of a noble art, and in elevating the standard of requirements of this very important class of public works. The subject has been divided into two parts, each complete in itself; the one general and descriptive, and the other analytical. The former is peculiarly intended to present to public com- mittees entrusted with the letting of bridge contracts such information as they ought to possess, while the latter is offered as an aid to engineers not experts in this branch of the profession, and yet who are often called upon to act as inspectors. The second part develops the strains in the ordinary forms of beams and trusses in an elementary manner, the principle of the lever being 8 PREFACE. applied throughout, to understand which the simplest arithmetical attainments are alone necessary. Great stress is laid upon the "strength of joints," since the essence of good bridge-building lies in their proper design. A joint must be as strong as the parts it serves to connect ; as in a chain, wherein a defective link determines its strength, so in a bridge the absence of a necessary rivet would determine its strength. First- class bridge-builders recognize this relation as an axiom ol their art, and it is oftentimes simply from a conscientious application of this vital principle that engineers, in mak- ing tenders for work, find themselves underbid by ignorant or unscrupulous builders, who have no other . ambition than that of getting work. Ordinarily, the cheapest proposal wins the day, simply because to the average committeeman one iron bridge is as good as another, no matter from what source its plan emanates. To such a man, difference in price has no other meaning than that of being a measure of the relative greed of con- tractors, and he does not realize that there exist precisely the same reasons for large variations of price in iron bridges as for the difference in price between the lowest grades of shoddy and carefully woven goods. That the wisdom of such a committeeman is evidenced by a remarkable freedom from bridge accidents through- out the country is no defence for the purchase of the PREFACE. 9 cheapest bridge, simply because it is a matter of exceed- ingly rare occurrence that a bridge is subjected to any thing near the load it ought to carry safely. The scat- tered travel of foot-passengers, or the uncrowded teams on the roadway do not test a bridge, and yet that is the usual condition of travel, particularly in country districts. Occasionally, circumstances arise when a bridge may become crowded, as was the case at Dixon, 111., when, on a quiet Sunday afternoon, a Truesdell bridge fell with a horrible crash, killing and wounding many of the citizens who had congregated on that ill-fated structure to wit- ness some unaccustomed, and therefore crowd-collecting, sight. The same story would be repeated throughout the land, were our ordinary highway bridges subjected to similar loading ; and it behooves all upon whom the responsibility of buying iron bridges rests to weigh well that responsibility, and not to be deceived with the idea that their duty to their constituents requires them to erect the cheapest structure offered. There is, however, considerable difference in price for good bridges, and a good substantial bridge can be built under any of the well-recognized types of trusses. Some designs require less material than others, and the proportion of parts relating to general forms, such as depth of trusses, panel lengths, etc., still further affects the amount of material required. Two iron bridges may be built on the same IO PREFACE. general design, and they may have the same amount of metal in each, and yet one bridge is better than the other, just in proportion as the workmanship, the mate- rial, and design of the joints are better. In fact, these elements may be so poor in the second bridge as to make it positively unsafe to use, and yet to the inexperi- enced eye one bridge may seem almost the counterpart of the other. If this book does nothing more than bring a realizing sense of the above facts home to those public officers on whom the responsibility of carrying out public improvements usually rests, the writer will feel abundantly compensated for his labors, for he feels well aware that if this advance in official sentiment is once attained, the next step of progress will certainly follow namely, the employment of experts to prepare well-defined specifications, and see that they are properly carried out. OP THH ~>3 UNIVERSITY PART I. GENERAL AND DESCRIPTIVE. THE essential elements of a good bridge consist in so applying the materials of construction to a given design as to have all parts of the work equally strong under the maximum loads that can ever come upon it, and that a proper relation, called the " factor of safety," should exist between the maximum loading and the strength of the structure. The term, factor of safety, as usually applied, means the number of times that the maximum load should be increased in order to break down a given structure, a ratio that varies very greatly in most Amer- ican highway bridges, particularly in the " cheap ones." This conception of the term, however, is apt to be mis- leading, since it refers to ultimate strength, and not to the limit of effective strength, which last involves the idea of elasticity. The elasticity of any material is sim- ply its recovering power from the distortion produced by the action of a force, as illustrated in the case of a rubber ball under the pressure of the hand. All mate- rials are more or less elastic, and experiments have shown that if this elasticity is not impaired, they are not injured for use. The strain at which the recovering 12 IRON HIGHWAY BRIDGES. power of a material is destroyed is called its limit of elasticity, which, when once exceeded, final rupture is simply a question of time. The true measure of value, therefore, of a material is its elastic limit, and the real factor of safety is from one half to one third the values employed when the factor is referred to breaking strength, since (so far as bridge material is concerned) about that proportion exists between the force necessary to attain the elastic limit and that which produces final rupture. When we speak of a factor of six, in the ordinary ac- ceptation of the term, it must not be understood that a given structure can be destroyed only when it is loaded with six times the load for which it has been propor- tioned. While it may not absolutely break down until that loading is reached, its value as a structure is impaired the moment the material commences to be strained beyond its elastic limit, which may be the case with only double the extreme load which it has been proportioned to car- ry. Custom, however, has so long made use of this term, "factor of safety," with reference to ultimate strength, that in order to avoid confusion it will be used in that sense throughout the following pages, and if only the preceding explanation is kept in view, it makes no difference how the factor is expressed. Factors of safety usually range from four to six, the most common one being five, and it is good practice to design a bridge with two or more factors, particularly in long spans, for the reason that certain parts can only be strained FACTOR OF SAFETY. 13 fully under the extreme conditions of loading (of very rare occurrence), while others are brought under their full work almost daily, as can readily be appreciated when the subject of loads on bridges is considered. The unit of intensity of a strain is expressed in pounds or tons, and the unit of area over which a strain acts is usually taken at one square inch, and in these units of pounds or tons per square inch, the factor of safety is applied. It has been before stated that material was uninjured when not strained beyond its elastic limit, and it might seem at first sight that the factor would be determined by dividing the ultimate strength by the elastic limit. Thus supposing an iron bar that took 60,000 Ibs. per square inch to tear it apart lost its elas- ticity just beyond a strain of 20,000 Ibs. per square inch, the apparent factor that should be used would be - = 3, or, in other words, the bar might be sub- 2OjOOO jected to a working strain of 20,000 Ibs. per square inch. This, however, would be a dangerous practice, since an allowance must be made for the imperfections of work- manship and material attending all human productions, as well as for endurance under the repeated application of moving loads. This allowance, experiment has shown, should be not less than one third greater than is expressed by the ratio of the ultimate strength to the limit of per- fect elasticity. Applying this principle to the case illus- trated, the factor of safety would become 4 instead of 3, and the working strain on the iron would be 15,000 Ibs. per square inch, instead of 14 IRON HIGHWAY BRIDGES. THE LOADS to which bridges are subjected, in addi- tion to their own weight, are of two kinds : that pro- duced by a uniform loading extending over the whole area of the structure, and that produced by a local con- centration of weight, such as may be produced by heavy stone and timber wagons, or the transport of boilers and machinery. The effect of any loading upon a bridge is further dependent on the span, for the longer the span, the greater is the fixed or dead weight, and therefore the less is the shock from passing loads felt. From this it follows that short spans should either have a higher factor of safety than long spans, or else they should be proportioned for much heavier loads. In the United States, short-span bridges are seldom built heavy enough, while, on the other hand, long-span bridges, say of 150 feet and over, are frequently made needlessly so, involving in consequence a useless ex- penditure. The circumstances of location must be very care- fully considered, since it is apparent that a bridge lo- cated in a country district, subject simply to the pas- sage of occasional loads, can never be strained like a bridge in a populous community, which may be called upon to bear the incessant traffic of a city, with its pro- cessions, and often the reckless haste of a fire service. Excepting in general terms, engineers are by no means agreed as to the exact loading for which highway bridges under different circumstances should be pro- portioned. The usual standard is to consider a span crowded with people, which experiments have shown LOADING. to vary within wicb limits, depending on the density with which a given surface is packed, and the weight of the individuals with whom the experiments were made. No probable contingency, however, will pack a crowd so as to bring a heavier weight than seventy-five or eighty pounds per square foot for a general load, and for local loads it is well to bear in mind that steam road-rollers, weighing fifteen tons on an area of sixty square feet, are being introduced in many suburban towns, for the compacting of Telford pavement* The following table, being substantially the same as was re- commended by a committee of bridge experts in a re- port to the American Society of Civil Engineers, will be found useful in preparing specifications for road bridges, as it gives a safe and economical loading for all circumstances under which bridges are usually built : ii. in. POUNDS PER SQUARE FOOT. For city and For towns and Ordinary coun- Span. other bridges where travel villages, and districts hav- try bridges travel infre- is heavy and ing well -bal- quent ind frequent. lasted roads. loads light. 60 feet and under. 100 Ibs. ioo Ibs. 75 Ibs. 60 feet to 100 90 75 66 100 feet to 150 80 66 5 150 feet to 200 70 60 5 200 feet to 300 66 5o 40 300 feet to 400 60 So 35 * An Aveling & Porter road-roller has fifteen tons on four wheels or rollers, each having a width of twenty inches. A roller used in England, made by the same parties, weighs thirty tons, nineteen of which are on two drivers, the width of each driver being thirty inches. 1 6 IRON HIGHWAY BRIDGES. The proper floor strength for all spans may be ob- tained by considering the loads on each pair of wheels, for each roadway, and this load on bridges of the first class may be taken at from four to five tons, on bridges of the second class three to four tons, and on ordinary country bridges two to three tons. This provision for local loads may seem extreme to many, but the jar and jolt of heavy springless loads comes directly on all parts of the flooring, at successive intervals, and ad- monishes us that any errors made should be on the safe side. From the above consideration of local loads on wheels, it follows that the cross floor-beams of a bridge are required to be of the same size and carrying capa- city, whether close together or far apart, being strained alike in any case. The longitudinal stringers, on the other hand, while increasing in size for the same loads as the floor-beams are spread farther and farther apart, are independent of their distance from each other. String- ers must be of the same strength, whether spaced two or four feet apart, since any stringer may support un- aided a wheel load midway between its bearings. If the wheel loads are assumed to be as high as has just been recommended, a factor of safety of four will be ample for the floor-beams and stringers, since the possibility of such loads coming upon them is very remote. IRON MANUFACTURE. I 7 f MATERIALS OF CONSTRUCTION. In all structures affecting the daily concerns of life, to the strength of which thousands of human beings in- trust their safety, the materials composing them must always be a subject of deep interest, and therefore it is of vital importance to disseminate as widely as possible a correct knowledge of their physical characteristics. And in this " Iron Age " upon which we are enter- ing, much will be accomplished when the community realizes that in regard to iron at least, a " little know- ledge is a dangerous thing," an aphorism applying with peculiar force to bridge-constructions. The first lesson to be learned is, that iron is a material, the qualities of which are as variable as the different localities of its production, and therefore that an iron bar is not neces- sarily as good if made in one place as another, sim- ply because it is iron. Iron may be very good or very bad, or it may have all intermediate degrees of quality, and yet, to an untrained eye, a sample of the two extremes would seem to be precisely alike. It must be understood that iron is a material the most sensitive to treatment known in the constructive arts. The least, and often infinitesimal variation in the fuel, ores, and working, will result in many variations of quality, and all are more or less useful for some purpose or other. It will be the effort of the writer, in as clear and untechnical language as he can command, to point out the leading characteristics of this metal, particularly in its application to bridge purposes, and he will be 1 8 IRON HIGHWAY BRIDGES. abundantly satisfied if attention other than professional is awakened to the responsibility attending its selection and use. Starting then from the ore, which is simply the pure metal combined with different degrees of earthy impurities, we have, as the first result of the contact of the ore with the fuel, the product from the blast-fur- nace called pig-iron, which commercially has different grades, numbered 1,2, 3, 4, etc., all produced through different proportions of the fuel used, the tem- perature, volume, and pressure of the blast in a given time. The low numbers are always the most expensive to produce, and are used for foundry purposes, and are known as " foundry pig," while the high numbers are converted into wrought-iron through the medium of the puddling-furnace, and are called " forge-pig." The foundry irons are often termed grey irons, and the forge- pig, white iron. Pig-iron (disregarding impurities al- ways present) is essentially a combination of carbon and metallic iron, which combination is partly chem- ical and partly mechanical. Foundry pig-iron may be recognized by its softness, and, when freshly bro- ken, by its presenting a fracture of an open, crystal- line texture, and of a dull grey color. Forge-pig is hard and fine grained, generally presenting a white- appearing fracture, and at other times a mottled one. The former flows readily in the moulds of the foundry, being very fluid when melted, while the latter, which IRON MANUFACTURE. 19 f melts at a lower temperature, is somewhat pasty and flows in a sluggish stream. The operation of produc- ing wrought-iron is simply the extraction from pig- iron of the carbon and other impurities, by means of the flame in a reverberatory-furnace, and stirring the charge of melted metal with iron bars, in order to ex- pose every particle to the action of the oxygen of the air, which, combining with the carbon, passes off" up the chimney as a gaseous product. The chemical operation thus performed is called decarburizing, which, were it possible to perfectly accomplish, and did the pig-iron contain no impurities, would result in pure metallic iron, which would be always alike in quality and cha- racteristics in all parts of the world. This, however, is never the case, and there results exceedingly wide varia- tions in the product of the puddling-furnace. Pig iron, like its namesake, who would not be driven to market, must be humored, and so metallurgists, accepting the situation, have endeavored to regulate the quality of their iron by a judicious mixture of neutralizing tenden- cies. In this they have been entirely successful, and all that an engineer has to do, is to say just what he wants his iron to withstand, and the service to which it is to be put, and he can have a grade of metal proper for such uses made to order. As is the quality of the pig- iron, so is that of the puddled product, which leaves the furnace as a loose, spongy-looking mass, called a " pud- dle-ball," still impure with cinder and slag. The next process is to consolidate the ball, and force out the im- 2O IRON HIGHWAY BRIDGES. purities which are mechanically combined in the inter- stices of the spongy mass. This is done by hammering, or more usually by a machine called a sneezer, which, as its name implies, squeezes out the scoriae, cinder and slag. The ball has now taken another shape, bei'ng con- solidated into an elongated mass, of such form as to en- able a still further compacting of its particles through the medium of the first set of rolls, called the roughing- rolls, to which the ball is immediately taken from the squeezer. The iron, after being passed through these rolls several times, becomes what is called a " paddled bar," and in appearance looks like a very rough and jagged-edged bar of flat iron about 20 feet long, and some 4 X | inches in section. At some mills these bars are called muck-bars. They are then cut up into short lengths, and made up into " piles," according to the shaped bar it is desired to make. The piles are heated in a heating-furnace, and when at a white heat are taken out, and passed back and forth through the finishing rolls, from which their marketable or commercial shape is derived. This is called best iron, and is the degree of refinement sold by manufacturers, when simply so many tons of iron are ordered. If made from good stock- that is, well-selected pig-iron such iron answers every requirement for ordinary purposes. But for a bridge, it is often required that this best iron should be again cut, piled, heated, and rolled into new bars, which process, while it does not change the quality of the iron in the least, still further refines it, and makes it more uniform WROUGHT-IRON. 21 in character, although, as may naturally be supposed, the cost of the iron is increased from ten to fifteen dol- lars per ton. This iron is known as " Best Best " iron. Uniformity of material is of very great importance in bridge-building that is, if parties desire their bridges to be as strong in one part as another ; and from what has preceded, it will be at once seen that this desirable end can not be obtained by open purchases in the market- that is to say, buying some bars here, and others there, wherever the different sizes can be obtained the cheap- est. The temptation to such a manner of purchasing is great, in times of close competition among bridge- builders, particularly when, in nine cases out of ten, the successful bidder is such simply from being the lowest in price. We come now to speak of the distinctive physical properties of iron, and firstly of WROUGHT-IRON. Take a number of miscellaneous bars of best mer- chant iron, fracture them short off, and there will be ex- hibited probably as many different appearances of the fracture as there are bars. Some specimens will present coarse crystals, whitish in color, others very fine ones, of a dark gray appearance, in some lights almost black, and in others lustrous like satin. Some specimens, again, may expose a fracture wherein coarse crystals are mingled with fine. Now, what does all this express ? It tells the expert that one iron is poor in quality, that it is hard, brittle, or weak, while he reads the second fracture 22 IRON HIGHWAY BRIDGES. exactly the reverse, and as that of an iron on which de- pendence can be placed for all purposes where strength is required. The specimen showing a combination of large and small crystals, means that the iron is not uni- form in quality, and that it needed further refinement. A fractured bar tells most every thing about the quality of iron, except that of uniformity, and it exhibits this at times, as in the case above illustrated. It so happened, in the assumed exposure of fracture, that the bar was broken at a point where it lacked uniformity, but if broken a few inches either side of this point, it might not have shown any coarse crystals. Good iron that has been insufficiently refined does not show its lack of uni- formity throughout the whole length of a given bar, but in spots more or less frequent, and it is simply a matter of chance if one of these raw spots, as they are some- times called, occurs at the point of fracture. If, now, in- stead of breaking the bars off short, we slightly nick them on one side and expose them to moderate blows, so as not to bend them too rapidly, fibre will be devel- oped in the iron of good quality, while the poor coarse crystal iron may snap off short again, after very few blows. The higher the quality of the iron, or the nearer it approaches purity, the more soft and silky will be the exposed fibre. The phenomenon of fibre can be readily understood, when it is remembered that all iron, whether pure, good, bad or indifferent, is built up, as it were, from crystals, which crystals have different degrees of fineness, depending upon impurities and the mechanical manipu- FRACTURE OF IRON COLD-BEND TEST. 23 lations during the different stages of conversion from pig iron to the refined bar. The process of rolling develops fibre by elongating these crystals, so that a bar of rolled iron may be likened to a bundle of metallic threads of dif- ferent degrees of fineness, according to the number of times the iron from which the bar has been produced has been put through the rolls. It is the ends of such threads that one observes when a bar is suddenly broken off short, looking as previously described, but when the bar is slowly broken, the threads, having time to arrange themselves in a new position, draw out past each other and expose fibre. It follows from what has preceded that great judgment must be exercised in criticising the quality of iron from its fracture, for crystalline fracture does not in itself indicate poor iron, nor does a fibrous one good iron. However, if care is taken to fracture the bar to be tested, under different circumstances, a fair idea can be formed of its quality and fitness for special purposes. Another method of reading the quality of iron is known as the cold-bend test, which requires no expert knowledge to understand. It consists in simply bending unnicked the bar under examination, by repeat- ed blows from a heavy sledge-hammer, over the corner of an anvil or its equivalent, until the two sides approach each other within a distance equal to the thickness of the bar. If the iron stands this treatment without show- ing any signs of fracture on the back of the bend, it can be rated as of the very best quality, possessing all the re- quirements for bridge purposes namely, toughness, due- 24 IRON HIGHWAY BRIDGES. tility, and elasticity. This test, of course, can not show uniformity, that being a matter depending on the num- ber of workings as before explained, and independent of quality. The cold-bend test is severer on a square bar than a round one, inasmuch as the fibres are very ir- regularly drawn out, being very much strained at the corners. Some very high-grade iron will even stand the cold-bend test where a screw-thread has been cut upon it, which is equivalent to numerous nickings. The annexed cut represents the appearance of a flat and of a round bar after the cold-bend test. FIG. 1. FIG. 2. COLD-BEND TEST. It was explained, under the head of the Factor of Safety, that the elasticity of a material was simply its recovering power after the removal of an extra- neous force, and that so long as the limit of its recovering power was not exceeded, no injury accrued to the material. This limit of elasticity varies consider- ably in the different grades of iron, and generally has a value about half the ultimate strength of the iron. After the limit is exceeded, permanent set occurs, and the value of the bar is destroyed. It is probable that a certain amount of permanent set takes place in iron even under the application of very light loads, say of two or three tons per square inch, but it is so inap- TESTING OF IRON STANDARD QUALITY. 25 ft preciably small, being detected only by the most refined measurements, that it need not be considered in practice. The usual method of testing a bar for its elastic limit, is to fasten to one end of the testing-machine, or to the bar itself, close to the point at which it is grappled, a rod or bar free to move at the other end, to which free end is attach- ed an index-point. Before the strain is applied, the test-, bar is scratched under this index, which mark, after the bar is put under strain, will gradually move past the stationary index, and if the strain has not exceeded the elastic limit of the bar so soon as it is removed, the mark will re- turn to its former position under the index. Successive applications and removals of the strain are required usu- ally to determine the elastic limit, else it might be un- wittingly passed under a continually increasing power. After becoming satisfied as to the elastic qualities of the bar, a final application of the strain can be made in order to tear the bar in two, care being taken to note how much it stretches before final rupture. This process of stretching to rupture, exhibits not only the ductility of the iron, but also the degree of uniformity, shown by a greater or less inequality in the amount of stretching at different portions of the bar. The beauty of the cold-bend test is, that it shows simply and inexpensively the same qualities (excepting unifor- mity) that the testing apparatus measures in pounds and inches, and for practical purposes nothing else is needed. The result of many thousands of experiments on Am- erican irons shows that for bridge purposes, bar-iron 26 IRON HIGHWAY BRIDGES. should stand at least 50,000 Ibs. per square inch before rupture, should have an elastic limit not less than 20,000 Ibs. per square inch, and should elongate at least twelve per cent of its length (or i^ inches to the foot), before ultimate strength is reached.* Most of the first-class bridge-builders use a higher grade iron than the above, which is given simply as a minimum quality for high- way-bridges, easily attainable. Angle-iron and plate- iron, as usually applied, are from ten to fifteen per cent weaker than good bars, and, therefore, bridges built from such irons should have proportionately just so much excess of metal over bridges built from bars, a require- ment that the buyers of iron bridges, in this country at least, have not as yet learned to insist upon. Before passing from this subject, it should be remarked that the tables of strength of wrought-iron are based upon exper- iments made on small bars, having cross-sectional areas of about one inch. Large bars will not show the same ultimate strength that small ones do, of the same make, a fact that must be borne in mind when specifications are being prepared. For example, the same iron in a bar having one inch area may require a strain equiva- lent to 10,000 Ibs. per square inch to rupture it, in excess of that required when formed in a bar having an area of four or five inches. Until a comparatively recent date, no attention was paid to the effect of the form of the specimen to be tested. Test specimens are simply short pieces of iron, three or more inches long, the middle of which is grooved down to exact gauge, and which be- * Very accurate gauging under a magnifying instrument will indicate a per- manent set long before 20,000 Ibs. per square inch is reached, and probably TEST SPECIMENS CAST-IRON. FIG. 2. FIG. I. comes the area to which the breaking strain is referred. The character of the grooving, whether long or short, affects, in a marked degree, the result of a test. If the groove is a short one, the iron will break at a much higher strain per square inch than if it had been long, and this result is due to the fact that a free stretch- ing of the fibres is prevented by the reinforcement de- rived from the metal contiguous to the ruptured section of the short-grooved specimen. This difference, due solely to the preparation of the specimen, will amount in some cases to as much as fifty per cent. The expla- nation of this apparent anomaly in the strength of iron may be made still clearer by an in- spection of the cut, where Fig. i re- presents a long-grooved specimen, and Fig. 2 a short-grooved one. The shoul- ders at either end are formed for the grappling-irons of the testing-machine. There are two terms continually met with among iron-workers name- ly, red-short and cold-short iron, which it may be advisable to explain. The peculiarity of the former is, that while very strong and tough when cold, it is difficult to work in the forge except under very high heats, otherwise it will crumble and waste, and for this cause has received the enmity of smiths. On the other hand, cold-short iron is brittle when cold, and absolutely unsafe to use where life depends upon its with not over a ton strain but ordinary methods, such as are used in the shops, will not detect a set below 20,000 to 25,000 Ibs. per square inch. SHORT AND LONG GROOVED SPECIMENS. 28 JRON HIGHWAY BRIDGES. integrity. The smith likes to use it, since it works and welds readily in the forge at low heats. The best manu- facturers aim to have a neutral product, which, if it has any tendency at all, is on the side of red shortness. Cast-iron in bridge-building is so little used at the present day, except in the form of bearing-blocks, poet- caps and bases, or washers, that little need be said about it. In its very nature, it is a brittle material, and even while apparently doing good service, may be dangerous- ly near failure. It has an irregular elasticity, and in cold climates it has been known to fracture through the freezing of water that had found its way into unpro- tected cavities. In the form of long columns, it is of course very inferior to wrought-iron. Such columns are exposed to cross strains, and have a tendency to fail by bending and not by crushing. Tension in some part always accompanies a cross strain, to resist which cast- iron is a very uncertain material. Castings may have initial strains through unequal cooling, or they may be thinner on one side than another, or they may be weak through concealed holes, " cold shuts," or cinder. No human foresight can remove these risks ; and especially in bridge-building is it important to reduce all risks to a minimum, and for this reason, if for no other, cast-iron should be discarded for such purposes, except in those places where it would be very expensive to forge wrought- iron, places where none other than a direct crushing strain can ever occur, as previously instanced. The iron from which castings are made should be selected with TIMBER. 29 f great care, and it should have sufficient meltings, 2 to 4, before being put into its final shape. Such castings, when broken, should present a fine-grained grayish frac- ture, and their skin should be generally smooth, but not smooth like stove-plate castings, as such iron is very un- suitable where strength is desired. Stove-plate cast- ings must be made from a very fluid iron, one that runs thin, and sharply fills the moulds, and such irons are very weak. Ordnance iron, with a tensile strength oc- casionally equal to that of inferior wrought-iron, is the best cast-iron possible to have, but it is expensive, and rarely used on that account. Such a grade of iron, how- ever, should always be insisted upon where bridges are permitted to be built having cast-iron top chords and posts. TIMBER. Whatever modesty is shown through conscious ignorance in criticising iron and its fabrication, it quickly disappears when the question of timber is un- der consideration, almost every one being positive as to what is good timber, and very frequently unreasonable exactions are imposed. The main trouble that arises, in the execution of contracts, arises from the interpretation given to the term merchantable, an expression some- what vague, without other limitations. All bridge-timber should be sound that is, free from loose or black knots, heart-cracks, and wind-shakes, and it should not be cut from logs obtained from dead trees. Seasoned timber, 30 IRON HIGHWAY BRIDGES. especially when it has been exposed to the direct rays of the sun during the process of seasoning, is apt to have more or less cracks, called season-cracks, which must not be confounded with heart-cracks and shakes. They can be distinguished from each other from the fact that the cracks due to seasoning are sharp, while those due to shakes are splintery the splinters, in many cases, being easily torn off. Well-seasoned timber wears much longer than green timber ; but since bridge-plank is seldom, if ever, kept in stock, and since public works rarely have their needs anticipated, lumber is almost al- ways procured fresh from the mills. The durability of timber would be very much enhanced if kept soaking in water for a few months after it is cut into plank, after which seasoning proceeds very rapidly, the water having acted as a solvent in ridding the pores, to a great extent, of sap and nitrogeneous matter, the decaying elements of wood. Sap-wood that is, the wood newest made and next the bark is not desirable, as it will wear away faster and decay sooner than the heart-wood, but practically it is impossible to obtain timber of any size and in large quantities entirely free from it, unless at a very great increase of cost. Sap-wood may be recog- nized as being lighter in color, softer, and of more open fibre than the heart-wood. Timber is regarded as mer- chantable when it has not more than three sappy cor- ners, although some inspectors do not permit of more than two ; but as bridge-plank usually wear out before they rot out, a latitude can with propriety be observed CLASSIFICATION OF BRIDGES. 3! here, and the plank laid with the sap corners down, thus : 1 the dark portion representing the sap-wood. Wane or bark edges are very apt to occur in otherwise first-class sound timber, but should not in- sure condemnation if only on one corner, if the plank can be laid with that corner down. If on two under corners, the plank would be next to the slab (or outside cut), and therefore almost all sap-wood, and should not be permitted to pass by the inspector. For stringer tim- bers, inspection ought to be somewhat more rigid than for floor-plank, but guided by the same common-sense principles, and the farther consideration, how much sur- plus strength the stringers possess. The kinds of lum- ber used are mostly oak and pine, both white and yel- low ; to these may be added, for plank purposes, beech, birch, and maple, and occasionally spruce, when two courses of plank are used, the upper one being of hard wood. All things being considered, the writer prefers close-grained yellow pine for floor-planks, it being much less expensive than a proper quality of oak, and besides less slippery for horses in frosty weather. As to artifi- cial means for preserving timber, a number of processes have been tried with success. The various methods of creosoting and burnetizing are the more common in use. The city of Boston required the latter process to be applied to spruce plank in some bridges recently built, as one eminently effective and cheap. Any process used, unless thoroughly well done that is, unless all the pores and cells vxt filled with the preservative material is 32 IRON HIGHWAY BRIDGES. even detrimental, since in such cases dry rot inevitably sets in at an early day. KINDS OF BRIDGES. The various kinds of bridges ordinarily met with may be classed under one of four heads, namely, the plain beam or girder, the beam truss, the suspension truss, and the arch truss or bowstring. The first class needs no explanation. The second form includes all trusses where both top and bottom chords are absolutely essential, while the third embraces those trusses wherein only the upper chord is essential. The bowstring is pro- perly not a truss at all, but simply an arch wherein the horizontal tie takes the place of fixed abutments. The office of all girders, whether plain or trussed, is to trans- mit weight to the points of support, which action de- velops two classes of strains, namely, horizontal and vertical (sometimes called shearing). The former are resisted by the top and bottom longitudinal chords or flanges, while the latter are taken up by the interme- diate bracing, called collectively the web, which applies to all the material lying between the chords or flanges, whether open as in a truss, or solid as in a plate-girder. The longitudinal strains in the chords are either com- pressive or tensile, and whichever may be the case, the quality of the strain is the same throughout the chord considered. The web is exposed to both kinds of strain, the parts of which, if a truss, are alternately in tension and compression in the march of a given weight to WEB SYSTEM. 33 either abutment. The tension members of the web are called ties, and they may be either vertical or inclined. The compressive portions of the web are called struts, or posts, and may also be vertical or inclined. When ties are vertical, the posts are inclined, and vice versa* or both may be inclined. Strut tie, as the name implies, means that a web member may act either by tension or compression. The point where a tie and a strut intersect in a chord, is called a panel-point, and the distance between two such points is called a panel-length. Again, a portion of the web system are called main braces, or ties, and a portion counter braces, or ties. The former embrace all parts of the web which carry that part of the weight going to the nearer abutment either side of the centre of the truss, and are lightest toward the middle and heaviest toward the ends of the span, while the lat- ter run in a contrary direction to that of the main braces, and carry that portion of the load going to the farther abutment, and they are heaviest at the centre and least at the ends of the span. Main braces may be made to act as counters, if they are constructed to act either by tension or compression. The office of the " counters " is simply to prevent distortion or change of form in a truss, and they are only necessary when the truss is subjected to the action of a variable load, as is the case on all bridges. They can only act when the main braces to which they are opposed are relaxed, and then have an action equal to the difference between the effects of the variable and fixed loads, acting in opposite direc- 34 IRON HIGHWAY BRIDGES. tions. In a bridge very heavy in proportion to the moving load, this excess is soon lost either side of the truss centre, when the counters can of course be left out. Ordinarily they are continued a short distance beyond theoretical requirements, in order to diminish vibration, which they materially assist in preventing when screwed up tightly. The usual forms of truss bridges are illus- trated by the succeeding figures, on each of which is re- presented, by means of lines of varying width, not only the parts strained the greatest, but also the kind of strain. Tension is shown in fine lines, and compression in full black ones. The weights producing strain are supposed to be located immediately at the panel-points, the whole materially aiding the mind in forming a very fair idea of how trusses really do act, when coupled with the descriptions and definitions just given. Figs. 3 and 4 represent plain girders for short spans, in which the flange and web parts are noted. Such gir- WEB OR STEM. ^^H^ ,,,f^& WEB OR STEM. FIG. 3. SOLID ROLLED BEAM. FIG. 4. COMPOUND RIVETED GIRDER. ders are often used of solid section, and are called rolled beams, being finished ready for use direct from the rolling- mills. They are made of varying sizes and weights, from the four-inch beam, weighing 30 Ibs. per yard, to the KING AND QUEEN POST TRUSSES. 35 9 fifteen-inch beam, weighing 200 Ibs. per yard. These beams, however, are more expensive than the compound riveted girder, made with plates and angle irons, but are 10 per cent stronger. The riveted girder can be made of any depth, and is therefore adapted for much longer spans than the rolled beams. Fig. 5 shows the simplest form of truss, and con- sists of a post and two inclined t. ties supporting the middle of a beam, that would otherwise be too weak to sustain a load. This supporting system in effect halves the span, the post performing FIG . 5 . KING POST TRUSS. the office of a pier, carrying one half the load of both subdivisions of the beam. Now, since all the load must finally rest on the two end supports or abutments, that portion that rests on the post can only reach them through the medium of the inclined ties, intersecting at its foot, each tie taking up half the load carried by the post. These ties are strained in excess of the load they transmit to the abutments in proportion to their deviation from a vertical line ; or, in other words, an inclined pull requires greater effort than a direct one, as almost eveiy one has experienced. Whenever a force is exerted at an angle, a horizontal effect is always produced, and in proportion to the angle at which it is applied. The flatter the angle, the greater the horizontal effect, and vice versa. In the truss before us, the abutment ends of the inclined ties, by virtue of 36 IRON HIGHWAY BRIDGES. this horizontal effect, pull toward each other, producing compression in the horizontal beam to which they are attached. This form of truss is called the " King Post " truss, and when inverted will be at once recognized as the commonest form of wooden trussing in existence. In that case, however, the vertical post becomes a tie, the inclined ties become thrust braces, and the beam is strained tensively, instead of compressively, since the horizontal effect of the inclined thrust braces is to tear the beam apart. Fig. 6. When an opening becomes too great to be spanned by a beam trussed with a single post, two posts FIG. 6. QUEEN POST TRUSS. are added, forming three spans, the posts being the piers as before, which piers are supported in turn by the inclined ties running up to the ends of the horizontal beam as before ; each tie sustaining the whole weight on one pier or post. This is a complete truss when both posts are loaded ; but if only one is loaded, the condition of affairs changes. The load is unbalanced on the other side of the centre, and the horizontal ef- fect of the inclined tie on the loaded side will be greater on the beam (which hereafter we will call the KING AND QUEEN POST TRUSSES. 37 upper chord) than that from the similar tie on the un- loaded side. The result will be a distortion of the frame, the loaded post sinking and the unloaded one rising. All that is necessary to prevent this destruc- tive effect, is to enable that portion of the load that must be carried by the further abutment, to go there by the most direct route, which is manifestly through the medium of a diagonal tie from the foot of the loaded post to the top of the unloaded one, or a diago- nal strut from the top of the loaded post to the foot of the unloaded one. This diagonal is the counter-diago- nal previously defined. Its introduction in the elemen- tary truss just described, and known as the " Queen Post Truss," is a pointed illustration of the value of the triangle in trussing, which is the only geometrical figure that resists change of form. Inverting this truss, as was done before with the King Post, we have the Queen Post in a more familiar shape ; and while the effect of the loads on the several parts is pre- cisely the same in amount of strain engendered, the quality is reversed. That is, the upper chord be- comes now the lower chord, and suffers tension, the inclined ties become thrust braces, the posts change to ties, and the lower chord beconies now the top chord undergoing compression. The counter- diagonals also become reversed as to tension or com- pression. The forms of trusses just described embrace all the elements of simple trussing, and an extension of these IRON HIGHWAY BRIDGES. principles is all that is necessary to meet the ordinary requirements of every-day practice. By adding to the number of posts, the Whipple or Pratt truss, Figs. 7 and 8, FIG. 7. FIG. WHIPPLE SINGLE CANCELLED TRUSSES. is formed, a plan of truss the popularity of which is well deserved. The inclination of the end posts, though not essential, results in a saving of material over vertical posts, but the latter form produces, in the judgment of many, a more pleasing effect. A study of the diagram will show how cumulative the horizontal effects of each diagonal main tie are toward the centre of the chords ; and also how it is that any main tie must carry all the weight between its own panel load and the centre of the span. Fig. 9. When a span becomes very long, and it is constructively and economically inconvenient to have WHIFFLE AND WARREN TRUSSES. 39 one system of triangles, two systems are introduced, complete and independent of each other, each one being FIG. 9. DOUBLE CANCELLED WHIPPLE TRUSS. formed of triangles having bases of two panel-lengths. The principle of the Queen Post still holds good as be- fore, as it would do if there were three or more series of triangles, each series doing its own work in transmitting the loads to the abutments, independent of any other. The truss illustrated in Fig. 9 is known as the double cancelled Whipple or Quadrangular truss, and has been used in spans of over 400 feet. Fig. 10 appears, at first sight, a greater variation from the elementary truss form previously described AAAAA FIG. 10. SINGLE TRIANGULAR OR WARREN TRUSS. than is really the case. The principle of the triangle being here developed to its utmost perfection, this form 4O IRON HIGHWAY BRIDGES. is usually known as the " Triangular " truss, although sometimes called the " Warren Girder." The marked difference between this form of truss and the Whipple and Queen Post trusses consists in the fact that the posts as well as the tension-rods are inclined, and if the angle of inclination is well proportioned, a considerable economy of material is obtained over that required by the straight post trusses. When a vertical post is used, the weight delivered to it by its tension-rod makes no progress whatever toward the abutment ; but in the case of an inclined post, by the time the weight has been transmitted to its foot, it has progressed toward the abutment by an amount equal to the horizontal reach of the post. When the span becomes long and the stretch of the triangles is so great as to necessitate an intermediate support for the flooring, a rod is dropped from the apexes of the triangles to form such support, FIG. II. DOUBLE TRIANGULAR OR LATTICE TRUSS. or two systems of triangles may be used corresponding to the double cancelled Whipple truss, as in Fig. 1 1. In the case of the trusses being beneath the roadway, the verti- FINK SUSPENSION TRUSS. 4! cal rod becomes a post, as the load then presses from above, instead of being suspended from below. In this form of truss, it will be noticed that the horizontal ef- fect at each panel-point is made up of two portions one due to the thrust of the posts, and the other to the pull of the ties, both being inclined and acting in the same direction just as a man pushing behind a wagon adds to the effect of a man pulling it in front. While the vertical post truss has only one increment at each panel-point, yet for the same depth of truss the sum of all the increments on either system will be the same at the centre of the chords. Fig. 1 2 illustrates the suspension truss, where only a top chord is essential, and is nothing more than an FIG. 12. FINK SUSPENSION TRUSS. ordinary roof truss turned upside down. This form was first developed for bridge purposes by Mr. Albert Fink, and it almost universally goes by his name. It is developed from the elementary truss, Fig. 5, as will be apparent on inspection. By imagining the King Post truss in Fig. 5 to become so long as to require inter- mediate support, it is accomplished in this case by add- ing sub-systems, acting precisely like the main system, 42 IRON HIGHWAY BRIDGES. only in a minor degree. The load on each post splits in half, as it were, at the post-foot, each portion being carried up the inclined ties to the top of the adjoining posts, each minor system thus adding to the weight im- posed on the next larger system, until the whole load is finally delivered to the abutment. The main system ex- tending over the whole span is called the primary sys- tem ; the systems extending over each half span are secondary systems ; those over each quarter of the span, are tertiary systems ; those over each eighth of the span, quaternary systems, and so on. The horizontal incre- ments of all the ties accumulate at the extreme ends of the top chord, producing uniform compression through- out its whole length. Fig. 13 is the familiar bowstring, which acts, as be- fore remarked, like an arch, and bears no relation what- FIG. 13. BOWSTRING TRUSS. ever to the typical form of trusses developed from Figs. 5 to 12. The essential parts are the bow and tie, the latter taking the place of fixed thrust abutments. The web for a uniform load need be nothing more than ver- tical rods, carrying simply the separate loads at the panel-points. Where the load is variable, as is always THE SELECTION OF BRIDGES. 43 . the case in bridges, and if the arch is not stiff enough in itself to resist distortion, diagonals must be introduced in the web performing simply the office of counter- braces. Like them, they are strained the greatest in the centre of the span and least at the ends. THE SELECTION OF BRIDGES should be governed by economy and adaptability to lo- cation, since no one of the well-recognized types of bridges is better than another. Apart from such mo- tives, any bridge designed on correct principles is a good one, whether a beam-truss, a suspension-truss, or a bowstring. On the contrary, any one is bad if impro- perly designed, and the principles of its construction ignorantly conceived. A general rule that will lead to satisfactory results is to ignore any plan of bridge that can not be accurately analyzed as to the character and amoimt of strain occurring in all its parts such, for instance, as the Truesdell bridge, scores of which have been built during the last fifteen years ; and assuming that the great majority are still in use, giving satisfac- tion to their users, yet their form of construction is one that removes them beyond the pale of the most refined analysis. They are purely empirical structures, and be- ing such their construction should under no circum- stances be permitted. It is bordering on criminality to build any structure on a plan that no human being can tell definitely any thing about, when there are so many plans that we thoroughly understand. 44 IRON HIGHWAY BRIDGES. METHODS OF CONSTRUCTION AND FORMS OF SECTIONS. The various systems under which iron-work is framed may be classified as the " pin connection," " screw-end connections," and all " riveted connections," which may be and often are combined, to a greater or less extent, in the same bridge. The first two systems are peculiarly American in their origin and practice, while the last is the system pursued almost entirely in England and on the Continent, although latterly the at- tention of American engineers has been drawn to a con- siderable extent to riveted work. As has been before intimated, the knowledge of a good bridge-designer will be shown in his details, more than in his mathe- matical expertness in figuring up strains ; and, perhaps, it will not be hazarding too much to say, by way of emphasizing this remark, that few iron highway bridges built in the United States are as strong at the joints as the parts they serve to connect. The very great diffi- culty in obtaining this joint strength in purely riveted work is due to the general nature of such designs. In the first place, as built in this country, the bars or pieces uniting at the panel-points do not assemble in the axial lines of the truss, thus producing a complexity of cross strains unknowable in amount. In a large bridge, in- volving heavy pieces and large joints, it is impossible to so dispose the rivets as to distribute the strain equally RIVETED WORK. 45 p among them, although they can only be proportioned on that supposition. It will be apparent to any one, on a moment's reflection, that when two pieces of iron are riveted together through the medium of a splice-plate, the rivets at the ends of the splice are the first ones to feel the effect of a strain in the bars, and consequently are brought into action before the rivets at the middle of the splice are affected ; and if the bars are large, the splice-plate long, and the rivets numerous, it is doubtful if the rivets in the middle of a splice do any service whatever ; certainly not before the iron has stretched considerably, in which case the first rivets may have upon them double the strain they were calculated to bear. As manufactured in this country, the holes of each piece ,are separately punched from wooden templates, and de- spite all the care exercised, the drift-pin must be always at hand to force the matching of the holes of contiguous plates, to admit the insertion of the rivet, thus developing initial strains on the iron impossible to compute, which may be regarded as another very serious indictment of riveted work. Workmen can not always be watched, and the eyes of even the fiercest inspector can not keep every hole and rivet before him. The carelessness of a work- man may be rapidly and nicely covered up with a neatly- shaped rivet-head, which tells no tale of the horribly muti- lated holes beneath, to which a cold-chisel had possibly been applied, or perchance the holes overlapped too badly for the drift-pin to even give an appearance of matching. Another imperfection very apt to creep in when hand- 46 IRON HIGHWAY BRIDGES. nveting is employed, and one, too, that is so thoroughly concealed as to be impossible of detection, is the imperfect filling of the holes. The chances of such a serious defect increase with the number of the plates riveted together, and owing to the shrinkage of the hot driven rivet- heads, they bind so closely to the surfaces of the outer plates, that striking with a hammer to test " looseness " is a very fallacious test. The high strain under which rivet- heads are left through shrinkage in cooling is often shown by their apparent brittleness when cut off by a cold-chisel. They will at times snap off like a piece of glass under the first blow. A hand-driven rivet will very frequently drop out from its own weight, when once the head is knocked off, showing that the shank of the rivet shrinks away from the holes, and when this is not the case, they are as apt to retain their position through the distortion caused by unmatched plates as to a perfect filling of the holes. In Europe, where the riveted system has been developed to its utmost perfection, these inherent defects are recognized, as is shown by the great care with which their riveted work is manufactured, such as drill- ing the rivet-holes through the plates and pieces to be joined while clamped in position, and thus overcoming almost entirely the evil effects of drifting and distorted rivets. Power-riveting is largely employed, as by that mode alone there is any reasonable certainty of filled holes. Did American girder-shops pursue the European system, our riveted bridges would cost much more than they now do, and they would be proportionately better. To THE AMERICAN SYSTEM. 47 do this, however, requires more than the customary standard plant namely, a punch, a pair of shears, and drift-pins, which any old boiler-shop can furnish. Before leaving the subject of riveted work, it is well to call attention to " field-riveting "-that is, where spans are so large that they must be shipped in parts, which are riveted together in the final position of the work. Whatever objection has been urged against skop-nvet- ing is intensified in a high degree when the field-riveter steps in to do his part of the work. He must work in constrained positions and in all sorts of weather. If the work in the shop has been well done, that in the field is pretty sure to be badly done ; and as this last applies principally to the joints, the most vital parts of the whole structure, the work must be judged entirely by them. In contrast with riveted work, we have the ma- ckine-m&die bearings and connections, which may be attained either by means offlms or screw-ends, or a com- bination of both. It is through the adoption of this constructive idea that the Americans have been able to surpass the rest of the world in bridge-building. This American system, as it is universally called, per- mits of the most economical use of material possible, is wonderfully well adapted for long spans, and enables the engineer to select the quality and shape of material best adapted for any given portion of his design. It is a system that permits of closer harmony between theory and practice than is possible to attain in the European method or its American imitation, concerning which 48 IRON HIGHWAY BRIDGES. enough has been said to show how lamentably deficient that system is in this particular. In a bridge on the American system, the strains, being axial, coincide with the skeleton diagram of the truss, and, further, the strains can be accurately computed, and need have no more mate- rial provided to meet their action than is absolutely neces- sary. The more usual mode of connection in this system is by means of pins, which joints, when well designed and executed, leave nothing to be desired. The main points to be considered are the sizes of the pins, the reinforc- ing of the upper chord and post-bearings, the fit between the pins and eyes, the proportion of the heads of the tension-bars, and the uniformity in lengths of similar parts in each panel. It is no part of a book of this character to give specific rules for the proper proportion of these parts, but the great importance of the subject, and the fact that the majority of American highway bridges are very deficient in "joint proportion," warrant an attempt to make clear the requirements of the pin- connection. Pins can not be made too large, and are governed in size by the largest tension eye-bars through which they pass. These occur in the lower chord or in the main diagonals at the ends of a truss. Whether a pin is a half inch more or less in diameter is an econo- my not worth consideration only be sure that the error, if any, is toward the larger diameter. Considering the very great importance of properly proportioned pins, it is somewhat remarkable that so little attention has been given to the subject. For years the crude con- PINS AND EYES. 49 elusions of Sir Charles Fox, drawn from very meagre experiments, made more than a dozen years since in England, have been a sort of blind guide for engineers. They have been supplemented within the last five years by the experiments of Mr. Berkeley, also English ; and although these last and more complete experiments have shown how erroneous Sir Charles Fox's rules are, yet those rules are still given in modern text-books as proper practice. Mr. Charles Bender, C.E., has very ably investigated the subject theoretically, and shows the various influences operating to modify the size of pins, according to the position of the different bars as- sembled upon them, and he shows the fallacy of deriving rules from experiments made upon bars having a uniform ratio of width to thickness, or on pins only exposed to di- rect shearing action. The best experiments and theoretical investigations go to show that the size of pins for flat bars should be not less in diameter than T 8 the width of the bar, and for square bars their diameter should be not less than if times the side of the square. It will be noticed that these proportions result in pins enormously in excess of what would be necessary for simple shear- ing. For example, a bar 4x1 requires a pin 3^ inches in diameter, the area of section of which is 8J square inches, while that of the bar is but 4 inches. Pins should be carefully turned to gauge, and fit the holes through which they pass with the least play with which it is pos- sible to put the work together, which the best practice has established at about - of an inch. Of as much 5O IRON HIGHWAY BRIDGES. importance as the pins, is the proper form to be given to the ends of the "links" or "eye-bars," the name usually given to the braces and lower chord bars. In order that the pin will not tear through the eyes before the body of the bar is at the point of rupture, experiment has shown that the link-heads must be full, and of gradual curvature, the proportions of which being dependent some- what on the mode of manufacture. Still further experi- ments are required on eye-bars of various sizes, to deter- mine with accuracy just what proportion should be given to the heads ; but so far as experience has gone, it points to a proportion in the case of flat bars of about 50 per cent of metal through the pin in excess of that through the body of the bar, and in front of the pin about the same as is contained in the body of the bar. Back of the pin, the curve uniting the head with the body of the bar should be a gradual one, so that the strain in the bar will not be too abruptly transferred around the pin. The annexed cut represents the end of an eye-bar, with a pin passing through it, the relative intensity of the surface pressure being indicated in shaded lines. It will be per- ceived how important it is to have tight-fitting pins, since the first pressure is simply a line of contact, the semi-circumference of the pin only coming into bearing when the pressure has upset the metal in front of the pin by an amount equal to the extent of play in the eye. Some engineers consider that the bearing surface should be determined by projecting the semi-circumference on the diameter, allowing nothing for frictional resistance EYE-BARS. when the pin and eye surfaces are in full contact. In that view of the case for flat bars, with heads uniform in thickness with the body, pins should have a diameter equal to the full depth of the bar; or, in case it is unadvisable to have such large pins, the required bearing area can be made up , FIG. 14. LINK OR EYE-BAR HEAD, SHOWING RELATIVE INTENSITIES OF PRESSURE ON PIN. eyes. When square bars are used, the eyes should be formed by long loop-welds, which gives, of course, ample mate- rial around the pin, being equal to the side of the square. Round bars should be forged with an equivalent flat head, as it is impossible to properly loop-weld a " round," and have a satisfactory flat bearing on the pin. The eyes of all links should be carefully bored to match the pin, with minimum clearance compatible with erection of the work. Since in all link bridges each individual bar is calculated to perform a given proportion of duty, uniformity of length, particularly in bars of the same panel, is of the first importance. Otherwise, an inequality of strain will result after the work is erected, the tighter bars taking all the load at first, only bringing the slack ones into play after they have stretched a sufficient amount so to do. These errors of length creep in from two causes 52 IRON HIGHWAY BRIDGES. namely, carelessness in centring the eyes from the master-gauge, and. the variations of temperature at which they are bored. The best shops use double-end boring- machines mounted on wrought-iron beds, and if care is taken that the bars have been long enough lying in the same temperature as that of the machine, the second class of errors are removed to a remote possibility ; the avoid- ance of the first being simply a matter of shop system, in checking measurements and using intelligent supervi- sion. Flat eye-bars (the form now almost universally used by the best designers) are manufactured in America, either by welding the eyes previously forged into shape to the ends of the bars, by die-forging under a steam- hammer, or upsetting by means of steam or hydraulic power. The former process is purely a welding process, and should be performed with great care in a hollow coke fire, the form of weld known as the split weld being used. The second process is a weld to the extent that a slab is forged down on the ends of the bar under the powerful blows of a steam-hammer, the shaping being performed at the same instant, the anvil and the hammer having matched die-faces, while the latter process con- sists in forcing the ends of the bar itself into properly- shaped moulds or dies under an intermittent or a steady, continuous pressure of a ram, the ends being previously heated to a white heat. All these processes are in use, and have given satisfaction ; but the two latter have decidedly the preference among engineers, owing to MANUFACTURE OF EYE-BARS. 5J f their greater reliability. The second method is the most flexible, in that there are no such limitations of ratio of width to thickness as the direct upsetting pro- cess necessitates. One fact in regard to upset-bars must not be overlooked, and that is the distortion of the fibre, and consequent change in the character of the iron. This is sure to be extreme, if the operation is performed under too low pressure, or if the bar is heavy and the head large, in proportion to what may be called the mass of the upsetting-machine. Where bars are wide and thin, there is a very great distortion of fibre since a large amount of iron must be forced back to fill the moulds, and which a slight etching with acid will develop very clearly. It is owing to the dete- rioration of the iron in the heads of upset-bars that American experiments have resulted in somewhat dif- ferent proportions from those made in England on bars of English manufacture. Whether upsetting is done by repeated impact, or by the steady, continuous pressure of the hydraulic ram fed from an accumulator, there is a marked difference in the result. Iron is most susceptible to change of form without deterioration when operated upon in a highly heated state, and since a bar commences to cool the moment it is taken out of the furnace, the most rapid means of shaping it will injure it the least. A fibrous bar, operated upon in a cold state, will be so modi- fied in its molecular arrangement as to become crystal- line. Again, in operating upon the end of a bar, just from the heating furnace, it must of course be firmly gripped 54 IRON HIGHWAY BRIDGES. behind the die, and where the iron is comparatively cold. In the case of slow, upsetting by impact, the iron is grad- ually crowded back from the soft end, the effect of each blow being less and less as the metal gets cooler and the fibres become compacted. At the end of the operation, the metal will have chilled off rapidly, and near the base of the upset be almost cold. At the point of " grip " the metal becomes more or less crystallized, according to the temperature at that point. In view of this effect of tem- perature on iron, it follows that upsetting should be only performed by continuous pressure, by means of which the iron may be driven back in the die at welding heat, at one stroke of the piston. Screw-ends are sometimes used for the upper ends of the diagonals, and form their connection with the top chord through the medium of a casting, which requires a very awkward and ugly enlargement to admit of their passage. Screw-ends should be enlarged over the body of the bar by upsetting, so that the cutting of the screw- threads will not diminish the sectional area. A serious objection to the use of screw- ends arises from the fact that they are a temptation to those custodians of public works who have a mania for screwing up any thing they can get a wrench around, and so, in their efforts to " ad- just " a bridge, they are very apt to leave the diagonals under different degrees of tension. To adjust screw-ends properly, the workman must combine the " feel " of the wrench with the striking of the bars, so as to judge of the tension by the sound, which involves somewhat of a mu- POSTS AND THEIR STRENGTH. 55 . sical ear, not possessed by every mechanic. Practically it is impossible to tap nuts so that they correspond with the threads of the screw. The dies will wear, no matter how carefully they may have been hardened, and the harden- ing process itself must affect the character of the threads. The post connection with a pin is made through the medium of " shoes " or " bases," either of wrought iron or cast, or both combined, depending on the form of post used. The bearing on the pin, or, in other words, the thickness in inches of that portion of the shoe through which the pin passes, should be not less than the com- pressive strain (as exhibited in the line diagram of strains which ought to accompany all proposals) in pounds, di- vided by twelve thousand times the diameter of the pin. The sections of posts in ordinary use are exhibited here- with in the order of their relative theoretical merit. The FIG. 15. SECTIONS OF POSTS OR STRUTS. first is the Phoenix hollow column ; the next four are made from solid rolled sections, and the last and weakest are compounded sections, as shown.* The resisting power of posts is based upon the ratio of their length divided by their diameter, and also upon the fact of their having round or square end connections. For the first five sec- * The last four sections are the forms of struts used in riveted work, and it needs not the eye of an expert to realize that they are immeasurably inferior ,to any of the preceding sections. 5 IRON HIGHWAY BRIDGES. tions, the diameter to be taken, in determining above ratio, is the least side of the least rectangle with which they can be circumscribed. For the other sections, two thirds of the least side must be taken for the diameter. While this method of determining effective diameters is not absolutely accurate, it is sufficiently near the truth to test the merit of competitive designs. Where a post bears directly on a pin, it should be regarded as having a round end. There is probably no property of iron about which less is positively known than its real strength when in the form of posts or columns. Certain general laws have been determined by the experiments thus far made, among the most important of which are the following : The strength of a column with square end bearings being called unity, that of a column with both ends rounded (like the ends of an egg) will be one third, and that of a column with one end square and one end round will be a mean between the first two. That is, the numbers i, f and \ represent the relative strength of columns, according as the bearings are square, one round and one square, or both round. The formula mostly in use for computing the strength of posts is an empirical one, invented by Lewis Gordon, of England, and is based upon the experiments made for the British Board of Trade, by Eaton Hodgkinson, about 1840. Gordon's formula is simpler in application than those de- duced by Hodgkinson, and, when properly applied, expe- rience has shown it to be abundantly safe. The original formula is as follows for square-end columns, and should STRENGTH OF COLUMNS. 57 9 be corrected for pin or round bearings by one of the three laws above given : T-V T . i j r ) 36,000 x area section Breaking: load for ( 7T ^ 2 s , . > = i /length of column\ wrought-iron i i + - ~j-- } 3000 \ diameter / The same formula for cast-iron, using 80,000 in nu- merator of fraction instead of 36,000, and -%fa in denomi- nator instead of ^oVo"- The constants in the numerator are intended to represent the average crushing strength of a short piece of the respective kinds of iron. Modern experiments have, however, shown that the ultimate crushing strength of American wrought-iron is much higher than that assumed in the formula namely, 36,000 Ibs. per square inch, by at least 20 or 25 per cent, In fact, so much depends upon the kind of iron, that no one constant is suitable for undeviating use. A column made from a hard iron inclined to granular, as it should be, will resist crushing better than a soft fibrous iron, or one of great tenacity, and consequently a much higher con- stant may be used. The following table has been com- puted from Gordon's formula, using 45,000 in numerator instead of 36,000, for wrought-iron that for cast-iron re- maining the same as in the original formula. It must be understood that any of the published tables for the strength of columns are purely tentative, to be modified by such light as farther experiments alone can give, and which it is hoped that the present Government Com- mission on the " Strength of Iron and Steel," appointed by Congress in the spring of 1875, will early institute. IRON HIGHWAY BRIDGES. TABLE SHOWING THE BREAKING STRENGTH PER SQUARE INCH OF WROUGHT AND CAST IRON COLUMNS, COMPUT- ED FROM GORDON'S FORMULA : Crushing strength of wrought-iron taken at 45,000 Ibs. per square inch. ' cast " " " 80,000 " " Values given are in pounds for each square inch area. Ratio of Length to Diameter. See page 56. i. Breaking Load : Square Ends. II. Breaking Load : Round Ends. in. Breaking Load : One Round, One Square. i Wrought Iron. Cast Iron. Wrought Iron. Cast Iron. Wrought Iron. Cast Iron. 10 15 20 25 30 35 40 45 5o 43562 41860 39717 37251 34615 31960 29355 26866 24545 64000 5I2OO 4OOOO 31220 24617 19692 I6OOO 13196 II035 I452I 13953 13239 I24I7 HS3 10653 97*5 8955 8182 21333 17067 13333 10407 8206 6564 5334 439^ 3678 20042 27906 26478 24834 23076 21306 19570 I79IO 16364 42666 34134 26666 20814 16412 I3I28 10668 8798 7356 FIG. 16. TOP CHORD SECTIONS FOR PIN CONNECTIONS. RIVETED SYSTEM The tipper chord has often a similar section to that of the posts, but when not circular is usually shaped like a box, the sides of which are channel or beam irons, and the top a broad plate. The under side of such a box, when open, should be stiffened with diagonal lattic- ing or broad batten-strips, so as to aid in the preservation TOP CHORD SECTIONS. 59 of its form under the compressive strain to which it is subjected. The allowable strain per square inch on chords is governed by the same rule as that for columns ; the ends being considered square, and the length of the chord the distance between two panel-points. The top chord may have simple machine-faced butt joints, or it may be made continuous in sections, the contiguous abut- ing surfaces being joined by fish or splice plates riv- eted or bolted to them. Such plates serve simply to keep the chord in position, and are not subjected to any strain whatever. Under this last arrangement, there would be attained all the advantages that can possibly be claimed for riveted work namely, perfect continuity of material. This principle, combined with the American system, re- sults in a structure that harmonizes theory and practice in the highest attainable degree. With some forms of compressive sections, like the Phoenix column, or the three-beam section, it is desirable, in fact necessary, that a casting be introduced to connect the several parts that cluster at the panel-points. This casting must have all its bearings machine-faced to match the faced ends of the chords and posts. In continuous box-shaped chords, the pin-holes must be reinforced with thickening plates, not only to increase pin-bearing, but also to distribute the pressure delivered to the chord at each panel-point over as much surface as possible. Further, it is advisable that the increased sectional area required at each panel-point, in approaching the centre, be placed in the sides of the box, as it is through the sides that the pin passes. It is 6O IRON HIGHWAY BRIDGES. not one of the least of the excellencies of the pin-con- nection system that the chords, posts, and tension-mem- bers may be made to unite at the centre of their several sections, and by proportioning the box chord as above this may be accomplished very fully. The advantage of a cast-iron joint box consists in the very perfect attain- ment of this principle, as such boxes insure an absolutely uniform distribution of pressure over the surfaces of con- tiguous chord sections. This principle is about as far lost sight of in riveted work as it is possible to be. In such work the chords have no stiffening along the inner edges of the vertical plates or sides to which the web system is riveted, and the increase of area is made by riveting on plates to the upper side of the top chord, or lower side of the bottom. The centre of section is not at the middle of the sides, as usually assumed, but approaches the top or bottom plates, and in large spans, where the strains are great, necessitating a large area of section (placed mostly in the above plates), the centre of section approaches the plates very rapidly. In applying the for- mula for posts, therefore, to such chord sections, the dia- meter used for determining the ratio of " length to diameter" must not be taken as equal to the side of the least circum- scribing rectangle, but must be a much smaller quantity. Just what this quantity is may be ascertained by reference to special treatises on engineering, since it involves con- siderations too technical to introduce into a book of this character. It will be sufficient for our purpose if the reader realizes that a box or trough-shaped compression AMERICAN AND RIVETED SYSTEMS COMPARED. 6 1 d chord, having most of its metal on the upper side, is weaker than one which has the metal equally distributed among the three sides, and for the weaker chord proper allowance must be made. In "pin-connection" chords, the pin-holes must be bored with the same care as eye-bars; the maximum play between pins and holes not being permitted to much exceed -^ of an inch. From what has been said, in describing the various systems of bridge-building in use namely, the " riveted," the " pin," and " screw-end" connections it will be under- stood how it is that the two latter can be worked very close to absolute theory, thus enabling material to be disposed in the best possible way to concentrate strains at centres of sections, and distribute them in axial lines through the various parts of the structure. Further than this, the shape of material used in designing on these systems is such that proper grades of iron are readily attainable. The riveted system has, of necessity, so many imper- fections of design, of workmanship and material, in contrast with the above, that, to obtain any thing ap- proaching equal strength on the same specification, it should only be used with a higher factor of safety. It is probable that this difference is not less than 20 per cent ; so that when a pin bridge is called for, having a factor of Jive, a riveted bridge can not be considered as approaching the same strength unless it is proportioned with a factor of six. The fact that a riveted bridge is stiff, or that its deflections may be small under a test, is no 62 IRON HIGHWAY BRIDGES. evidence of strength, which last depends upon other considerations than those applying to stiffness. The stiffness of a girder depends upon the average sectional area of the flanges and web, while the strength is measured solely by the net sectional area at any point. A girder, for example, having uniform flange areas from end to end, would be stiffer than one having this area only at the centre, and diminishing with the diminution of strains toward either abutment, but it would not be stronger. The amount of metal at the weakest point determines the strength of the girder, and since this is a matter independent of stiffness, it follows that the ad- vocates of riveted work practice a deception on the public (perchance themselves) in pointing to the wonder- ful stiffness of the lattice bridge, as a triumphajit refuta- tion of the damaging criticisms made by those who have well weighed the respective merits of the various methods of bridge-building. THE FLOORING SYSTEM. If there is one part of a bridge more than another that can be claimed to be of supreme importance, it is the flooring system, to a careful proportioning of which more attention has been paid during the last few years than ever before. A good, stiff floor is a pretty fair criterion of the rest of the work, as well as a comfort to the travelling public. The various elements of the floor system are the cross-beams, the stringers, the connection with the trusses, the sway-brac- ing, and the floor-covering. The cross-beams, often called floor or needle beams, FLOORING SYSTEM. 6 (f may be either solid rolled flange-beams, single or in pairs, or beams of lighter section deeply trussed ; or, finally, riv- eted plate web-girders, the two last being better than the fi rs t not that they are necessarily stronger, but from the great depth thereby attainable, there is less spring to FIG. 17. 12. 0. 8. 0- HALF SECTION PLAINFIELD BRIDGE. SIDE VIEW PLAINFIELD BRIDGE, 104 FEET SPAN. BY THE AUTHOR. 64 IRON HIGHWAY BRIDGES. them under rapidly moving loads, with a proportionate gain in stiffness. In the best designs, cross-beams are located at panel-points, and they must be proportioned to carry the wheel-loads previously indicated. When sidewalks are to be carried outside of the trusses, the floor- beams of the roadway are prolonged on either side to sup- port them, although occasionally circumstances may arise when the sidewalks must be supported by independent cantilevers bolted or riveted to the outside faces of the truss-posts. All things being considered, the compound riveted girder is probably the best form for floor-beams, because they can be made deep. A good depth for such girders in the middle is one tenth the width of roadway, but for long panels and heavy loads a still greater depth will often be found more desirable. A short distance either side of the centre, the bottom-flange may be tapered up gradually to the point of support. This form, even when not dictated by motives of economy, is very much more sightly than if the flanges are kept horizontal and parallel from end to end/ The thickness of the web in such girders is usually from J to T 5 T of an inch, and the flanges should be so arranged as to be formed from but two angle-irons, the section of which must, of course, be determined by the extreme strain at centre of beam, This is a matter easily attained, since the sizes of angles vary so much that any desired area may be found in the lists of the principal manufacturers. The objections previously advanced against riveted work have least force in such girders as are above described, there being but a FLOOR-BEAMS AND THEIR RIVETING. 65 single line of rivets which unite the solid flanges to the web, and the number and proportion of the rivets can be computed with a fair amount of accuracy. Special atten- tion is called to the idea of solid flanges, implied in the recommendation for using but two angle-irons, as opposed to a very common practice of using light angles, and in- creasing the sectional area toward the centre of the beam by riveting on plates to the angles, whereby the complex- ity of riveted work is introduced, which it is desirable to avoid in every instance where possible. Sufficient attention is rarely paid to the riveting, the pitch of the rivets (that is, the distance from centre to centre) being usually too great. Thin webs require close riveting, and the rivets should be well driven, by power if possible, since in this way alone can any reliability be placed upon the holes being well filled. No exact rule can be given for the pitch of rivets, as it is a matter of computation in pounds, of just how much horizontal strain is delivered by the web at any given point to the flanges. As this web-strain increases to- ward the ends of a girder, the rivets should be placed closer as the ends are approached. The pitch will vary from 3 to 6 inches, depending upon the above considera- tions, and the smallest size rivet that should be used in the flanges is f of an inch, which becomes ^ greater after being driven, where the hole is properly filled. The web requires occasional stiffeners, usually two, intermediate between supports, for ordinary widths of roadway, and one at either point of support. If the web is of such 66 IRON HIGHWAY BRIDGES. thickness that the distance between the flange angle-irons is not greater than thirty to thirty-five times that thick- ness, no stiffeners will be required. Since there is no difficulty in obtaining the pieces composing a compound girder in one length between bearings, nothing has been said about joints. Should these occur, either in flange or web, pains must be taken to have splices of ample size, and a full complement of rivets, to thoroughly trans- mit the strength of the solid sections so united. Solid rolled beams are 10 per cent stronger than riveted beams, but are much more expensive per pound, the difference at present (1875) being 25 per cent and upward.""" Such beams, in double-track roadways, from their shallowness, spring too much, throwing the trusses into an annoying vibration, to say the least, even from light passing loads, and conveying an idea of weakness, which the structures may not really possess. The connection of the floor-beams to the trusses, for deck-bridges, is a very simple matter, as they are then directly bolted to the top chord. For through bridges, or half-deck bridges, they are either hung from the pin by means of hanger-bolts, or they are riveted or bolted to the posts. When hung from the pin, the hangers are best of the f] form, the legs being long enough to pass down the full depth of the floor-beam at that point, through a washer-plate (by preference of wrought-iron) * Since the above was written, the price of beams has been reduced fully the amount of this difference. STRINGER-BEAMS. 67 on which the beam rests. The end of each leg is furnish- ed with a nut, sometimes with a jam-nut in addition; which, when drawn up, holds the beam securely in place. Inasmuch as these hangers are short, and always feel at once the effect of the passing load, they should be of first- quality iron, and not be strained in excess of 8000 Ibs. per square inch at the root of the screw-thread. They should have a flat bearing on the pin, and may be either single or in pairs. When the beams are riveted to the posts, usually between them, the connection is made by means of angle-iron brackets, one on either side of the web, arid in length equal to the whole depth of the beam at the bearing, and since this attachment depends solely on the strength of the riveting, and since the riveting must be done on the ground after the work is in posi- tion, an excess of rivets should be arranged for, to com- pensate for the imperfections of field-riveting, which is usually more difficult to get at than in the shop, and consequently not so well done.* The horizontal or sway bracing may consist of very light rods, if the floor is well laid, forming as it does a very effective system of bracing against lateral movement. Rods from f to i inch round will cover all but extreme requirements, and they are attached by any convenient means to the floor-beams near their point of support. They require a screw-adjustment of some kind, turn- buckles or end-screws, in order that they may be drawn up taut. On top of the floor-beams, and lengthwise with the bridge, are laid the stringer-beams. These beams * See Plainfield Bridge, page 63. 68 IRON HIGHWAY BRIDGES. may be either of wood or iron, and are spaced from two to three and a half feet apart, depending on the character of the flooring and the loads to which the bridge is liable to be exposed. If stringers are proportioned for wheel loads, as has been recommended, their size is independent of their distance apart, since, however great their number, a wheel may be immediately over any one, straining it to the maximum. Where a roadway is regulated by guard- timbers, confining the wagon-tracks to a fixed position, the stringers may be made heavier immediately under the track-way, and lighter under the rest of the flooring. For wooden stringers, white or yellow pine is the best kind of timber, such varieties of timber being obtained of straighter grain than most any other, and consequently are peculiarly well adapted for resisting the effect of transverse strain. Stringer timbers should be inspected with greater care than is given to the floor-planks, not only on account of their position as beams, but also be- cause floor-planks, under most circumstances, will wear out before they will rot out, while the stringers, not being exposed to the abrasion caused by horses and vehicles, become destroyed by decay, the date of such destruc- tion being dependent on the practical knowledge of the timber inspector. Wooden stringers should be uni- formly notched down on the cross-beams, which not only aid in retaining them in their position, but also insure uniformity in the level of their upper surfaces. The fol- lowing table will be found convenient in determining the size of timber to be used for different panel-lengths : PROPER SIZE STRINGERS FOR GIVEN WHEEL LOADS. 69 Table giving proper size of wooden stringers, for supporting different assumed wheel-loads, supposed to be concentrated in the middle of a panel, the timber being strained to 1200 Ibs. per square inch. LOADS ON ONE WHEEL. Span or panel-length. 500 Ibs. 1000 Ibs. 1500 Ibs. 2000 Ibs. 2500 Ibs. 10 feet. 2x8 3 x 8 3X9 3x9 3 x 10 12 " 2x8 3 x 8 3 x 10 3 X 12 4 x 12 14 " 2x9 3x9 3 x ii 3i x 12 3 x 13 18 " 2 X 10 3 x 10 3 x 12 3 x 14 4 x 14 20 " 3 x 10 3 x 12 4 x 12 4 x 14 4 x 16 Iron stringers are simply rolled I beams, of proper strength for the wheel loads, and may be had of any depth from four inches (weighing ten pounds per foot), upward. Where they rest upon the floor-girders, they should be secured by means of bolts, clips, or brackets. * Table giving proper size of iron stringers, for supporting different assumed wheel-loads, supposed to be concentrated in the middle of a panel, the iron being strained not over 12,000 Ibs. per square inch. LOADS ON ONE WHEEL. Span or panel- length. 500 Ibs. 1000 Ibs. 1500 Ibs. 2000 Ibs. 2500 Ibs. 10 ft. 12 " 15 " 18 " 20 " 4" 61bs.p.ft. 4" 6 ' 5" 10 " 6" 1 3 7 "i8 " 4"iolbs.p.ft. 4" 10 " " 5" 10 " " 6" 13 " 7"i8 " 4" 10 Ibs. p. ft. 4" 10 " 5" 10 " " 6" 13" ' 7"i8 " 5"iolbs. p.ft. 5" 1 2 " 6" 1 3 " " 7*18 " f 1 8 " 5" 1 2 Ibs. p.ft. 6" 13 '* " 6" 13" 7" 18 " " 7 "i8 " " FLOORING. The flooring of common road-bridges usu- * The sizes of beams recommended in the table are the nearest mercantile sizes that fulfil the requirements. This in some cases necessitates the use of beams in excess of that called for by the loads. It was thought best to use none lighter than the seven-inch beam for the twenty-feet panel-lengths, since shallower beams would be apt to spring to an undesirable extent. 7O IRON HIGHWAY BRIDGES. ally consists of one course of plank, laid transversely to the stringers, and about three inches in thickness. Occa- sionally two courses are used, in which case it is a good plan to apply to the lower course some of the wood-pre- servative processes, and the cost of such application can be balanced by using a cheaper grade of timber than would otherwise be proper such as spruce. If wooden stringers are used, they may also be chemically treated, when the sub-floor can be regarded as measurably per- manent, the only renewals being that of the upper hard- wood plank, as it becomes worn. When two courses are used, the lower one should be not less than two and a half or three inches in thickness, and the upper two inches, which last, if laid diagonally to the lower course, will materially stiffen the floor as a whole. The planking is spiked directly to the stringers, if of wood, with spikes having a length of about double the thickness of the plank. When two courses are used, each course should be spiked down independently. It is not necessary to spike at each stringer intersection, every other one being sufficient ; but where spiked, there should be two spikes used, one at either edge of the plank. Where iron stringers are used, the simplest method of securing the floor-plank is to lay a spiking timber on either side of the roadway, and one or more between, to which the planks are fastened in the usual way. This arrangement avoids the necessity of using hook head-bolts, clinch- spikes, and other troublesome devices required if the at- tachment is made directly to the iron. On either side of GUARD-TIMBERS LAYING SIDEWALKS. 71 the roadway there should be bolted to the flooring, guard- timbers of hard wood, with the inside edge chamfered off to make a finish. These guards should be located far enough from the trusses to prevent the wheel-hubs from striking them, and they should be raised by means of blocking, at intervals of five or six feet, about three inches, to aid the drainage, and add to their effective height. Pieces of the floor-plank, about eighteen inches long, will be found convenient for this blocking. The guard-timbers had best have lap-joints, which laps should be about twelve inches long, and secured with two bolts. Where there are sidewalks, it is desirable to have them raised above the level of the roadway, which can best be done by means of hard-wood bolster-pieces, at intervals of about four feet, laid transversely with the stringers, and of a depth equal to the desired elevation of walk. With sidewalks projecting beyond the trusses, necessitat- ing a stiff independent railing, a rail-base should be fast- ened with two bolts to the ends of the bolsters, and have a projection of about three inches. This rail-base is usu- ally from twelve to sixteen inches in width, the upper edges being neatly chamfered, and the exposed surfaces planed. On the inside edge of the bolsters, and bolted to them, next the trusses, there should be a deep guard- timber, at least twelve inches higher than the walk, and if desired, as an additional precaution, a few slats can be spiked between the sidewalk and roadway-guards, cover- ing the otherwise open space between them, unless it happens that the roadway-plank are fitted around the 72 IRON HIGHWAY BRIDGES. posts, and carried close up to the sidewalk. With the above arrangement for supporting the- sidewalk, it is ne- cessary to lay the plank (about two inches thick) longi- tudinally with the bridge, spiking to the bolsters with two spikes at each intersection. It always makes the most satisfactory walk to have the planks narrow, and edged to a uniform width. They should be laid one half inch apart to form drip-spaces, and in first-class work the upper surfaces of the planks should have been planed before laying, as well as that of the rail-base and inner guard. The planed surfaces ought to be well oiled, not alone as an inexpensive finish, but also to protect the plank in a measure from sun-cracking. The best kind of wood, be- yond all question, for sidewalk plank, is yellow pine. The cornice, of i^-inch clear pine, is fastened to the ends of the bolster-pieces, and a bold moulding is nailed under the projection of the rail-base. A very slight ex- pense will provide a neat scroll " drop " opposite the end of each floor-beam, which, trifling as it is, materially adds to the appearance of a bridge. The above descrip- tion of the floor may be considered a standard method for the general type for road-bridges ; but in important city bridges, floors should be made very much more durable than has thus far been customary in this country, except in a very few localities. It is true that durable floors, either of wood or stone paving, add vastly to the cost of a structure, increasing as it does the dead load to be carried, but in many cases it is warranted by PERMANENT FLOORING. 73 the circumstances of heavy travel, the interruption to which through frequent repairs (as would necessarily be the case for an ordinary wooden floor) would cause great FORMS OF WROUGHT-IRON FLOOR-PLATES. FIG. 18. FIG. 19. FIG. 20. BUCKLE-PLATE. CORRUGATED PLATE. ZORE, OR FRENCH SECTION. inconvenience. Any kind of paving that may be used requires an iron floor, which may be made of wrought- iron plates, -^g- to T 5 ^ of an inch in thickness, in the form of broad corrugations laid transversely, or buckle-plates, which are rectangular plates about 3 ft. square, domed or crowned under pressure a height of three or more inches at the centre, and having flat edges on all four sides, to allow of riveting to the stringer-beams. The general appearance of these plates is that of a flattened dome. After the floor is thus formed, it must be levelled off with well-made cement concrete, to a depth of four inches and upward, to form a bottom for the paving. This concrete must be prepared with great care, as upon its excellence depends the protection of the iron plates from water, which, at the best, it is very difficult to keep from working its way through the roadway ; and as floor-plates are made from comparatively thin iron, perfect immunity from rust is the price of their durability. In view of 74 IRON HIGHWAY BRIDGES. this fact, as an additional precaution, after the concrete has been levelled off, or rather crowned to the usual street regulations, and had time to harden, it is well to coat the whole surface of concrete about an inch thick with as- phalt mixed with fine ashes, to add to its body, flashing it up at least six inches against all projections where it would be possible for water to trace through and get at the iron of the flooring system. On the surface thus pre- pared, the roadway, gutters, and sidewalks are laid as in the ordinary street, only with greater care. A proper provision for drainage must not be overlooked, and fre- quent spouts ought to be introduced to carry the water rapidly away, clear of the trusses. While Macadam and stone-block pavements have been used for bridge-plat- forms, they are enormously heavy as compared with wood, and, while more expensive in themselves than a wood-block pavement, add very largely to the genera! cost of all the iron-work, owing to their excessive weight. Under most any circumstances, wood blocks are the best for bridges, and if they have a good, uniform bottom to rest upon, the conditions that have caused the failure of the wood-block pavements in most of our cities are re- moved. Blocks four inches deep will answer all require- ments for ordinary traffic, and a depth of six inches the heaviest. The blocks should not rest immediately upon the prepared floor surface, but on tarred, well-seasoned plank, one inch thick, with a thin layer of fine sand in- terposed between the asphalt and the plank. BEAM-BRIDGES. Special notice is directed to the BEAM-BRIDGES. 75 construction of beam-bridges, as an economical substi- tute for the ordinary stone arch and culverts so much in use throughout the country. Apart from economical considerations, they afford an increased water-way, and thus avoid the liability to disastrous overflows during sudden freshets, as is almost sure to be the case when a freshet meets with an obstruction like an arch, which, if made large enough to easily pass extreme floods, would become comparatively a very expensive affair. There is hardly a town or village through which a brook runs, that has not suffered more or less damage through the incapacity of arch culverts to carry off the water of an unusual freshet. Beam-bridges can very readily be carried up to spans of 25 or 30 feet, and if properly designed, and the exposed parts occasionally painted, can be regarded as durable as the old-fashioned stone arch. The flooring of such bridges may be simply plank (Fig. 21), or it may be made permanent, as before de- scribed, with iron floor-plates and paving (as in Fig. 22). i i FIG. 22. BEAM-BRIDGE NICHOLSON PAVEMENT ON BUCKLE PLATES. 76 IRON HIGHWAY BRIDGES. A very excellent floor is one made with brick arches turned between the beams, and laid in cement mortar, very similar to the ordinary fireproof floor (see Fig. 23). aiiML^illi^ ^^i^^^lij^i^ FIG. 23. BEAM-BRIDGE TELFORD PAVEMENT ON BRICK ARCHES. The arches are levelled off with concrete, and the pav- ing, or Telford, laid on the concrete surface previously coated with asphalt. For these bridges, solid rolled beams or compound plate-girders are used, spaced from 3 to 5 feet apart, with tie-rods at intervals connecting their lower flanges. The compound beams, not being restricted in depth, and costing less per pound, will usually be found the most desirable. The temptation to use thin web-plates in such girders, from motives of econ- omy, should be avoided, as a percentage of rust must be provided for, either on account of possible neglect, or from carelessly-laid brick-work and concrete, allowing water to trace in alongside of the inaccessible plates. Before brick arches are turned, a further precaution than those named should be used, and that is to thickly coat the girders with a tar paint of some kind. Perpetuating the life of iron-work is very often simply a matter of inex- pensive, preliminary precaution, which, if once realized, would be oftener put in practice than it is. WIDTH OF ROADWAYS AND SIDEWALKS. As to the proper width of roadways and sidewalks, where street regulations do not impose carrying the whole width of the street over the bridge, the circum- stance of location is very occasional where more than two wagon-ways are necessary. Eighteen feet between the side-guard timbers are amply sufficient for all ordi- nary traffic, and in many cases sixteen feet will be found sufficient. A greater width of roadway (excepting sufficient width is added for a third wagon-track) involves an unneces- sary expenditure of money, since the bridge, being pro- portioned for a certain number of pounds per square foot, each unnecessary foot in width, requires just so much more material, which rapidly becomes transformed into dollars, without a particle of advantage accruing. The great difference will be found in the floor, since the cross- beams increase in weight very rapidly, as the width of the roadway increases, and the number of stringers is also increased. A rule then to determine how wide a roadway should be made is to determine the minimum width, with a margin for clearance, for one wagon-way. Then two or three times, this, according as there is a double or triple wagon-way to be accommodated, will give the distance between roadway-guards. Sidewalks, if on either side, need not be made wider than four feet in the clear; but if only one sidewalk is to be provided, 78 IRON HIGHWAY BRIDGES. having to accommodate travel in opposite directions, a width of six feet in the clear will be found sufficient. When bridges are of such span as to necessitate a height of truss requiring overhead sway-bracing between the trusses, a clear height of from thirteen to fourteen feet above the flooring will be found to answer all but extreme requirements. WEIGHTS OF MATERIAL, ETC. In designing a bridge, the weight of the flooring must be first computed, and it is a fixed quantity, inde- pendent of the span, for the same width of roadways, sidewalks, and panel-lengths. It forms the principal part of the dead load in spans up to about 100 feet, and in addition to the weight of material of which it is com- posed, some consideration must be paid in northern cli- mates to snow-loads, which add to the dead weight ten to fifteen pounds per square foot. It is impossible to give a reliable rule for the dead weight of the iron and other materials entering into the construction of a bridge, depending as they do upon peculiarities of form and construction ; but the following data, as far as it goes, will assist any one in determining this important preliminary in proportioning the parts of a given design. A yard of wrought-iron, having one square-inch section, weighs ten pounds. So that, know- ing the area in inches of a given piece of iron, all that is necessary is to multiply it by ten and divide by three, to THE MAINTENANCE OF IRON-WORK. 79 f have the weight per lineal foot. A cubic inch of cast- iron will weigh ten per cent in excess of one quarter of a pound. The weight of timber varies according to its condition, whether dry or wet, a fair average being given as below : White pine, 3 Ibs. per sq. ft., B.M. 6 Ibs. for 2 in. plank, 9 Ibs. for 3 in. Yellow " 4 " " " " 8 " " " " 12 " " " Oak " 41 " " . " 9 " " " " 131 " " " FOR PAVEMENTS. Wooden block, as Nicholson, 25 to 35 Ibs. per square foot, according to depth of blocks. Telfora and Macadam 130 Ibs. per cubic foot. Stone block 150 " SUPPORTS OF PAVEMENTS. Wrought-iron Buckle-plates, etc., depending on thickness : a square foot of one quarter inch plate-iron weighs 10 Ibs. Brick-work, when turned arches are used 120 Ibs. per cubic foot. Concrete, for levelling off no to 130 " " " " Gravel.. 120 " " " " Hard asphalt 140 " " " " THE MAINTENANCE OF IRON-WORK. This subject has not received the degree of attention which so costly a structure as an iron bridge warrants. Too often insufficient painting is allowed to remain as the only protection for years, the fast-accumulating rust either not being noticed, or is not seen, owing to the peculiar color of the paint which may have been used. Because a bridge is an iron one, it does not imply that it 80 IRON HIGHWAY BRIDGES. requires no further care after it is once finished*. When iron is neglected, it is only a question of time as to its final destruction. A large bar will rust out only less rapidly than a small one, or a thick plate than a thin one, and there are circumstances of location that will cause rust- ing to proceed with varying rapidity. It is with a view to permanence of iron structures that it is recommended in no case to allow of plates or parts to be used less than one quarter of an inch in thickness, and perhaps five six- teenths of an inch would be still more desirable as a minimum thickness. It is further advisable to have iron bridges so designed that all parts of the work should be open to inspection, and within reach of the paint-brush. When not so designed, concealed surfaces should be her- metically sealed, so that by no possibility can moisture find its way within to work a sure destruction. Town authorities should insist upon more care being exercised at the construction-works, in preparing iron for shipment, than is usually given to such matters, particularly in times of close competition, when the profit of a con- tractor is made up from small economies. This extra care will amply repay the very small addition to the price that it would necessitate. At the manufactory, each individual piece can be ex- amined and protected with a care impossible to exercise after the parts are all assembled in position at their final location. All new iron, as it comes from the rolling-mill, has a scale on its surface easily detached under vibra- tion. More or less falls off while it is undergoing fabri- PAINTING OF IRON-WORK. 8 1 , cation into shape, but enough usually remains on, to render ineffective the paint with which it may be coated. This scale should be thoroughly removed at the shop by scraping, or with wire brushes, after which a priming coat will take hold. Some authorities recommend that before scraping off the scale, the iron should be allowed to rust slightly, as giving a better hold for the paint. In any case, the paint should be thoroughly well rubbed into the surface, and the boiled oil and turpentine with which it is mixed, and on which its value largely depends, should be of the first quality. All things considered, the mineral paints prepared from iron ores are the best priming paints, since they are inexpensive, and therefore unadulterated, which can not be said of many of the red leads (a favor- ite priming paint with some engineers) in the market. Before shipment, iron surfaces that have had machine-work put upon them, called bright iron, should be coated with tallow, to which a body of white-lead has been given. After a bridge has been erected, it should have at least two coats of tinted lead paints, care being taken that the brush reaches all the crevices about the joints. The color of the final coat or coats had better be of such a tint as will show the first indication of rust. All tints bordering on cream, buff, and different greys, answer this purpose excel- lently well ; and as an additional advantage, these tints form a pleasing and appropriate ground for decorative effect, occasionally required for first-class city bridges. It is recommended that all iron bridges should have two addi- tional coats of lead paint the second season after their 82 IRON HIGHWAY BRIDGES. erection, which will last several years before requiring renewal, and it would be good practice for the authorities of every county to examine their bridges systematically every spring for signs of rust, which, if discovered, should be attended to as soon as possible. In this way their bridges (if originally good ones) can be made to last for- ever. THE ARCHITECTURE OF BRIDGE- BUILDING. In the true sense of the term architecture, unadorned construction is as much a part of architecture as the more popular idea that it simply covers the art of producing pleasing effects. A man can not be a good architect before he is a good constructionist, no matter how dextrous he may be in devising graceful forms, or artistic in his selec- tion of colors. In bridge-building, there is little room for artistic architecture, and any pleasing effect produced must grow out of consistency of design, and a thorough knowledge of the peculiarities of materials of construction and color. To an educated person, correct construction always produces a sense of satisfaction, for in it is involved the idea of proportion and appropriateness for the ser- vice to which it is put. Concealment of constructive forms, by mouldings, panels, or other devices, to suggest something else than what the construction really is, is vulgar as well as dishonest. To construct a girder bridge, and give it the appearance of being an arch, il- lustrates what is here meant by falsity in architecture, BRIDGE ARCHITECTURE. 83 specimens of which more than one of our public parks contain. Possibly to bridges more than to any other class of public works does the Ruskinian axiom (which can not be repeated too often) apply : " Decorate the construction, but not construct decoration." Such a principle conscientiously kept in view can not but result in else than good work. Its violation results in a sense- less fraud, demoralizing to the taste of the community where such violations may occur. Public works, in a certain sense, play a part in the education of a people, and their authors and builders have consequently, to that extent, a responsibility in addition to the mere utilitarian idea of endurance and safety. The ideas herein ad- vanced are not novel ones by any means ; but they can not be enforced too often, when in this boasted age of culture and civilization a community will permit the huge architectural fraud of the Fairmount Bridge over the Schuylkill at Philadelphia, and hardly yet completed. Constructively, this bridge, with its double tier of floors, spanning the Schuylkill, in a single stretch of 340 feet, is a monument to its designer and an honor to Ameri- can engineering. Instead, however, of letting the enor- mous trusses stand in all their grandeur, depending wholly upon judicious painting and the design of the cornices and railing, etc., for their aesthetic effect, thousands of dollars have been spent in actually cover- ing up the trusses to a great extent with sheet-iron, form- ing an arcade as it were of great massiveness, by arching between the posts of the trusses, the arches springing 84 IRON HIGHWAY BRIDGES. from large Roman sheet-iron capitals about half way down the posts ! The result is that, at a little distance, the spectator beholds an arcade, without any visible means of support for a distance of 340 feet. To be thoroughly consistent, the architect (heaven save the name !) of this constructed " decoration " should have at least sanded his sheet-iron when painted, and marked out in strong lines the joints that masonry of similar forms suggests. About one mile north of this bridge, a noble structure spans the Schuylkill, the Girard Avenue Bridge, as it is called. As an engineering accomplish- ment, it stands in no comparison with the bridge at Fairmount, the spans being much smaller, and only a single roadway (of paved granite) is carried on the upper chord, it being a " deck-bridge." Architecturally, it is certainly one of the finest, if not the very finest, bridges in America ; while in the same sense the Fair- mount bridge is the worst, and probably the worst in the world. The Girard Avenue is an example of pure decorated construction, and the writer is aware of no place in this country where the principles for \vhich he has been contending can be so well illustrated as in the case of these two Philadelphia bridges. A thirty-minutes' walk will carry a spectator between these two extremes of very good and very bad bridge architecture. As before remarked, a truss-bridge presents little opportunity for architectural effect, further than what is due to correct construction, and the taste shown in the colors with which it is painted. In a through bridge, BRIDGE ARCHITECTURE CONTINUED. 85 and where the span is such as to necessitate a depth of truss requiring overhead sway-bracing, neat corner- brackets (either of wrought or cast iron) connecting the vertical posts with the horizontal struts of the upper sway-bracing, may be appropriately introduced, since they act as knee-braces, materially stiffening the trusses against vibration. They may be made constructively useful and artistically pleasing. In those designs involv- ing the use of cast-iron joint-boxes between the upper chord sections and posts, these boxes may be cast with neat mouldings and necks, forming capitals for the posts, in any conventional architectural forms. The effect of such caps should depend entirely on the strength of the mouldings, and not on detached leaves and pieces screwed on after the casting is finished. When trusses terminate in vertical end-posts, there is considerable room for good effect, in making the neces- sary stiffening end struts or portals of such form as to embody true architectural expression. Such a design may be worked out either in cast or wrought iron with an appropriate degree of elaborateness. In doing so, however, the main lines of the portal must form an in- tegral part of the construction, contributing to stiffness, and any appearance of brackets, arches, scroll-work, etc., hanging from a horizontal strut, must be avoided. The capitals of end-posts, when vertical, can be made a very prominent feature of the portal design, inasmuch as a large casting is usually required at the juncture of the end-post and top chord to accommodate the large main 86 IRON HIGHWAY BRIDGES. end-braces terminating at that point. When economy of design dictates the use of 'inclined end-posts, the por- tals will produce the most favorable effects, by confining the architectural effort to the expression derived from the simple bracing-bars. An arch-portal of angle or T iron, with the spandrils filled in with lattice-work, or broken up into triangles with bracing-bars, is simple and expressive, and exceedingly appropriate. The lattice intersections can be ornamented by small rosettes or bosses, and the two halves of the portal-arches can be united properly with a half-circle or other form of centre-piece, while at the springing, where they are bolted to the sides of the end-posts, a neatly-designed bracket or shoe will not be out of character. It is exceedingly difficult to design the portals for inclined end-posts so as to look well, since they are viewed obliquely, and it will be found in such cases that simplicity of design growing out of an agree- able arrangement of constructive necessities will always give the best results. The appearance of a roadway-bridge having sidewalks is very much enhanced, and at a very small cost, by neatly-designed railings, with a deeply- moulded fascia-board, to which may be added scroll- drops opposite the ends of the floor-beams. It is not necessaiy that such railings should be ex- pensive, a light lattice railing of wrought-iron, with one or more intersections, with or without rosettes, always looking well and harmonizing with the constructive character of a truss. The cheap gas-pipe railing is so positively ugly that its use ought te be banished to those BRIDGE ARCHITECTURE CONTINUED. 87 country districts where it is rarely seen. Well-designed newel-posts, lamp-posts, and brackets are features of a design where a cultivated taste may be exercised, and form no small part of the prominent accessories of public works of this character. This matter of treating bridge constructions as architectural works, in the true sense of that term, deserves the most thoughtful consideration of engineers and committees, as bridges nearly always form prominent objects of observation in cities and towns, particularly when across large watercourses. They are seen by every one, and therefore in those portions and surroundings capable of aesthetic treatment, some regard should be paid to appearances. A plain four-walled building as a court-house for example might answer every requirement for public purposes, but the demands of modern civilization require that a large expenditure must be made for what is called " architectural effect," in order that a certain gratification may be derived by the community where it occurs, springing from the con- templation of pleasing forms. Nothing has been said about masonry design, as in these pages we are simply dealing with the superstructure, but as the masonry forms part of a bridge design when taken as a whole, the form of piers, abutments, character of masonry, coping, etc., it must not be forgotten, leave abundant room in many cases for the exercise of correct aesthetic treatment. There are very few who can not appreciate a well-pro- portioned pier, with its ice-breaker, heavy coping and belting courses, well-laid, rock-faced work, and chisel- drafted corners. 88 IRON HIGHWAY BRIDGES. v TESTING. As to the utility of testing individual pieces of work during manufacture, opinions differ, but it is unquestion- ably a wise procedure, in the case of welds in main ten- sion bars, as imperfections of workmanship and material (if any exist), undiscoverable by the eye, will be very apt to be developed under strain. To avoid injury, it is ad- visable that this proving should not be carried beyond say nine tenths of the elastic limit ; thus a bar with an elastic limit of 20,000 Ibs. per square inch should not be tested much beyond 18,000 Ibs. After erection, all bridges should be tested with loads approaching as near as possible the maximum loads for which they were de- signed. Railroad-bridges are very readily tested, but highway-bridges can only be tested at considerable ex- pense. Pig-iron, or paving-blocks when convenient, are probably the best artificial loads that can be used, as they are readily handled and distributed. An excellent, though expensive, method of testing, and one of universal appli- cation, is to distribute gravel in a uniform layer over the whole area of roadway, and of such thickness as to equal the load which the bridge was designed to carry. Inas- much as the weight of gravel and earth varies according to locality and degree of moisture when excavated, before a proposed test is made, a cubic foot of the testing mate- rial must be weighed to determine the proper thickness to be put on the bridge. In order to judge the result properly, means must be used to measure the deflection TESTING OF BRIDGES. 89 f of the structure undergoing the test, which may be done by observations with a levelling instrument, or when convenient (as in most cases) by planting a pole or measuring-rod alongside of the span at the centre, as follows : After the bridge is completely finished, and come to a natural bearing under its own dead load, ob- serve the position of any part, say the lower chord at cen- tre, with reference to the position of the instrument or measuring-pole. Then apply the test load, and measure the amount of deflection caused thereby. Remove ,the test, and observe again how near the bridge returns to its first position. This it will do if the bridge is well built, less a small fraction due to that peculiar quality of wrought- iron which is called " permanent set," which takes place under comparatively very small strains. The set here spoken of must not be confounded with that taking place after the elastic limit is reached, but simply means that the various parts of the bridge have come to a working bearing. If the test load is now applied for the second time, as it always should be, it would be found that the deflection would be precisely the same as it was before, under the first test, and so also the amount of re- covery after the load was removed. To make a real test, this second application of the load, with accompany- ing observations, should not be omitted. To illustrate : suppose, at the first loading, the deflection was two inches, on its removal the span recovered itself within one eighth of an inch. This proportion of the deflection is permanent, due to the span coming to its bearing, and 9O IRON HIGHWAY BRIDGES. will forever exist. The second loading would now pro- duce a deflection of i inches instead of 2 inches, as at first, the total i$ plus \ of an inch being precisely the amount of the original deflection. Upon removal of the load, the recovery \vould be i inches, the same as before. Bridges ought always to be built with a camber or up- ward curvature, which camber at a minimum should not be less than the deflection caused by a maximum load- ing. Beyond this the amount is purely a matter of taste with the designer, it having nothing whatever to do with the strength of the work.* BRIDGE-LETTINGS. In the matter of " Lettings," it frequently happens, that parties with the best intentions make mistakes against themselves in their award, simply from ignorance of what they really do want, and by so doing are apt to work an injustice toward competing parties, that is pro- vocative of suspicion and ill-feeling all around. With a view to aid in a clear understanding of how bridge-let- tings should be conducted, in order to secure the best re- sults at the least cost, the following forms of invitation and specification have been prepared, in the hope that they will save \vell-meaning committeemen much per- plexity. While the forms recommended are brief in expres- sion, they cover aH the salient points necessary for a fair competition. The specifications are general, and should * All bridges, besides being tested for deflection, under a dead load, should be tested to see that they are measurably free from vertical and lateral vibra- tion, owing to lack of counter and horizontal bracing. The best test for this purpose, is to have a couple of heavily loaded carts driven rapidly back and forth over the roadway. THE CONDUCT OF BRIDGE-LETTINGS. 91 be made so, as the best work is obtained by permitting bridge-builders to have full latitude of design, under no other restriction than that of requirements and material. These should be made so clear that no refuge for evasion may be found under technicalities. To make a just com- parison of prices, competing parties must estimate upon precisely the same basis, or endless confusion will result in any effort to make a fair canvass of tenders. It is re- commended, in all cases of a bridge-letting, to call in the services of an expertnot simply a general engineer, but one familiar with the science and practice of bridge- building, for the purpose of examining the strain-sheets submitted with the tenders, and comparing them with the specifications on which bids were taken. His services should be continued throughout the building of the bridge, the work on which, however, should not be commenced before all detail drawings have been made by the con- tractor, and submitted to the expert for criticism and ap- proval. If it is inconvenient to employ such an inspec- tor through the continuance of the work, he should be called in at its completion, to make a thorough examina- tion as to the material and execution, in accordance with the contract and specification. A suggestion was made in a report* to the American Society of Civil Engineers * Report on the " Means of Averting Bridge Accidents," by James B. Eads ; C. Shaler Smith, of St. Louis ; I. M. St. John, of Louisville ; Thomas C. Clarke, of Philadelphia ; James Owen, Newark, N. J. ; AIL P. Boiler, Octave Chanute, and Charles Macdonald, New- York ; Julius W. Adams, of Brooklyn, and Theodore G. Ellis, of Hartford, Ct Transactions American Society Civil Engineers, 1875. 92 IRON HIGHWAY BRIDGES. on the subject of " Bridge Accidents," which deserves the very serious consideration of town authorities. It was to the effect that every bridge built should have a tablet fix- ed upon it in a conspicuous place, on which should be in- scribed the name of the builder, the expert inspector, the names of the committee or corporation officers under whom built, the load for which it was proportioned to carry, with factor of safety and date of erection. Such a method of procedure tends to fasten responsibility, which is a powerful incentive to honest, conscientious work, and if every State passed a law covering the above suggestion, there would in a short time be a surprising improvement in the design and construction of highway bridges, al- though that improvement would be accompanied with an increased cost. It will be noticed, in the last clause of the form for " Invitation," bidders are requested to be present at the opening of the bids, and hearing them read. This is simple justice ; and when one considers the time required to make plans and estimates, even for a small piece of work, to say nothing of the expenditure of money inci- dent thereto, with probable travelling expenses in addi- tion, no fair-minded man can object to rendering at least what satisfaction may be derived from the public opening of tenders. Bids secretly opened always lead, whether justly or unjustly, to the suspicion of unfair practices, an imputation that can be readily removed by the method of publicity suggested, a method which can be objected to FORM OF INVITATION AND SPECIFICATION. 93 by no one, unless those whose mode of doing business seeks darkness rather than light. PROPOSED FORM OF INVITATION TO " BRIDGE-BUILDERS. The undersigned committee of .................. will meet at .................. at .... o'clock, on the .... day of ...... , for the purpose of receiving plans and proposals for the furnishing of all material, the con- struction and erection of a wrought-iron bridge over ...................... , agreeably to the specifictions hereto annexed. Parties tendering must furnish a clearly made-out strain-sheet of their design, with the data on which it was computed, and showing also the areas of ma- terial proposed to be given to each part. Bidders are requested to be present on the above occasion, when all the proposals will be opened and read in their presence. The right to reject any or all bids is reserved. Signed by the Committee, PROPOSED FORM OF STANDARD SPECIFICATION FOR OR- DINARY HIGHWAY BRIDGES, WHEN INVITING TENDERS. GENERAL DESCRIPTION. The bridge will be a (through or deck) bridge, consisting of .... spans, and will have a roadway of .... feet between guards, with .... sidewalks of .... feet in the clear each. Sidewalks to be raised .... inches above level of roadway. The distance from grade to bed of stream (or from 94 IRON HIGHWAY BRIDGES. grade to grade of roads crossing each other) is .... feet. From grade to highest water is .... feet, and the centre line of the bridges makes an angle of .... degrees (to the right or left), with the face of abutment or piers. LOADS TO BE CARRIED. The bridge must be propor- tioned to carry, in addition to its own weight, .... Ibs per square foot (see table, page 16) of moving load, starting at one end, and moving over until the whole span is covered, in addition to which the flooring system must be proportioned to carry .... tons (of 2000 pounds) on each pair of wheels for each wagon-way, and due con- sideration must be given to the effect of this concen- trated loading upon the posts and tension-braces of the trusses. The stringer-beams and floor-beams (to be wood or iron, as desired). FACTOR OF SAFETY. Under the above loading, the factor of safety referred to Ultimate strength, shall be for the chords (4 or 5), for the web system 5, and for all parts of the floor system (5 or 6). MATERIAL. The wr ought-iron used shall be of that quality best suited to the purpose, the test for bars being that pieces cut therefrom shall be capable of being bent cold without fracture, until the two sides of the bend shall approach each each other within the thickness of the bar. No iron in small bars to be used with an ulti- mate strength of less than 55,000 pounds per square inch, or an elastic limit of less than 24,000 pounds per square inch. Castings must have a clean skin, free from holes or cinder and expose when broken a fine-grained grey CONSTRUCTION. 95 fracture. Lumber must be of a good, merchantable qua- lity, sound and free from black or loose knots and wind-shakes, and not have sap on more than three cor- ners for planks, or on two for stringer-timbers, or wany edges on more than one corner. For roadway plank the lumber will be of three inches thick, for side- walk plank, two inches thick of , and for string- ers pine will be required. CONSTRUCTION. In pin-connection designs, the pins must be carefully turned to match the holes of the seve- ral parts of the trusses through which they pass, with a minimum play of a scant -fa of an inch, and in diameter must not be less than T 8 the width of the largest bars they connect, if of flat iron, or if the bars are of square iron the diameter must not be less than if times the side of the largest square. The heads of eye-bars must have at least 50 per cent of effective section more than in the body of the bar. The bearing surfaces of the compression members on the pins must be effectively re- inforced, so that the minimum thickness in inches of such surface will not be less than the result derived by divid- ing the maximum strain as shown on the strain-sheet in pounds, by 12,000 times the diameter of the pin. All bearing surfaces must be machine-faced, and any dis- crepancy in length between all parts in the same panel must not exceed T a T of an inch. Where rivets are used, serving to transmit strain, and not simply for the purpose of securing- parts in position, they should be pro- portioned as to number and size by considering the work- 96 IRON HIGHWAY BRIDGES. ing value of each rivet to be equal to its diameter, mul- tiplied by 12,000 pounds, multiplied by the thickness of the thinnest plate. The plates and angle-bars subject to tension, under such riveted construction, must have an allowance made up for the area cut out by the rivet-holes. Pin-connection work and solid section iron will be considered to have an advantage of 10 to 20 per cent over and above riveted or compound work. The spac- ing of the rivets must not exceed five inches between centres, and in the flanges of plate-girders this pitch must be reduced as the ends are approached, according to the value obtained by the above rule for the propor- tioning of rivets. Before shipment, all iron must have a thorough coating of mineral paint, well rubbed in, and all bright work must be protected with white-lead and tallow. To the above specifications must be added the degree of finish required, such as the painting after erection, the manner in which sidewalk is to be laid, whether the plank is to be planed, etc. ; also the kind of railing desired, whether plain or ornamental, and proposed arrangements for lighting. ^ : OP THE UHI7BRSIT7 PART II. THE STRAINS IN GIRDERS AND SIMPLE TRUSSES. ALL questions involved in the consideration of this subject resolve themselves into mere questions of lever- age, of greater or less complexity. It is by means of the law of the lever that we are enabled to determine pre- cisely what portion of a given weight resting on a beam is sustained by either point of support, which is the first thing to be determined before the strains can be computed. The law is simply this : " The weights bal- ancing each other at either end of a beam or lever over any point, are to each other inversely as their distances (called lever-arms) from the point or fulcrum." For ex- i * "- t FIG. 24. ample, supposing we have a beam held up as in Fig. 24, with a weight at either end, the point of support be- Q8 IRON HIGHWAY BRIDGES. ing to one side of the centre, say at J the length of the lever from one end. Then, in order that the lever be balanced, the weight at B must be J- the sum of A and B, and that at A, that sum ; for always B multi- plied by | S must equal A multiplied by i S, and the sustaining force P must, of course, equal the sum of A and B. For example, suppose P, or A plus B, is 1 2 tons, and the span S is 20 ft. For equilibrium, the proportion of the 1 2 tons at A is in excess of that at B, precisely in the proportion that the lever of B exceeds that of A in this case, 3 times. A, then, must be 9 tons, and B 3 tons, and J S multiplied by 9 equals 45, being the same as f S multiplied by 3. Again, supposing that there is but one weight, and two points of support, as in the r ............... * ...................... 1 lllllllllllllllllllllllllllllllllllllllllllHllltllllUlllllllilW FIG. 25. figure, the condition is precisely the same as before, only reversed, and, according to the law of the lever, we find that for equilibrium a force must be applied to A equal to | of P, and at B equal to J- P. This last example is precisely the same case as that of a beam or truss of any kind, only A and B are now called the reactions of the abutments, the sum of which must always be equal to the weight or weights causing them. In order then to know just how much of the weight at any point of a ABUTMENT REACTIONS PRINCIPLE OF MOMENTS. 99 beam is supported by either abutment, all that is neces- sary to be done is to multiply the shorter or longer seg- ment into which its centre of gravity divides the beam (according to the above law) by the weight, and then divide by the product by the sum of the segments, which is, of course, the same as the span. For example, sup- ... 20 FIG. 26. pose we have a beam A B (Fig. 26) 20 ft. long, and there is a weight of 12 tons, J the distance from B, or 5 ft. Then each abutment supports or "reacts" a certain amount of this weight proportional to its distance from either end, the sum of these reactions being equal to the weight. A supports or reacts according to the rule : 12 tons x 5 ft. , -r, 12 tons x 15 ft. i5ft. + 5 f t .- == 3 tons; and B supports - I5 - ft . + 5ft . =9 ton s- Adding these two upward reactions, there results a total of 1 2 tons, the same as the whole load at P acting down- ward. Any number of weights are to be treated in the same way, the sums of their separate reactions being the total reactions or weight supported at each abutment Any weight or force multiplied by the leverage at which it acts is called the moment of that weight or force. The leverage or lever-arm of any force is the perpendicular distance let fall from the point around which its moment 100 IRON HIGHWAY BRIDGES. is taken (or the "fulcrum") upon the direction of the force. Thus if we have a force P (Fig. 27), and the ful- FIG. 27. crum about which it acts is A, then / is the lever-arm of that force, and P multiplied by / the moment. Since the tendency of a force acting with a lever is to produce motion, and it being evident that all the forces acting at any given point of a beam or truss can not act in the same direction, it follows, if equilibrium is to be maintained, the sum of all tendencies to move in one direction must equal those in the opposite direction, or their algebraic sum be zero. The ordinary crowbar (Fig. 28) is a familiar eve,ry- FIG. 28. day example of the " principle of moments" above ex- plained. Suppose a man presses down with a force of loo Ibs., distant 4 ft. from the fulcrum A. The moment ACTION OF FORCES ON A BEAM. IOI 9 of this pressure is 100 Ibs. multiplied by 4 ft, or 400 feet- pounds, as it is called, and it acts, with reference to the fulcrum, toward the left. The weight that will just balance this moment acts toward the right, with a lever of 6 inches, or one half a foot ; and since the moment of this weight must equal the moment of the pressure, the weight itself must be 800 Ibs. For 800 Ibs. multiplied by one half of a foot equals 100 Ibs. multiplied by 4 ft. To absolutely move or destroy the equilibrium of a weight of 800 Ibs. circumstanced as above would require the man to just exceed a pressure of 800 Ibs., barring the resistance due to friction. In any beam or truss, there are two sets, as it were, of forces in action, called exterior and interior forces ; one tending to break the beam through bending, and the other tending to resist breakage. The former are de- rived from the weight of the beam and the loads placed upon it, and the other from the resistance of the mate- rial, in which is involved the form of cross-section. When a beam is bent by the imposition of a load, it is accompanied with a pulling apart of the fibres on the convex side, and a crowding together of those on the concave side. The one signifies tension, and the other compression, and in passing from one extreme to the other, there must necessarily be a set of fibres without strain. Where these unstrained fibres occur is called the neutral axis of the beam, and its position is, in all cases when the load is vertical, in the centre of gravity of IO2 IRON HIGHWAY BRIDGES. the beam-section. The annexed illustrations (Figs. 29 and 30) show in an exaggerated way this extension .. UNLOADED. LENGTHENED FIG. 29. FIG. 30. and shortening of the fibres, and it will be noticed that the fibres lengthen or shorten proportionately to their distance from the neutral axis. The relative intensity of the strain is also measured by the relative changes in length of the fibres. At the neutral axis, the fibres being unchanged in length, there is no strain ; but on the ex- terior surfaces, the top and bottom of the beam, the fibres are lengthened or shortened a maximum amount, and the strain is there a maximum. In further illustra- tion of this principle, suppose there is a rectangular beam (Fig. 31) of which A B C D represents a side view, with the neutral axis M N passing through the centre of gravity. When the beam is loaded with a weight W, it will deflect, due to the shortening or compressing of the fibres on the upper surface, and lengthening those on the STRENGTH OF BEAMS OF RECTANGULAR SECTION. 1 03 lower, as before explained. Let a b and a' b' represent the extreme changes in length of the fibres on the outer surfaces. Then, since the strain at centre is nothing, if W we draw two triangles either, way from the centre to the points of extreme strain, the strain on any fibre will be represented by the length intercepted by the sides of the triangles aO and 6Q and a'O and b'Q. Summing the changes of length of all the fibres in either triangle, there results the representation of the to- tal amount of the tensile and compressive strains, or, what is the same thing, the sum of the strains may be re- presented by the areas of the triangles, their mean effect taking place at the fibres of mean length, or the centres of gravity of the triangles, which is one third their height from their bases, or two thirds the distance above or be- low the neutral axis. This mean effect is represented in the figure by the forces P and P 7 . These two forces, acting in opposite directions, and parallel to each other, constitute what is called a couple, their leverage of action being their distance apart, which lever is also the effective depth of the beam. To determine the resistance of a rectangular cross-section, let C equal stress on out- IO4 IRON HIGHWAY BRIDGES. side fibre represented by ab or a'b', d depth of beam, and let the width of beam be taken as unity. Then from what has preceded we have the average force P or P' (equal to the areas of either triangle or \ C X k d = P) multiplied by the leverage of action, or the distances apart of the centres of gravity of the triangles. That is to say, P= Cxi dx^d^ C d\ For any breadth b other than unity, this expression becomes p b d* f^ aiea of cross-section \y j r^ / \ r "6~^ ~ ~i- _+ l-l^-l-l-l^lHl^ ,/ 7 ty of which is in the middle of beam, or %* tiJx. >! ^ ! leverage of action to produce mean moment FIG. 33. of rupture is \ /. / wl* 2R - w X--- "7 1 " ' 3 ' Beam loaded at centre with W, and sup- i/ 2 w w >/ 2 w ported at both ends, length /. Lever- age of action \ /for the reaction of either k // abutment, the fulcrum being immediate- / ly under the weight. FIG- 34 ' / W/ _ , .__ 4 R M mix = |W x i /== = R and w = y- (4) Beam uniformly loaded with w per unit of length, giving wl for total load 9 fi v \ wl --'A supported at both ends. Maximum iiliiiiiiiiill moment under centre gravity of load, ^ -/2 I i v ^...... ....... 7 ' .-----. -..^ jy y/ lever i /. Reaction of either abutment FIG. 35. ^ the whole load. M max = -!-// X i/less \ wl X i / _ wl^_ ^._^_ R nd ~~~A~' 8 "" 8 a * The value eighteen times the breaking force used in determining constant C is derivable as follows see Fig. 34 : Let W = breaking weight at centre of bar. C = required constant or modulus of rupture, (Continued on page 106.) IO6 IRON HIGHWAY BRIDGES. It will be noticed this last expression is obtained by subtracting that portion of the load between the abut- ment and centre that acts in a contrariwise direction to the reaction of the abutment. If the loads are placed in any other position, or are only partial, M can always be found by first finding the reaction of either abutment (page 101), and multiplying that reaction by the distance from the abutment to the point where M is wanted. The reaction being upward, if there are any weights (which act downward} between the abutment and point of desired M, they must be mul- tiplied into the leverages with which they act around that point, and their sum deducted from the product of the reaction and its leverage before found. This is the principle that had to be applied to the circumstance of loading shown in Fig. 35. As an example of the applica- tion of these formulae : suppose in all cases the material is a pine stick 10" X 10" X 10 feet or 120 inches long. We require to know the breaking load under each con- dition of loading, C being 7000 Ibs. See formula (i) : I0 No. 2. W = = 6 X X0 X - 97" lbs.-hung at one end. per H. neal inch = 19,440 Ibs. uniformly distributed. No. 4. W = ^ = 4 x Tx X i a T = 3 8 ' 888 lbs '~ supported in middle. No. 5. = = 8x7 rxr 4 Z XIO = 6 48 Ibs. per li- neal inch = 77,760 Ibs. uniformly distributed. The bar being one foot long between bearings, and one inch square, we have the moment due to external forces i W X i span 3 W. 'A 6 And the moment due to internal forces R = r- C = C. Since M must equal R, we have | C 3 W ; or C 18 W. PRACTICAL APPLICATION OF FORMULA. 107 p Now, assuming a safety factor of five, the safe load to which the above stick should be subjected would be : One end fixed, the other free ; weight at free end *944 Ibs. One end fixed, the other free ; weight distributed. 3888 Ibs. Both ends supported ; weight concentrated at middle. 7777 Ibs. Both ends supported ; weight uniformly distributed. . . 15,555 Ibs. It will be noticed from this example that, taking the first case as having a strength of one, with the second condition of loading and support, the stick will sustain twice as much, with the third four times as much, and with the fourth condition eight times as much. The third and fourth conditions are those that apply to the longitudinal stringer-beams of a bridge, and from formu- las 4 and 5 has been computed the following table for different spans or panel-lengths and depths of stringers, the thickness being for a unit of one inch. The modulus of rupture C for pine has been taken at 8000 Ibs, with a factor of safety of six. TABLE GIVING A SAFE CENTRE WORKING LOAD IN POUNDS FOR ANY DEPTH OF PINE STRINGER AND A UNIFORM WIDTH OF ONE INCH. CLEAR SPAN IN FEET. Inches. 6 feet. 8 feet. 10 feet. 12 feet. 14 feet. 16 feet. 18 feet. 20 feet. 6 8 9 10 12 14 16 443 602 787 996 333 454 593 750 927 266 363 474 600 74i 1067 302 395 500 617 888 1209 338 428 529 7 6l 1036 I-JCA 375 463 666 907 118? 411 591 805 ICK2 527 717 Q^8 108 IRON HIGHWAY BRIDGES. For safe, uniformly distributed loads, double the loads given in the table. To use the above table, the weight to be carried in the centre of a given span is first determined, and then select any depth for the beam, and follow along the hori- zontal line until below the span at top of column. The number there found will be the safe load in pounds for a beam of the given depth and one inch thick. Divide the weight to be carried by the number of pounds found from the table, as above, and the result will be the width in inches required for the beam. Thus, for example, it is required to know how thick a piece of timber should be that is 10 inches deep, spanning 12 feet to carry 3000 Ibs. hung in the middle, or, what is the same thing, 6000 Ibs. uniformly distributed. Opposite 10 in the first col- umn and below 1 2 in the fifth column, we find 6 1 7 Ibs., the safe load for one inch thick. Dividing 3000 by 617, we find the timber should be a shade less than 5 inches thick. The following table is given as showing judicious sizes for the wooden stringer-beams for the various classes of bridges, and for varying panel-lengths. In judging this table, it is to be considered that the standard wheel loads recommended in Part I. are extreme, and therefore very occasional, so that a much lower factor can safely be used for such loads. Under these circumstances, if the stringers are of good timber, they can safely be proportioned for a working stress of 1500 Ibs. per square inch. FLANGE-BEAMS. I0 9 Span or panel-length. Size Stringers for City Bridges. Size Stringers for Town Bridges. Size Stringers for County Bridges. 8 feet , 1 X IO 3 x 10 7 v Q 4 x 10 4XIO 9 v IO 4 X 12 ^4 x 12 3xii 14 4x13 4X12 ^ X 12 16 4 x 14 4x13 4 X 12 18 . 4 X K 4 X 14 A X [ 20 4 x 16 4 X 1 5 4 X I-l Thus far we have been dealing with rectangular cross-sections ; but bearing in mind the explanation made as to the stresses on the different fibres of a beam with reference to the neutral axis, it will be at once seen how wasteful it is to have so much material near the neutral axis, where it is of so little service. If the material were so disposed as to be principally in the upper and lower portions of the beam, the strength of the beam would be largely added to. With wood, other than a rectangu- lar section is evidently out of the question ; but in iron, the true form for the most economical distribution of material is a necessity in practical construction, and is readily attained by concentrating most of the metal in the upper and lower portions or the " flanges," the stem or web being just stout enough to properly unite them, and to resist the tendency of one part of the beam to slide vertically or horizontally past the other under the direct action of the load, called the shearing tendency. For example, the accompanying cut, Fig. 36, represents the vertical shearing tendency of a load, which is least at the centre and greatest at the abutments, as each section either side of centre must take up the shear of each I IO IRON HIGHWAY BRIDGES. preceding one. Solid rolled beams are manufactured in this country from 4 inches deep, with 3-inch section, to FIG. 36. 15 inches deep, with 2oinch section. Their ordinary length up to and including the 9-inch beam is 30 feet. The beams exceeding 9 inches have an ordinary length of from 20 to 25 feet, according to weight. Beams are often rolled beyond the commercial ordinary length ; but the cost of extra lengths increases very rapidly with such excess. To determine the " Moment of Resistance " of flanged beam sections, we must consider first the resistance due to the rectangular web, and, secondly, that due to the flanges. The resistance due to the web portion has already been shown to be equal to one sixth of its area multiplied by its height, being the same as a rectangular section. That of the flanges is the area of either one multiplied by the distance apart of their centres of gra- vity, which, when added to the resistance of the web, gives the total resistance of the section. The web should not be taken the whole depth of the beam, but only from flange to flange. Thus, suppose we want to know " R " for the beam proportioned as in Fig. 37: MOMENT OF RESISTANCE FLANGE-SECTIONS. Ill < 5 /N. FIG. 37. area web = * multiplied by 13" equal 14 083 Area flange = s" x i " 5" multiplied by 14" equal 70.000 Resistance of section " R " 84.083 The quantity thus obtained has only to do with the shape of section, the efficiency to do work being dependent on the quality of the material. R must there- fore be multiplied by a coefficient expressing this quality before the strength of the beam becomes known. For wrought-iron, this coefficient, within safe limits, varies from 10,000 to 15,000 Ibs. per square inch, depending upon the requirements of any given specification. The above process for obtaining the value of R varies so fractionally from absolute truth that the refinement of calculation to obtain mathematical exactness is entirely unnecessary, while the ease of its application is so great that but a few moments of the simplest arithmetical processes are all that is required to compute the resisting value of any beam cf the usual patterns. The formulae already given for different circumstances of loading, page 105, may be divided by the assumed maximum strain per square inch allowed on the iron, which amounts to the same thing as multiplying R by the same quantity, and is the most convenient way of introducing the above coefficient. As an example in applying the above principles for determining the proper size of beam for any given load, let us take the condition of loading given by equation 5, page 105. Let the load to be carried be 40,000 pounds, uniformly distributed, 112 IRON HIGHWAY BRIDGES. and the maximum allowable strain be 10,000 Ibs. per square inch ; span, 15 feet, or 180 inches. Then formula 5 would read : A/rmax 40,000 Ibs. multiplied by 180 inches _ p _ 8 multiplied by 10,000 Ibs. per sq. in. ~ A beam must therefore be designed having this value of R, precisely as described on page in. It will be noticed that the section there computed falls a little short of a moment of 90, which would be attained by increasing the flange areas ten per cent. Since each beam- section has its own value of R, the following table gives this value for all shapes of " Phoenix " beams, and is about the same for the same sizes of other makers : TABLE GIVING THE VALUE OF R FOR ALL SECTIONS OF AMERICAN BEAMS. Total depth in inches. Weight per foot. Area of one flange. Distance be- tween cen- tres of flanges. Area of stem. Depth of stem. Moment of re- sistance, R. 15 66* 6.IO 13.80 7.80 11.875 IO2.20 IS 50 4-312 14.04 6-375 12.750 75-44 12 561 5-755 IO.92 5-49 9.250 72.85 12 4H 3-790 ii. 16 4.92 IO.OOO 51.48 10* 35 3-380 9-74 3-74 8.625 38.96 9 50 5.50 7.90 4.00 6.375 48.70 9 28 2.78 8.30 2.84 7.000 27.00 2 3 i 2.37 8.38 2.26 7.250 22.88 g 2l 2.035 7.42 2.43 6.500 18.11 7 1 8* i. 80 6.44 1.90 5.500 13-63 6 i6f 1.82 5.50 1.36 4.375 11.25 5 12 1.175 4.60 1.25 4.000 6.37 5 IO 995 4.62 1. 01 4.063 5.38 4 IO 1.14 3.58 .72 2.900 4.50 6 545 3.65 .71 3.250 2.45 To use the table, compute the maximum bending moment as before explained, and select the beam having the largest value of R nearest to the computed one, in case there is none having the exact required value. COMPOUND GIRDERS. 1.13 COMPOUND GIRDERS. For beams compounded from plates and angles, the process for determining R is precisely the same as for any other beam. Inasmuch as compound beams are specially designed for any given case, it is necessary to determine from R the area of the flanges and web, from which the proportions of the parts can be made out. It must be remembered that M or R do not represent strain, being independent of depth, but can be converted into flange strain by dividing by the depth in inches. Assume, therefore, any depth for the girder (bearing in mind that the effective depth is the distance between centres of gravity of the flanges*), divide R by this depth, and the result is the strain on either flange ; and if the maximum allowable strain per square inch has not already been introduced in determining R, the strain above found must be divided by this maximum unit strain to determine the square inches that must be .given to the flanges. * To find the centre of gravity of a flange com- posed as in Fig. 38, and representing a plate web- girder, assume any axis, as XY. Area of the whole flange = M = m * m. Let / equal distance centre of gravity of m from axis. .< // 000 lbs> The horizontal strain on d e and b c will be 39,000 x 20 13,000 x io /: - OOO Ibs io The horizontal strain on e f,f h, h z\ and eg will be 39,000 x 30 - 13,000 x 20 13,000 x io __ ygoQO io " / I3O IRON HIGHWAY BRIDGES. 2d. Web Strains. The web strains must be com- puted separately under each condition of loading. The posts and braces are strained the greatest when the moving load covers the segment from which any given diagonal slopes. Thus the diagonal e c is strained the greatest when c and all points to the right are loaded with moving load ; f g when g and all points to its right are loaded, etc. While the web strains can be readily calculated by finding the horizontal components for each maximum condition of loading, and converting them into longitudinal strains, as was done for the Queen Post truss, the method is somewhat tedious when there are a number of panels, and a separation of dead and live loads must be made. For trusses with parallel chords, the following method will be found most conve- nient, and is the one usually employed. It is based on considering the load on each panel-point, tracing its action on the posts and ties, and summing their effects or, in other words, finding the vertical components, which are the post strains. Taking first the dead load, there is w at each panel-point, or, under the example, 3000 Ibs. Since three panel loads are supported by each abutment, the loads, and therefore the strains, are symmetrical with the centre, and it is only necessary to compute the strains for one half the truss. At the point c, 3000 Ibs. is taken up by the inclined tie e c, and delivered to the vertical post e b, which has a compression, therefore, of that amount ; the tension on the tie being 3000 Ibs. X its length 14.1 ft. 1t r^\ i i j depth of truss* or 3Oo X 7^7 = 4230 Ibs. This panel load STRAINS IN WHIPPLE TRUSS. 131 is again progressed to the abutment by the tie d b, which also has upon it another panel load at b of 3000, making 6000 Ibs. delivered to the end-post d o. The strain on this tie is, therefore, just double that on the preceding tie, or 8460 Ibs., to which must be added the effect of the third panel load sustained by the vertical tie d a, or 4230 Ibs. for the compressive strain for the inclined end- post, making a total for that post of 12,690 Ibs. For the moving load alone, advancing from the left abut- ment, we have, when it reaches the points, 10,000 Ibs. By the law of the lever, % of this is supported by the left abutment, and \ by the right abutment. Since the whole of this load ascends the vertical a d, the \ that goes to the right can only do so by passing down the diagonal d b to the foot of the post e b, when the diagonals in the opposite direction progress it toward the right abutment. The strain in d b from this action of the load is one of compression ; but since the dead load strains this diag- onal tensively largely in excess of this compressive effect, the latter is entirely neutralized. Advancing to each panel-point in succession with the load of 10,000 Ibs., and distributing the load by the law of the lever, the strains on the various parts will be as follows, from the live load alone : On od:\ (6 + 5+4 + 3 + 2 + 1) io,oooX J T V compression = 42,300 ad: one panel load, tension =10,000 db: M5+4 + 3 + 2 + 1 ) i,oX J ^- J =30,214 e b: | (4 + 3 + 2 + 1) 10.000 compression^ 14,280 ec: sameas*x-W tension =20,143 132 IRON HIGHWAY BRIDGES. fc: fg-' hg: hj: 10,000 sameas/!55 Ibs. compression. " 3. 10 x 1677 = 16,770 Ibs. tension, and I x 1677 1677 Ibs. comp. " 4. 10 x J 677 = 16,770 Ibs. comp., and I x 1677 = 1677 Ibs. tension. " 5- 6 x 1677 = 10,062 Ibs. tension, and 3 x 1677 = 5031 Ibs. comp. " 6. 6 x J 677 = 10,062 Ibs. comp., and 3 x J 677 = 5931 Ibs. tension. " 7. 6 x 1677 = 10,062 Ibs. comp., and 3 x 1677 = 5931 Ibs. tension. " 8. 6 x J 677 = 10,062 Ibs. tension, and 3 x J 677 = 5931 Ibs. comp. " 9. 10 x 1677 = 16,770 Ibs. comp., and I x 1677 = 1677 Ibs. tension. " 10. 10 x J 677 = 16,770 Ibs. tension, and I x J 677 = 1677 Ibs. comp. " ii. 15 x 1677 = 25,155 Ibs. comp. " 12. 15 x 1677 = 25,155 Ibs. tension. To the above values must be added, for final maximum web-strains, the effect of the permanent load, 3000 Ibs., at each apex, which, converted into longitudinal effect as above, is 3354 Ibs. This is done in the following table : I 3 6 IRON HIGHWAY BRIDGES. NAME OF FROM MOVING LOAD ALONE. FROM DEAD LOAD ALONE. ALGEBRAIC SUM OF MOVING AND DEAD LOAD. DIAGO- NAL. _J_ i _|_ Com- pression. Tension Com " pression. Tension. Com- pression. Tension. Ibs. Ibs. j Ibs. Ibs. Ibs. | Ibs. i .... 25,155 .... 8,385 j 33,540 2 25,155 .... 8,385 .... 33,540 none 3 1,677 16,770 .... 5,031 none 21,801 4 16,770 i,677 5,031 .... 21,801 none 5 5,031 10,062 1,677 3,354 n,739 6 10,062 5,031 1,677 n,739 3,354 7 10,062 5,031 1,677 .... n,739 3,354 8 5,031 10,062 .... i,677 3-354 u,739 9 16,770 1.677 5,031 21,801 none 10 1,677 16,770 .... 5-031 none 21,801 ii 25,155 .... 8,385 33,540 none 12 25,155 .... 8,385 33-540 It will be seen from the above table how the com- pression due to the variable load in diagonals 10 and 3 is more than neutralized by the tension from the fixed load. Diagonals 5,6, 7, and 8, however, must be capable of acting either by tension or compression, since the effect of the variable load preponderates over the dead load that works against it. In other words, the necessary counterbracing is confined to the last diagonals named. When the span becomes so great as to make the tri- angles of the Warren system too large, another series may be introduced, each one being computed indepen- dently of the other, care being taken not to omit their joint effect on the chords. By increasing the number of sys- tems of triangles, the lattice-truss is formed ; but this is FINK SUSPENSION TRUSS. 137 not a commendable form of truss, since the intersections of the different systems must be riveted together, which vitiates more or less the calculations, based, as they neces- sarily must be, upon the hypothesis of an independent action of each system of triangles. FIG. 48. THE FINK SUSPENSION TRUSS (Fig. 48). This form of truss is only well adapted for deck spans, and is pre- cisely the same truss as the ordinary iron roof turned upside down, with the reversal of the quality of strains. The maximum chord strains and all parts of the primary system (marked i) occur when all points are loaded. On the secondary system (marked 2), maximum strains occur when all the panels embraced in that system alone are loaded, and so on. Let the load on each apex be w, then posts 3 support w only ; posts 2 support w + -J- w, delivered to it from each sub-post 3, or 2 w ; post i sustains its own w, + \ of the load on each sub-post 2, + \ the load from each adjoining sub-post 3, in all 4 w. The suspension rods are strained in proportion to their inclination or j^^*- Example. Span, 120 feet; 8. panels, 1 5 feet ; height of centre-post, 1 5 feet ; load on each apex, 10,000 Ibs. ; ratio of length of any rod to post 138 IRON HIGHWAY BRIDGES. 61.8 ft. of system to which it belongs, -|y ft> - 4.12; ratio of horizontal to vertical, ff- 4. i st. Strain on posts compression. Sub-system, 3 w= 10,000 Ibs. ; secondary, 2 2 w = 20,000 Ibs. ; primary, i - - 4 w = 40,000 Ibs. 2d. Longitudinal tension in suspension bars. Suspension bars, sub-system i . . . - 10,000 x 4-J2 = 20,600 Ibs. " " secondary system 2 . 20,000 x 4- 12 = 41,200 " " " primary " 3 . \ 40,000 x 4- 12 = 82,400 " Strain in panel a will be, therefore, 82,400 Ibs.; in b = 82,400 + 41,200 = 123,600; in c = 123,600 + 20,600 144,200 Ibs. The horizontal chord strain will be uniform throughout, and is the sum of the horizontal compo- nents of the several systems. From sub-system 3 \ 10,000 x 4 = 20,000 Ibs. " secondary system 2 .... \ 20,000 x 4 = 40,000 " " primary " I .... ^ 40,000 x 4 = 80,000 " Total chord strain, 140,000 Ibs. FIG. 49. THE BOWSTRING TRUSS (Fig. 49). The maximum horizontal strain occurs when all panels are loaded both with fixed and moving loads, and is uniform THE BOWSTRING TRUSS. '39 throughout the length of the tie or bottom chord. The longitudinal thrust through the arch varies with the inclination of the arch-segments, being equal in amount to that of the horizontal strain at the centre only. To find the horizontal strain at the centre under uniform load, " multiply the abutment reaction (in this case 2\ panel-loads) by its lever or \ span, from which subtract the intermediate panel-loads, multiplied by their leverages, acting in the opposite direction to the reac- tion, and divide the result by depth of truss." The ex- treme longitudinal thrust in the arch occurs in the last segment, being the one of greatest inclination, and is at once found by " multiplying the reaction by the lever of one panel-length, and dividing by the perpendicular let fall from the point around which the moments are taken upon the direction of the segment" Or the longitudinal strain in any segment may be found by multiplying the maximum horizontal strain by the length of segment, and dividing by its horizontal stretch. In the web, under uniform loading, there is no other strain than tension on the verticals, amounting to a panel-load, and the diagonals are unnecessary ; but under a variable load, moving from end to end of the truss, the verticals are brought under a compressive strain through the medium of the diagonals, the strain on which may be most conveniently computed as follows : For each position of the load as it advances from point to point, determine the abutment reaction as for an ordi- nary truss on the principle of the lever. From this I4O IRON HIGHWAY BRIDGES. compute the horizontal strain at the extreme point of loading, and also at the next panel-point beyond. The difference between these two strains will be the hori- zontal component of the diagonal of the panel between the points where the horizontal was computed. This has now to be converted into the direction of the diago- nal for its longitudinal strain, from which the vertical effect of compression on the post is readily derived. Since tension forever exists on the verticals from the dead load, the amount of tension of one panel dead load must be deducted from the compression above found for maximum compressive effect that can come on a post. As an example of the application of these principles, assume a bowstring truss, with 6 panels of 1 5 feet, and 13 feet deep at centre. Also let dead load w = 5000 Ibs. per panel, and live load w' = 15,000 Ibs. per panel. The lengths of the verticals and diagonals as marked on the diagram : Maximum horizontal chord strain Reaction. (u>+w')x 2\ panels x 45 ft. /. (w + a/) X (1 + 2)15 ft.. JQ g g j^g Maximum thrust in last segment f g of arch = 2 panels X 15 ft. 20,000 X 2J + 15 _ ,, "~6^"ft.~~ 6.7 ^>940 0& Maximum tension on verticals w + w = 20,000 Ibs. Constant tension from dead load alone w 5,000 Ibs. Maximum tension on b c' occurs when variable load is at b alone ; reaction left abutment = -f w' = 12,500. Horizontal tension at 6=***^=&&= 2 5,000 Ibs. THE BOWSTRING TRUSS. 14! Horizontal tension at c I2 -5QQ * 30 15.000 x 1 5 _ 150,000 cc 11.7 = 12,820 Ibs. 25,000 less 12,820 Ibs. = 12,180 Ibs. the horizontal component. 12,180 X ff- ~ longitudinal tension in b c' = 15,328. Maximum tension on cd', moving load at b and c. Reaction left abutment = w' + f w' = 22,500 Ibs. Horizontal strain at c . . gjogjj so- 15.000 x 15 = 3 g 46o Horizontal strain atrf . . 22>5 x 45 ~ IS ' x I5 (I + 2 ) 13 25,9- 38,460 less 25,900 = 12,560 Ibs. = horizontal compo- nent of c d. 12,560 X f = longitudinal tension in ^^16,713 Ibs. Maximum tension on d e , moving load at b, c, and d. Reaction left abutment ^-t|i- 3 w' 30,000. Horizontal strain at d = 3 t000 x 45 ~ I *>JL1L 13 Horizontal strain at e = 30.000x60-15.^5(1 51,923 less 38,461 = 13,462 Ibs., horizontal component 13,462 X {-- = longitudinal tension, 17,052 Ibs. Maximum tension on e f ; all points but / loaded with w\ Reaction left abutment 5 + 4 + 3 + 2 w ' = 35,000. TT i_ 1 ' Horizontal strain at e = = 64,103. 35.OOO X 6O - I5,OOO X 15 (l -4- 2 + 3) 142 IRON HIGHWAY BRIDGES. Horizontal strain at/- 3^gggJLJlzii^pj.s(L+ a + 3 + 4) = 50,000. 64,103 less 50,000 = 14,103 = horizontal component 14,103 x |f = longitudinal tension in ef', 15,983. The compressive strain in verticals from a moving load occurs when all panel-points between any given one and the abutment are loaded. Thus d d' is com- pressed the greatest when b and c or e and f are loaded. The strain (supposing the load is at b and c) on d d 1 will be the vertical component from d e, less the tension of one panel of dead load. It is necessary, then, to find the longitudinal strain on the different diagonals when the panel-points beyond are loaded, and that of the given diagonal unloaded. On c d' , when b alone is loaded, reaction = -| w' 12,500. Horizontal strain at c = "SODJCJS.OOOXJIS = 1 d = 45 -15.000x30 12,820 less 8654 = 4166 = horizontal component, which multiplied by |^ = 5521 = longitudinal strain. Converting this last strain into vertical strain by multi- plying it by the ratio of diagonal to vertical, or ^|, the compression on post c c f from line load is obtained. Since there is always a tension caused by one panel of dead load, the compression above found must be reduced by that amount, to obtain the maximum compression. THE BOWSTRING TRUSS. 143 On d d' , when b and c are loaded, reaction = 1 w = o 22,500. Horizontal strain at d= 22 ' 5 x 45 ~ I5 ' x 'il'-Ji*) = 13 2 5 Horizontal strain at e = 2 -^^*- 6 ^-^A I 5 (* + 3) = I9.H5- 25,963 less 19,145 = 6818 = horizontal component. Multiplying this component by -ff- = 5900; less 5000 = maximum compression on post d d' = 900. On e e' , when b, c, and d are loaded, reaction = J 2 - w 30,000 Ibs. Horizontal strain at _ 30.000 x 60 - 15,000 x 15 (i + 2 -f 3) _ ,,0 s 11.7 ~ o 5 4 DI - Horizontal strain at r _ 30,000 x 75 15,000 x 15 (2 H-3 + 4) _ / - ~~7.5~ " 3' Ooa 38,461 less 30,000 = 8461 horizontal component. Converting this horizontal strain into vertical, there re- sults for compression on posts from live load 8461 Ibs. X ^f =4230 Ibs. Since the tension induced by dead load is 5000 Ibs., there can, therefore, be no compression whatever on post e e'. On b b' or f f, there can be no other strain than that of tension from w + w'. If the bowstring is inverted, the strains may be com- puted in the same way as above explained, but are re- versed in quality. The horizontal tie will become a compression chord, and the arch will be under tension. 144 IRON HIGHWAY BRIDGES. The posts, in this case, will be compressed from the dead load, the effect of which is therefore added to that of the diagonals (being of the same quality), instead of being subtracted as before. For a deck span this adaptation of the bowstring truss is to be commended as economical in material and pleasing in appearance. RETUKN TO BORROWED LD21 32m 1,'75 (S3845D4970