LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Class CONCRETE BRIDGES AND CULVERTS NET BOOK This Book is supplied to the trade on terms which do not admit of discount. THE MYRON C. CLARK PUBLISHING CO. Graduate of Toronto University CHICAGO AND NEW YORK THE MYRON C. CLARK PUBLISHING Co. LONDON E. & F. N. SPON, LTD., 57 Haymarket 1909 a < CONCRETE BRIDGES I AND CULVERTS FOR BOTH RAILROADS AND HIGHWAYS BY H. GRATTAN TYRRELL Civil Engineer Graduate of Toronto University CHICAGO AND NEW YORK THE MYRON C. CLARK PUBLISHING Co. LONDON E. & F. N. SPON, LTD., 57 Haymarket 1909 COPYRIGHT 1909 BY H GRATTAN TYRRELL PREFACE. Bridges of solid concrete are superior to those of any other material. They are as permanent as stone, and have a less cost. Masonry bridges and aque- ducts built by the Romans are still standing, and some of them in use. A few old cast iron bridges re- main, dating back a century or more, but a majority of the modern ones built of wrought iron and steel have a very limited existence. Forty years ago, steel bridges were believed to be permanent structures, but it is now well known that they do not generally last longer than from twenty to thirty years. Solid concrete bridges are superior to those in which reinforcing metal is required for resisting tensile stresses in the arch ring. Continuous water- soaking reduces the adhesion of concrete to steel by about 100 per cent, and the effect of shocks and vi- brations also tends to destroy the bond. It fre- quently occurs that cracks develop, sufficiently large to admit water, and when water and moisture reach the reinforcing metal, it is then only a few years be- fore the metal is destroyed by rust. An old wire suspension bridge that recently failed, was examined and reported on by the writer, and it was found that failure occurred because of the rust- ing and breaking of the wire cables embedded in the anchorage. When the bridge was built, it was doubtless considered that the cables when painted 194738 iv PREFA CE. and embedded in concrete, were secure against cor- rosion. Sufficient caution was not taken to exclude moisture from the anchorages, and the bridge failed as stated above, by the rusting and breaking of the embedded metal. It is evident, therefore, that the most enduring bridges are those of solid mason- ry, where no metal is required. Many of the largest masonry bridges built in re- cent years, have arch rings built of solid concrete, without reinforcing metal for resisting direct stress- es. Details of some of these are given in Table Xo. I. Even in arches with reinforcement, the best de- signers are now proportioning the arch rings, so the line of pressure for uniform loads will at all times fall within the middle third of the arch ring, and require no reinforcing for these loads. In the Engineer's Pocket-Book, Mr. Trautwine makes the following statements: "Nearly all the scientific principles which constitute the foundation of Civil Engineering, are susceptible of complete and satisfactory explanation to any person who really possesses only such knowledge of arithmetic and natural philosophy, as is taught to boys in pub- lic schools. The little that is beyond this, may safe- ly be intrusted to the savant. Let them work out the results, and give them to the engineer in intelli- gible language. We can afford to take their word, because such things are their specialty. The object has been to elucidate in plain English, a few im- portant elementary principles, which the savants have enveloped in such a haze of mystery, as to PREFA CE v render pursuit hopeless to any but a confirmed math- ematician." Several complete and very comprehensive trea- tises have already been written, covering the mathe- matical theory of arches, and as far as this feature of the subject is concerned, there is little left to be desired. Tn the preparation of this manual, the effort has therefore been made, to as far as possible eliminate mathematical formulae, and to present the subject in the simplest possible manner. Only such material is given as is directly required in the design and construction of ordinary concrete or masonry arches, so it will be unnecessary for the busy engineer to spend valuable time and thought in the perusal and study of obstruse mathematical treatises. Practi- cing engineers have but little time for mathematical investigation, and generally must accept formulae as given to them by others. A real need for this book is believed to exist, ow- ing to the increased use of concrete bridges. The designs and data tables for culverts and tres- tles are original with the author, and are here pre- sented for the first time. They are the result of his own practice in the design and construction of railroad structures. In the preparation of this manual, I have received valuable assistance from my wife, Maude K. Tyrrell, a graduate of the Chicago Art Institute, and ex- perienced in architectural design. I am indebted also to the following gentlemen for assistance as vi PREFACE. noted : To Julius Kahn for two views of concrete trestles, to Whitney Warren, Architect, for views of the proposed Hudson Memorial Bridge, to Messrs. Lea and Felgate for views and drawings of the Rocky River Bridge, to George S. Webster for a photograph of the Walnut Lane Bridge at Philadelphia, and to H. Haw T good for the illustrations and drawings of the Santa Ana Bridge. 1 am also indebted to the Engineering News for drawings of the proposed Hudson Memorial Bridge, the Spokane and the Grand Avenue Bridges, and to the Engineering Record for two drawings of the Rocky River Bridge and drawing of Edmondson Avenue Bridge. H. G. Tyrrell. Evanston, Illinois. November, 1909. \ TABLE OF CONTENTS. PART I. PLAIN CONCRETE ARCH BRIDGES. Page. Composition i Advantages of Masoniy Construction 1 Uncertainty of Masonry Arches 4 Form g Hinged Arches 10 Position of Springs n Abutment Piers n Height of Bridge 12 Rise arid Span 12 Crown Thickness 14 Thickness of Crown Filling 16 Spandrels 16 Various Forms and How to Draw Them 20 Ellipse 20 Multi-Centered Arch. Three Centers 20 Multi-Centered Arch. Five Centers 22 Parabolic Arches 23 Hydrostatic and Geostatic Arches 24 Selection of Most Suitable Form 27 External Loads and Forces 29 Mathematical Theory of the Arch 32 Stability Requirements 33 Ultimate Values 34 Working Units 35 Line of Resistance. Full Loading 36 Line of Resistance. Partial Loading 45 Point of Rupture 50 Determination of Arch Thickness 51 Backing 52 Waterproofing and Drainage 52 Intermediate Piers 53 Abutment Piers 54 Abutments 55 Foundations 58 Expansion 60 Surface Finish 60 Cost of Concrete Arch Bridges 63 vii viii CONTENTS. Page. Design for a 60 ft. Arch Bridge 65 Uneven Loading 68 Required Arch Area 69 Intermediate Piers 69 Abutment Piers 70 Illustrations of Concrete and Masonry Bridges 71 Ponte Rotto, Rome 74 Bridge of Augustus at Rimini, Italy 76 Hudson Memorial Bridge, New York City 78 Auckland, New Zealand, Bridge 80 Rocky River Bridge, Cleveland, Ohio 81 Walnut Lane Bridge, Philadelphia 85 Connecticut Avenue Bridge, Washington 87 Big Muddy River Bridge, Illinois 89 Santa Ana Bridge, California 91 Table of Concrete Arch Bridges 95 PART II REINFORCED CONCRETE ARCH BRIDGES 100 Historical Outline 102 Advantages of Reinforced Concrete 106 Adhesion and Bond 108 Metal Reinforcement Ill Reinforcing Systems 117 Concrete Composition 120 Loads 121 Units Ultimate and Working 125 Theory of Arches 128 General Design 136 Hinged Arches 140 Ribbed Arches 141 Intrados Form 145 Spandrels 147 Piers and Abutments 148 Costs of Reinforced Concrete Arch Bridges 150 Estimating 154 Approximate Estimating Prices 155 Table of Approximate Quantities 158 Potomac Memorial Bridge Design 159 Jamestown Exposition Bridge 161 Franklin Bridge, Forest Park. St. Louis 161 Jefferson St. Bridge, South Bend, Indiana 16 Gary, Indiana, Bridge 163 Como Park Foot Bridge, St. Par.l 163 Boulder Faced Bridge, Washington 166 Grand Rapids Arch Bridge 166 CONTENTS. ix Page. Bridge at Venice, California 169 Garfield Park Bridge, Chicago 169 Stein-Tenf en Bridge. Switzerland 173 Table of Reinforced Concrete Arches 174 PART III. HIGHWAY BEAM BRIDGES. Comparison of Arch and Beam 181 Beam Bridges 183 Method of Design 185 PART IV. CONCRETE CULVERTS AND TRESTLES 189 Required Size of Culvert Opening 191 Reinforced Concrete Box Culverts 194 Loads 195 Economic Length for Slabs and Slab-Beams 198 Reinforced Concrete Slab Table No. VI 198 Single Box Culverts, Slab Type, Table No. VII 205 Double Box Culverts, Slab Type, Table No. VIII 207 Single Box Culverts, Beam and Slab, Table No. IX 209 Double Box Culverts, Beam and Slab, Table No. X 211 Comparative Culvert Costs, Various Forms 213 Other Common Culvert Forms 216 Culvert Data, Table No. XI 227 Concrete Railroad Trestles 228 Economic Span Lengths 230 Description of Various Trestle Designs 230 Design A 230 B 235 C 235 D 238 E 238 F 238 G and H 242 Comparative Trestle Costs 242 x LIST OF ILLUSTRATIONS. PART I. SOLID CONCRETE ARCH BRIDGES. Frontispiece Potomac Memorial Bridge, Washington. Fig. Page. 1. Ellipse 20 2. Three Centered Arch 21 3. Five Centered Arch 22 4. Parabolic Arch 23 5. Hydrostatic Arch 26 0. Comparison of Above Curves 27 7. Pressure Curve, Full Loads 38 8. Alternate Pressure Curve, Full Loads 44 9. Pressure Curve, Partial Loads 46 10. Design for Twin Arches 48 11. Abutments 57 12. Design for Railroad Bridge 62 13. Ponte Rotto, Rome 73 14. Bridge of Augustus at Rimini, Italy 75 15. Hudson Memorial Bridge 7t 16. Monroe St. Bridge, Spokane, Wash 79 17. Rocky River Bridge, Cleveland 82 18. Rocky River Bridge, Cleveland 83 19. Rocky River Bridge, Cleveland ; 84 20. Walnut Lane Bridge, Philadelphia 86 21. Connecticut Avenue Bridge, Washington 88 22. Big Muddy River Bridge, Illinois 90 23. Santa Ana Bridge, California 92 24. Santa Ana Bridge, California 93 PART II. 25. Design for Concrete Highway Bridge 99 26. Theory of Arches 134 27. Grand Avenue Bridge Design, Milwaukee 143 28. Jamestown Exposition Bridge 160 29. Franklin Bridge, Forest Park, St. Louis.... 162 30. Jefferson Street Bridge, South Bend, Indiana 164 31. Gary, Indiana, Bridge 165 32. Como Park Foot Bridge, St. Paul 167 33. Boulder Faced Bridge. Washington 168 34. Grand Rapids Arch Bridge 170 35. Bridge at Venice, California 171 36. Garfield Park Bridge, Chicago 172 PART III. 37. Three Span Beam Bridge 180 38. Single Span Slab Bridge 182 39. Single Span Beam Bridge 184 LIST OF ILLUSTRATIONS. xi PART IV. Fig. Page. 40. Richmond, Va., Trestle 188 41. Augusta, Ga., Trestle t 190 42. Relative Cost of Slab and Beams 200 43. Single Box Culverts, Slabs 202 44. Double Box Culverts, Slabs 203 45. Single Box Culverts, Beams 204 46. Culvert Cost Chart 213 47. Culvert Cost Chart 217 48. Concrete Box Culverts, Slabs 218 49. Concrete Box Culverts, Beams 220 50. Beam Top Box Culverts 221 51. Concrete Box Culverts, Slab Type 222 52. Concrete Box Culverts, Beam and Slab , 223 53. Rail Top Culverts 224 54. Reinforced Concrete Arch 225 55. Beam Top Culvert 226 56. Parabolic Arch Culvert 226 57. Sewer Type Arch Culvert 227 58. Concrete Trestle, Design A, Rail Top. 231 59. Concrete Trestle, Design B, Beam Top 233 60. Concrete Trestle, Design C, Steel Beams 234 61. Concrete Trestle, Design D, Beam Top 236 62. Concrete Trestle, Design E, Slabs with Rods 237 63. Concrete Trestle, Design F, Beam and Slabs 239 64. Concrete Trestle, Design G, Slabs 240 65. Concrete Trestle, Design H, Beam and Slab 241 66. Concrete Trestles, Comparative Costs 243 PART I. PLAIN CONCRETE ARCH BRIDGES. Composition. Masonry arches were formerly built almost en- tirely of brick and stone. In recent years, however, owing to the increased production of cement and modern methods of making concrete, including the crushing of stone and the mixing and handling of materials, a large number of our modern bridges are built of concrete. Brick arches lack the bond of stone. They are usually laid in concentric rings, the edge of the brick appearing in the soffit of the arch. Occasionally the bricks have been laid dry, and grout run in to fill solid all cavities. As brick is a softer material than stone or concrete, its use does not appear to have any special advantage. All masonry arches, whether built of brick or stone as block structures, or made of concrete in a solid monolith, carry their loads entirely through com- pression in the arch ring, and while the mortar joints would doubtless resist considerable tension if so required, no reliance should be placed on the ten- sile strength of such joints. Advantages of Masonry Construction. Tn many respects a masonry arch is superior to either a steel bridge or a combination of steel and concrete. Some of these advantages may be enu- merated as follows : Cement hardens with age, and consequently the older the bridge, the stronger it becomes. Therefore, if it successfully sustains its first test load it will always be secure. This condition is reversed in steel structures, which CONCRETE BRIDGES AND CULVERTS. deteriorate with age through the action of rust and the loosening of rivets and pins. As travel increases, concrete bridges become stronger to support it; neither is there any yearly expense for painting or other maintenance. They can generally be built from local ma- terial, and largely by local and unskilled labor. The building and completion of such bridges is not dependent on mills, shops, or the operation of trusts, as is frequently the case with steel struc- tures. In this respect, concrete bridges have an advantage over those of combined steel and concrete, for in the latter case, it is frequently necessary to await the convenience of the shops for the reinfor- cing steel. A consideration that should appeal to the purchasers of bridges is, that local labor and ma- terials for concrete structures can usually be secured and used, and the money expended by a municipal- ity goes back to its own people, instead of going to distant points in payment for manufactured steel. Arches in general, which form is usually adopted for masonry bridges, present a more substantial and pleasing appearance than can be secured by any form of truss, even though an arched truss be con- sidered, for in a truss, the outline of the arch is not so evident as in a solid structure. For railroad bridges the arch of solid concrete is superior to the reinforced, in that its greater weight and mass more readily absorb the vibrations and shocks due to the passage of heavy trainloads and engines. Concrete bridges require no floor renewals as steel bridges PLAIN CONCRETE ARCH BRIDGES. 3 frequently do, and they will generally cost from 10 to 30 per cent less than stone. They are fire proof and have no steel, either in the form of principals or reinforcement, to rust. They can be widened at any time without tearing down the original bridges, as must be done with bridges of wood and steel. Bridges of solid concrete are particularly suitable for permanent railroad structures. Many railroad companies are realizing their superior advantages and are replacing their steel bridges with new ones of masonry, and while these concrete bridges are frequently reinforced with steel, the main arches are in most cases, designed to resist only compres- sive stresses, with no need for steel in tension except to better unite the arch and to prevent cracking from change of temperature. Many iron and steel rail- road bridges in America have been replaced two or three times by heavier steel ones during the past thirty or forty , years, in order to renew worn out structures or to provide for heavier loads. When it is remembered that several masonry bridges in Europe that were built 2,000 years ago, are still standing and in use, it is evident economy for per- manent roadways, to rebuild ordinary spans in ma- sonry. Views of two old Roman bridges are shown on subsequent pages. Ponte Rotto at Rome, shown on page 73, was first completed in the year 142 B. C., and while it has been damaged several times by floods, owing to its unfortunate location, three arch spans still remain in good condition. The Bridge of Augustus at Rimini, supposed to have been built 4 CONCRETE BRIDGES AXD CULVERTS. about 14 A. D., during the reign of Emperor Augus- tus, has five arch spans. The piers are very heavy and support semicircular arches. The bridge is fine- ly ornamented, is still in good condition and in use at the present time. A view is shown on page 75. Uncertainty of Masonry Arches. As compared with steel frames, the design of ma- sonry arches is uncertain. The hypotheses upon which the design is based are only approximate as- sumptions, and when constructed, the action of the arch under loads is unreliable. In the former case, with single truss systems and truss lines meeting in points, with working unit values closely known by long series of experiments in both tension and compression, the designing of such frames has be- come almost an exact science. It is different with masonry arches, as their conditions under loads are too little known to arrive at any exact method for proportioning them. Moreover, even if these con- ditions were more definitely known, the same incen- tive for reducing the quantities of material does not exist in masonry as in steel structures, because of the comparative cheapness of masonry. Some of the indefinite factors in the design of masonry arches are as follows : (1) The condition and amount of the external forces are not definitely known. For instance, in an arch with spandrel earth filling, the amount of the conjugate horizontal pressure of the earth against the extrados of the arch is comparatively unknown. PLAIN CONCRETE ARCH BRIDGES. 5 If the filling were a liquid, the external pressure Avould then be normal to the extrados and its amount would be definite. This condition does not ordinarily exist, and the nearest approach to liquid pressure is from spandrel filling of clean dry sand. It is well known that earth filling, which, when new- ly placed, will stand at no greater slope than one and one-half to one, will after it becomes set, sup- port itself for a time, at any rate, with almost verti- cal faces. Hence, conjugate pressure which may have existed at first, while the arch was under con- struction, may vanish later. In the case of an arch under a deep embankment, it is plainly evident that such an arch does not support the entire weight of earth filling above it, as the earth to some extent arches itself. The case of a tunnel arch is an excel- lent example. Such an arch is proportioned to carry only a small part of the load above it, de- pending upon the nature of the overlying material. Further, where the masonry is continuous over the piers, especially where a large amount of backing is used, the material tends to cantilever itself from the piers, and thereby relieve the arch of much of its load, or if the amount of backing and filling above it be large, these materials may to a great ex- tent arch themselves from pier to pier, and thereby relieve the real masonry arch. The external span- drel walls may also act as arches and carry a con- siderable load. The above remarks apply to bridge arches. In the case of arches in buildings, the con- dition of the external loads or forces is even more in- 6 CONCRETE BRIDGES AND CULVERTS. definite. Take, for example, the case of an arch car- rying a wall load above it. It is customary to con- sider that the arch carries the entire weight of such a Avail. The fact, however, is that an unbroken wall supports itself almost entirely, by acting as a mason- ry beam or by arching itself, and the only portion supported by the arch is a triangular piece of ma- sonry directly above it. This is true for a wall without openings. When openings occur the above consideration will be effected, depending upon the location of the openings. If they occur in such po- sitions as to evidently interfere with, and destroy the beam or arch-action of the superimposed ma- sonry, then the entire weight of masonry may come on the arch. There are many bridge arches now standing that would doubtless fail, were they sub- jected to the entire weight of the materials above them. After striking center, the arch itself has set- tled, and much of the imposed load is transferred to the piers by the cantilever or arch action of the backing and fill, or the arch action of the spandrel walls. (2) Another unknown factor in the design of ma- sonry arches is the strength of masonry. Experi- ments have been made principally on small sam- ples tested in machines with pressures normal to surface, all of which conditions are quite different to those of actual arches under loads. The material is then concentrated in bulk, with pressures inclined to bearing surfaces and with loads more or less of a vibratory nature. PLAIN CONCRETE ARCH BRIDGES. 1 (3) It is usually assumed by engineers and an alysts, that the joints of block structures such as masonry arches will resist no tensile stress. This is a precaution on the side of safety, but may be far from true. With a rich quality of concrete, we know that properly formed points will actually re- sist considerable tension, provided they remain in- tact. (4) The position of the line of resistance in the arch is not definitely known. This is largely due to the continuity of the arch at the center, and the square bearings at the piers or springs. To obviate this difficulty, some European engineers have built masonry arches with hinges at the crown and springs, thus fixing the position of the line of resist- ance at these points, but in America such provisions are not generally used. (5) Imperfect workmanship in the cutting of the stones and the fitting of the joints is another factor causing the actual line of resistance to move from its supposed position to a different one, where the joints come to a firm bearing. (6) The removal of the arch center and the set- tling of the arch to its permanent position, also effects to some extent the theoretical considerations. It appears therefore that any effort at ultra re- finement in arch design is a waste of energy, for the actual conditions existing in a completed structure may not even approximate those assumed. 8 CONCRETE BRIDGES AND CULVERTS. Form. The form or general outline is the first considera- tion in the design of a masonry arch. Semicir- cular and semi-elliptical arches, commonly known as full centered arches, spring from horizontal beds, while segmental arches spring from inclined beds called skewbacks. The old Roman arches were near- ly all semicircular. In bridges and viaducts where piers are used, full centered arches or those which spring from horizontal beds, are preferable to seg- mental arches springing from inclined beds, for the reason that full centered arches produce a less over- turning moment on the pier, and their attachment to the piers with horizontal beds is simpler than with inclined springs. The thrust on piers, however, depends upon the rise of arch, which is not neces- sarily the distance from spring to center intrados. The effective rise is the vertical height from spring to crown, measured on the linear arch or line of pressure and any minor curve joining the arch soffit to the pier, is not effective and must not be con- sidered as part of the rise. Segmental arches have a shorter curve than elliptical for the same span, or for the same length of soffit the segmental arch results in a wider span. For small spans such as commonly used for culverts, segmental arches con- tain from 25 to 40 per cent less masonry than semi- circular arches, though common practice makes the segmental arch ring 10 to 25 per cent thicker than the semicircular. For fluid pressure the proper form of arch is the semicircle. The effect of earth PLAIN CONCRETE ARCH BRIDGES. 9 fill or other loads at the haunches, tends to raise the line of pressure to the approximate form of an el- lipse, while the effect of a uniform load, such as the weight of earth fill and pavement above the crown, together with a uniform live load, tends to depress the line of pressure to the approximate form of a parabola. The combined effect of these two loadings is to bring the line of pressure more nearly to the segment of a circle. , The most economical form is a linear arch of the given span for the required loading, in which the thickness is proportional to the thrust. In such an arch every part of the cross- section would be stressed alike. One authority rec- ommends that the form of intrados for arches with earth filled haunches be midway between a circular segment and ellipse. Any variation from regular curves that is sufficient to be apparent to the eye, is a violation of a principle of design and should not be permitted. The many three and five centered flat arches already in existence are sufficient to clear- ly prove the utter failure of such forms to produce artistic or satisfying effects. If multi-centered flat arches must be used, they should be drawn from as many centers as possible. Three and five centered arches are suitable when the form approaches a semicircle. An economical form of arch with cantilever brack- ets at the ends has lately been built over the Yermil- lion River at Wakeman, Ohio. The bridge has cross walls with open spandrels, a clear span of 145 feet, and end cantilever brackets 37 feet long. The meth- 10 COXCRETE BRIDGES AND CUU 7 ERTS. od necessitates the use of reinforcing metal at the floor level for the purpose of tying the brackets to the main span. A somewhat similar plan was adopt- ed in the Topeka bridge, but in the latter case the concrete cantilevers were for retaining walls only. The cantilevers were tied together with rods to pre- vent spreading from the pressure of the earth filling. In the case of arches such as culverts under high embankments, the segmental arch with its horizon- tal thrust is economical. The arch thrust resists and counteracts the earth pressure on the sidewalk from without. Hinged Arches. A practice that has long been followed in Europe, is to provide stone or metal hinges at the crown and springs. The use of such hinges locates definitely the position of the line of pressure at these points, and thereby removes one of the common uncertain- ties of masonry bridges. Hinges are particularly desirable where the nature of the soil is yielding or uncertain. Any lateral movement of the abutments causes the arch to sink at the crown when the centers are removed, and such sinking produces cracks that are unsightly and possibly dangerous. When hinges are used, the joints are filled in solid w r ith cement mortar, after the centers are removed and the arch ring has assumed its final position. For additional loads, the entire area of both hinges and mortar fill- ing will then be available for resisting arch thrusts. PLAIN CONCRETE ARCH BRIDGES. 11 Position of Springs. The arch springs should be located as near to the foundation as conditions will permit. This will reduce the overturning effect on the pier to a mini- mum, and produce a more stable construction. Some of the conditions governing the position of the springs are as follows : Over streams the spring must be sufficiently high to allow ample water way, and clearance for the passage of boats or drift ; over roads or highways the springs must be sufficiently high to provide proper head room and clearance for the passage of pedestrians and vehicles, and over railroads, for the passage of cars. In the last case, there must be a clear head room of at least 21 feet at a distance of five feet from the face of piers. This allows clearance for the largest box cars and additional space for trainmen on the roof. Abutment Piers. For long bridges or viaducts with a series of arches, abutment piers, or those of sufficient thick- ness to resist the pressure of a single arch, should bo placed at frequent intervals. Where the spring lina is located so near the foundation, that piers need not be excessively thick, it may be desirable to have all piers of the abutment type. Then, during the course of construction, the spans may be built inde- pendently and false work removed when desired, without reference to the adjoining spans, or after the completion of the bridge if one span should be destroyed by flood or other cause, the other spans 12 CONCRETE BRIDGES AND CULVERTS. would still remain intact. If all piers in an arch viaduct are of the ordinary type, to support vertical loads only, and one span should be destroyed, then the remaining spans would also fall, one after the other in succession, by the overturning of successive piers. Height of Bridge. In most cases, the height of the bridge or level of the roadway will be previously determined. In some cases, however, the floor grade may be varied more or less by grading the approaches to suit other con- ditions. It may be that money spent in raising the approaches and the level of the bridge floor, will be saved many times in the cost of the masonry. Rise and Span. The span is the clear distance betw r een vertical faces of piers or abutments, and the rise is the height of crown above springs, measured on the line of pressure, and not on the arch intrados. Curves joining flat arches to piers are not part of the effective rise. The length of span and rise of arch will be among the first considerations. In many cases, the natural conditions will determine one or both of these di- mensions. If the bridge is short, a single span may be sufficient. If it spans a street or rapid stream, where piers are impracticable, the conditions will require only one span. In long viaducts, the dividing of such a structure into spans of proper length is an important matter. The economic span PLAIN CONCRETE ARCH BRIDGES. 13 length depends chiefly upon the total height of structure above foundations. Generally, high struc- tures require longer spans, and lower structures, shorter spans. For steel bridges with vertical reac- tions, the economic length of span for various heights is well known or may easily be determined, but with arches there are other considerations. The usual practice is as follows : Place the springing lines on the piers down to the lowest point possible consistent with the necessary clearance, and after allowing for the thickness of the arch ring and fill- ing at the crown, draw in spans, the length of which are from two to five times the rise of the arch, pref- erence being given to spans of twice the rise or to semicircular arches. Certain other conditions, how- ever, may determine the length of span. For exam- ple, in a long viaduct over railroad yards, it may be desired to span a certain number of tracks with each arch, or to have as few piers as possible to in- terfere with additional tracks or switches. In that case, the length of span may be fixed arbitrarily re- gardless of the rise or height of bridge. Tn fixing the lengths of a series of arch spans, the Romans made those spans nearest to the center of the river, longer than the shore spans. The plan is still in general use, and it has the merit of causing the span at a distance from the shore observer, to appear at least as long as the nearer ones. When a uniform span length is used, the effect of perspec- tive is to cause those spans near to the river center 14 CONCRETE BRIDGES A\'D CULVERTS. which should be of greater importance, to appear shorter than they really are. To balance the pier thrust from unequal spans, the shorter one may have a smaller rise with greater earth filling and consequently greater loads. Several of the large railroad companies have re- cently adopted standard segmental culvert arches having a rise of one-fifth the span. In many other bridges this proportion is exceeded, especially where natural or other conditions govern. General- ly speaking it will be found cheaper to make long spans with few piers, provided sufficient rise is available. Crown Thickness. In the preliminary design it is necessary to know approximately the required crown thickness or depth of keystone, and also the amount of earth filling over the crown, to determine the remaining distance from crown to spring or the available height for the rise of arch. The crown thickness may be found approximately by reference to tables of existing arches, or from some reliable empirical formula. Trautwine's formula for such thickness is as fol- lows, a development of the formula for various spans and rises being given in the Engineer's Pocket Manual. Depth of key in feet= -\Radius-fhalf span +.0 f tt 4 The above is for the tirst class cut stone work, either circular or elliptical. For second class ma- sonry, increase the results from the above formula PLAIN CONCRETE ARCH BRIDGES. 15 by one-eighth, for brick, by one third; for large elliptical arches some engineers increase also the above values by one-third. Rankine's rule for croAvn thickness is: For single spans A '.12 Radius For several spans -* .17 Radius It becomes necessary therefore to determine the radius at the crown. This can be done graphically. The crown radius for an ellipse can be found as described later and shown in Figure 2. It is com- mon practice with small segmental arches to make the arch ring from 10 to 25 per cent thicker than semicircular ones. The crown thickness may also be found approxi- mately by first determining the approximate crown thrust. This is easily computed by finding the cen- ter bending moments for all loads, the same as for a beam, and then dividing by the rise, or the approxi- mate crown thrust ma^ be found from Navier's formula, T />r, where T is the crown thrust, p the average pressure per square unit on the arch, and r the radius of arch at crown. It will be noted that the proper value for the crown thrust is that one which produces equilibrium about the point of rup- ture, and not about the springs. The experience of the Writer in using Trautwine's tables of sizes and quantities for masonry arches is that Trautwine's figures are about one-third larger than the best practice now in use by the large rail- road systems for the design of concrete arches. 16 CONCRETE BRIDGES AND CULVERTS. Thickness of Crown Filling. An assumed depth for this filling is required as noted above, in order to determine the available height for the rise of the arch. For highway bridges, a depth of filling including the pavement, of from one to two feet will be sufficient, but for railroad structures a greater depth is necessary in order to form a cushion for the ties and absorb and distribute the shock from passing trains. For this purpose a depth of from two to four feet, or ordi- narily of two feet below the ties will be sufficient. To secure this cushion effect, the filling in some re- cent concrete railroad bridges has been as great as five feet. Spandrels. Bridge spandrels are either filled solid with earth held in place by side retaining walls, or the floor over the spandrels is supported on a series of in- terior walls and arches, which may or may not ap- pear on the exterior. The solid earth filling is gen- erally used for small spans and flat arches. But for large arches and especially semicircular ones, the open construction will be cheaper. In certain cases of comparatively flat arches, even where it would be more expensive than solid filling, the open spin- drel construction may be desirable for the purpose of reducing the load on the foundations. This was the case with an elliptical arch bridge recently PLAIN CONCRETE ARCH BRIDGES. 17 built by the Illinois Central Railroad Company over Big Muddy River, containing three spans of 140 feet each, with 30 feet rise. It was found that the open spandrel construction reduced the loading on the piles by about six tons per pile. Which one of these methods to use in any particular case, can be determined by making comparative designs and es- timating the costs. In many cases, however, the choice can be made by inspection. By building open chambers crosswise of the bridge and having the openings appear on the spandrel faces, a design is produced that presents a lighter appearance and at the same time shows plainly the plan of construction. When a heavier and more massive appearance is desired, then the side w r alls may be used and all spandrel openings closed. In large arches approaching the semicircular form, if open spandrels are used and the interior spandrel walls run parallel w r ith the axis of the bridge, these walls then act as backing and produce the necessary conjugate thrusts on the haunches below the points of rupture. The need of providing for necessary conjugate thrusts is important and must not be over- looked. Cross spandrel walls and open chambers or arcades may be used above the point of rupture, but below 7 that point the construction must be solid. This type of construction is well illustrated by the Connecticut Avenue bridge at Washington, shown on page 88. 18 CONCRETE BRIDGES AND CULVERTS. An improved method of designing spandrels is il- lustrated in the Piney Creek Parabolic Arch bridge in Washington. The floor slabs are carried on an interior system of beams and columns supported on the arch ring, and the spandrels are enclosed with thin curtain walls. A design similar to this for a segmental arch was prepared by Mr. Thacher for the Bellefield bridge in Schenley Park, Pittsburg. This system is a very economical one and has the advantages of leaving the interior construction open at all times for inspection, and of producing a less amount of load in the spandrels for the arch to carry. The curtain walls are also thinner than re- taining walls for earth filling and cost proportion- ately less, and the pavement may be laid at once without waiting for the filling to settle. When the pavement is laid, there will never be any liability of the road settling, as often does occur when pave- ment is laid on earth filling, even though such fill- ing be well rammed and permitted to settle a long time before laying the roadway. The use of the open spandrel construction with either cross walls or columns avoids any uncertainty in reference to horizontal conjugate pressure from spandrel filling, and also prevents water collecting and soaking into the arch masonry. When it is de- sired to secure a greater diversity in design, the face walls may be omitted and the interior arcade or colonnade construction artistically treated for the PLAIN CONCRETE ARCH BRIDGES. 19 purpose of producing a more pleasing architectural effect. In comparing the relative costs of colon- nade and arcade construction for spandrels, en- closed column construction will generally be found the cheaper, for the beams and columns may be left rough, and the spandrel curtain wall only will need a finished surface. Cross arcade construction has the economy of small dead load, but all open span- drel walls are exposed to view and may require fin- ished surfaces or possibly architectural treatment. Open chambers may be enclosed at the top, either by means of arching or by using flat slabs of stone or reinforced concrete. The upper surface is then waterproofed by applying a layer of rich mor- tar and surfacing with neat cement, on top of which is poured a layer of tar or pitch. The surface may then be leveled with gravel and sand, and the pave- ment laid. Another reason for selecting either the solid or the open spandrel type is for the purpose of adjust- ing the imposed loads on the arch to the form selected. This may be necessary to secure stability and will be considered later under the head of load- ing. In designing the side spandrel walls to retain earth filling the usual rules for retaining walls will apply. Practice is to make the thickness of such walls at the base 40% of the height. They should be firmly doweled or otherwise secured to the arch masonrv, 20 CONCRETE BRIDGES AND CULVERTS. Various Forms and How to Draw Them. The forms adopted for the intrados of masonry arch bridges are generally circular, segmental, elliptical, or multi-centered. These four types can be reduced to two, circular and elliptical, for the seg- mental arch is merely a segment of a circle, and the multi-centered arch is merely an approximate ellipse. The two general forms are, therefore, the circu- lar and the elliptical. Methods of drawing the ellipse and the multi-centered curve are as follows: Ellipse. Let AD and CD be the semi-major and semi-minor axes of an ellipse at right angles to each other. Draw circular arcs Fig. 1 with radii AD and CD, respectively. From points where a common radius intersects the two circular arcs, draw vertical arid horizontal ordinates. The in- tersection of these ordinates gives points on the ellipse. Multi-Centered Arch Three Centers. These curves are sometimes called basket-handled arches. The method of drawing a three-centered PLAIN CONCRETE ARCH BRIDGES. 21 c arch is as follows : Let AD and CD be the semi-major and semi-minor axes, respectively, of a true ellipse. The form of the true ellipse is first drawn by the method given above. This is show r n in Figure 2 by the full line. The approximate form is then o drawn as follows : Assume any two equal distances CB and AE less than half of the semi-minor axis. Join BE and bisect the line BE at F. Through F draw a perpendicu- lar to BE, intersecting the line CD at 0. The two points and E will be centers of two circular arcs which will form an approximate ellipse. By first selecting the position of the point E so the circular arc described from E as center will conform as closely as possible with the true ellipse, satisfactory curves will easily be found. The full line on Figure 2 shows the true ellipse and the dotted line the ap- proximate. Fig. 2 22 CONCRETE BRIDGES AND CULVERTS. Five-Centered Arch. A method for drawing a five-centered arch is as follows : In order to check on the work, it is advisable to first draw the form of the true ellipse by the method given above. In Figure 3 the two curves so closely correspond that only one can be shown. On the [transverse axis AO draw the rectangle AGCO, equal in height to the semi-minor axis OC of the ellipse, and draw the diagonal AC. From G draw a line GHD per- pendicular to AC and intersecting the center line CO of the span produced at D. From as cen- ter, with radius OC, draw the circular quadrant as shown. Describe the semicircle ARL and produce the line OC to its intersection with the semicircle at L. From O as center, describe the arc at M with radius equal to CL, andD as center de- PLAIN CONCRETE ARCH BRIDGES. 23 scribe arc rtM, with DM as radius. On the axis AO lay off AN equal to OL. Then from II as center, with radius HN. describe the arc Na, cutting Ma at a. The three points IT, a and D, with correspond- ing ones in the other quadrant are the five desired centers from which to draw the approximate ellipse. This method of drawing a five-centered arch as ap- proximate to an ellipse must not be confounded with the method given later for drawing a hydrostatic arch. The crown radius of the ellipse will be less than the corresponding radius of the hydrostatic arch. Parabolic Arch. The parabola is not frequently used in masonry bridges, but the formula for drawing it is given. It is as follows : * 3 * ' o The various let- ters refer to di- mensions shown in the accompanying Figure 4. = *& F*i The line OR is divided into any number of convenient equal parts, which are numbered 1, 2, 3, etc., beginning at the point nearest O. Then to find the value of y, for the various ordinates x, the numbers 1, 2, 3, etc., may be inserted in the above equation for values of x, and the total number, which in the illustration is 6, will be inserted for the value 24 CONCRETE BRIDGES AXD CULVERTS. of a. The upper line in Figure 4 shows the corres- ponding form for a true ellipse. A very simple graphical method of drawing the parabola is to lay off on the vertical line RS the same number of equal divisions as drawn on the horizontal axis OR, and from draw radiating lines to the various division points on the vertical axis RS. From the various points on the horizontal line OR draw vertical lines intersecting the radiating lines from 0. The points at which these vertical lines intersect the radiating lines are points on the required parabolic curve. Hydrostatic and Geostatic Arches. In selecting the most suitable form for the in- trados of an arch, the following consideration of the above two forms of curves will be serviceable. The hydrostatic arch is the form of a linear arch under varying pressures which are always normal to the line of arch. This condition corresponds to that of an arch submerged below the surface of water. As the depth below the surface increases these normal pressures increase proportionately, and as the external pressures are always normal to the surface, the amount of pressure in the arch is con- stant, and is equal to the produce of the external pressure at the point by the radius of curvature. The equation is T=pr, and is known as Navier's Principle. Since the essential principle of the hy- drostatic arch is that fluid pressure is normal to the surface, the thrusts at all points of the arch PLAIN CONCRETE ARCH BRIDGES. 25 ring are, therefore, constant, and cannot vary with- out the application of oblique or tangential pres- sures. Since T is constant, r will vary directly as /> These radii may be found for varying depths below water level, and the corresponding curve plotted. It will be noted that the thrust T at the crown, is equal to the total horizontal pressure on the ex- trad os of half the arch. Ordinarily, however, arches are subjected to earth pressure rather than water. The external forces fire, therefore, no longer normal to the extrados o the arch, but bear a relation thereto, depending on the nature of the overlying material. In the case of earth or gravel filling, having an angle of repose of one and one-half to one, it is known that the hori- zontal pressure exerted against vertical surfaces is about one-third of the weight of the material above the point under consideration. The formula is H=-^-. o The linear arch supporting a filling of clean dry sand would be the true form of the geostatic arch. If p is the horizontal intensity of force in the hydrostatic arch, and p' the corresponding force in the geostatic arch, then p=Cp f . It will be seen, therefore, that the geostatic arch bears the same relation to the hydrostatic arch as the ellipse does to the circle. A linear geostatic arch may, there- fore, be drawn for any assumed value of C, such as 3, which experiments show to be about the right factor for earth or gravel filling. In drawing this linear arch all the vertical co-ordinates of the hydro- CONCRETE BRIDGES AND CULVERTS. static arch are retained, and conjugate pressures changed according to the formula p=Cp f . For arches under heavy banks of earth the geostatic arch can be drawn from the hydrostatic arch. If the height is fixed, the form of curve and proper width can be found to properly withstand the earth pressure. For bridges, these principles are useful chiefly for arches under high embankments. In his book on Civil Engineering, page 420, Ran- kine gives the following approximate method for drawing the form of a hydrostatic curve about five centers by means of circular arcs. The two radii r' "]?" and r are first computed from the accompanying formula. This fixes two of the centers and the third is found at E as shown. The equations for radii are as follows : * 5 r>= 1 - 30 a DE == AF BD / a 3 x a - PLAIN CONCRETE ARCH BRIDGES. 27 In Figure 5, let FB be the half span and FA the rise of the proposed arch. Make AC=r, and BD r', the radius of curvature at the crown and springing as calculated from the above formulae. Then C will be one of the centers and D another. About D, with the radius DE, describe a circular arc, and about C, with radius CF, describe another circular arc. Let E be the point of intersection o f these arcs. The points D, E and C will be the re- quired centers. Many semi-ellip- tic arches ap- proach very near- ly the form of a hydrostatic arch. A comparison be- tween Rankine's approximate curve and the true one are shown in Figure 6. The upper or outside curve is the approximate curve as given by Rankine. The center curve is the true hydrostatic arch plotted from a succession of radii, and the inside curve is a true ellipse. Selection of the Most Suitable Form. Full centered arches, either circular or elliptical, produce the least overturning moment on the piers, and w T ill generally require less pier masonry than Fig. 6 28 CONCRETE BRIDGES AND CULVERTS. segmental arches. If the arch thrusts against nat- ural rock skewbacks or abutments, the amount of such thrust is then a matter of little importance as far as the abutment is concerned. The attachment of segmental arches to piers usually requires tilted beds to bring the joints at right angles to the line of pressure. This is a condition that does not occur in full centered arches. In flat ellipses the pier thrust is greater than with semicircular arches, the position of thrust approaching more nearly that of a segmental arch. It has already been shown that, for arch culverts carrying heavy earth banks, the segmental form of arch will be more effective and less expensive. It produces heavy thrusts on the abutments, which thrusts counteract the inward pressure of the earth on the side retaining walls. At the same time there is a shorter length of curved work to build than with a semi-circular form. The cost of segmental culverts has been shown to be only about 60% of the cost of the corresponding semicircular ones. After drawing a trial linear arch or line of re- sistance for any particular case, the form of this trial curve will suggest the most suitable form for the intrados of the structure. For a bridge with spandrel filling and loads increasing from the center to the springs, the elliptical form or a corresponding multi-centered arch will probably lie nearest to the linear arch, while for an arch with open spandrels the condition of loading will be more nearly uni- form, and the curve will be flatter at the haunches PLAIN CONCRETE ARC PI BRIDGES. 29 and approach the form of parabola. In such cases the segmental form would probably be used instead of the elliptical. The elliptical form requires less filling in the haunches than the segmental arch, and has, therefore, less weight to carry. At the same time it gives a greater amount of clearance under- neath, A semicircular or Roman arch with a large rise generally requires the smallest piers, and in a high viaduct, where the piers are an important part of the total cost, this form will be economical. The exact line of resistance for an arch under a high embankment is the geostatic arch. It may, how- ever, be assumed as an approximate ellipse. The form of the intrados under earth whose angle of repose is 30 degrees will then be determined by the equation : Vertical axis r- Horizontal axis A In designing culvert arches it will be advisable for the engineer to consult standard plans for such structures. Many considerations will appear that might not at first occur to the designer. External Loads and Forces. It has already been shown that both the amount and direction of the external forces acting on a masonry arch are indefinite. In an arch supporting a masonry wall it is usually assumed that the arch carries the entire weight of wall above it. This is on the side of safety, but is certainly not correct. The wall will, to a great extent, support itself. 30 CONCRETE BRIDGES AND CULVERTS. either acting as a beam or arch, and the probability is that the weight of only a small portion of the wall directly above the arch is all that is carried directly by it. Arches under high embankments certainly do not support the entire weight of earth above them. The earth corbels or arches itself, as is plainly seen in the case of a tunnel, where only a small portion above the crown is supported by the tunnel center. It is customary to consider that arch bridges with spandrel filling support the entire weight of such filling on the arch ring. The fact is, however, that the backing and fill either arch themselves, to some extent, from pier to pier, or if the backing is continuous over the pier, the backing itself will then form a cantilever and carry much of the spandrel loads. The English engineer, Brunei, many years ago designed and built a semi-arch of brick, with hoop iron bond, 60 feet in length, which supported itself entirely by cantilever action. Since the introduc- tion of reinforced concrete as a desirable material for arch construction, it has become common prac- tice to build cantilever arms or brackets on the shore ends of arch spans, showing that the canti- lever principle is just as sure to come into action when continuity over the piers exists, as it is that the arch thrust itself is in operation. A good illus- tration of this cantilever construction is shown in a bridge recently built over the Vermillion River at Wakeman, Ohio, and described in Engineering-Con- tracting, February 4, 1909. Somewhat similar canti- PLAIN CONCRETE ARCH BRIDGES. 31 lever arms were used for retaining walls at the ends of the reinforced concrete arch bridge at Topeka, Kansas. Not only is the amount of vertical loading from the filling unknown, hut the horizontal conjugate pressure on the masonry haunches is also indefinite. We know that nearly all semicircular arches, or those of similar form, after the centers are removed, will settle at the crown and recede laterally at the haunches. The effect of this settlement is to bring conjugate pressure on the backings, and, therefore, it is certain that pressure exists there, but the amount of such pressure is unknown. Semicircular arches require backing below the point of rupture to produce conjugate pressure equal in amount to the crown thrust. This must be secured, either from backing, fill or spandrel walls. If the point of rup- ture in segmental arches is at or near the skewback, the conjugate thrust then comes from the abutment, and little or no backing or corresponding walls will be required. "While conjugate pressures are neces- sary for stability below the point of rupture, it has been demonstrated that conjugate tensions are nec- essary above that point, and to secure that result, rods have been used. The intensity of conjugate thrust from earth filling with an angle of repose of 30 degrees is one-third of the vertical. It is good practice to cut the voussoir stones on the extrados of the arch into steps with horizontal Lnd vertical faces, so the pressures on these may be normal to the surfaces. 32 CONCRETE BRIDGES AND CULVERTS. Scheffler's Theorem assumes that all external loading acts vertically. This is an error on the safe side and will require abutments slightly heavier than when conjugate horizontal forces are consid- ered. It has already been stated that elliptical arches have less fill or material above them, and conse- quently less weight to carry, than either segmental or parabolic arches. In the case of arches supporting earth filling, the form of such filling will, to a large extent, deter- mine the proportion of weight that bears upon the arch. A long bridge will carry the entire weight of material above it, while a culvert under a high bank will carry only a portion of the material above it. Sewer arches exist which would be unstable without earth pressure, showing clearly that con- jugate earth pressure does exist. Mathematical Theory of the Arch. The theory of arches is very complex and in- tricate. Analysts have given much thought to the matter, and many volumes have been written, when in reality, the complete determination of the force polygon, and the corresponding line of resistance in the arch, constitute all the calculations involved in the practical design of a masonry arch. All methods of computation are approximate only. The thick- ness of arch is first assumed by comparison with tables of existing arches or by the use of some em- pirical formula. Lines of resistance are then drawn PLAIN CONCRETE ARCH BRIDGES. 33 for this arch, and if these lines do not fall within the middle third of the arch ring, the form is changed and a new line of resistance is drawn for the revised form. The calculations resolve them- selves into a series of trials. No effort will be made here even to review the many theories of the arch. For such investigation the student is referred to the writings of mathematicians. Their conclusions only will be given in this book. The theory is based upon the assumption that joints will resist no ten- sion. Stability Requirements. The requirements for complete stability in a ma- sonry arch are three in number : (1) There shall be no rotation of one part of the arch about another. (2) There shall be no sliding of one surface upon another. (3) The unit pressure shall be such that no crush- ing of the arch material shall occur. To insure the first requirement it is necessary that the line of resistance shall lie entirely within the arch ring, and to insure further that the pres- sure shall be distributed across the entire section of the arch, and no tendency to opening of the joints occur, it is necessary that the line of resistance shall lie within the middle third of the arch ring. To avoid sliding of one joint upon another, all joints, including those in the arch and in the abutment, shall make angles not less than 70 degrees with the 34 CONCRETE BRIDGES AND CULVERTS. line of resistance. The friction coefficient for ma- sonry joints is from 40% to 50%. To avoid crush- ing of the arch material, the cross-section of the arch shall be sufficient, so that the intensity of pressure at the outer edge shall not exceed a certain safe work- ing unit. With these three requirements fulfilled, the stability of the arch is assured. If a line of resistance cannot be drawn within the middle third of the arch ring, then it is necessary to change either : (1) The thickness of the arch ring, (2) The form of the arch, or (3) The distribution of the loading. Practice in the design and construction of con- crete arches varies in reference to the absence or presence of joints in the arch ring. In large struc- tures, where the entire concrete cannot be placed from one mixing, it is customary and sometimes necessary to provide joints in the arch ring, and as an additional precaution against sliding of such joints, they may be doweled or dovetailed together. Ultimate Values. The ultimate crushing values of the common arch materials are as follows : Granite . . .5,000 to 18,000 pounds per square inch Limestone .4,000 " 16,000 " Sandstone .3,000 " 10,000 " Concrete ..2,000 " 4,000 " Brick 300 " 600 " PLAIN CONCRETE ARCH BRIDGES. 35 Working Units. The working unit strength of these materials at the outer edge is taken at one-tenth of the ultimate, and as the maximum pressure at the outer edge when pressure at the inner edge is zero, is twice the mean or average pressure, this corresponds to using a mean unit pressure of only one-twentieth of the ultimate. The necessity for this high factor will be seen from the following considerations. Experi- mental data on the strength of masonry in bulk is comparatively small. Most experiments have been made on sample pieces of the material held properly in position with pressures applied normal to sur- faces. Also the crushing strength of masonry in bulk is much less than that of the separate material of which it is composed, because of the presence of mortar joints. On the other hand, experiments were made on sample cubes of material, while in the arch the material is used in large mass, and is, therefore, stronger than cubes. Errors in workman- ship and in fitting of joints may cause excessive pressure to occur on some parts of joints, and little or none at all on other parts. The entire system of external loads is, therefore, uncertain. Working units may safely be taken as follows : Granite 500 to 1,500 pounds per square inch Limestone ..-.300 " 1,000 " Sandstone ....200 " 800 " Concrete 200 " 500 " Brick . .80 " 100 "-. " " " 36 CONCRETE BRIDGES AND CULVERTS. A maximum pressure of 400 pounds per square inch is good practice for concrete arch rings, and is suitable for a mixture of 1-2-4 well and carefully laid. The above pressures refer to the maximum pres- sure at the outer edge and not to the mean or aver- age pressure, which would be only one-half of the above. These units will give a factor of safety of ten in compression. The requirement that the line of resistance shall fall within the middle third of the joint produces a factor of safety against rota- tion of three, and the requirement that the angle between the face of joints and the line of resistance be not less than 70 degrees produces a factor of safety against sliding of from one and one-half to two. Determination of Line of Resistance. Ordinarily, the consideration of two cases of load- ing will be sufficient. (1) A uniform dead and live load over the entire structure, and (2) the entire dead load with a maximum live load over one-half of the span only. The absolute maximum stresses from partial loading may be obtained when the live load is applied to somewhat less than one-half the span, as .4 to .45 of the length, but for practical purposes it is sufficiently accurate to consider half the span loaded. In certain cases it may be neces- sary to consider the maximum dead load with a single concentrated live load at the center. PLAIN CONCRETE ARCH BRIDGES. 37 Find first the line of resistance for the maximum dead and live loads over the entire structure. An approximate thickness will have been assumed for the arch ring at the center, also the depth of the earth filling above as previously described, and an approximate form of arch will have been selected. If the bridge has spandrel filling, the first operation will be to divide the loaded area above the intrados into a number of vertical strips, to compute the weight of material in each of these strips and the live load on them. In order to simplify calculations, a portion of the bridge one foot in length at right angles to the paper will be considered. Each re- maining portion will be a duplicate of this. It may be necessary to draw a separate line of resistance under the side spandrel walls, because the weight of wall masonry is, greater than earth fill. The amount of conjugate pressure of the backing on the haunches is then considered. For gravel and earth the intensity of this pressure per square foot or other unit may be taken at one-third of the weight of filling and live load above the extrados at the strip under consideration. Then the product of this horizontal intensity and the area of the vertical projection of that portion of the extrados under the strip will give the amount of the conjugate thrust. This will be repeated for all other strips and a complete set of loadings found, which should all be written in their respective places. PLAIN CONCRETE ARCH BRIDGES. 39 Proceed next to construct a force polygon by drawing the various loadings to a convenient scale. As arches are generally symmetrical about the center and horizontal at that point, the crown thrust for uniform loadings will likewise be hori- zontal. The pole in the force polygon will, there- fore, be on the same horizontal line with the upper end of the first load line at A. The amount of this crown thrust is unknown, and the pole distance can, therefore, be only assumed for the present. Take any pole, as that shown at P' on Figure 7, and draw the corresponding force polygon. Draw also the corresponding line of resistance or funicular poly- gon in the arch ring, starting from any point within the middle third at the crown. The resulting funic- ular polygon is that shown at ay f . It is evident that the pole distance assumed was not the correct amount of the crown thrust, for the line of resistance or polygon falls entirely outside of the arch ring. Project the last line of the funicular polygon till it intersects the line of crown pressure produced at the point g. This gives the position of the resultant of the assumed loads, and its direction will be par- allel to the line AB in the force polygon. The posi- tion of this resultant is constant, regardless of the force polygon. Therefore, the corresponding line of any other funicular polygon produced, such as that through 3', will likewise intersect at the same point. Therefore, through y draw such a line, and 40 CONCRETE BRIDGES AND CULVERTS. from B in the force polygon draw BP, intersecting the horizontal through A at P. The distance AP measured to the same scale as the load line will represent the true amount of the crown thrust. The other lines radiating from P to the various points on the load line will truly represent the amount of thrust at the various points in the arch. A check on the crown thrust may be made by finding the bending moment at the center for all the loads in the same way as for a beam, and dividing this moment by the rise of the arch. It will be remembered, however, that the rise is not neces- sarily the distance from spring to crown, for in flat arches, and especially in elliptical forms, the line of resistance does not fall as low as the springs. The correct rise of an arch is the rise of the line of resistance and not the rise of intrados from spring to crown. It will be seen by inspection that a position of the point y was selected so the line of pressure would not pass outside of the middle third of the arch. It approaches nearest to the limit under the strip d. The point opposite to this limiting position is called the point of rupture, and is the point at which the arch first tends to open at the ex- trados. If the line of resistance from the assumed point 3; had fallen outside the middle third of the arch ring at d, a new point w r ould then have been assumed so as to bring the line of resistance en- PLAIN CONCRETE ARCH BRIDGES. 41 tirely within the middle third at the point of rup- ture. As this point v would approach very close to the middle third for an arch of uniform thick- ness from crown to spring, the ring is thickened at the haunch to keep the line of resistance well within the middle third. The line ay, which falls entirely within this limiting space, is, therefore, a true line of resistance for the maximum assumed dead and live loads. It was necessary to determine the crown thrust or pole distance by trial, because there are four unknown quantities, the tw T o vertical and the two horizontal reactions of the arch, and to determine these there are only the three equa- tions of equilibrium, 2x=Q, 2y=Q, 2m=Q. The line BP applied at the point 3.', represents truly in both direction and amount, the thrust of the arch on the abutment. This may be resolved into ver- tical and horizontal components as shown. Numerous ingenious methods have been adopted for simplifying the computations. For instance, some writers prefer to construct what they call a reduced load contour. This consists in first finding the actual loads of arch ring, fill, live loads, etc., for each vertical strip, and reducing the height above the extrados to a corresponding height, pro- vided the load was caused entirely from stone or material of the same nature as the arch ring. Plot- ting these various heights to scale above the in- trados, and connecting the points so found, pro- 42 CONCRETE BRIDGES AND CULVERTS. duces a line which is called the reduced load con- tour. Then by making the divisions two feet in width, and scaling the length of the two sides of each strip, the sum of the lengths scaled will repre- sent the area of the enclosed strip. Sometimes the areas are plotted on the load line of the force polygon instead of the weights. Practice varies somewhat in reference to the selecting of the proper point in the middle third of the arch crown from which to draw the line of resistance. When a hinge occurs at the crown there is then no uncertainty as to the correct position of the line of thrust. Some designers consider that the position of the line of resistance is such as to make the crown thrust a minimum without causing tension on any part of the section. To satisfy these conditions, the line would pass through the upper extremity of the middle third at the crown, and at the springs or at the points of rupture, the line of resistance w r ould pass through the inner extremity of the middle third. Professor Church says that the true line of resistance is that one corresponding most nearly with the center line of the arch. The intensity of the unit pressure on a surface may be found from the following formula : W 6Wd ~~ L " L' where p is the maximum unit pressure at any part of a joint, W the total pressure, d the distance of PLAIN CONCRETE ARCH BRIDGES. 43 the center of pressure from the center of the arch ring, and L the depth of the arch ring. The formula is general for all positions of d, provided the joints can resist tension. If they cannot resist tension, the formula is still general for the values of d up to one-sixth of L. If d exceeds this amount the max- imum pressure is then given by the formula : 2 W P '' ~ 3 (one half L d) The amount of crown thrust or pole distance may be found analytically by taking moments succes- sively around the various load points in the arch. The crown thrust will be found a maximum when moments are taken about the load point opposite to the point of rupture. This is an analytical method of locating the point of rupture. If the arch had hinges at the crown and springs, as are commonly built in Europe, the cro\vn thrust could then be definitely figured. The presence of such hinges greatly facilitates the computations for partial loading, for then, not only the amount of the crown thrust, but also its direction, are un- known. It is no longer a horizontal thrust. The above method of drawing a line of resistance for uniform loads applied to a pair of segmental arches is illustrated also on the left hand arch of Figure 10. 44 CONCRETE BRIDGES AND CULVERTS. A modification of the above method of determin- ing the crown thrust and drawing the line of re- sistance is shown in Figure 8. The space above the arch ring is divided as before into ten equal divi- sions and the total load on each calculated and indi- cated in the proper places. Beginning at the point R, which is the upper extremity of the middle third at the crown, the loads for half the arch are meas- Fig. 8 ured off to scale on a vertical load line Re. From R and e draw lines at 45 degrees with the vertical intersecting at 0, and from draw lines to the points a, b, c and d. Construct a polygon with sides parallel to the lines Oa, Ob, Oc, Od and Oe and ex- tend the two extreme lines of this polygon to their intersection at D. Through D draw the vertical CE, PLAIN CONCRETE ARCH BRIDGES. 45 intersecting the horizontal line R at C. The line CE marks the center of gravity of the loads on the five arch divisions. Through C draw the line CS so that the line of resistance, when drawn, will lie within the middle third of the arch ring. After drawing the line of resistance, if it should be found that any part of it falls without the middle third, a new position must then be assumed for the point S. Through e draw the horizontal line EF, inter- secting CS prolonged at F. The line FC will repre- sent truly to scale the amount of the crown thrust. From R lay off on a horizontal line through R, the distance RP, equal to FE, and join P with the points a, b, c, d and e. From R draw the line of resistance with sides parallel to the lines Pa, Pfr, etc. If any part of this line of resistance falls outside of the middle third of the arch ring, a new position must then be assumed for the point S, and another line of resistance drawn, falling entirely within the mid- dle third. If no such line of resistance can be drawn, then either the form of the arch or its thick- ness must be changed until a line of resistance can be drawn lying entirely within the middle third: Line of Resistance Partial Loading. Consider next the case of a maximum live load over half the span, acting in conjunction with PLAIN CONCRETE ARCH BRIDGES. 47 the maximum dead load. Both halves of the arch must then be considered. As before, the portion of the bridge above the intrados is divided into vertical strips, and the vertical and conjugate load- ings written down in their respective places. A load line, ABC, is drawn, and any trial pole, P', assumed. With this position of pole, the funicular polygon shown in dotted lines is drawn. By using a little care, the point x may be selected, so the curve on the left will fall within the middle third, or tangent to it. It will be seen that this line of resistance shown dotted, falls outside of the middle third in two places and intersects the outer vertical through e' at 3-. This curve cuts the center line of arch at /'. See if it is possible to draw another line of resistance, so that it will -cut the center of the span at the point t and pass through the point y. From P' draw a line parallel to t' y' intersecting AB at D, and from D draw r another line DP parallel to ty. The new pole will lie on the line DP. Also through P' draw a line parallel to xy' intersecting the load line in Q, and from Q draw another line QP parallel to .vy, intersecting the line DP at P. The point will be the correct position of the pole, in order to have the line of resistance pass through the three points, .r, t and y. The distance H in the force polygon may be verified analytically as fol- lows : PLAIN CONCRETE ARCH BRIDGES. 49 From this equation the value of H may be found. and the point P will lie on the line QP at a distance II from the load line. The line of resistance xty is tangent to the line of middle third in the strip d. The point where lines become tangent might have been taken as the required point through which, with x and /, it was desired to pass a line of re- sistance. The corresponding line would have been found in a manner similar to that described. It will be seen that the line xty lies entirely within the middle third of the arch, and the arch as drawn is, therefore, stable. If it had been found impossible to draw a line of resistance within the limits of the middle third, it would have been necessary to change either (1) the form of the arch; (2) the thickness of the arch; or (3) the distribution of the arch loading. A similar method applied to seg- mental arches is shown in Figure 10. In this case the bridge was designed to carry a double line of railroad, with tracks 15 feet apart on centers. It was assumed that the ties and earth fill- ing distribute the weight of each track and the live load thereon evenly over one-half the width of the bridge. This assumption may not be true, but it is as reasonable an approximation as can be made. The live load w r as assumed equal to Cooper's stand- ard E 50, and for 35-foot spans is equivalent to a uniform live load of 10,000 pounds per lineal foot, which was considered evenly distributed over a width of 15 feet, amounting to 667 pounds per lineal 50 CONCRETE BRIDGES AND CULVERTS. foot in width of bridge. For partial loading, the equivalent uniform live load on half the span was assumed at 11,500 pounds per foot of track. Point of Rupture. The point of rupture is that point of the arch ring. at the haunches where the joints tend to open at the extrados, or where the line of resistance lies closest to the inner edge of the arch. By some writers this point is considered the real springing point of the arch, and any part of the arch below the point of rupture is considered as part of the pier or abutment. Its position can best be deter- mined graphically when drawing the resistance line, and, as far as the arch itself is concerned, the line of resistance is required only above the point of rupture. It is, however, continued further for de- termining the stability of the pier. The following empirical rule gives approximately the required thickness for circular segmental arch rings at the point of rupture. In the following equation crown thickness, d=required thickness at point of rupture, when 1*1 m^ _ > = 1 then d=2.00 t span = then d=1.40 * = j- then d=1.24 t = T Vthend=1.15* In reference to the necessary thickness of the arch ring at various points between the crown and PLAIN CONCRETE ARCH BRIDGES. 51 springs, the vertical projection of every section cut- ting the arch ring normal to the line of resistance must be at least as great as the vertical depth of arch ring at the crown. The position of the point of rupture generally occurs at about that point of the arch where the normal to the line of pressure makes an angle of 45 degrees with the horizontal. It may be said that it never falls lower than an angle of 30 degrees with the horizontal and generally between 35 and 45 degrees with the horizontal. Determination of Arch Thickness. The amount of pressure at the various points of the arch have now been determined. It will be seen that these pressures increase from crown to spring in proportion to the rise of the arch. In semi- circular arches the thrust at the spring may be three to four times the thrust at the crown. The relative position of the center of arch and the line of resistance must be examined and suitable unit pressures selected for the various points. If the line of resistance is at either limit of the middle third, the mean unit pressure will then be one-half of the maximum at the outer edge. This is the usual assumption. Then the area obtained by dividing the total pressures by the working units will be the required area of material at various points of the arch. Most authorities on the subject recommend liberal sizes, not only because the usual arch material is not expensive, but also on account 52 CONCRETE BRIDGES AND CULVERTS. of the uncertainty of so many conditions in connec- tion with the whole matter. Backing. Reference has already been made to the point of rupture. It is that point on the extrados of the arch where the joints tend to open, and it occurs opposite that point where the line of pressure ap- proaches nearest to the intrados. It is known in the failure of flat arches that the joints open at the intrados of the crown, and extrados at the two points of rupture, and the haunches recede later- ally, allowing the central part of the arch to fall. In order to resist and counteract this lateral move- ment of the haunches and apply horizontal conju- gate thrust thereto, that part of the extrados from the point of rupture down to the pier is filled gen- erally with backing of rubble masonry or concrete laid in horizontal layers. Semicircular arches re- quire backing sufficient to produce conjugate pres- sures equal to the crown thrust. Segmental arches which have a horizontal thrust component at the spring requires less backing than semicircular ones. Waterproofing and Drainage. Previous mention has already been made of waterproofing. This is necessary to prevent water soaking into the joints and freezing, thereby tending to disintegrate the masonry. A\ 7 aterproof- ing is necessary also 'to prevent drainage water leak- ing through the arch and discoloring or otherwise disfiguring the structure. To prevent such leakage PLAIN CONCRETE ARCH BRIDGES. 53 it is customary to cover the upper surface of the arch and backing with a layer of bituminous con- crete or clay puddle. Clay should contain enough sand to prevent the clay from cracking when dry. Waterproofing may be accomplished by applying a layer of rich mortar and surfacing it with neat cement, on top of which is poured a coating of tar, pitch or asphaltum. The upper surface of the back- ing must have sufficient slope to carry drainage water to the gutter, where it may be discharged through pipes built into either the arch soffit or the side spandrel walls. Intermediate Piers. In making preliminary designs of piers, use may be made of empirical formula to determine approx- imate sizes. Rankine's rule is to make the thick- ness of piers at spring from one-sixth to one-seventh of the span or arch for intermediate piers, and one- fourth of the span for abutment piers. Intermediate piers must be of sufficient area to resist crushing from the maximum loads, and in proportioning the base of pier the weight of the pier itself must be added to the imposed loads. Intermediate piers must also have sufficient stability to resist the over- turning effect of unbalanced thrusts on the adjoin- ing spans. Such unbalanced thrusts will occur if the adjoining spans are of different lengths, or if one only, is subject to live load. For such condi- tions the center of pressure shall fall within the middle third of pier base. Piers must be given 54 CONCRETE BRIDGES AND CULVERTS. sufficient spread at the base, so the pressure on the foundation will not exceed a safe unit. To neutral- ize the effect of unequal thrust on the piers from spans of different lengths, the shorter span may have a less rise with a correspondingly greater amount of filling. This will tend to produce a thrust from the smaller span sufficiently large to equal that from the longer one. Another method is to incline the shorter span upward so the thrust will act on the pier at a point somewhat higher than the corresponding thrust from the longer span. In writing on this subject, Rankine says: "Each pier of a series should have sufficient stability to resist the thrust which acts upon it, when one only of the arches which spring from it is loaded with a travel- ing load. That thrust may be roughly computed by multiplying the traveling load per lineal foot by the radius of curvature of the intrados at its crown in feet." The mathematical investigation of piers is shown in Figures 7, 9 and 10. Abutment Piers. Bridges having a series of spans should have abut- ment piers at intervals in order that the possible fail- ure of one span would not cause the entire structure to fail. Abutment piers are useful also in allowing false work centers to be removed from some of the spans, without waiting for the completion of the en- tire structure. When spring lines can be located close to the foundations, it may be advantageous to make all piers, abutment piers. This was the case PLAIN CONCRETE ARCH BRIDGES. 55 in the long masonry viaduct recently built at Santa Ana in California, on the line of the San Pedro, Los Angeles & Salt Lake Railroad. (See Engineering Record, September 9, 1905.) When it is imprac- ticable to make all piers abutment piers, it will then be well to have every third or fifth one of the type. Such piers may be designed with a factor of safety against overturning of from one and one-half to two. It will be noticed that the point of intersec- tion of the arch thrust with the load line through the center of gravity of the piers, falls lower in the abutment pier than in the intermediate ones,. owing to the greater width of pier. This is an advantage and will bring the resultant pressure nearer to the center line of the pier base. Trautwine's approxi- mate formula for the thickness of abutment piers at the springing is to make the thickness equal to one-fifth of the crown radius plus one-tenth of the rise, plus tAvo feet. Abutments. In proportioning abutment piers, it is not neces- sary to keep the resultant pressure within the mid- dle third of the base, if the maximum pressure at the outer edge does not exceed the allowable unit pressure. Trautwine's empirical rule for the thick- ness of abutments at the springs is the same as was given above for abutment piers. This approximate size will assist in establishing the correct or final one and the rule gives a thickness intended to be sufficient without depending upon the existence of 56 CONCRETE BRIDGES AND CUU 7 ERTS. earth pressure from behind. Abutments sustaining high banks of loose material, must be proportioned, not only for the arch thrust, but also as retaining walls. There is frequently more masonry in the abut- ments of a bridge than in the span itself. For this reason it is desirable to consider carefully any op- portunities for saving material in the abutments. Placing the arch spring down near the ground, greatly reduces the overturning moment on the abutments and causes a considerable saving of ma- terial. In bridges with several arch spans, even though the spring lines on the piers must be high to secure a clearance underneath the bridge, the springs at the end abutments may sometimes bo kept down lower than the corresponding springs on the pier, or if abutments must be high, it may be economical to use ribbed abutments, cored out aivl reinforced with metal bars, if necessary. The use of pavement ties of either wood or metal, will cause the arch thrusts to counteract each other, and thereby greatly reduce the size of abutments. This expedient has not been used to any great ex- tent until recent years, and even now is used chiefly for bridges of reinforced concrete. A wide and shallow waterway is more effective than a narrow but higher one of the same area. Fig- ure 11 shows some possible abutment forms. At A and C are shown abutments where the concrete in front of dotted line, not only is of no service or benefit, but actually decreases the area of waterway PLAIN CONCRETE ARCH BRIDGES. 57 and at the same time adds to the cost of the struc- ture. It will be seen, however, that the abutment A is one of the most common forms used in nearly ARCH ABUTMENTS. all old arch bridges. If for any sufficient reason, vertical sides are desirable or necessary, it will be economy to build independent side walls, as shown 58 CONCRETE BRIDGES AND CULVERTS. at B, rather than waste material by making the whole abutment solid. At E are shown old and new methods of construc- tion. The dotted lines showing an abutment built on level foundation is the method given by Traut- wine and the one generally used until recent years. It will be seen, however, that the forms shown at E in full lines is equally effective in transmitting thrusts to the soil, and requires somewhat less ma- terial. If vertical sides are not required, some ad- ditional material may be saved by using the method shown by dotted line at C. D is suitable for arches with considerable rise on hard soil or loose rock, and F shows a form of abutment in which the arch thrusts against solid rock. In designing abutments, it is safer to discard tho effect of conjugate earth pressure on the arch ex- trados. The abutments will then be somewhat heavier, but the error w T ill be on the side of safety. Rankine says that the thickness of abutments is often from one-third to one-fifth of the radius of curvature at the crown. Flaring wing walls, 25 feet in height or less, rigidly connected to the abutment face, will ordinarily be safe with a base equal in width to one-fifth of the height. This is only half the thickness usually given to retaining walls, and is less because of the angular connection to the abutment face. Foundations. Piers and abutments must have sufficient spread at the base, so the load on the foundation will not PLAIN CONCRETE ARCH BRIDGES. 59 exceed a safe unit. For soil, this will not ordinarily exceed from two to four tons per square foot at the outer edge of the pier, where pressure is the great- est. If piles are used, the same precaution will be taken. Sloping piles have occasionally been used in arch foundations for resisting the arch thrust, but they are more difficult to drive than plumb piles. The Jamestown Exposition bridge, Figure 28, has 26 plumb and 126 batter piles under each abutment. The maximum allowable load on piles should not exceed from 15 to 25 tons each, depend- ing upon the penetration of the pile at the last blow of the hammer. Allowance must be made for the resultant pressure on the base falling outside of the center. It need not necessarily be confined to the middle third, provided the pressure on the founda- tions at the outer edge is not excessive. In his treatise on Masonry Construction, Profes- sor Baker gives the following values for safe bear- ing power of soils : Tons per square foot. Rock equal to best ashlar 25 to 30 Rock equal to best brick masonry 15 to 20 Rock equal to poor brick masonry 5 to 10 Clay, dry thick beds 4 to 6 Clay moderately dry thick beds 2 to 4 Claysoft 1 to 2 Gravel and coarse sand well cemented 8 to 10 Sand compact and well cemented 4 to 6 Sand clean and dry 2 to 4 Quicksand, alluvial soil, etc !/2 to 1 60 CONCRETE BRIDGES AND CULVERTS. Expansion. It is well to provide for possible expansion, so cracks will not appear in the finished surface. In tho case of the Connecticut Avenue Bridge at Wash- ington, shown on page 88, one-half inch expansion joints are provided throughout the entire height of the spandrels, from spring to the floor over the piers and across the roadway. These arches are 150 feet in length and semicircular. After the completion of the concrete arch bridge over Big Muddy River on the Illinois Central Railroad (See Engineering News, November 12, 1903) an examination was made during a period of several months, and almost no expansion whatever was discovered. Surface Finish. Various methods have been adopted for procuring satisfactory surface finish on concrete structures. Among these methods may be mentioned cement washing, tooling, sand blasting, rough casting or slap dashing, scrubbing, cold-water painting^ and acid treating. The Connecticut Avenue Bridge at "Washington has corners and moldings made of con- crete blocks, and to remove form marks the body and flat face work were bush hammered. The Walnut Lane Bridge at Philadelphia has a rough surface finish similar to pebble dash, but of coarser grain. The surface shows stone chips not larger than three-eighths of an inch in diameter, formed by washing the concrete face before the ce- ment had hardened. A more expensive method of PLAIN CONCRETE ARCH BRIDGES. 61 securing a finished surface is to build all exposed surfaces of cut-stone work, or a combination of stone and brick, using concrete for the body of the work only. The Green Island Concrete Bridge at Niagara Trails has surfacing on the spandrels and piers of cut stone, and other bridges have been simi- larly built at Indianapolis and elsewhere. Many bridges generally known as stone masonry bridges are stone only on the surface, with the body of pie^s, arches and backing composed entirely of co^c^ete. The Rockville stone arch bridge built by the Penn- sylvania Railroad Company over the Susquehanna River is of this construction. It has stone facing throughout, including the soffits, spandrels and piers. In building an ornamental concrete foot bridge over two lines of railroad at Como Park, St. Paul, to avoid the appearance of form marking on the finished surface of the bridge, the entire surface of the lagging and moulds was lathed and finished with fine plaster. In the National Zoological Park, Washington, is a concrete bridge faced on the span- drels and parapets with natural boulders, which ex- tend down six inches or more below the concrete soffit. In San Francisco are several concrete bridges with rustic surface finish, made to represent natural boulders, but really formed of moulded concrete. These boulder and rustic surfaces are appropriate for certain wooded parks or rural places, but are not suitable for general adoption. Engineering-Contracting for January 6, 1909, con- tains illustrations of concrete surface effects secured PLAIN CONCRETE ARCH BRIDGES. 63 by various methods on laboratory samples. It will be understood, however, that better results would be obtained under these conditions than could be ex- pected on larger surfaces where one of its chief diffi- culties is to produce uniform effects. Stony Brook Bridge in the Boston Fenways has granite trimmings with spreckled brick facing, while the arch soffits are lined with glazed brick of vary- ing patterns and colors. There is a very artistic three-span arch bridge over the river at Des Moines, Iowa, that has vitrified brick facing. The spans are each 100 feet in length and elliptical in form. The brick facing with trim- mings of a lighter color presents a very pleasing appearance. Another method of preventing form marks from appearing on the concrete surface is to cover the lagging with a layer of fine clay and overlay the same with building paper. Cost of Concrete Arch Bridges. The cost of concrete bridges varies with local re- quirements and conditions. The following original formula gives the cost of solid concrete arch bridges for both railroads and highways. The formula is ===*' 100 where C is the cost in dollars per square foot of road- way, H the general height of the bridge at the center, W the total width and F a variable factor given by the following table: 64 CONCRETE BRIDGES AND CULVERTS. 200, then F is 1.5 " 1.0 " .65 " .48 " .42 " .JIG " .32 "' .285 " .202 and . F' is .00 ' .224 " " .95 "' .20 < " .04 ' : .18 " " .03 .104 " " .02 .152 " " .01 .141 " " .88 " .133 " " .80 '* .125 " ' .85 " .110 " " .82 .113 " " .80 As the height of the bridge multiplied by its width gives the cross sectional area, the function HW may be represented by the letter A. Factors F refer to arch bridges with complete soffit slabs, while factors F' refer to arch bridges with partial soffit slabs, such as used in the Walnut Lane bridge in Philadelphia, and the Detroit Ave. bridge in Cleveland. The cost of concrete bridges is affected more by natural conditions and the selection of the economic forms than by the live load to which these bridges When A is 200, ft 500, Cf 1000, ( ( " 1500, t ( " 2000, i ( " 2500, " 3000, a " 3500, te " 4000, - t i " 5000, (( 0000. K " 7000. (( " 8000, (( " 0000, ( i " 10000, (( " 11000, i t " 12000, it " 13000, a " 14000, PLAIN CONCRETE ARCH BRIDGES. 65 are subjected. This is shown by the above formula applying equally to concrete arch bridges for both railroads and highways. The weight of concrete and other materials is greater than the imposed live load and the live loads are not, therefore, the chief considerations in deter- mining the ultimate cost. The formula clearly shows that concrete arch bridges vary in cost in proportion to the product of their weight and width. Bridges with a small cross sectional area cost as low a price as $2.50 per square foot of floor surface, while large monumental bridges may cost as high as $16.00 per square foot. The formula also clearly shows the great economy in using partial in place of complete soffit slabs, and this economy may be still further increased by the use of ribbed arch designs. Kibbed arches are not, however, generally suitable for construction in solid concrete and the treatment of this style of arch will therefore be taken up later, with the design of arches in reinforced concrete. Table No. 1, giving details of concrete bridges, gives also the total cost of these structures. Design for a Concrete Arch, 60 Feet Center to Cen- ter of Intermediate Piers. Clear Span 53 Feet. Rise 10 Feet. The bridge consists of a series of arches to carry a street over a number of railroad tracks. The span was arbitrarily fixed at 60 feet center to center of intermediate piers, or 53 feet in the clear. This provides clearance for four lines of tracks, 13 feet 66 CONCRETE BRIDGES AND CULVERTS. apart on centers. For a low structure of this height, shorter spans might have been more economical, but this length was selected that the clearance way for the tracks would not be too greatly obstructed with piers. The headroom underneath is shown on Fig- ure 7, and is the height generally required by rail- road specifications, being 21 feet from the top of rail in the center of track nearest to the pier. The elliptical form was selected for the reason that, with the given clearance, it allows the springing line to fall lower than any other form and in this case is 15 feet above the ground. As the viaduct is a long one, it was desirable to keep the entire height and the corresponding cost down to the lowest possible amount. A minimum rise of one-fifth the spaa was therefore selected, amounting to 10 feet from spring to crown. The rise is the semi-minor axis of the ellipse and not the effective rise of the line of pressure, which is used later in determining the crown thrust and pier reactions. The approximate rule for the thickness of intermediate piers is to make the thickness of such piers one-sixth to one- seventh of the length of span. This would produce a thickness of pier from 7 to 8 feet at the spring and 7 feet was selected for a trial. To determine an approximate crown thickness, Rankine's rule was used. For a series of arches, it is -\r ^ Radius. This requires that the radius be known. Lay out an ellipse graphically by the method of five centers, and the radius is found to be 72 feet. Eankine's PLAIN CONCRETE ARCH BRIDGES. 67 rule, as above, gives a thickness of 3.5, while Traut- wine's rule for the approximate thickness is given in his book, page 617, and is 2.2 feet. Try a thick- ness of 2.5 feet. The grading of the bridge up to a higher level in order to secure a greater rise for the arch was considered, but as this increased the quan- tities of material in the superstructure, and would effect a saving only in the abutment piers, the pl?i was not adopted. A thickness of crown filling of 2.5 feet was assumed from the extrados of the arch to the pavement surface. The entire portion of the bridge above the intra- dos was then divided into strips, and the weight for each of these strips calculated, on the assump- tion that earth filling weighs 100 pounds per cubic foot, and masonry 160 pounds per cubic foot. A live load of 150 pounds per square foot was assumed on the roadway. The weight was computed for each strip and noted on Figure 7 in their respective places. The amount of conjugate thrust was then found by taking the intensity of such thrust at one- third the weight of earth and live load above it. These were also noted in their proper places. Center lines were then drawn through each strip, and a load diagram constructed by drawing in order the various vertical and horizontal loads from A to B, as shown in Figure 7. A trial pole P' was selected and lines drawn connecting each of the load points on aB with P'. The corresponding funicular poly- 68 CONCRETE BRIDGES AND CULVERTS. gon ay was drawn with lines parallel to the lines in the force polygon AP', BP', etc. This is evidently not the correct position of the pole, for the result- ing funicular polygon lies almost entirely outside of the arch. By prolonging the last string of the funicular polygon to its intersection at g with the horizontal through the arch center from a, we find the point of application of the resultant of all the imposed loads, which is at g. The direction of the resultant pressure would be parallel to AB. As the position of this point is constant for any other posi- tion of pole, we may draw through y a line yg. This will represent the direction of the actual pressure of the arch on the abutment. Through B in the force polygon draw a line parallel to yg intersecting the horizontal through A at P. The point P will be the correct position of the pole, and the distance AP measured to the same scale as the line AB, will rep- resent truly the amount of the crown thrust. In this case it is 42,000 pounds. This investigation is for a portion of the bridge one .foot in length at right angles to the diagram. Pressures at the var- ious points in the arch correspond to the lengths of lines in the force polygon. At the pier for full loading, the pressure is 48,000 pounds. Uneven Loading. Lines of resistance were next drawn for unsym- metrical loading as shown in Figure 9. This has already been quite fully described under the head of Partial Loads. PLAIN CONCRETE ARCH BRIDGES. 69 Required Area in Arch. Using a maximum pressure of 400 pounds per square inch as a safe working unit on concrete at the outer edge, or 200 pounds per square inch mean 42000 pressure, the required area in the arch is 200 or 210 square inches. This requires a depth of arch of 18 inches. We have already assumed a depth of 30 inches so the arch is secure against crushing. With a depth of 30 inches, the mean pressure on the concrete is only 116 pounds per square inch, instead of the 200 pounds which is proposed. Intermediate Piers. First figure the required size of pier to sustain the total load in compression. The total weight from the arches and the live load is 54,000 pounds. As- sume the material of the pier to be concrete, with an allowable unit pressure on the outer edge of 400 pounds per square inch. For a mean working pres- sure assume half of this amount, or 200 pounds per square inch. The required area in the pier at spring- ing to sustain direct loads is therefore or 200 270 square inches. As the assumed width of pier at the top was 7 feet, the case of full uniform loading is evidently not the governing consideration. Consider next the case of equal spans thrusting on the pier, one with full dead and live load and the other with dead load only. The thrusts in these 70 CONCRETE BRIDGES AND CULVERTS. two cases are 48,000 and 42,000 pounds respectively. The total load on the pier at the level of the ground is therefore as follows : Pounds. From fully loaded span 26,000 From partly loaded span 23,000 Weight of pier .18.000 Total 67,000 By combining this load with the arch thrust, we find the resultant pressure, the line of which inter- sects the base at ground level one foot from the cen- ter of the pier, which is well within the middle third. This result may very easily be checked ana- lytically. The width of pier at base is 14 feet, which was found as follows : The total pressure on the soil is : Pounds. From bridge 54.000 From pier 27,000 Total 81,000 Allowing a mean pressure of 6,000 pounds per square foot on the soil, the required width of pier is 8 1000 or 13.5 feet. If the soil will not sustain GOOO 6,000 pounds per square foot, which, allowing for uneven pressure, equals 4 to 5 tons per square foot at the outer edge, piles will then be required. Abutment Piers. In proportioning the abutment pier, stability is the chief consideration. It must be stable against PLAIN CONCRETE ARCH BRIDGES. 71 the thrust of arch from one side only. This arch thrust intersects the center of -the pier at a distance of 14 feet above the ground. The overturning moment from this thrust is therefore 33000 X14, foot pounds. Using a factor of one and one-half against overturning, the necessary moment of stability is 33,OOOX14Xli/>, or 69,300 foot pounds. Next pro- ceed to find the half width of pier base at ground level. Calling this half width A% the required mo- ment of stability in foot pounds is 230000? +(2o;X22Xl60)a; = 69,300 foot pounds. In the above, 22 is the total height of the pier from the top of the ground to the top of the backing, and 160 is the weight of the pier material per cubic foot. From the above we obtain a quadratic equation, and solving, we find the value of x to be 8.45 feet. This would be for a pier w r ith vertical sides. For sloping sides, take a half width at the base of 9 feet, as shown in Figure 9. This size of pier is then amply stable against overturning. Coring out the haunches by means of interior spandrel walls, would evidently be no economy in so flat an arch. The cost of such walls and arching would be greater than the saving in the arch ring from the reduced dead load and the less amount of filling. Illustrations of Concrete and Masonry Bridges. The foregoing table gives a list of arch bridges, the main arches of which are built of solid concrete 72 CONCRETE BRIDGES AND CULVERTS. without metal reinforcement. In one of these, how- ever the railroad bridge over the Vermillion River at Danville reinforcement was actually used in the main arch, but was adopted only for the purpose of better uniting the concrete and preventing cracks from change of temperature. In several of the other bridges, noted in the table, metal reinforce- ment was used in spandrel arches, or other minor parts, but as already stated, the main arches have been designed with no provision for tension in any part of the arch section, and consequently no need for reinforcing metal to resist direct stresses. The table is not intended to be comprehensive or complete, but gives some details of a few of the largest concrete spans, the main arches of which are designed without reinforcement. In reference to the Hudson Memorial Bridge, noted in this table, and illustrated on page 77, the design calls for a large amount of metal reinforcement, not for the purpose of resisting any tensile stresses in the arch, but rather to supplement the concrete in resisting direct compression. This is a new principle in arch construction, not previously used. Illustrations and descriptions of two old Roman bridges are also given for the purpose of calling attention to the superiority and permanence of ma- sonry bridges over those of any other known type or material. They have existed for centuries, and such bridges should endure after metal bridges have disappeared. a 8 74 CONCRETE BRIDGES AND CULVERTS. Ponte Rotto, Rome. As it stands to-day, this old bridge has three stone arch spans, and a suspension bridge, spanning the gap where other arches originally stood. The pres- ent bridge stands on the site of the old Pons Aemil- iiis, built B. C. 178-142, which was the first stone bridge over the Tiber at Rome. The three remain- ing arches date from Julius ITT, and are richly orna- mented. Two arches were carried away by a flood in 1598, and have never been replaced. The bridge seems to be unfortunately located, as it has been carried away at least four times, the first time in A. D. 280. It was erected by Cains Flavius, and is probably the first appearance of the arch in bridge construction. It has semicircular arches and a level roadway. The two end arches were shorter than the three intermediate ones. It is called also Pons Palatinus, Senators' Bridge, and Pons Lapi- deus. The bridge is similar in construction to the other old stone bridges of Rome, and is built of peperino and tufa, faced with blocks of travertine anchored into the body of the masonry. It will bo seen from the illustration that the spandrels and parapets are highly ornamented with carved panel work and each of the piers above the arches and foundations are penetrated with smaller arch open- ings. The panel work has disappeared fromlhe left shore span and plainly reveals the plan of construc- tion. It will be seen that the arch ring is built of 76 76 CONCRETE BRIDGES AND CULVERTS. different material and differently laid than the filling above it, and that numerous openings occur in the backing which were doubtless used for the purpose of anchoring the ornamental facing to the body of the structure. It is well known that, in the construction of bridges and aqueducts built by tho Romans and others-in early times, a large amount of concrete was used. Bridge of Augustus at Rimini. The old Roman bridge crossing the River Mara- chia at Rimini, is supposed to have been built during the reign of Emperor Augustus, about 14 A. D. It has five arch spans, with very heavy piers. The de- tails that still remain show that originally the bridge was very ornamental. There are niches at the piers, and the heavy' stone cornice is carried on numerous brackets. The arches are all semi- circular, the end ones having a span of 23 feet, while the three intermediate ones have spans of 28 feet. Henry Hudson Memorial Bridge. (Reinforced Concrete Design.) It is proposed to erect on an extension of River- side Drive in the City of New York, a Memorial bridge over Spuyten Duyvil Creek, to commemorate the explorations and discoveries of Henry Hudson. The design accepted by the Municipal Art Commis- 78 COXCRETE BRIDGES AND CULVERTS. sion of the City of New York is herewith shown. Previous designs showing the principal span framed in steel were rejected as being inappropriate for a great memorial bridge. There will be one span with a clear length of 703 feet, and seven other semicircular arch spans with clear lengths of 108 feet. The total length of the structure will be 2,840 feet. The main arch span will have a rise of 177 feet, and will contain a large amount of steel, used, not as concrete reinforcement ordinarily is, to re- sist tensile stresses, but rather to assist in resisting the compressive stresses in the concrete, and there- by reduce the amount of masonry. The arch will have a crown thickness of 15 feet. There will be two decks, the upper one carrying a CO-foot road- way and two 15-foot sidewalks, while the lower deck will be 70 feet in width, and will carry four lines of electric railway. It is the intention to omit the construction of the lower deck at the present time. The design provides for a clear headroom of 183 feet under the main arch. The main piers will be 180 feet in width. The estimated cost is $3,800,000. The illustration shows the bridge as it will appear to an observer looking out over the Hudson River, with the Palisades in the distance. The de- sign was made by the bridge department of the City of New York, at which time C. M. Ingersoll was Chief Engineer, L. S. Moisseiff Engineer in Charge, Wm. H. Burr, Consulting Engineer, and Whitney PLAIN CONCRETE .ARCH BRIDGES. 79 Warren, Architect. The next longest masonry arches of the world are as follows : Feet, span. Stone arch bridge over Adda River 230 Stone arch bridge at Luxemburg, Germany 278 Stone arch bridge at Plauen, Germany 295 Concrete arch bridge at Gruenwald 230 Concrete arch bridge at Walnut Lane, Philadel- phia 233 Stein-Teufen bridge, Switzerland 259 Concrete arch bridge at Rocky River, Cleveland. 280 Aukland, New Zealand 320 Aukland, New Zealand, Bridge. A reinforced concrete arch bridge is being built on the North Island, at Aukland, New Zealand, with a clear span of 320 feet the longest in existence. Several longer ones have been projected, one over the Mississippi River at Fort Snelling, Minn., w T ith two spans of 350 feet, but none built. The Aukland bridge has, besides the 320-foot center span, two 35- foot and four 70-foot spans, with a total length of 910 feet. It is 40 feet wide, and the roadway is 147 feet above the valley. The two arch rings are hinged at the springs and center. It was commenced in February, 1908, and the contract calls for comple- tion in two years. It adjoins a residential district, and at one end are the graves of New Zealand pioneers. 80 CONCRETE BRIDGES AND CULVERTS. Monroe Street Bridge, Spokane, Wash. In the city of Spokane, Wash., plans are prepared tor building a four-span concrete bridge to carry Monroe street at a height of 140 feet above the Spo- kane River. The main arch has a clear span of 281 feet, and is divided into two ribs, 16 feet wide and 6 feet thick at the crown. It will have open span- drels and overhanging sidewalks, with Dutch towers at the ends for public lavatories. The bridge will replace the old steel cantilever built 17 years ago. It will have a 50-foot roadway and two 9-foot side- walks, making a total width of 71 feet and a total length of 791 feet. The main arch will be segmental and the remaining ones semi- circular. The deck will be carried on solid cross spandrel walls, 20 feet apart. The ground on the north side of the river is naturally suited for an arch bridge, but on the south side the plan proposes an abutment carried down to 140 feet below street level, consisting of four parallel walls, each 4 feet in thickness, joined by numerous cross struts and braces. See Fig, 16. J. C. "Ralston, City Engineer. Rocky River Bridge, Cleveland, Ohio. A concrete arch bridge with the longest masonry span in America is now being built over Rocky River on Detroit avenue, at Cleveland, Ohio. It will have a central span of 280 feet and five approach spans of 44 feet each. It will carry a 40-foot road- way and two sidewalks 8 feet wide each. The total width over railings will be GO feet and the total length 708 feet. The, main span consists of two sep- SI .7*' S a III 84 CONCRETE BRIDGES AND CULVERTS. arate arch rings 18 feet wide at the crown, and placed 16 feet apart. On these arches the deck is to be carried on cross-spandrel walls. The roadway level is 9-4 feet above the surface of low water and the pavement will be of brick, with two lines of track for heavy suburban cars. Beneath the floor are to be two subway chambers, 3 feet by 11 feet for the placing of pipes and wires. The main arch rings will contain no steel reinforcement, as the cal- culations show that no tension can at any time oc- cur in any part of the arch. The sidewalks project out over the face walls about five feet, and are sup- ported on brackets. The entire structure will be built of concrete. It will be quite similar to and 47 feet longer than the Walnut Lane Bridge at Phila- delphia. The only longer masonry arch span in ex- istence is the one at Plauen, in Germany, with a span of 296 feet, built of hard slate. Other pro- jected long-span bridges are that over the Neckar River at Manheim, with a span of 365 feet, and the Hudson Memorial Bridge in New York City, with a span of 703 feet. The Rocky River Bridge was de- signed under the direction of A. B. Lea, County Engineer, by A. M. Felgate, Bridge Engineer. It is under construction by Schillinger Brothers, con- tractors of Chicago. Wilbur J. Watson, Engineer. Walnut Lane Bridge, Philadelphia. Walnut Lane crosses the Wissahickon valley on a new concrete bridge at a height of 147 feet above the river bed. At the time of completion it was the to o *J Q 86 CONCRETE BRIDGES AND CULVERTS. longest concrete masonry bridge, having a clear span of 233 feet. It consists of two separate arch rings, 18 feet wide at the crown, increasing to 21 feet 6 inches at the springs. At the crown the two rings are separated by a space of 16 feet. The double rib construction is similar to that used in the stone arch bridge at Luxemburg, Germany, hav- ing a span of 275 feet. The main arch is an approximate ellipse, has a rise of 73 feet, and carries 10 cross w r alls which support the floor system. There are also five semicircular approach arches with clear spans of 53 feet. The bridge con- nects Germantown and Roxborough, two residential suburbs of Philadelphia. It has a 40-foot roadway, and two 10-foot sidewalks. The entire structure is solid concrete, not reinforced, excepting in certain minor details. The surface finish is rough, some- what similar to pebble dash, but of coarser grain. The exposed surface shows stone clips of not over three-eighths inch in size, formed by washing before the cement had hardened. The total length of bridge over all is 585 feet, and the cost $259,000. George S. AVebster, Chief Engineer, Bureau of Sur- veys. H. H. Quimby, Bridge Engineer. Reilly & Riddle, Contractors. Connecticut Avenue Bridge, Washington. Connecticut Avenue, one of the chief thorough- fares of Washington, is carried over Rock Creek valley near its junction with the Potomac on a new concrete arch bridge, about three miles from the lit 88 CONCRETE BRIDGES AND CULVERTS. Capitol building. The roadway is 120 feet above the valley below, and is carried by five semicircu- lar arches of 150-foot span, and two end arches of 82-foot span. It has a 35-foot roadway, and two sidewalks 8 feet wide each, making a total width of 52 feet, a clear length between abutments of 1,068 feet, and a total length of 1,341 feet. It w r as com- menced in 1889, and completed in 1908. The main arches are hingeless with -no reinforcing, but the spandrel arches have steel reinforcement. As the bridge is located in a fine residential district, its aesthetic appearance was a matter of considerable importance. The face rings of the arch, pier cor- ners, mouldings and all trimmings below the granite coping, are moulded concrete blocks. The remaining part of the exposed concrete surface is bush ham- mered, for the purpose of presenting a more uniform and pleasing appearance. The cost of the falsework was about $50,000, but on this there was a salvage of about $15,000. The cost of framing the false- work was $9 per thousand feet of lumber. Moulded cement blocks cost $15 per cubic yard. The total cost of the structure complete was $850,000, equal to $639 per lineal foot, or $12.30 per square foot of floor surface. It is built from a modification of the prize design submitted by the late George S. Morri- son. The original competitive designs estimated to cost from $370,000 to $1,100,000 were published in Engineering News January 27, 1898. It was built under the direction of Col. John Biddle, Engineer Commissioner of the District of Columbia. "W. J. SiS bb at 5 w 90 CONCRETE BRIDGES AND CULVERTS. Douglas. Bridge Engineer. E. P. Casey Consulting Architect. Big Muddy River Bridge, Illinois. Two tracks of the Illinois Central Railroad are carried over Big Muddy River near Grand Tower, Illinois, on a new three-span concrete arch bridge. It was built in 1903 to replace an old steel bridge, and for this reason the piers remain in their original location. The bridge has three clear openings of 140 feet, and a total length of 463 feet between faces of abutments. It is 32 feet wide, contains 12,000 cubic yards of concrete, and cost complete $125,000. The arches are true ellipses with semi-minor axes of 30 feet. The old piers were 9 to 10 feet in thick- ness, and the new ones, which were built around the old ones, are 22 feet thick. The main arches are solid concrete, the only reinforcing being in the spandrel arches supporting the floor, and this was used for convenience in erection. As built, with spandrel arches and openings, the cost was some- what greater than if it had been filled. The de- signer explains that open spandrels were used for the purpose of reducing the load on the foundations. Big Muddy River Bridge was designed by II. W. Parkhurst, Engineer for the Illinois Central Rail- road Company. Santa Ana Bridge, California. This structure carries the new line of the San Pedro, Los Angeles and Salt Lake Railroad, over Santa Ana River, near Riverside, California. The I i 91 fl S w PLAIN CONCRETE ARCH BRIDGES. 93 bridge has a total length of 984 feet, and the deck is 55 feet above the water. It was built during the years 1902 to 1904 under the direction of Henry Hawgood, who was then Chief Engineer for the above railroad company. It contains eight semi- circular arches of 86 feet clear span, and two end spans of 38 feet. The piers are 14 feet in thickness, making the distance on centers of main piers 100 feet. It is made of solid concrete without reinforce- ment, contains 12,500 cubic yards of concrete and cost $185,300. The thickness of arch at crown is 3 feet 6 inches, and the width across soffit is 17 feet and 6 inches. A letter from Mr. Hawgood to the author in ref- erence to this bridge states as follows: "The Santa Ana viaduct has given entire satisfaction from an operating standpoint. There has been no cost for maintenance during the five years it has been in service, whereas a steel bridge would certainly have involved some expense during the same period. In positions such as the Santa Ana Viaduct where there is no limitation as to headroom, I consider the simple concrete structure without reinforcement a better structure than one reinforced. The greater weight of concrete required forms a much heavier mass to take up the impact of heavy high speed trains. The absence of vibration is very marked. It is a parallel condition to a heavy anvil under a steam hammer the heavier the anvil, the longer it will last." 94 CONCRETE BRIDGES AND CULVERTS. TABLE I LIST OF CONCRETE BRIDGES 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Hi 17 IS 19 20 21 22 23 21 2f) 2(5 27 2S LOCATION. Over. i 02 8 d & Length of Span, ft. | Total Length, ft. j Hudson Mem., New York. Spuvten Duvvil. a n 1 7 1 703 108 320 177 2840 it n tt tt Auckland, N. Z. . 910 ? 35 n < 4 1 5 1 ^ 2 1 1 2 1 1 1 5 2 5 2 2 1 3 1 1 3 1 2 70 280 44 233 53 230 210 211 68 187 165 164 150 82 150 120 30 144.6 140 141 139 60 127.6 20 "so" 22 73 26.5 42 87' "708 '585 "720 ',500 Detroit Avenue, Cleveland Walnut Lane, Philadelphia Rocky River.. . . Wissahickon. . . . Tsar Gruenwald Bavaria T^lm, Germany Railway Yards . Iller River . Kenipton, Germany it it Lautrach " K a Neckar . . . 32 13.5 16.4 75 41 40 18.5 30 14 44 30 22.5 280 1341 1450 1450 1450 483 150 542 542 Neckarhausen, Germany Munderkingen, Wurtemburg Connecticut Ave., Washington. . . . it tt Portland, Pennsylvania Danube Rock Creek it it Delaware River . Thames a tt Vau xhall, London Grand Tower, Illinois Big Muddy River Danube Jnzighofen, Germany Edrnondson Ave., Baltimore Borrodale Scotland Gwynns River .. tt a Borrodale Burn a n a a PLAIN CONCRETE ARCH BRIDGES. 95 TABLE I Continued LIST OF CONCRETE BRIDGES M 3 1 53 H Form of Curve. | Highway or Railroad 4 I Engineer. Reference. N., Eng. News R., " Record Number. 80 u 40 tt 60 60 60 60 20 46 54 183 t 147 H. H. it 't IT. H. H. H. R. R. 3,800,000 Moiseeiff u N., Nov. 21, '07 R., Dec. 28, '07 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 1908 it 1909 1906 1904 1905 1906 94 94 147 147 Sec;. C. E. C. ' C.' ' 208,300 Felgate Webster Morsch 262,000 N., Jan. 31, '07 N., Jan. 31, '07 N., Feb. 23, '05 N., Mar. 15, '06 65,000 45,000 13.8 15 8 26 52 52 31 34 34 40 Seg. 1906 1903 1893 1907 R. R. H. H. H. 21,600 Leibbrand Leibbrand Morrison N., May 2, '07 120 ' C.' ' c 21,420 850,000 N., Mar. 26, '08 65 65 65 El. 1908 1908 1908 1899 R R Bush Bush Bush Binnie Parkhurst Leibbrand R., Aug. 15, '08 R., Aug. 15, '08 R., Aug. 15, '08 R R R R 33 12.5 60 60 45 20 70 70 E. Seg. C. 1902 1895 1909 1898 R. R. H. H. 125,000 6,650 183,300 N., Nov. 12, '03 N., Sept. 17, '96 R., June 19, '09 R. R. Simpson N., Feb. 9, '99 96 CONCRETE BRIDGES AND CULVERTS. TABLE I Continued LIST OF CONCRETE BRIDGES 1 % LOCATION. O.er. No. of Spans. Length of Span, ft. | I 9q Sixteenth St , Washington Piney Creek. . . . 1 125 39 272 30 Kirchheim, Wurtemburg Hainsbur 01 New Jersey Neckar Paulins Kill . . . 4 5 124.6 120 19 60 450 1100 3 9 fl 100 1100 ?3 Miltenburg, Germany Main r 112 17.7 733 34 c 107 35 36 Pittsburg Pennsylvania Silver Lake 102 100 50 600 37 n Thebes Illinois Mississippi e t. 1 80 100 40 50 ?9 ' a 11 65 32.5 40 Danville Illinois . . Vermillion i 100 40 330 41 2 80 30 42 43 Mechanicsville, New York Anthony Kill. . . 9 1 100 50 14 Imnau Bavaria . . Eyach 1 98 9 8 110 45 46 Wyoming Ave., Philadelphia Brookside Park, Cleveland . . . Frankford Creek Big Creek . . 2 1 98 92 28 9 200 125 47 Riverside California. Santa Ana 8 86 43 984 48 38 19 l f Boulevard Philadelphia Tacony Creek . . 3 80 14 350 51 Long Kev Florida. Atlantic 180 50 25 10500 51 Mannheim Neckar. . . . 1 365 rco Larimer Ave Pittsburg Beechwood Boul 1 300 53 Spokane Spokane 1 115 791 54 1?,0 60 55 tl 1 100 50 190 PLAIN CONCRETE ARCH BRIDGES. 97 TABLE I Continued LIST OF CONCRETE BRIDGES d 25 19 34 34 23 i i o 8 1 1 1906 S98 1908 Highway or Railroad M I Engineer. Reference. N., Eng. News R., " Record 3 |Z5 50 40 115 115 22 Par. Seg. C. H. H. R. R. 50,000 46,600 Douglas R., Jan. 26, '07 N., Mar. 29, '00 R., Aug. 15, '08 29 30 31 32 33 34 35 36 37 Bush Seg. 1899 H. 101,000 Fleischman N., July 25, '01 54 54 28 28 33 33 70 70 C. C. C. c. 1905 R. R. Brown R., May 6, '05 1903 R. R. Nobel N., Nov. 20, '02 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 90 1905 R. R. Duane R., Mar. 3, '03 El. R N., Nov. 5, '03 8.2 80 12.7 17.6 '100 15 15 32 12 55 "30 30 Seg. "EI." c. c. Se, 1896 1908 1905 1904 1904 1908 1904 H. H. H. R. R R. R H. R. R 4,285 102,000 185,000 Leibbrand Quimby Zesiger Hawgood N., Feb. 16, '99 R., Feb. 27, '09 N., May 10, '06 R., Sept. 9, '05 100,000 Webster Carter 'Whi'ted " Ralston R., Mar. 13, '09 N., Oct. 19, '05 Proposed Projected 1909 tl It H. tt (t 71 it n 140 C. ... 1 PART II. Reinforced Concrete Arch Bridges. Reinforced concrete arch bridges as usually built, are a combination of arch and beam, and contain most of the properties of both types, the arch or beam properties predominating according as they have a large or small rise in proportion to their span. Flat arches act more like beams, regardless of' theory. Reinforced concrete was first considered merely a cheap substitute for stone, but its own merits are now recognized and it is used in a manner ac- cording with its properties. A principle of architectural design demands that imitation of one material by the use of another shall not be made, and, therefore, in designing con- crete bridges, there should be no effort to imitate stone, but to treat the design simply and truth- fully, keeping all lines in harmony with the mate- rial used. The extent to which concrete and reinforced con- crete are now being used in preference to stone or steel, may be judged from the fact that, during the year 1908, there was at least twenty times more cement manufactured and sold than in the corre- sponding period, ten years previous. As methods of design and construction become generally un- derstood and as workmen become more accustomed to handling concrete, there will be a still greater number of bridges built of this material. Long REINFORCED CONCRETE ARCH BRIDGES. 101 spans exceeding three to four hundred feet, will probably continue to be framed in metal, but there is reason to believe that all ordinary town and county bridges and the majority of railroad bridges will be built as permanent structures. Reinforced concrete is a good combination of materials. Concrete has a high compressive strength, but is weak in tension. Steel rods im- bedded in concrete have a high tensile strength, but are weak in compression. The steel, therefore, strengthens the concrete, and the concrete stiffens the steel, the strength of one thus supplementing the weakness of the other. Since the beginning of the competitive practice in bridge building, many bridges have been built which are deficient in both strength and design. There is no doubt that competition is responsible for many economic features in steel bridge design and has helped to a great extent in developing eco- nomic methods. It was found about the year 1900, that steel bridges were being built entirely too light and competition was responsible for the con- dition. Previous to that time, the various bridge companies were accustomed to submit competitive plans, and generally the lowest bid and conse- quently the weakest bridge was the one accepted. From that date the policy began to change, and instead of calling for competitive designs, a com- petent engineer was employed to prepare plans and competitive prices were then received on his plans. The policy of employing an engineer whose prin- 102 CONCRETE BRIDGES AND CULVERTS. cipal motive was to produce an economic design, has resulted in a much better class of bridges than under the old competitive system. Concrete bridges are now in the same stage of development as were steel bridges ten years ago. Many concrete bridges have been and are still be- ing built, which are lacking in architectural de- sign and some are lacking in strength. The prin- cipal reason for these defects is that reinforced concrete bridges are obliged to compete with struc- tures of wood and steel. When towns and other municipalities realize the chances they are taking in accepting competitive designs, the method of securing an acceptable one will then be changed and a competent engineer will be employed to pre- pare the plans. Competitive prices will then be re- ceived on these plans, but competition will cause no reduction of the cost by weakening any parts of the bridge. At the present time, stone and con- crete bridges exist, having factors of safety varying from three to one hundred and fifty, and there is, therefore, a very evident need for better and more rational methods of design. Historical Outline. Since the early days of stone bridge building, rods and bands of hoop iron have been used near the extrados of the arch from the piers and abut- ments, to or slightly beyond the point of rupture. It was found when the temporary arch centers were removed, that the arch settled at the crown and REINFORCED CONCRETE ARCH BRIDGES. 103 there was a tendency for the masonry joints to open at the extrados haunches. To prevent these joints from opening, iron rods have long been used. There was then no general effort made to strengthen the masonry arch, excepting as stated above. Con- crete arches are reinforced with metal not only at the extrados from the piers to the points of rup- ture, but are also strengthened at all places where there is any possibility of tension in the arch ring. Jean Monier first began using reinforced concrete in Germany in the year 1867, by making large flower pots and urns of cement and concrete with a single layer of wire netting embedded therein. Monier was a gardener, but he foresaw a success- ful future for this combination, and in the next ten years he built a number of tanks, bins and other small structures of the composite material, and secured patents from the German Government on his invention. Introduction of this construction in Germany was slow, and it was not until 1894 that the Monier patents were introduced in the United States. This system of reinforced concrete contained a single layer of wire mesh with wires of the same size in both directions. Professor Melan realized the weakness of the Monier system and patented another and improved method of re- inforcing arches, by which curved steel ribs were placed lengthwise of the arch and imbedded in the concrete two or three feet apart. In his first de- signs, curved 1 beams were used and are still used under his patents for small spans. For larger spans 104 CONCRETE BRIDGES AND CULVERTS. with a greater thickness of arch ring, he proposed a system of light latticed girders spaced from three to five feet apart, which system is still in use. These patents were introduced in the United States by Herr.von Emperger in the year 1893, and under these patents many of America's best concrete bridges are built. In the year 1894, when American engineers began to seriously consider building and replacing old bridges in the new T type, it was esti- mated that Europe had not less than two hundred of these bridges built mostly on the Monier system. ("A bridge which is believed to be the first of rein- ;forced concrete in the United States, was built in \ Golden Gate Park, San Francisco, in 1889. It has / a 20-foot span, 4 feet 3 inches rise, and a width of v64 feet. It is an ornamental bridge with curved wing walls built with imitation rough stone finish. A second one in the same park and of similar de- sign was built in 1891. In 1895 a 70-foot span arch was built by Ilerr von Emperger, carrying a drive- way over Park Avenue in Eden Park, Cincinnati. The bridge is located in the park at a place much frequented, and an effort was made to make it both strong and beautiful. The balustrade is highly or- namental and the spandrel walls are decorated with panels. The intrados of the arch is much flatter than appears necessary and certainly a greater rise would have presented a more pleasing effect. During .the first ten years after the introduction of the Melan patents in the United States, there were not more than a hundred reinforced concrete REINFORCED CONCRETE ARCH BRIDGES. 105 bridges built. The fact that a more general intro- duction of this system was not made, was probably due to the lack of more definite knowledge and data in reference to the action and behavior of this construction under live loads. European engineers were likewise embarrassed by lack of knowledge, so much so, that during the years 1890 to 1895, the Austrian Government undertook extensive experi- ments on full-sized concrete arches. The result of these experiments was entirely satisfactory, and complete reports of the investigations were pub- lished in many of the engineering journals of Amer- ica and Europe. From the completion of these ex- periments in 1895 to the present time, the building of bridges in concrete and reinforced concrete has been on the increase, and there are now more than a thousand of these bridges in the United States. Previous to these experiments, no satisfactory progress was made either here or abroad. At first it was customary to use reinforcing steel in the arch ring only, but later structures and most of those now being built have metal reinforcement throughout. Masonry bridges and buildings are still existing that have stood for many centuries, while steel bridges built less than forty years ago, have already worn or rusted out and have been replaced. Two of these bridges have already been illustrated in Part I of this book, and there are positive rec- ords of many others quite as ancient which are still in existence. Pont du Gard, an old Roman aque- duct bringing water to the city of Nimes, France, 106 CONCRETE BRIDGES AND CULVERTS. is supposed to have been built about the time of Augustus in the year 19 B. C. The Aqueduct of Vejus, consisting of a series of high arches, and the dome of the Pantheon at Rome, with a span of 140 feet, are at least 1,800 years old and all of these structures are even now in a fairly good con- dition. These and many others quite as old are built of coarse concrete masonry. Several American railroad companies, after re- peatedly renewing their metal bridges to support increased loads and rolling stock, have at last re- sorted to building their bridges in masonry, know- ing that when properly built, they will remain as permanent structures for centuries. Advantages of Reinforced Concrete. The general advantages of masonry as compared to steel framing have already been referred to on page 1. These advantages referred particularly to plain concrete rather than to reinforced con- crete bridges. It was stated there, that arch bridges of solid concrete were superior to all others, and particularly superior to arches where tension oc- curs in any part of the arch ring. In pointing out the commendable qualities of solid concrete, it is not intended to deny the merits of reinforced con- crete. On the other hand, reinforced concrete arches have some decided advantages over solid concrete. Some of these advantages are as follows : (1) Working units for reinforced concrete may be higher than for plain concrete. REINFORCED COXCRETE ARCH BRIDGES. 107 (2) Higher units produce a thinner arch ring, and consequently less dead load and lighter abut- ments. (3) Flat arches may be safely used, which would be impossible in solid concrete. (4) Because of their lighter weight, it is practica- ble to build spans of much greater length. (5) All cracks of every description can be avoided in reinforced concrete arches. (6) They have the strength of steel with the solid- ity and substantial appearance of stone. Bridges of both plain and reinforced concrete have also the following merits : (1) They have no noise or vibration and are not only cheaper but more durable than stone. (2) Concrete bridges with solid decks permit the use of ordinary ties for railroad tracks, which cannot be used on steel bridges with open decks. (3) The floors of concrete street bridges over rail- road tracks are not damaged by the action of gas and fumes from locomotives, as is the framing of these bridges when built in steel. (4) Concrete bridges require but very little skilled labor. (5) A concrete arch bridge so designed that ten- sion cannot occur at any time or under any condition of loading, is the most permanent bridge of all. If no tension occurs, cracks will not form to permit moisture to reach and corrode the reinforcing steel, and when 108 CONCRETE BRIDGES AND CULVERTS. the metal is permanently protected and secure from the atmosphere and moisture, it should endure for centuries. Deck bridges are in nearly all cases preferable to those where the travel is carried between lines of side trussing and beneath systems of overhead brac- ing. Such truss and bracing systems are a danger and menace to travel, particularly on crowded thor- oughfares, and obstruct the space required for vehicles. Trussing and bracing are also an ob- struction to observation and the clearance required through the bridge prevents the use of lateral brac- ing necessary to stiffen the frame. Concrete arch bridges, when deck structures, are free from the disadvantages mentioned above. Through bridges should never under any condition be used for im- portant locations unless the underneath clearance or structural requirements positively prohibit the use of a deck bridge. For all ordinary locations and length of span, there appears, therefore, to be no good or sufficient reason for building unsightly frame structures when more permanent and artistic ones can be made at the same cost. Adhesion and Bond. Rich cement concrete in w r hich iron or steel is embedded has an adhesion thereto of from 500 to 600 pounds per square inch of exposed surface. Ad- hesion of concrete to metal occurs only when the metal is thoroughly embedded and the concrete has REINFORCED CONCRETE ARCH BRIDGES. 109 opportunity to surround and grip the bars. If a metal bar is placed simply in contact with soft concrete there will be but little adhesion. For the purpose of illustration, if steel plates are placed on edge and concrete filled in between, but not un- der or above them, after the concrete has hardened it will be a comparatively easy matter to loosen the concrete and break the adhesion. This weak- ness is due to the fact that the concrete is simply in contact with the metal but does not grip or sur- round it. In contrast to this condition, if a bar be thoroughly embedded and surrounded w T ith rich concrete, it will adhere so securely to the rod, that a pull of from 500 to 600 pounds for every square inch in contact will be required to extricate the rod from its bed. In order to develop the full strength of the rod up to its elastic limit, it is necessary that the embedded length must at least equal twenty to twenty-five times the diameter of the rod. This is on the assumption of perfect ad- hesion between the metal and concrete. The mix- ture as ordinarily used, instead of fine mortar, con- tains more or less voids, which may be considered equal to 50% of the entire surface in contact. To allow for watersoaking, a still further reduction of 50% must be made. In ordinary work as found in actual structures, the adhesion between the con- crete and metal, instead of being from 500 to 600 pounds per square inch, as for fine test samples, would, therefore, not exceed from 125 to 150 pounds per square inch. By using a factor of 110 CONCRETE BRIDGES AND CULVERTS. safety of five a working adhesive unit will not ex- ceed from 30 to 40 pounds per square inch of sur- face in contact. The length, therefore, that rods must be embedded in ordinary concrete to develop their full strength up to the elastic limit is about four times twenty-five, or one hundred times the diameter of the rod. It has been positively proven by numerous ex- periments that concrete adheres as securely to smooth rods as it does to rough ones. Frequent and continued shocks and vibrations tend to de- stroy the union between the two materials, and ex- periments show that continuous watersoaking from six to twelve months reduces the adhesion by about 100%. Poor workmanship in placing and ramming the concrete is also probable and for these reasons, it is desirable to use reinforcing rods that are roughened or twisted, so the bar may have a direct mechanical grip on the concrete in addition to its adhesion. "When this roughening of the bars is secured without decreasing their cross-sectional area, the entire area of the bar is then available for tension and no strength is lost by the expedi- ent. Roughening the bars can, therefore, do no harm and it may be a source of extra strength. As- suming that the rough rods cost more than plain ones, the consideration in making a choice between the two, is simply whether the extra expense for rough rods is warranted by the additional strength that they may give. AVhilf3 watersoaking decreases the adhesion between the two materials, the upper REINFORCED CONCRETE ARCH BRIDGES. Ill concrete surfaces are usually waterproofed, and the probability is, that instead of weakening from watersoaking, the strength of the concrete and its adhesion to the steel will increase. The conclusion, however, is that rough rods are preferable. They cost but little more, can do no harm and may be a benefit. Metal Reinforcement. Reinforcing steel in concrete bridges is intro- duced for any or all of the following reasons : (1) To resist tensile stresses due to bending mo- ments, (2) To prevent cracks occurring from change of temperature, (3) To form a temporary working platform at the roadway level. There is no sufficient reason from a scientific standpoint for the use of high tension bars or rods for concrete reinforcement. After years of investigation and experiment, brittle metal w r as dis- carded for structural use and the only reason for a return to the use of high tension bars now, is a commercial one and not scientific. It is well known that in re-rolling bars to produce surface roughen- ing, the tensile strength of the metal is increased Instead of admitting the inferior quality of their products, interested parties have endeavored to ex- plain that this increase in tensile strength, and cor- responding decrease in ductility is a benefit. Medium steel with an elastic limit of 32,000 pounds per square inch, or soft steel with a corre- 112 CONCRETE BRIDGES AND CULVERTS. spending elastic limit of 28,000 pounds, are the proper grades of metal for all ordinary concrete reinforcement. These may safely be stressed up to half their elastic limit under working loads. If, for any sufficient reason a high tension metal is desirable, then some grade of wire is preferable to bars. It is difficult, however, to secure good con- tact between wire mesh and concrete, for the small openings in the mesh make it difficult to tamp the two materials well together. If a mesh must be used, then a large mesh is preferable to a smaller one. In nearly all positions, whether tensile stresses are liable to occur or not, the presence of metal in concrete will add to its strength and perma- nence. Only in such places where there is insuffi- cient space for its insertion, will it be a detriment. The rule generally is "when in doubt, use rein- forcement ' '. The old Monier system of arch reinforcement, consisting of a single layer of wire mesh with wires of the same size in each direction, is evidently wrong in principle. The amount of metal required crosswise and longitudinally of the arch is not nec- essarily the same, for the area in each case must be suited to its need. For resisting bending mo- ments in the arch ring, when the line of pressure falls outside of the middle third, the size of rods will depend on the magnitude of the bending mo- ments. It was customary at first to reinforce only the arch ring, but now all parts of reinforced concrete REINFORCED CONCRETE ARCH BRIDGES. 113 bridges, excepting perhaps the balustrade and other ornamental features, are provided with metal for the purpose of better uniting the whole into a solid monolith. It is particularly desirable that rein- forcement be placed at all points where local loads are liable under any circumstances to produce bending or tension. Where cross spandrel walls bear upon the arch ring, these walls should not only be well anchored to the arch, but additional metal may be required beneath these concentrated loads. The best practice at the present time in reinforcing concrete arch rings is to use two com- plete systems, one at the extrados and the other at the intrados of the arch. Some designers prefer to reinforce the extrados only from the springs to, or a little beyond the point of rupture, omitting the metal at the extrados crown. The saving by this omission is not great and generally is not suffi- cient to warrant it. At all points where light walls or sections join to heavier concrete masses, heavy reinforcement should be used. In setting and drying, concrete acts much in the same way as cast iron, and unless the light sections are well tied to the heavier ones, cracks at the junction will occur. This is illus- trated where ring walls join to the abutments. If for any reason, it is impracticable to anchor the wing walls to the abutment face, it is then prefer- able to leave an open joint, for otherwise an irreg- ular crack will occur, showing weakness either in the design or in the construction. 114 CONCRETE BRIDGES AND CULVERTS. As the amount of adhesion between steel and con- crete depends directly upon the amount of steel surface in contact with the concrete, it is prefer- able for securing the greatest bond, to use a larger number of small bars rather than a smaller number of larger ones. It is desirable also to have the cracks in the concrete as small as possible, so water will not enter the cracks and corrode the metal. Upon this feature the duration of a concrete struc- ture depends. Tf water is allowed to soak into the cracks and corrode the reinforcing metal, it will then be only a few years until the strength of the member will be destroyed by rust. It is necessary, therefore, that sufficient reinforcing metal be used in order that cracks will not be excessive. Several leading designers of reinforced concrete are now specifying that tension in the concrete shall be considered, and enough metal used so the tension in the concrete will not exceed a safe unit, which is usually placed at about 50 pounds per square inch on the cross-sectional area of the concrete in tension. The object in this is to prevent cracks from forming and to exclude all moisture from the metal. This is doubtless the ideal condition, for when perfectly embedded and protected from mois- ture, steel is known to be indefinitely preserved. When insufficient steel is used, large cracks will form on the tension side and the bridge is then no more a permanent one than an ordinary steel bridge, or not even as permanent. When a steel bridge is exposed to moisture the steel can be ex- REINFORCED CONCRETE ARCH BRIDGES. 115 amined and painted, whereas in a reinforced con- crete bridge, the steel is concealed from view, can- not be inspected, and its collapse is the first warn- ing given that the metal reinforcement has been destroyed. The best results are, therefore, secured by allowing no cracks whatever, but if cracks must form, to have these cracks so small that water can- not enter them. Tt is better to have a large num- ber of very small cracks than a small number of large ones. A requirement upon which the strength of rein- forced concrete directly depends, is the amount of contact between the two composing materials. Every effort should be made to have this contact as perfect and complete as possible. In deciding upon a working unit for adhesion of concrete to steel, it is customary to consider that imperfect workmanship in ordinary structures w r ill cause only about one-half of the exposed metal surface to be actually gripped by the cement. If a higher de- gree of workmanship be secured, then the strength of the structure will be increased accordingly. It is considered that watersoaking still further de- creases the adhesion by another 100%. Therefore, if perfect adhesion on rich samples between the two materials is from 500 to 600 pounds per square inch, the ultimate adhesion in actual structures can- not be taken greater than from 125 to 150 pounds per square inch. To develop the full tensile strength of bars embedded in concrete, it is easy, therefore, * compute the length that these bars must be em- 116 CONCRETE BRIDGES AND CULVERTS. bedded. Using an ultimate adhesive unit for ordi- nary structures of 150 pounds per square inch, one inch square bars would be gripped to the extent of 600 pounds per lineal inch of bar. Therefore, to secure the full elastic strength of the bar up to -32,000, the rod must be embedded a number of inches, equal to 32,000 divided by 6,000, or 53 inches. Where arch rings join to piers and abut- ments, it is customary to run the reinforcing steel well into the piers to develop the full strength of the metal. Experiments show that adhesion to steel is much greater before the steel is painted than afterward. A slight coating of rust has been found to add to, rather than to detract from, the adhesive strength. Loose scales or Hakes of rust must not be permit- ted, but a slight rusting is no disadvantage. Ex- periments have been made on rusted steel imbedded in rich cement, and after a period of several months when the steel was removed and the cement broken away, it was found that the steel appeared clean and free from even the slight rusting that existed when it was first imbedded. Light reinforcing frames are frequently used in the spandrels of reinforced concrete bridges, not only to strengthen the concrete, but also to provide a temporary working platform at the roadway level. This plan is illustrated by the Illinois Cen- tral Railroad Company's bridge over Big Muddy River near Grand Tower, Illinois. Bridges built by Herr Wunsch in Germany were mostly of this REINFORCED CONCRETE ARCH BRIDGES. 117 type. The metal in such cases must have sufficient strength to act as compressive members. In the Big Muddy River bridge, the engineer used old rails for the spandrel frames, and when completed, these were encased by the concrete spandrel col- umns. Reinforcing Systems. The principal reason for the existence of the many patented systems for concrete reinforcement is the patent royalty secured therefrom. There are a few essential requirements, and where these are fulfilled, the reinforcement is satisfactory. Chief among these requirements are : (1) The metal shall be rough or have a mechanical union with the concrete, (2) Reinforced beams shall have stirrups for trans- mitting shear components from the main ten- sion members into the web of the beam. In connection with the latter requirement, it is preferable that the stirrups be rigidly connected to the tension member, in order to secure a positive transmittal of the shear components. The various reinforcing systems may be roughly classified under two headings. (1.) Slab Reinforcement, (2) Beam Reinforcement. Under the first heading are included the various kinds of expanded metal. Light rods are suitable for slabs, as are also twisted bars and plain flats with rivet heads thereon. For beam reinforce- ment, the opportunity for patented systems is 118 CONCRETE BRIDGES AND CULVERTS. greater, and a large number are now on the mar- ket. Among these may be mentioned Twisted rods. Corrugated bars, Diamond bars, Thacher bars, Cup bars, Twisted Lug bars, etc. All of these are rods and bars without provision for stirrup connection. In addition to these, there is quite a variety of patented bars on the market, either in the form of truss frames or with stirrup connections. In this latter class may be placed the Kahn bar, the Cum- mings Girder Frame, the Unit Reinforcing Frame, the Luten Truss, the Monolith Frame, the General Fireprooling Company's Girder Frame and others. For slab reinforcement, a coarse wire with its high tensile strength and corresponding high elastic limit, is economical. It does not have the disadvantage of high tension bars, for while bars are brittle and lack ductility, wire is elastic and has always been and probably will continue to be a desirable tensile metal. It bends easily, will not crack in handling and gives a large external con- tact area in proportion to its section. Certain kinds of wire mesh have the principal strands in one direction, united by a lighter weave at right angles to them. This type of wire mesh is made with the principal wires in various sizes and is well suited for reinforcing bridge floors. Where floor panels are square and floor beams in both directions, it is then economical to use a wire mesh with wires of the same size in each direction. Most of the various expanded metal systems, while they have a lower tensile strength, have sufficient stiffness to REINFORCED CONCRETE ARCH BRIDGES. 119 support their own weight during construction, and are rougher and have a greater mechanical bond than wire. An excellent example, showing the vari- ous methods of reinforcement for concrete bridges is a ribbed design, for Grand Avenue Viaduct in Milwaukee, shown in Figure 27 and more fully de- scribed in the Engineering News, February 14, 1907. As the shearing stress in curved arch slabs is quite small, there is but little need for metal in the web. The Melan system has continuous lines of double angle bars at the extrados and the in- trados of the arch, connected by light lattice work, and these are manufactured complete in the struc- tural shop and shipped to the bridge site ready for erection. These frames are blocked up vertically on the arch centers from three to five feet apart crosswise of the bridge, and they are connected at intervals with bars or frames which take the place of expansion rods. These shop-riveted frames con- siderably simplify the work of field erection and avoid the complexity and confusion which is liable to occur when a large number of disconnected small bars are used, but much of the web material and the shop labor of riveting is unnecessary for re- sisting stresses. In some of the designs, Mr. Thacher has used plain flat bars adjacent to the extrados and intrados placed about two feet apart. These bars are roughened by having rivets driven at fre- quent intervals, rivet heads projecting to form the mechanical bond. 120 CONCRETE BRIDGES AND CULVERTS. The Kahn bar with light connected diagonals, is well suited for arch reinforcement, as the web members securely tie the reinforcing bar into the body of the arch, but any system of rough bars or rods which are completely imbedded in and sur- rounded with concrete and which have the neces- sary cross-sectional area, regardless of whether they have a web connection or not, are suitable for con- crete arch reinforcement. Concrete Composition. It is customary with some engineers to specify several degrees of richness for the concrete in a single bridge. Mixtures varying from one part of cement with two of sand and three of gravel and stone, varying through several different grades to corresponding mixtures of 1, 5 and 10, are all specified in the same bridge, the richer concrete for the spandrel or arch ring and the poorer for the abutment foundation. The policy is generally un- warranted. Anyone who has observed the ordinary methods used, and the way in which concrete goes into structures, should realize that exact methods which can reasonably be applied to single truss systems, and specifications for various grades of metal, are not appropriate or suitable for use in the design of concrete bridges. Generally it is quite sufficient to specify only one or two kinds of con- crete mixtures, the richer for the superstructure and the poorer grade, if another, for the founda- tion. Examination of test records on the strength REINFORCED CONCRETE ARCH BRIDGES. 121 of concrete mixtures, varying from 1, 2 and 3 to 1, 3 and 6, does not show enough variance in strength to warrant a change of working unit. Therefore, instead of several mixtures with only slight variations, it is better to specify a single mixture. It is frequently cheaper for the con- tractor to put in all mixtures of the richer grade, than to make numerous changes. A more impor- tant consideration than the quality of the concrete, is the securing of contact between the concrete and the metal. In proportion as this is well or poorly done, the permanency of the bridge depends. Loads. The principal loads on masonry arches are the dead weight of the arch itself and the superimposed material above it. It is better to consider only vertical loads as acting on ordinary earth filled flat arches, for the conjugate horizontal forces are small and may be neglected. The amount of horizontal thrust from earth filling is indefinite, for the earth will recede more or less horizontally, allowing the arch to settle at the crown. Therefore, neglecting these horizontal earth pressures is an assumption on the side of safety. It must be noted, however, that the above statements apply only to flat arches when the proportion of rise to span is small. When the arch has a greater rise equal to or approaching half the span, the conditions are greatly changed, for below the point of rupture the horizontal thrusts are so great that solid masonry filling is required. 122 CONCRETE BRIDGES AND CULVERTS. The side retaining walls of earth filled arches fre- quently act as arch ribs and carry a large propor- tion of the weight of the earth filling. The distri- bution of loads in earth filled arches is uncertain and the proportion borne separately by the arch ring and the side walls acting as arch ribs, is un- certain. To avoid this uncertainty some engineers are now designing the side retaining walls with one or more expansion joints in each wall, to pre- vent these side Avails from having any arch action. The entire dead weight and imposed loads must then be supported by the arch ring. There is no doubt that the side retaining walls are capable of supporting large loads as arch ribs, but it is im- portant to know definitely which members of a structure are in action. Any type of construction in which the action of stresses is indefinite, is in many ways undesirable. The condition is similar to that of multiple systems for metal truss bridges. Multiple systems are no doubt economical, but it is usually impossible to know what proportion of the load is carried by each system. This lack of definite knowledge is often the cause of failure, and it is desirable in the design of masonry as well as steel structures to have the condition of loads as nearly fixed as possible. For this reason many arches are designed with cross-spandrel walls elim- inating entirely any possibility of external hori- zontal pressure on the arch ring. The weight of earth filling varies according to its nature from 100 to 120 pounds per cubic foot, REINFORCED CONCRETE ARCH BRIDGES. 123 and the weight of concrete from 130 to 160 pounds per cubic foot, depending upon the density of the stone. Other loads such as that of pavement, rail- ing, water pipes, etc., must be taken according to their actual weights. Approximate general rules for moving live loads are as follows : (a) Light carriage travel is equivalent to 100 pounds per square foot. (b) Heavy carriage travel is equivalent to 200 pounds per square foot. (c) Electric railroad travel is equivalent to 500 pounds per square foot. (d) Steam railroad travel is equivalent to 1,000 pounds per square foot. There is usually sufficient earth filling above the arch ring to distribute any concentrated loads, and particularly for railroad bridges where the ties and rails assist in spreading the load out over a greater area. It is usually safe, therefore, to consider all live loads as uniformly distributed. These rules apply only to earth filled arches, for the loads on arch rings which have open cross-spandrel cham- bers or arcades occur beneath the spandrel walls, and are plainly concentrated loads. The system of loads should be carefully considered for each case, and the designer should be satisfied in refer- ence to the safety of his assumptions, for local loads might easily occur which would require special pro- vision. The bending moments on arch rings for moving loads are a maximum when the uniform live load 124 CONCRETE BRIDGES AND CULVERTS. covers from two-fifths to three-fifths of the span, but it is usually considered as covering one-half of the span. The weight of loaded electric cars varies from 1,000 to 3,000 pounds per lineal foot of track, one- half of this load being borne on each rail. The weight of ordinary light electric cars fully loaded will not exceed 1,000 pounds per lineal foot, but it is now customary to proportion the better class of street railroad bridges to carry loaded freight cars which it is often convenient to switch over electric railroad tracks. The additional cost of proportion- ing bridges for this extra load is comparatively small. The electric railroad companies themselves so often require large quantities of coal delivered at their power plants, that they are usually will- ing to pay the extra cost of a bridge over which their tracks run, in order to have coal cars deliv- ered directly to their plants. Temperature stresses in masonry arch rings are frequently as large or even larger than the bending stresses from partial live loads. Masonry bridges are not subject to so great a range of temperature as metal bridges, for masonry is a poorer conductor of heat than metal and the intrados of an arch is not exposed to the direct rays of the sun, neither is the extrados or any .part of the arch ring ex- cepting the ends appearing at the spandrel. For this reason it is safe to assume a maximum tem- perature range of from 50 to 60 degrees between the highest and the lowest temperatures of the REINFORCED CONCRETE ARCH BRIDGES. 125 arch material. Temperature stresses may be en- tirely eliminated by the use of hinges at the springs and crown, but the practice with American engin- eers is to spend more money in making the founda- tions secure, and thereby avoid the need of hinges. The money that would be spent on building hinges is put into the foundations. As temperature rises, the arch expands and rises at the crown, but when the temperature falls, the arch contracts and it must necessarily fall at the crown. This rise and fall of the arch, due to at- mospheric conditions, is the cause of temperature stresses. Addition must be made to the live loads to pro- vide for the effect of impact. The amount of this impact is determined from the formula Impact load= L+D where L is the live load and D the total dead load per horizontal square foot on the arch. Units Ultimate and Working. Permissible working units for plain concrete arches have already been given in Part I. Rein- forced concrete arches may have higher values, owing partly to the fact that the reinforcing steel will resist some compression and also because rein- forced masonry is a more secure monolith. Con- crete has an ultimate compressive stress of from 2,000 to 2,800 pounds per square inch. A working unit for plain concrete in compression was given 126 CONCRETE BRIDGES AND CULVERTS. at 400 pounds per square inch; for reinforced con- crete it is safe to assume 500 pounds per square inch for combined, direct and live load bending stresses. For combined, direct, bending and tem- perature stresses, it is safe to assume a working unit of from 600 to 700 pounds per square inch. American engineers generally are accustomed to using much lower working units in concrete than are used by European engineers. There is probably sufficient reason for these lower units, for the qual- ity of work done in America is not so fine as is produced in France and Germany. In designing the Grand Avenue bridge, now being built in Mil- waukee, the concrete working units used were 500 pounds per square inch, and 600 pounds including temperature stresses. Perfect adhesion of rich concrete to steel varies from 500 to 600 pounds per square inch. It has already been shown under the heading "Adhesion", that 30 pounds per square inch of exposed surface is a safe and usual work- ing adhesive unit. The ultimate shearing strength of concrete is 400 pounds per square inch and a safe working unit is 50 pounds per square inch. A safe working stress for steel in compression is one-half its elastic strength, or 14,000 pounds per square inch for soft steel and 16,000 pounds per square inch for medium steel. The ultimate tensile strength of good concrete is 200 pounds per square inch, and for the purpose of preventing cracks forming on the tension side of beams or members REINFORCED CONCRETE ARCH BRIDGES. 127 subject to bending, provision may be made for tension in the concrete, not exceeding 50 pounds per square inch. The object in this is plainly to prevent cracks from forming, which would admit water or moisture and expose the metal to the dan- ger of corrosion. The provision is a safe one, but as the modulus of elasticity for steel is not more than twenty times greater than for concrete, the steel in the tension side of the beam would then be stressed to only twenty times the tension allowed on the concrete, or 20 times 50, which is 1,000 pounds per square inch, instead of 16,000 pounds per square inch. Some engineers propose a method of proportion- ing concrete sections by the use of ultimate units applied to three or four times the actual loads. This method is inconsistent. Bridge engineers have long been accustomed to using safe working units for structures which are only a fraction of the ultimate values, using different working values where neces- sary for the dead and the live loads. The same system used in designing steel bridges should be applied also to concrete bridges, and all sections proportioned according to safe working units after addition has been made to the live loads for impact. It is evi- dent that when a tension unit of 16,000 pounds per square inch is used for dead load stresses and a corresponding tension unit of only 8,000 pounds for live load stresses, that provision is made by these varying units for impact amounting to 100%. It is simpler and more accurate to follow the method 128 CONCRETE BRIDGES AND CULVERTS. of the more recent steel bridge specifications and apply impact addition, using the same unit stresses for both dead and live loads. Theory of Arches. The exact theory of arches is very complex. Sev- eral comprehensive books have been written on the subject and the theory will be referred to only briefly here. For a full discussion and explanation of the various theories, the reader is referred to any of the mathematical treatises on the elastic arch. The subject has been treated generally by two methods, the analytical and the graphical. Most, if not all writers and designers using the analytical method follow the theory as developed and explained by Professor Charles E. Green in his book entitled "Trusses and Arches", while expo- nents of the graphical method use the one out- lined by Professor William Cain in his ''Theory of Elastic Arches". The complexity of the subject is responsible to a great extent for the lack of a more general in- troduction of reinforced concrete arches. They are really a combination of arch and beam. Plain con- crete arches have already been discussed in Part I, and reinforced concrete beams are considered in Part III. The reinforced concrete arch is propor- tioned to act both in direct compression and as a beam, to resist bending stresses from uneven load- ing on the arch ring. The arch is distinguished from the beam by hav- ing horizontal or inclined thrusts at the springs, in REINFORCED CONCRETE ARCH BRIDGES. 129 addition to the A r ertical reaction of the abutments. Arches are classified under three headings accord- ing as they are fixed or hinged- (1) Arches with no hinges, (2) Arches with tw r o hinges at the springs, (3) Arches with hinges at the two springs and hinge at the crown. They are classified also under two general heads into (1) Slab Arches and (2) Ribbed Arches. The stress conditions in the arch vary greatly, depending upon the presence or absence of hinges. The space allotted to this book w r ill not permit of more than a very brief review of the principles involved. The principal part of the computation for a reinforced concrete arch consists in finding (a) the horizontal thrust, (b) the end reactions and (c) the bending moments at various points in the span. After these haA r e been found, it is then a compara- tively easy matter to proportion the metal and con- crete to resist the stresses. The method consists in drawing the correct line of pressure for the given arch arid loading, and determining its proper posi- tion in the arch ring. When this has been done, it is easy to find the bending moment at any point of the arch. Most of the uncertainties of masonry arches which have been enumerated in Part I apply equally to reinforced arches. The elastic theory applies not only to arches in which bending moments are 130 CONCRETE BRIDGES AND CULVERTS. resisted by the arch ring, but may be used also for arches of solid concrete with no tension in any part of the arch ring or where the line of pressure lies in all cases within the middle third of its depth. The theory is applicable both for two-hinged and for fixed end arches. rches with fixed ends have five unknown quan- tities, (a) equal horizontal thrusts at either end, (b) two vertical end reactions and (c) two bending moments at the springs. Where there are no hinges in the arch, the reac- tions are not transferred to the abutments in ac- cordance with the law of the lever. Since there are five unknown quantities, there must in addition to the two equations of equilibrium, 2x=0 and ^0 be three more equations found. These are deter- mined from the conditions of equilibrium for fixed end arches, which are as follows : (1) The angle of inclination that the springs make with each other must not change. (2) The relative elevation of the two end abut- ments must not change, and (3) The length of span must not change. These are mathematically expressed by the formu- lae : 2$ n M= 0, 2$ n MX 0, 2% n Mi/ =0. In the above formulae, M is the general value of the bending moments, n the length of a short por- tion of the arch ring, and x and y, the horizontal and vertical coordinates to the center of n, meas- REINFORCED CONCRETE ARCH BRIDGES. 131 ured from the origin at the springs A or B. Fixed end arches have high temperature stresses, two to four times greater than for two-hinged arches. The abutment reactions for arches with either two or three hinges, follow the law of the lever, which greatly simplifies the mathematical calcula- tions. Two-hinged arches have only three sets of un- known forces, (1) The horizontal reaction and (2) The two vertical end reactions. As there are hinges at the end and a condition of continuity cannot exist there, the two additional unknown quantities, the two unknown bending mo- ments at the springs do not now exist. This is the theoretical assumption, but it is not exact, for even with pin bearings at the end, there is a large amount of friction on the pins and the bending mo- ments will not entirely disappear. The assumption, however, for two-hinged arches is that there are only three sets of unknown forces. Therefore, in addition to the two usual equations of equilibrium 2x=Q and 2y = 0, there is only one other equa- tion required, and this can be found from the con- dition that the length of span must not change. The span length should not change or no sliding of either abutment should occur in order that the arch ring between the springs shall remain intact. The third equation required for the solution of 132 CONCRETE BRIDGES AND CULVERTS. the two-hinged arch is, therefore, expressed as fol- lows : Hinged arches are not frequently built in America, but some designers for the purpose of simplifying calculations, consider the arch ring as hinged at the springs. The condition of stress in three-hinged arches is definite, for the moments both at the springs and crown are zero, and the position of the line of pres- sure is, therefore, fixed at these three points. Tho equations of equilibrium for three-hinged arches are, therefore : The thrusts, bending moments and shears may bo found most easily by Professor Cain's graphical method, after which the section may be most easily proportioned analytically. It has already been stated that the graphical method consists in draw- ing the correct line of pressure for the given arch and loading and determining its proper position in the arch ring. The following method is used for determining the form of arch and the thickness of the arch ring for uniform loading. It avoids the usual trial method given in Part I for solid concrete arches. The position of the springs must first be assumed as well as an approximate crown thickness and the depth of earth filling above it. The remaining height from spring to crown intrados will be the REINFORCED CONCRETE ARCH BRIDGES. 133 rise of the arch. The method depends upon the equation, M HT, where M is the bending moment, H the crown thrust or pole distance of the force polygon, and T the vertical ordinate to the pressure curve at the point where the moment is taken. The bending moment at the center is the same as for a simple beam and dividing this moment by the arch rise gives the crown thrust or pole distance H. The bending moment at any other point of the arch is equal to the pole distance IT multiplied by the vertical intercept at that point in the funicular polygon. The moments are, therefore, computed for as many points as desired and dividing these moments by the pole distance H, which has already been found, gives the required ordinates T to the funicular polygon, which is the line of pressure for the full assumed loading. The pressure curve is then plotted from the ordinates found and this will give a curve for uniform loads. The height T referred to above is the distance to the line of pressure measured from a horizontal line through the point of rupture, which is not nec- essarily at the abutment face. The correct crown thrust cannot be obtained by using a distance T to any point below the point of rupture. When the point of rupture falls within the abutment face, the span length must be taken as the distance be- tween the points of rupture, and not the clear dis- tance between abutments. 134 CONCRETE BRIDGES AND CULVERTS. For full dead and live loads, the line of pressure should wherever possible, lie within the middle third of the arch ring, and reinforcement used only for resisting bending stresses due to partial live loads. In Figure 26, the weight of the arch ring may be assumed at its mean thickness at the quar- ter point, and the arch ring weight assumed ap- proximately as a uniform load. The weight of earth filling, pavement and other material between the Fig. 26 extrados and roadway level, as well as the uniform live load, is also uniform, and the center bending moment for these uniform loads is expressed by the equation: M w s 2 M= - 8 For a parabolic arch, the spandrel area shown REINFORCED CONCRETE ARCH BRIDGES. 135 O "R hatched in Figure 26 is equal to - . The center of 6 gravity of this area is equal to one-eighth of the span length from the abutment face. Therefore, the bending moment at the center from spandrel 25 R S 2 filling is equal to . The total moment is, JLU therefore, equal to the sum of moments from uni- form loads and from the spandrel filling. Dividing the center moment by the rise gives the crown thrust or pole distance II for the force polygon. This is a very convenient analytical method for determining the correct arch form for any system or arrangement of loads. A combination of the an- alytical with the graphical method will simplify computation, as some results, like finding the crown thrust, may be determined most easily by the an- alytical process. In practice, it is usually sufficient to find the sum of all moments and thrusts at three different points the center, the quarter points and springs. The thickness of arch ring at other points below the crown must be such that the vertical heights D, shall not be less than at the crown. The bending moment at any point of the arch ring from partial loading is equal to the pole dis- tance or horizontal thrust at the center, multiplied by the vertical intercept* between the neutral plane and the line of pressure at the point considered. The correct position of the line of pressure for partial loading will already have been drawn upon 136 CONCRETE BRIDGES AND CULVERTS. the arch ring, and the vertical intercept may be scaled and will be positive or negative according as the pressure curve lies above or below the neu- tral axis of the arch. The determination of the thrusts and moments may be simplified by considering the arch as a par- abola. This is approximately true when the rise is small in comparison to the span. The stability of an arch is secured when it will resist the stresses resulting from thrust and bend- ing from any system of loads, when the line of pressure is drawn in such a position as to produce the least possible bending moment, or when the line of pressure is drawn the nearest possible to the center line of the arch. General Design. The introduction of bridges of combined metal and concrete has thrown open a wide field for im- provement in design. So long as it was necessary to build bridges of stone, the art showed no great improvement over the work of the ancients. In recent years, however, the increased production of cement with its decreased cost, as well as the in- vention of improved stone-crushing machinery and appliances for mixing concrete, have tended to make larger structures possible, even in solid ma- sonry. The greatest progress in the art has been made since the completion of the Austrian experi- ments iii 1895. Reinforced concrete has made it possible to discard old, conventional forms and to introduce new and lighter types of bridges sup- REINFORCED CONCRETE ARCH BRIDGES. 137 ported by arch ribs, carrying open spandrel framing to support the roadway. The enormous reduction in the dead weight of the superstructure has caused a proportionately large saving in the foundations. A large number of improved methods of design have already been tried successfully and there is prospect of additional progress in the future. "With the new material designers are following to some extent the outlines used for metal bridges, so there are now numerous examples of bridges built in con- crete-steel, not only in the form of light ribbed arches, but also as solid and ribbed cantilevers, girders, trusses, etc. The new material is, in fact, being used according as its own properties will per- mit. The general subject of arch bridge design is divided into four parts, (1) The parapet or deck, (2) The spandrels, (3) The arch ring and (4) Temporary arch centers. In beginning the general design, the final object should at all times be kept in view. The first and chief object in building all bridges is to construct and support a platform at the proper elevation, of sufficient capacity to safely and securely conduct travel over certain openings. A second object which is too often neglected, is the desirability of making the bridge pleasing in appearance, in har- mony with its surroundings and a credit to its builders. 138 CONCRETE BRIDGES AND CULVERTS. When once started, the design should be contin- ued in logical sequence. The width of bridge and the kind of pavement required, should be selected with the necessary filling beneath the pavement to support the roadway or the railroad ties. After deciding upon the kind of deck required, the most economical method of supporting this deck must be determined. It may be carried on solid earth filling or on a series of walls or columns, and these may be continued to the ground in the form of a trestle, provided the height from deck to ground is small. If the height be great, these walls or columns may then be supported on other ribs or frames, such as arches or trusses, and the loads from these may in turn be transmitted to the ground through walls or piers of the most econom- ical form. There is no good reason why the span- drel columns of a concrete bridge cannot be sup- ported in other ways, excepting on slab or ribbed arches. Trussed frames or girders are possible forms, though they would not be as pleasing in appearance as a continuous arch. It is possible that arches with double ribs or drums separated by systems of framing may be used, following the outline of a double-braced metal arch. If the de- sign is developed in successive steps, beginning with the roadway platform, and transmitting the loads continuously in the most economical man- ner through various kinds of framing into the foundations, the result will be both scientific in con- struction and satisfying to the engineer. It is a REINFORCED CONCRETE ARCH BRIDGES. 139 deplorable fact that the design of many bridges is begun by first locating the foundations and de- veloping the design upward from the ground, in- stead of from the deck downward. This one error accounts for the absence of economy in many struc- tures. The old empirical rules for masonry arches, which required more masonry in the abutments than in the arch, are unscientific and useless for reinforced concrete. All through bridges are ob- jectionable. They are a menace and an obstruction to travel, are lacking in lateral stiffness, and the trusses or framing interfere with the river view, which is generally and should always be an inter- esting feature of a river bridge. If a bridge has several spans and one span has movable bascule leaves or other kind of draw, the outline of the draw span should conform and har- monize with the rest of the bridge and its pres- ence should be indicated by ' piers or towers at either side of the opening. The underneath out- line for double bascule leaves in a single span may easily be made in the form of a continuous arch, corresponding to the intrados curves of other spans in the bridge. Unsymmetrical arch spans may be used at the ends of viaducts crossing deep ravines. They cause a large saving in the abutments by permitting higher springs at the abutments than at the piers. The half shore span adjoining the pier may be made with intrados curve to correspond with the next 140 CONCRETE BRIDGES AND CULVERTS. adjoining span, thus producing symmetry about the pier center. As the end arch span lacks symmetry in the arch, it is necessary for appearance, that the design shall be symmetrical about the pier. The Kissinger Bridge, twelve miles southeast from AVabash, Indiana, is of unusual design. It has a IG-foot concrete roadway slab balanced on a single center concrete web 12 inches in thickness, supported on a segmental concrete arch, 8 feet in width. It is a single span highway bridge, with 60-foot opening and was built in 1907. All tow r n or city bridges should have open cham- bers beneath the floor for pipes and wires. They may either have removable iron covers, or be paved over, with manholes or entrances provided at either end. Hinged Arches. There is a difference of opinion with regard to the use of hinged or fixed arches for masonry bridges. Hinges, by which is meant the insertion of heavy stone or metal blocks at or near the cen- ter line of the arch, remove one of the principal uncertainties of arch construction, by fixing the position of the line of pressure at the springs. The presence of a hinge at the crown tends to consid- erably reduce the rigidity and increase deflection, and is not alwaj T s to be recommended. Hinges may be introduced at the springs in such a manner as to insure absolutely within small limits the posi- tion of the line of pressure there. Fixed ends tend to greatly increase the amount of temperature REINFORCED CONCRETE ARCH BRIDGES. 141 stresses and they have no advantages over hinged ends. Alter the centers are removed and the arch ring has come to or nearly to its final position, the open joints at the hinges should then be filled solid with cement, so the entire cross-section at the hinges will be available for full loading. The pres- ence of hinges or the assumption of their presence at the springs, simplifies the computations and re- moves one of the chief uncertainties of concrete arch design. The American practice has been to avoid any extra expenditure on hinges, but to put it into the foundations, insuring their stability against movement. There are numerous unfortu- nate cases where the foundations have been in- sufficient. Several spans of a bridge over the Illi- nois River at Peoria were recently destroyed, owing to the undermining of foundations. Hinges are de- sirable chiefly where it is known that the soil is yielding and the abutments are liable to recede lat- erally, allowing the arch to fall at the crown, and cause unsightly and possibly dangerous cracks. A method employed by certain German engineers is to place hinges at the point of rupture. This was done in a bridge built at Kempten, Bavaria, over the Iller River, and described in the Engineering News, May 2, 1907. Ribbed Arches. The principal economy in reinforced concrete bridges comes from the use of ribbed arches. Most of the surplus material, both in the structure itself, and in the spandrel filling, may then be eliminated, 142 CONCRETE BRIDGES AND CULVERTS. and as weight of superstructure decreases, the cost of foundations decreases in proportion. The use of ribs instead of slabs, is a more scientific type of construction and allows the strongest supporting members to be placed exactly where required. Ribbed concrete arches are purely a product of this new material and are possible in concrete only when properly reinforced with metal. Concrete ribbed bridges are built mostly in the form of arches, though other forms, as cantilevers, have also been used with varying degrees of success. Many bridges designed as arches have cantilever action also, or when the rise is small in proportion to the span, the stresses are chiefly the result of bending, and regardless of theory the span acts then more as a beam than as an arch. The uncertainty in refer- ence to cantilever or beam action of arches can be removed by building an open vertical joint between the arches over the piers, the presence of which will positively prevent any cantilever action. While such a joint removes a serious uncertainty of de- sign, it is very doubtful whether or not this expedi- ent is desirable, for the cantilever action frequently adds as much strength to the bridge as does the arch and when properly designed and built to re- sist both sets of stresses, the presence of cantilever action adds greatly to its strength and permanence. The Walnut Lane bridge at Philadelphia, and the Rocky River and Piney Creek bridges now un- der construction, illustrate to some extent the sa\- ing which may be accomplished by the use of ribbed 144 CONCRETE BRIDGES AND CULVERTS. in place of slab arches, and yet all of these three bridges are only partially ribbed. They each con- sist of a pair of twin arch rings separated by a distance of from 10 to 20 feet, which space be- tween the rings is spanned by simple floor con- struction. The saving in the arch ring by this ex- pedient is from 25% to 30% of the cost of the ring, which saving would be still further increased by using entire ribbed designs. The Luxemburg stone arch bridge in Germany with a span of 275 feet, and completed in the year 1903, is of the same type. An unusual example of ribbed arch design pre- pared by Mr. Turner of Minneapolis, is shown in Figure 27. It is one of several designs submitted for the Grand Avenue viaduct in Milwaukee. The main compression members are octagonal and are hooped. The use of ribs instead of slabs makes it possible to place members of the proper strength where re- quired, as for example under lines of street railway track, where heavier ribs are usually required than under other parts of the roadway. Sidewalks may be bracketed from the outer ribs and properly tied into or across the floor, and the whole design exe- cuted in a more scientific and economical manner. The principal objection to the use of ribs is the extra cost of the required wooden forms, which of course is much greater than for plain curved slabs. Notwithstanding this objection, important concrete arches of the future will possibly be built with ribs, particularly when the proportion of the rise to span is large. REINFORCED CONCRETE ARCH BRIDGES. 145 Intrados Form. A low flat opening is the best form for the pas- sage of water. A rectangular opening for culverts with the height greater than the width, will cost less than when the width is the greater of the two dimensions. This is clearly shown by the culvert design given in Tables VII, VIII, IX and X of Part IV, but the decreased cost is secured at the expense of efficiency. Intrados forms should be as nearly as possible ex- act mathematical curves, but if these cannot be secured, they should then approach so nearly to the exact curves that the lack of regularity may not be detected by the eye. Three and five centered flat arches as approximation to the ellipse, are usually unsatisfactory because the breaks in the curve can be detected. If a flat ellipse is desired, the curve should be an exact ellipse and not an approxima- tion. Ellipses which are too flat are not artistic. A rise of from one-fourth to one-sixth of the span will give a better appearance. Natural conditions or grade lines will frequently prevent even this amount of rise, and it must then be determined by stability requirements, which should not be less than from one-eighth to one-tenth of the span. The steel arches of the bridge across the Mississippi River at St. Louis have a rise of one-eleventh of the span and there is at Steyr, Austria, a reinforced concrete bridge of 139-foot span, the rise of which is only one-sixteenth of the opening. Earth filling in the haunches tends to make the 146 CONCRETE BRIDGES AND CULVERTS. line of pressure approach the form of an ellipse, while the uniform loads including the weight of arch ring,, filling above the extrados, pavement and full live load tends to depress the line of pressure to the approximate form of a parabola. The com- bined effect of these two tendencies is to produce a curve approximating a circular segment. The resulting curve will lie nearer to the ellipse or to the parabola, according as the effect of haunch fill- ing or uniform load predominates. The trial method of determining the intrados curve is no longer necessary, for a direct method has been given. Under the head of ''Theory of Arches", a method has been explained for deter- mining the amount of crown thrust by dividing the center bending moment by the rise. The simple beam moment at any other point is equal to the crown thrust or pole distance H multiplied by the vertical ordinate in the funicular polygon, which is the intercept between the closing line and the pres- sure curve. Therefore, dividing this bending mo- ment by the crown thrust or pole distance, gives the proper ordinate or rise for the center line of the arch at the point considered. This method makes it possible, after having first assumed the approx- imate form, to determine directly without trial, the exact intrados curve for uniform loading. When the exact linear arch has been found, the bridge will present a better appearance if a regular curve be drawn, such as a segment or ellipse, even though the use of a regular curve makes the arch some- REINFORCED CONCRETE ARCH BRIDGES. 147 what thicker in certain parts than is required. After having drawn the correct linear arch, the thickness of the ring for uniform loads should be proportioned directly to the thrusts. The computations are much simplified if the curve be considered a parabola, and this assumption is approximately true when the rise is small in comparison with the span. Parabolic and seg- mental arches require little metal reinforcing, while elliptical and other flat arches may require a greater amount. Some designers prefer to use an intrados curve, lying half way between a segment and an ellipse and found by bisecting the vertical intercepts be- tween these two latter curves. Mr. Burr's Potomac Memorial Design No. 3 has an elliptical intrados, with a rise of one-fourth the span, and a segmental extrados. Spandrels. The principles already given for the spandrel de- sign of solid concrete arches, apply also to arches of reinforced concrete. If side spandrel walls are used, provision should be made for expansion or these side walls will crack. A dovetailed expan- sion joint is the most satisfactory one, for sufficient space can be allowed in it for expansion, while the two wall sections are held securely together. If an expansion joint is not provided, an open crack is liable to develop between the spandrel wall and the arch, and if an effort be made to prevent such an opening by clamping the spandrel with metal 148 CONCRETE BRIDGES AND CULVERTS. ' ties to the arch ring, the stress in the arch then becomes indeterminate, as a portion of the load will be carried by the arch action of the spandrel wall. Joints in continuous walls should occur at in- tervals not exceeding 20 to 25 feet. It has been found by experience that temperature cracks occur in solid walls at about these intervals and if artifi- cial joints be formed, the developing of unsightly and irregular cracks will be avoided. All exposed flat concrete surfaces should be pan- eled to avoid monotony. It is difficult to build plain surfaces perfectly straight or plumb, and the use of panels with pilasters and belt courses assists to conceal irregularities and imperfections in flat surfaces, that otherwise might be quite apparent. Open spandrel arches in the haunches produce a light and artistic appearance, but they are not prac- ticable for flat arches. Spandrel walls may be built either as curtains to obscure the open chamber framing, or as retaining walls to support earth filling. As retaining walls they may be built either as solid gravity walls, or as lighter reinforced walls with counterforts. In any case it is better that the centers be removed and the arch allowed to settle before building the spandrel walls. Piers and Abutments. On the stability of the foundations, the strength of the whole superstructure depends. The piers and abutments include all of the structure from REINFORCED CONCRETE ARCH BRIDGES. 149 the ground up to the point of rupture. The total angle included between normals to the points of rupture, never exceeds 120 degrees and is usually from 90 to 110 degrees, the real theory of arches applying only to material between these limits. The part below the points of rupture must be designed in connection with the substructure. The greatest economy in the design of abutments is secured by using low springs. If higher springs are desired, they can be secured by false side walls as explained and illustrated in Part I. Great sav- ing can be effected in high abutments by coring out the rear and transferring the thrust to the soil through vertical walls bearing on a foundation slab of reinforced concrete. Abutment wings may be built as cantilevers from the arch, extending into the embankment only far enough to hold the slope. They contain much less masonry than the old style of gravity retaining wing walls. Cantilever wing walls should be tied together with rods be- neath the roadway, to resist the outward thrust of filling. This method was adopted in the Topeka bridge. The recent failure of the Peoria bridge over the Illinois River, has called attention to the need of having absolutely secure foundations. The Peoria bridge was destroyed, not because of any lack in the design of the superstructure, but because of the undermining of its foundations. Flaring gravity wing walls are more economical than straight ones of the same type and better 150 CONCRETE BRIDGES AND CULVERTS. direct water to the opening, but straight wings usually present a better appearance. River piers require cut-waters at the upper end which should be capped with stone or steel, well anchored into the masonry. Some bridge piers have been given a different batter on the two sides for resisting the unequal thrust on the sides from spans of different lengths. The piers must have sufficient thickness to resist the uneven thrust caused by full live loading on one span and no live load on the other. Piers must be designed, not by empirical rule, but according to the stresses that they actually have to resist. The presence of reinforcing rods for resisting temperature stresses in piers, is desirable though not necessary. Piers are usually well protected from the direct rays of the sun, and rods are more useful to unite the mass into a solid monolith than for resisting temperature stresses. The design of piers for reinforced concrete bridges does not differ greatly from the design of piers for masonry bridges, and most of the discus- sion of this subject for Concrete Bridges, applies equally here. Cost of Reinforced Concrete Bridges. There are numerous considerations that affect the cost of reinforced concrete bridges, among which are the nature of the soil, the nearness or accessi- bility of materials, presence or absence of switch- ing facilities, the design of the bridge whether solid filled or open spandrel, the height, width, finish, REINFORCED CONCRETE ARCH BRIDGES. 151 paving, wings, etc. They will, however, rarely if ever cost more than bridges of solid concrete. An original formula for the cost of solid concrete bridges has been given in Part I, but for convenience it is repeated here. It is as follows : 100 Where C is the cost of the bridge in dollars per square foot of roadway, W, the total width of deck in feet, II, the height of deck above valley or river bottom, and F, a variable factor the value of which is as given below, The function HW, or the product of height by width, is the cross-sectional area, and may be represented by the letter A. Factors F, are for bridges with solid slab arches, while factors F' are for bridges w r ith partial slabs, like the Walnut Lane bridge at Philadelphia, or the Rocky River bridge at Cleveland. Values of Factors F, and F'. When A is 200, then F is 1.5 500, " 1.0 1000, "' M 1500, " .48 2000, .42 2500, .36 3000, .32 3500, " .285 152 CONCRETE BRIDGES AND CULVERTS. When A is 4000, then F is .262 and F' is .96 5000, " .224 " .95 6000, " .200 .94 7000, .180 " .93 8000, " .164 " .92 9000, " .152 " .91 10000, " .141 " .88 11000,. " .133 " .86 12000, " .125 " .85 This formula will give costs that should rarely if ever be exceeded. Generally, however, econom- ically designed reinforced concrete bridges should cost from 25% to 50% less than the costs given by the formula for bridges in solid concrete. In a few cases, the cost of bridges in reinforced concrete have exceeded that given by the formula, but these cases are rare. Where the height does not exceed 15 to 20 feet, the cost will usually vary from $2.00 to $4.00 per square foot of floor surface, while for greater heights it may be twice these amounts. The total cost, as well as the cost per square foot of deck for a miscellaneous lot of reinforced con- crete bridges is given in Table No. II. The square foot cost is based upon the total length of bridge over parapets or foundations, and not upon the length of opening. If based on the latter length, the costs per square foot would then be greater. The cost of IS concrete arch highway bridges, built by the city of Philadelphia, is reported in Engineering Record January 23, 1909. The report states that the bridges were mostly single span with REINFORCED CONCRETE ARCH BRIDGES. 153 ornamental balustrade, washed granolithic surfaces and paved decks. The costs based upon the total length of bridge vary from $1.73 to $7.39 per square foot, or an average of $3.50 per square foot, while the costs based upon the width multiplied by the clear length of opening vary from $3.10 to $9.74, or an average of $6.25 per square foot. The total cost based upon the yardage of concrete in the structure varies from $8.50 to $11.25 per cubic yard. The report states further that if large spalls or stones were embedded in the concrete to save cement and mixing, the cost would then be reduced by about 20%. Compared with steel, reinforced concrete bridges usually cost about the same as steel bridges with solid floors. The report referred to above states that those built in Philadelphia proved to be cheaper in first cost than plate girder bridges by about 25%, but if maintenance expense is considered, the saving is still greater. Comparative estimates for the Memorial Bridge at Washington, one design for which is given in the frontispiece, showed that the reinforced concrete designs cost 45% more than corresponding designs in steel. A bridge over the Hudson River at Sandy Hill, N. Y., consisting of 15 ribbed arch spans of 60 feet each, cost only $2.30 per square foot and a steel bridge for the same loads w^ould have cost as much. Bids received for a bridge over the Mississippi River at Fort Snelling Minn., consisting of two arch 154 CONCRETE BRIDGES AND CULVERTS. spans 350 feet in length each, showed that the bridge could be built in either steel or reinforced concrete at about the same cost. A concrete design for the Richmond trestle shown in Figure 40 is reported to have been accepted in preference to steel, simply because it was the cheaper. Estimating. It is customary to estimate the total cost of floor slabs, including concrete, metal reinforcement and forms, at 25 cents per square foot of floor for the slab only. This figure is made up as follows : Concrete, 6 inches 12 cents Metal 5 cents Wood forms 8 cents Total 25 cents The cost of forms varies considerably, and for floor slabs may cost from 8 to 20 cents per square foot of floor. If the slabs are estimated separately, then it is necessary to estimate also the cost of floor beams and spandrel columns. It is usual to estimate the cost of forms for beams and columns of ordinary size, not exceeding about one and a half foot in cross-section, at 50 cents per lineal foot. To this must be added the cost of the con- crete and steel in the member. The total cost per lineal foot of girder or columns would then be as follows : Concrete 1 cu. foot 25 cents Steel 15 cents Forms 50 cents Total . 90 cents REINFORCED CONCRETE ARCH BRIDGES. 155 TABLE II APPROXIMATE ESTIMATING PRICES Price delivered. Price in Place. Earth filling. . . $0 50 to $1 00 per yd Excavating, ordinary. . . 50 cu ft. " under water (including cost of cofferdam) . . . 4 00 cu ft. Wood piling 35 lin ft Sheet piling . 40 00 per M. Concrete piling 1 25 per ft. Concrete in foundations . 6 00 " yd. " in arch rings 8.00 " " including steel reinforcement . . . 12.00 " " Concrete including steel reinforcement and centers. 18 00 " " Steel reinforcement, riveted work " rods, plain 70. 00 per ton 30 00 " " " patented rods 50.00 " " Brick, common . $6 00 to $10 00 per M 20 00 per M. " face. 30 00 " " 45 00 " " " moulded " enameled 50.00 " " 70.00 " " 70.00 " " 100.00 " " Concrete blocks, 10 inches thick Sand .25cu. ft. 75 to 1 25 " yd .SOcu.ft. Gravel. . 1 25 " " Cement, Portland " non-staining. . 1 . 35 per barrel 3 25 " Crushed limestone 1 20 per yd " granite 3 00 to 3 50 " " Bedford limestone. . 1 30 per ft 1 CO per ft. Carthage limestone. . . . 2 00 " " 2 " " Kasota or Mankato stone Granite 2.50 " " 2 50 to 3 00 " " 2.80 " " 3 SO " " Bedford ashlar facing, 4 to 8 inches thick. 1.00 sq.ft. Bedford stone carving 4.00 " " Concrete floor slabs ( concrete, steel, forms) .25 " " Concrete girders and columns (concrete, steel and forms) . . . 1 00 lin. ft. Concrete columns, spiral wound 1.70 " " 156 CONCRETE BRIDGES AND CULVERTS. TABLE II Continued APPROXIMATE ESTIMATING PRICES Price delivered. Price in Place. Bridge pavements, wood block " " granolithic walks. . . " " brick asphalt " stone block " " granite block Railing, three lines pipe " plain iron lattice " fancy iron lattice " artificial stone Balusters, turned Bedford stone Hand rail and base rail Stone coping Intermediate rail posts End newels Lamp posts Trolley poles Lumber in cofferdams " " arch centers " " forms Beam and column forms Metal lath and plaster, interior " " " " exterior Expanded metal No. 10, 4-inch mesh. . . " light Nails and spikes Tar paper Toch Bros, waterproof paint, No. 10. . .' Bay State coating (for concrete surfaces) $22.00 .035 per sq.ft. .02 " " $1.50sq. yd. 1.50 " " 2.50 " " 3.50 " " 3.00 " " 4.50 " " 1.00 per ft. 2.00 " " 5.00 " " 6.00 " " 1.00 each .60 per ft. 2.00 " " 8. 00 to 12. 00 each 10.00 "100.00 " 100.00 " 75.00 " 40. 00 per M. 32.00 " " .08 sq. ft. .SOlin. ft. .50 per sq.yd. .03 perlb. .OOSper sq.ft. 1.25 "gal. .02 "sq.ft. 20.00 15.00 REINFORCED CONCRETE ARCH BRIDGES. 157 If the girder or column is larger than 12 inches square, the cost of the concrete will then increase in proportion to its area. In making up a tender on a prospective contract, it is necessary that all items of expense be included and provided for. Some of the extra expense items, that are not included in the regular estimate, are as follows : Superintendent. Foreman. Timekeeper. Traveling Expenses. Bond. Cost is 1 per cent, on amount of bond, which is usually 25 per cent, of contract. Telephones. Watchmen. Fire Insurance. Liability. Cost is 2* to 3| per cent of amount of pay roll. Permit and License. Water. Setting out survey. Rent of, or depreciation on plant. Office and Storage sheds. Material tests. Models. Signal lights. Pumping and Baling. Refilling and Leveling. Shoring. Removing Rubbish. Incidentals. Surfacing. These items must be provided for and the amount of profit desired added to the total. The approximate estimating prices given above, should be changed to suit local conditions and the varying state of the market. Prices of material and labor change according to location and time, and prices that are suitable in the East may not hold 158 CONCRETE BRIDGES AND CULVERTS. for work in the West or South. The greatest care is necessary in estimating the foundations, for the part that is unseen is uncertain. It is well to make unit prices for a greater or less amount of founda- tions than is shown on the plans, for frequently more is required than is anticipated. Table of Approximate Quantities. The following table gives the approximate quan- tities in Reinforced Concrete Arch Highway Bridges for clear spans varying from 20 to 150 feet, and a clear width of roadway of 16 feet. They have solid earth filled spandrels with rein- forced concrete side retaining walls and the rise of arch is one-tenth the span. They are proportioned for a live load of 200 pounds per square foot on the roadway. The quan- tities of material in the abutments are only approx- imate. TABLE OF APPROXIMATE QUANTITIES. Steel, Bars 12 in. c. c. Clear Span in Feet. Crown Thickness in Inches Concrete in Arch, Cu. Yds. Concrete in Abutments, Cu. Yds. Size. Area in Sq. Ins. 20 9 2 x M .50 30 89 30 11 2 x A .62 45 118 40 13 2j^ x .78 63 140 50 15 2 ^ x jHi .93 89 162 60 16.5 3 x A .94 118 205 70 18 3 x H 1.13 150 240 80 19 1.31 186 280 90 21 3 iz x .i. 1.53 220 320 100 22 4 x y s 1.50 265 360 110 24 4 x A 1.75 312 410 120 26 1.69 360 460 130 28 4 J^z x -fs 1.97 415 515 140 30 5x^ 1.88 475 570 150 32 5 x A 2.19 540 630 REINFORCED CONCRETE ARCH BRIDGES. 159 Potomac Memorial Bridge Design. This is one of several designs submitted to the United States Government in the year 1900 for a proposed memorial bridge across the Potomac River at Washington. It has a clear width of 60 feet, con- sisting of a 40-foot roadway and two 10-foot side- walks. The total length of open bridge is 3,400 feet. It has one deck and no provision for car tracks. There are six segmental reinforced con- crete arch spans of 192 feet clear length and 29 feet rise, with 53 feet clearance underneath. A double leaf trunnion bascule draw span is centrally located between the arch spans, having a clear open- ing of 159 feet and a distance between centers of trunnions of 170 feet. The Washington approach consists of twelve semicircular reinforced concrete arch spans of 60 feet clear length, and 550 feet of embankment, while the Arlington approach has fif- teen similar spans and 1,350 feet of embankment. The entire exterior surface is shown faced with granite. The face rings for main spans are 5 feet 6 inches deep at the crown and 9 feet 6 inches at the springs. Each main span has five concrete-steel arch ribs 30 inches deep at the crown and 7 feet 3 inches at the springs, supporting a system of in- terior steel columns carrying the floor beams. Span- drel curtain walls with expansion joints rest upon the arch rings and are faced with granite. The design shows asphalt 'lOO 48 14 ' C.' ' Seg.' 443 401 '265 219 26 68 36 19 21 22 90 36 Playa del Key, Cal Vermillion River . . Wakeman, Ohio Routo Waidhofen, Austria Steyr, Austria 8.5 16.2 18.9 16.3 14.6 11.4 15 12 11.4 23 18 14.4 9.6 11.3 13.3 14.3 23.5 40 11.5 10 165 244 693 'ieo 404 .214 '716 '222 371 19.7 74 40 12.8 17 20 64 54 11.8 12 10.5 40 41 19 24 32 "43" 39 .25 30 "56" 16 Seg. 3C. Branch Brook Park, Newark . . Topeka, Kansas Kansas River Yellowstone River Jacaquas River. . . . Grand River Ravine Pena River Miami River Niagara River .... St. Joseph River '. . White River Route Wildegg, Switzerland .. Yellowstone Park Porto Rico Lansing, Michigan Lake Park, Milwaukee Portugal Third St., Dayton, Ohio Boulevard, St. Paul Green Island Jefferson St., South'Bend. '.'.'.'. Emerichsville Ind. . 'l4!6 14 14.4 9.5 11.7 'i70 240 522 50' 16 45 55 25 21 30 3 C.' Morris St., Indianapolis Huntington, Indiana Buda Pesth, 4 Austria Canal Dover, Ohio. ..'.'.'.'.'. '.'.'.'. Danube River Tuscarawas River . REINFORCED CONCRETE ARCH BRIDGES. 175 TABLE III Continued LIST OF REINFORCED CONCRETE BRIDGES Crown Thickness in Inches. 1 I 02 Distance Apart. fi w ' W 1 3 1 Engineer. References. B.C., Eng.-Con. N., " News R., Record .d s i w Cost Per Sq. Ft. 1 l l 10 g 1909 H. $80,000 Morsch N., Aug. 5, '09... 1 2 3 IS H 4 .... 1907 H. $42,400 De Mollius N., Apr. 2, '08... Rib. $5.50 5 g 21 100 H 7 22 18 S7 1899 90S H. R R 35,000 Leffler. . . . N., Apr. 10, '02 . . R Apr. 24 '09 Rib. 3.05 8 9 10 54 '94' ... . 1907 906 'Seoneid'Eng.'Co'.!! De Palo . N., July 26 '06 'Rib! Rib 11 12 13 ... . 1908 H. H 16,870 Watson E.G., Feb. 24, '09 Rib. Rib 3H. ? H 3.66 14 15 24 '26' 19 36 36 36 897 895 897 H. H. H. ' 84,000 150,000 Reynolds Keepers & Thacher 'R'.,' Aug.' 12', "'65'.: R., Apr. 16, '98 . . N.,Apr. 2, '96.. '4'!65 5.40 16 17 18 19 9 7 890 H. ?1 24 28 9 1 ix'ji' 24 30 1904 1901 H. H. 59,440 Crittenden Judson N., Jan. 14, '04 . . R., Aug. 3, '01 . . N Aug 1 '01 'MO 22 23 24 25 32 1902 1904 1901 1906 H. H. E. R. H. 31,000 184,000 Newton Eng. Co. . . Turner E.G., Mar. 17, '09 R., Nov. 25, '05. R., Mar.' 4, '06'.!' 'Rib! ' '4!is 25 26 27 28 29 i ii ii ii ^0 ** " " K Rib 31 > 40 e'x'ji' 36 1909 900 H. H. 18,800 102,070 C. A. P. Turner . . . R., Apr. 3, '09 . . N., Dec. 6 '00 2.12 6.60 33 34 38 F, R Hammond R., Feb. 16, '01 . . .... 35 36 H. 37 H. 38 20 4? 901 H. 32,000 Melan N., July 16, '03 3 77 39 21 20 a 12 907 900 H. H, Luten 40 41 94 I 9 24 in 12 905 H. 105,000 Thacher R., Feb. 9, '07.. ^- - 43 176 CONCRETE BRIDGES AND CULVERTS. TABLE III Continued LIST OF REINFORCED CONCRETE BRIDGES Number. PLACE. Over. No. Span . 02 *s 1 1 % i 1 "c 1 4 ^ 55 52 40 SO 42.7 7.5 28 18 22 54 16 56 50 54 53 16 36 26 27 45 I Z 3 o 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 7^ 75 76 78 79 80 81 82 Canal Dover, Ohio Pelham " Draw Span Tuscarawas River. Chester Bay Passaic River Wabash River .... Des Moines River. . Hoosatonic River . Sangamon River . . 1 (i 1 1 1 2 2 2 3 1 2 2 1 2 1 2 2 2 12 1 2 2 2 3 1 2 2 1 5 1 2 1 3 1 8 10 1 2 1 70 105 62 108 100 95 80 75 100 100 100 93 95 90 90 86 80 74 75-90 88 83 76 69 88 87 83 79 85 83.5 81 81 80 80 77 75 75 75 73 75 10 16.5 'l2" 15 13 T27.7 23.9 [20. 10 30 11 15.7 11.5 10 9.3 8 22-25 "9 .'5 "8 11 8.5 8.2 8 9.7 15 8 7 7 11 11 14.7 522 807 360 686 360 124 640 'm 620 1200 588 317 493 144 494 107 187 130 305 30 30 20 28 24 32 15 60 "26" 30 tt 45 30 i< 18 30 18 20 16 18 18 30 'EL" 3 C.' 3C. 3C.' 5 CY Seg. Seg.' Seg. Paterson, New Jersey Wayne St., Peru, Indiana Sixth Ave., Des Moines, Iowa. . Stockbridge, Mass Decatur, Illinois Yorkton, Indiana . Cartersburg, Indiana Washington St., Dayton Waterville, Ohio '.'..... Main Street, Dayton it i> 134 m '"ii" '"x" 8 18 24 12 33 36 1903 1906 1897 1906 1901 1903 1901 1906 1905 R. R H. 21,803 33,900 16,500 ' 'l7,5bo' ' 48,000 Luten Douglas Riboud R., Aug.ie, '02. N., Aug. 14, '02 Rib. Rib. Marsh Bridge Co. Leonard R.,' Feb.' 24, '06 ! 1897 H. Concrete Steel Co. 178 ' CONCRETE BRIDGES AND CULVERTS. TABLE III Continued LIST OF REINFORCED CONCRETE BRIDGES 1 83 84 85 86 87 88 89 DO 91 92 93 94 9,5 96 97 98 9i) 100 101 102 103 104 105 100 107 IOS 10':) 110 111 112 113 114 115 116 117 118 119 120 121 122 PLACE. Over. i & 3 2 4 5 3 '3 3 3 7 1 2 4 2 2 1 3 3 1 11 3 7 15 1 2 7 11 1 1 18 1 1 2 2 2 1 CO 8 js 75 75 70 95 74 74 74 72 72 70 70 70 70 70 70 70 70 69 66 66 62 60 60 59 54 50 50 50 50 45 45 40 43 42 40 38 42 39 35 38 & 'A J I 240 565 284 284 '586 163 300 201 240 89 242 270 845 755 1025 92 161 446 613 83 l6i9 65 150 53 "56 82 216 1 ^ 32" 56" 70 60 54" 46 33 16 26 64 32 24 14 20 52" 35 33 16 23 23 17 25 26 45 16 20 15 6 63 16 48 1 6 C 3 o Par El. El. 3C. 3C. ' C.' ' C. 5 C.' 3C. Par. 3 C.' Se^ 3 C.' Seg.' Seg. ' C.' ' "Big Four" bridge near Terre Haute "is" 12" 9.5 9.5 "j, 2 10 14 20 7 18 10.5 9 7 14 12 8.5 15 8.5 8 4 12.5 11 12 6.2 5.7 8.5 6.8 4 "7.'e 7.2 6.5 7 24 "26 18 18 "20 "19" 45 15 24 13 14 20 "30 32-40 24 "is" 22 22 "22" 12 11 "s 'J7 Wabash, Indiana Mission Ave., Spokane Olive Ave., Spokane Meridian St., Indianapolis Illinois St. Northwestern Ave., Indianapolis Derby Conn. Charley Creek Spokane River. . . Fall Creek Waterloo, Iowa ^ Eden Park, Cincinnati Logansport, Indiana Park Drive Pine Creek Trinidad, Colorado Wabash, Indiana Seventeenth St., Boulder, Col Miners Ford Guaya River Porto Rico Boulevard Bridge, Philadelphia Jacksonville, Florida Herkimer, K Y Sandy Hill, N. Y." '.'.'.'.'.'.'.'.." Franklin Bridge, St. Louis Lima, Ohio Plainwell, Michigan Maryborough, Queensland ComoPark, St. Paul Atlantic Highlands, N. J Glendoin, Cal Forest Park, St. Louis London, Ohio Cruft St., Indianapolis Oconomowoc, Wisconsin Columbia Park, Lafavette. .... Interlaken Bridge, Minneapolis Plainfield, Indiana Chicago, C. & E. I. Ry . . . . '.'.'.'. R. R. Tracks W. Canada Creek . Hudson River. . . . Park Stream Kalamazoo River . Mary River Tracks Grand Ave San Gabriel River . River Tes Feres . . Trim Creek. ".'..'... REINFORCED CONCRETE ARCH BRIDGES. 179 TABLE III Continued LIST OF REINFORCED CONCRETE BRIDGES Crown Thickness in Inches. 1 i ro "a'x'i" "i6"'i 10" I I 1 1 1 ^ w S ffi O s / Engineer. References. E.G., Eng.-Con. N., " News R., ' Record a id t & 1 J 1 'l8 '27' 16 16 '14 15 14 40 14 18 14 13 "is" 21 ii 20 18 18 10 10 'ii' 14 9 24 '36 36 "8"' 36 12 12 18 24 12 12 'ii' '36' 8 21 24 36 '(}' 12 12 1900 1900 1902 1895 1905 1905 1905 1906 1907 1901 1903 1902 1906 1897 1907 1903 1896 1904 1896 1902 1907 1905 R. R H. ' ii.' ' H. R. R. H. 'H.' ' H.' ' E. u R. H. E. R. H. F. B. H. E. R. E/R. H. Duane 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 1C6 107 108 109 110 111 112 113 114 115 116 117 118 19 120 21 22 Hilty 55,000 ' 54,400 50,900 Mclntyre Ralston Jeup Jeup Concrete Steel Co. . N., Dec. 5, '07. 'N.,'Apr.'ii,''6i" N., Apr. 11, '01.. E.G.',' Mar. '17,' '07 R., Feb. 13, '04 N., Oct. 3, '95. '2': 65 2.90 2166 4! 75 3^40 i&xii 9" I H m & &i ""\y* "8"'l * Frame 6 ;/ j- ....... H 54,000 25,680 149,900' 77,000 5,640 ' '19,900 75,000 ' '12,600 Concrete Steel Co.. Von Emperger. . . . Wells Hibbard R., Sept. 22, '06.. R., Feb. 10, '06. Kahn National Bridge Co. Luten Ju son Con crete Steel Co. . Osborn N.,' Aug.' 'i,' ; oi ; '. R., Apr. 20, '06 . . E.G., Sept. 2, '08 . Burr Dean Luten Courtright Brady MelanCon.'Co'..'!. Mercereau N., May 9, '07 . R., Dec. 10, '98 . N.,'May'l2,"'04^ R.,Nov.l7, '00. N., Apr. 6, '05 . 2.15 1.84 '1^96 5.30 '4!31 Luten N.,' Oct.' 19,' ''99.': 10 is 14 13 26 H 5 12 '4 6 8 1902 1900 1905 H. H. R/R. Luten Hewett Luten 6.55 12,000 E.c!,Sept.2, '08 i PART III. Highway Beam Bridges. Comparison of Arch and Beam. The advantages of arch bridges have already been described in Part I of this book, and original formulae have been given from which the approximate cost of concrete bridges may be determined. One of the chief merits of arch bridges is that when properly designed, they may be made beautiful in outline. Some of the advantages of beam bridges are as follows: (1) It is possible in a beam bridge to locate the grade of the bridge floor much lower and nearer to the high water level or other clearance line than can be done when an arch is used; (2) foundations for beam bridges may be built on soil that is more or less yielding, which cannot be done with arch bridges, unless hinges are used at the center and spring. The lateral thrust of arches on soft foundations is liable to cause serious injury to the structure, while the corresponding amount of settlement under the abutments of beam bridges produces no injurious effect. A frequent objection to the use of beam bridges is that they are not susceptible to artistic treatment. It will be seen, however, by referring to Figures 37, 38 and 39, that beam bridges may be designed that are equally pleasing in appearance to arch bridges, and for many locations are more suitable. In making a selection between an arch and a beam design, the chief consideration will generally 181 HIGHWAY BEAM BRIDGES. 183 be their relative cost. The cost of concrete arch bridges has already been given by the formulae referred to above, and for the purpose of compar- ison, the costs of concrete beam bridges, in spans ranging from 4 to 40 feet in length, are given in the tables on Figures 38 and 39. The estimated costs of these beam bridges include the filling, pave- ment and two lines of railing, but do not include lamps or other purely ornamental features. On Figure 38 is given also a table of approximate costs for concrete abutments of various heights, which estimates also include railing and pavement to- gether with earth excavation and back filling in the abutments. These estimates will enable the de- signer to compare the relative cost of arch and beam bridges, and to select the form which he finds most economical. TABLE IV SPAN 2 ABUTMENTS Estimate Length Thick Rods Steel Lbs. Cone. Cu. Yds. Cost Ft. In. In. Sq. In. cc. 4 6 K 10 112 1.5 $ 70 6 6 % 10 232 2.2 110 8 7.5 X 8 365 3.7 150 10 9 % 7 510 5.5 200 ]2 11 % 6H 612 8.1 250 11 12.5 74 7 970 10 8 310 16 14 % 6 1 4 1160 13.9 370 18 16 % 5L/ 2 1540 17.7 410 20 18 % 5 1880 22.2 510 Height Cost 4 $ 280 5 340 6 410 7 510 8 650 9 770 10 880 11 1030 12 1190 Beam Bridges. Concrete beam bridges have been built in spans up to 70 feet in length, but they are not generally economical for lengths exceeding 35 feet, for above this length arch bridges will cost the least. HIGHWAY BEAM BRIDGES. 185 The economical lengths and forms for concrete beam bridges are as follows : Simple slabs are eco- nomical for spans up to 12 feet. Beam bridges similar to Figures 37 and 39, supported on parallel longitudinal beams, are economical for spans from 12 to 25 feet in length, while above 25 feet it is economy to use two lines of heavy side beams carry- ing light cross beams supporting the floor slab. To determine the economic span length to use in a long bridge containing several intermediate piers, TABLE V Span Side Beam Center Beam Estimate Cone. Rods Cone. 1 Rods Cone. Steel Cost Ft. Ft. In.Sq. Ft. In. Sq. Cu. Yds. Lbs. 8 12x20 2- 3 12xlfi 3- k 3.8 656 $ 164 10 12x20 2- % 12x18 3- M 4.9 850 207 12 12x20 3- % 12x20 4- % 6.1 1160 256 14 12x20 3- % 12x23 4- % 7.3 1360 304 16 1HX21 3-1 12x27 4- % 8.9 1780 360 18 14x22 3-1 14x28 4- 7 8 11.2 2000 420 20 14x25 3-1H 14xM2 4-1 13.3 2550 490 22 14x28 3-1*8 14x35 4-1 15.5 2800 545 24 14x31 4 - 14x39 4-1H 16.2 3350 603 26 14x34 4 - 14x42 4-1*8 20.7 3620 682 28 14x37 5- 14x46 6-1 23.8 4-460 775 30 16x38 5 - 16x46 6-1 28.2 4770 855 32 16x41 6- 16x50 ,6 -1H 32.0 5800 960 34 16x44 6-1 16x54 6-1*8 35.7 6200 1090 , 36 16x48 7-1 16x57 8-1 39.8 7000 1140 38 16x52 7-1 18x58 8-1 45.5 7450 1244 40 16x56 T-1H 18x62 8-1*8 51.2 9400 1400 the rule is to select such a span length that the cost of one span will be approximately equal to the cost of a pier. Methods of Design. Single span concrete bridges of either slab or beam design must be considered non-continuous, but for a series of spans the effect of continuity in the beams may be considered. To provide for this continuity, it is customary to pro- 186 CONCRETE BRIDGES AND CULVERTS. portion the beams for only 80% of the maximum bending moment. The floor slabs must be pro- tected from injury by a sufficient depth of earth filling, which is shown 12 inches on Figures 38 and 39. This provides depth enough for bedding ties of street railway tracks. A suitable pavement or wearing surface may be laid on this earth filling which may be renewed as required. It is permissible and good practice in designing small concrete beams which are united by slabs, to consider the effect of a portion of the floor slab and to proportion the beams as T beams. Large longitudinal beams carrying floor loads directly to the piers, should be proportioned as simple beams without considering the effect of the adjoining slab. They will then have additional strength due to the presence of such slab. The bridges shown in Figures 38 and 39 are de- signed for total loads of from 400 to 500 pounds per square foot of floor surface. It is customary to provide for impact either by adding a percentage to the live load or by using a factor of 2 for dead load stresses, and a corresponding factor of 4 for live load stresses. It has been proven by numerous experiments that the adhesion of concrete to metal is sufficiently great so no additional bond is required, but as voids in the concrete are liable to occur and it is difficult to always secure the highest grade of work- manship, it is desirable to use rough bars with mechanical bond. As provision must also be made HIGHWAY BEAM BRIDGES. 187 for shear by the use of inclined or bent rods and stirrup irons, it is desirable in all large beams, to use reinforcing bars which have the inclined stir- rups or shear members rigidly connected to the main tension metal. In all bridges where appearance is any consider- ation, the railing should be designed with care so the design may properly harmonize with the rest of the structure. Generally speaking, the balus- trade that presents the best appearance on a con- crete bridge is one composed of either natural or artificial stone, but it is also evident (Figure 39) that an equally artistic effect may be secured with an ornamental metal railing and stone or concrete posts and pedestals. Open balustrades are usually preferable to solid ones, not only because they are susceptible to more artistic treatment, but also be- cause their light and open design emphasize by con- trast the solidity and strength of the supporting structure beneath them. Solid balustrades are per- missible chiefly for through bridges, where the con- crete side girders standing above the roadway form a sufficient protection. The exposed girder surface may then be paneled or otherwise ornamented. S w 188 PART IV. Concrete Culverts and Trestles. Since the introduction of reinforced concrete as a building material, many railroad companies are re- building their permanent bridges and culverts in concrete, either plain or reinforced. The use of re- inforced concrete for culvert construction has be- come almost general with the raihoad companies, while the building of trestles in this material is grad- ually coming into favor. Many old wooden struc- tures, both of the open and the gravel deck types, are being repjaced by better ones of concrete ma- sonry 7 . Amor.g the railroad companies that are using reinforced concrete extensively for the con- struction of trestles may be mentioned the Illinois Central, the Cleveland, Cincinnati, Chicago & St, Louis (Big Four), and other branches of the New York Central Railroac system. A notable concrete trestle or viaduct that has attracted much attention is the one recently built at Richmond, Virginia, for the Richmond & Chesapeake Bay Railroad Com- pany. This viaduct is 2,800 feet in length, and varies in height from 18 feet at the ends to 70 feet near the middle, and is shown in Figure 40. At At- lanta, Georgia, there is a reinforced concrete viaduct carrying Nelson street over the tracks of the South- ern Railroad. It contains 10 spans of various lengths from 20 to 75 feet, has a total length of 480 feet, and is shown in Figure 41, The main line of the Big Four Railroad is carried for a distance of iS9 190 CONCRETE BRIDGES AND CULVERTS. 1,200 feet across the Lawrenceville Bottoms on a reinforced concrete trestle 20 feet in height. This entire region is periodically flooded with backwater from the Ohio and Miami rivers, making it neces- Fig. 41. NELSON STREET VIADUCT, ATLANTA, GEORGIA. sary to build, not only this road, but all others in the vicinity at an elevation of 30 feet above low- water level of the Ohio River. On the following pages are designs and estimates for about 1,000 railroad culverts and trestles, and CONCRETE CULVERTS AND TRESTLES. 191 the estimated costs are given on charts shown in Figures 46, 47 and 66. Tt will be seen that the trestle designs are equally suitable for culverts, and may be adapted for that purpose by increasing their width to correspond with the depth of structure below the base of rail, or to conform to the depth of the embankment. When used as culverts, abutment wing walls must be added and the nature of the foundation soil may be such as to require culvert pavement. These modifications in the trestle estimates may easily be made either for one or more openings, and adapted for either single or double box culverts. The culvert designs are shown with a minimum depth of filling of not less than 3 feet above the con- crete top. This depth is desirable not only for the purpose of distributing the live load from the engine and train Avheels, but also for the purpose of form- ing a cushion to absorb and distribute the shock and impact from rapidly moving trains. Trestle de- signs G and H, Figures 64-65, are shown with a 3-foot depth of filling. It frequently occurs, how- ever, that thin floors are necessary and only suf- ficient depth can be secured for the usual 15 inches of ballast. This arrangement has been shown in trestle designs A to F inclusive. (Figures 58 to 63.) Required Size of Culvert Opening. The most important consideration effecting the final cost of a culvert is the selection of its form and size. It frequently occurs that structures of 192 CONCRETE BRIDGES AND CULVERTS. too large a size and excessive cost are specified, when smaller ones \vould be ample to carry off the greatest rainfall. The selection of the proper size of culvert is of much greater importance than any consideration of design. If a culvert costing $10,000 be specified, where a smaller one costing only $5,000 would bo sufficient, the loss by such an error would evidently be $5,000. On the other hand, if the size of struc- ture as specified be used, the engineer may by care- ful estimating, select a form with the required wa- terway, and with a cost of only $8,000. The saving in this case is only $2,000, whereas, if greater care had been given to the selection of the proper size, there might have been a saving, not only of this $2,000, but of $5,000 additional. It will be seen, therefore, that the one consideration outweighing all others in effecting the final cost is the selection of a structure with the necessary waterw r ay. In the State of Wyoming there are four bridges within a short distance of each other, carrying a road over the same stream. The last of these bridges to be built has two spans 65 feet in length, or 130 feet extreme. The second bridge has two 40- foot spans, and is SO feet in length. The third has a single CO-foot span, while the fourth is an old 30- foot wooden truss, which has for fifty years proved itself sufficient to meet even flood conditions. There are, therefore, in close proximity to each other four bridges over the same stream, the longest of which is four times greater than the shortest, and the long- CONCRETE CULVERTS AND TRESTLES. 193 est one was the last one built. After selecting a length of structure four times greater than required, it is possible that the engineer may have spent con- siderable time and thought in his endeavor to build this bridge at the least possible cost, and may have succeeded in saving a few hundred dollars on his original estimate. A bridge 130 feet in length would cost approxi- mately $7,000, while a 30-foot bridge would not ex- ceed $1,500. This saving is, therefore, only a frac- tion of the saving that might have been effected, had a 30-foot bridge been used, which length had proved sufficient for half a century. The most reliable data on which to base the size of a prospective structure is the high-water level of previous years. It is frequently possible to obtain such data from local records, or to determine the size from that of other bridges passing the same flow of water in the near vicinity. In the case re- ferred to above, if the engineer, before building the 130-foot bridge, had made sufficient inquiry, he could easily have learned that a 30-foot span had carried the entire stream discharge for fifty years, and was therefore large enough for the rainfall of the future. It is not economy to provide openings of sufficient size to carry the rainfall of freshets or cloudbursts that may not occur oftener than once in a century. For such unusual occurrences it is better to make occasional repairs than to invest additional money in larger structures than may ever be required. 194 CONCRETE BRIDGES AND CULVERTS. when such money might be drawing interest to cover the cost of an occasional repair. Where reliable data in reference to the maximum rainfall cannot be obtained, it is customary for the railroads to build temporary wooden trestles at the proposed bridge or culvert site, and to make these trestles unnecessarily long, so there will be no doubt whatever of the openings being large enough. These temporary bridges will last from six to ten years, and during this period careful observations of the water flow may be made, and other data secured from which to determine the necessary culvert area. As the cost of these temporary trestles will not ex- ceed $10 per lineal foot their entire cost may easily be saved by selecting the minimum required size for the permanent structure. Where no reliable data in reference to the volume of water is obtainable, the culvert area may be com- puted approximately by a empirical rule know r n as Meyer's Formula, which is as follows: The Re- quired Culvert Area=^ Drainage area in acres X F, where F is a coefficient varying from unity for flat country, to 4 for rolling or mountainous country, from which rainfall is discharged at a greater ve- locity. The proper value for this coefficient for any particular location must be selected entirely by the judgment of the engineer. Reinforced Concrete Box Culverts. The following series of designs for single and double box, reinforced concrete railroad culverts, in- CONCRETE CULVERTS AND TRESTLES. 195 eludes between 800 and 900 separate estimates, and is therefore very comprehensive and complete. The charts of comparative costs, Figures 46 and 47, show these to be more economical than any other form of culvert, excepting perhaps reinforced concrete oval culverts of the form shown in Figure 57. While arch culverts of this latter form may contain less ma- terial than box culverts of equal area, they are more difficult to build because of their curvature, even though collapsible centers be used. Several large railroad systems in America are now using arch cul- verts of this general form, in place of the old seg- mental or semicircular types, which contain more masonry in the abutments than in the arch wing. Loads. There is much uncertainty in reference to the amount of load carried by the cover of a rail- road culvert. The amount of this load depends to a great extent on the depth of the culvert top below the base of rail. The greatest load occurs when the depth of filling above it is a minimum, for then the culvert top is subjected to the entire load from the locomotive wheels and their impact. On the con- trary, when the culvert is buried beneath a deep embankment, the live load and impact is so distrib- uted and dispersed that only a part of this load goes directly to the culvert. Various writers have en- deavored to show that these loads are distributed crosswise of the embankment, and slope outward from the railroad ties at the rate of one foot hori- zontal for every two feet vertical. The pressure on the base of these triangles varies from zero at the 196 CONCRETE BRIDGES AND CULVERTS. outer point to a maximum under the end of tie. This assumption is only an approximation, though a rea- sonable one. Unfortunately, however, the author of this hypothesis assumes that the earth pressures slope outward at each side, but makes no provision for similar distribution lengthwise of the embank- ment. It is quite evident that whatever distribution of loads does occur, must occur equally in all direc- tions, and the assumption referred to above is there- fore incorrect. Where a culvert has a small depth of filling above it, the entire weight of such filling is then sup- ported by the culvert, but if located at the bottom of a high embankment, the culvert then carries only a portion of the live load above it, supporting also a portion only of the earth embankment. The amount of this portion depends upon the nature of the embankment material. If this material is ce- mented well together, it will then tend to support itself by acting either as an arch or beam, and there- by relieving the culvert of much superimposed load. The most reasonable assumption is to consider that the culvert carries the weight of a triangular sec- tion of the embankment, the sides of which slope outward from the vertical in the ratio of one foot horizontal to two feet vertical. If the embankment material is composed of clean sand, a larger propor- tion of the imposed material will then be borne by the structure. In view of the uncertainty of various conditions effecting the amount of load on culvert tops, it has been determined that these loads can CONCRETE CULVERTS AND TRESTLES. 197 never exceed the values occurring under a minimum depth of earth filling. An assumed live load on each track equivalent to Cooper's engine load E. 50, spread out by the ties, rails and ballast, produces a distributed load on the culvert top of 1,100 pounds per square foot. To this has been added impact, amounting to 50% of the live load, or 550 pounds per square foot. Adding to these the weight of ties, rails, ballast, earth filling and concrete in the culvert top, pro- duces a total load of from 2,100 pounds per square foot for small culverts with thin slabs, to 2,400 pounds per square foot for larger spans with a greater thickness of concrete. The following box culvert tops are therefore proportioned for total loads of from 2,100 to 2,400 pounds per square foot. From the theory of horizontal earth pressure, it is known that the thrust per square foot on an em- bedded vertical surface is equal to one-third of the corresponding horizontal pressure on a unit of area at the same level. This condition exists w r hen the embankment is composed of clean, dry sand with an angle of repose of about 30 degrees. The proper amount of pressure to assume on the culvert side is therefore from 700 to 800 pounds per square foot, or one-third of the corresponding roof loads. As the sides are, however, subjected to vertical loading and impact from moving trains, the assumed side pressure has been taken at one-half of the vertical, or from 1,050 to 1,200 pounds per square foot. On account of the liberal provision for impact, 198 CONCRETE BRIDGES AND CULVERTS. amounting to 50% of the live load, high working values have been used for concrete and metal reinforcement. A reasonably rich concrete mixture, such as 1-3-5, has an ultimate crushing value of 2,800 pounds per square inch. One-fourth this amount, or 700 pounds per square inch, is there- fore assumed as a working unit for concrete, anl 12,000 pounds per square inch as a working unit for reinforcing steel. Economic Length for Slabs and Beams. There is evidently a limit where economy ceases in the use of flat slabs for supporting loads in bending, and above that limit the economical construction is a combination of beams and slabs. For the purpose of determining these economic lengths, a slab table (Table No. VI) has been prepared, giving the amount of concrete and steel and the estimated cost per square foot for spans varying in length from 4 to 24 feet, and total imposed loads of from 2,100 to 2,400 pounds per square foot. TABLE VI REINFORCED CONCRETE SLABS SIMPLE SPANS TOTAL LOADS 2100 TO 2400 LBS. PER SQUARE FOOT. Span. Effective Depth. Total Cost per Depth. Sq. Bars. square ft. Cents. 4 6 8 10 12 14 16 18 20 22 24 6 9 12 15 18 21 24 28 31 34 37 7 . 5 8.4 i 10.5 7 s 13.5 " 8 17.0 1 20 . 1 23.0 1 28 . 1 M 30 . 5 1 \i 33 .5 1 M 37.0 1M 40.0 l l /i n. 7 } 2 in apa rt. 30 . 6 43 6 56.0 71.6 85.7 97.7 110.2 131.5 146.5 159.0 170.0 4 CONCRETE CULVERTS AND TRESTLES. 199 A corresponding set of ten tables was made giv- ing the amount of material and the estimated costs per square foot for a combination of beam and slab construction, with spans varying from 6 to 30 feet in length, and beams spaced from 6 to 18 feet apart, on centers. The cost results from these ten tables are given on the chart, Figure 42. The thickness of slabs and beams are proportioned so the stress at the outer edge will not exceed 700 pounds per square inch from dead, live and impact loads. The thicknesses were determined from the writer's orig- inal formula where M. is the bending moment in inch pounds, d the distance from slab top to center of ten- sion bar, and K a variable factor. It is advisable to neglect the effect of continuity in proportioning slabs, even though a considerable amount doubtless exists, Avhich would reduce the slab thickness by about 20%. Slab thicknesses are, therefore, given, as required for non-continuous beams. From the comparative cost chart, Figure 42, the following conclusions are obtained. For loads of from 2,100 to 2,400 pounds per square foot : Simple slabs are economical for clear spans up to 7 feet in length. Slabs with beams 6 feet apart are economical for spans from 7 to 14 feet in length. 200 CONCRETE BRIDGES AND CULVERTS. i (X 1 / / / / / / ^ / /* / C Y / / w ,1< f / ' /} }/( ^ vi y / ' / % // - 7 / / j /, // ) k | 3 / / / $ // k. f / 7 / S '/ / . ft z 1 * ' r 3 f / 7 / / f 6 E 1 K / / / ty / ^ r ,/ q / / { l/ / '/ / tV: x / / / / z / ^ / i 1 j / / / ^ It ^ t t / hW / / / / j / <3 { f [ / { { / $ 2 x > M / / > / y / S sp ^ f / v // / \ 7L / / y 4 / * ? -i y / / A // Vy / / / / 4 ft ' > s /(, // ^ /] / iV / / / ^ i\ / I/ ZE / 4 ^ / > f / 4^ / / / * / 9 / / L '* 1 r J & Vj / / t > . <,' /i ^ c s/ c R r g a. /: y 0. / / / | / s r L < ^ / 2 s. / ^ I y / / / / ' ^ x r / . ' / ^ P/ fl i 2 / j ^ Comparative Cost per Sq. Ft. Combination of Slabs and Beams for Various Beam Spacing also Cost of Simple Slabs. Total loads 2100 to 2100 Ibs. sq. ft. / I / L / / \ 1 y /y L ) y 1 /*? J.$o J-20 1.10 I-OO -Bo So 7o 60 5o Zo' Fig. 42. CONCRETE CULVERTS AND TRESTLES. 201 Slabs with beams 7 feet apart are economical for spans from 14 to 20 feet in length. Slabs with beams 8 feet apart are economical for spans from 20 to 30 feet in length. The comparative cost chart, Figure 42, was ob- tained from 130 separate estimates, and the conclu- sion from it is that slabs for the above loads are not economical for greater lengths than 8 feet or greater thicknesses than 12 inches. Figures 43, 44 and 45 are typical drawings for single and double box railroad culverts for both slab, and a combination of beam and slab construc- tion, and Tables VII, VIII, IX and X give the cor- responding sizes, quantities and costs for culverts varying in area from 4 to 480 square feet. These tables give separately the quantities and cost for the two portals and for the culvert barrel per foot of length, and also the lengths and total costs of culverts for six different heights of embankment, varying from 10 to 50 feet. The single and double slab culvert tables contain 34 different sizes each, varying from 2 feet by 2 feet to 12 feet by 12 feet for each opening, while the combined beam and slab culverts contain 30 corre- sponding sizes each, varying from 8 to 20 feet in width, and from 4 to 12 feet in height. The esti- mated costs of these culverts for banks 20, 30, 40 and 50 feet in height are shown in Figure 46. These curves represent the cost of the economic forms, which generally have openings of a greater height than width, such as 4 feet wide by 6 feet high, either 202 Is.; Illil 204 CONCRETE BRIDGES AND CULVERTS. TABLE VII REINFORCED CONCRETE, SINGLE BOX, RAILROAD CULVERTS SLAB CONSTRUCTION TO ACCOMPANY FIGURE 43 1 -S ^r ~ 4 Top and Bottom Sides. [Quantities, per liri. ft. 2 Portals. af 09 Square Rods. c.c. (Concrete, In. Square Rods C.C. Concrete.C.Y. A 1 M Concrete.C.Y. A 1 cc I 1 2 2 4 6 ^/2 /f 6" 6 V4" 12" .19 22 2.43 1 . 78 14 2 " 'J 6 " i// . jo .23 26 2.91 3.40 27 3 3; 2 6 83^9 " *4 18 .28 35 3.69 3.55 23 4 " g 9 " " " 7 " 15 .34 43 4.50 4.00 32 5 4 12 " " " S 12 .42 51 5.39 4.50 200 44 6 " t] 15 " " 9 10 .51 62 6.55 6.00 250 58 7 4 2 8 93^ 71 / (5 18 .36 58 5.25 3.85 40 8 " 3 12 " " " 7 15 .42 55 5.60 4.30 34 9 " 4 16 8 12 .50 65 6.66 5.50 250 54 10 5 20 " " 9 " 10 .59 75 7.75 6.80 300 66 11 " 6 24 " " " 10 8 .69 92 9.26 8.70 500 89 12 5 3 15 103^-7 8 15 .55 66 7.06 5.00 500 72 13 4 20 " " 9 12 .64 75 8.10 6.70 600 65 14 " 5 25 " " " 10 " 10 .74 86 9.42 8.50 800 84 15 " 6 30 " tt tt 10 8 .79101 10.3710.40 1000107 16 " 8 40 " i " 12 6 1.04132 13.6013.00 1600136 17 (5 4 24 12:% 7 10 7 ^ 12 .83113 11.2210.00 900116 18 36 " it tl 10 " 10 .96134 12.9712.40 1200147 19 " 8 48 " " " 12 8 1.20168 16.3013.70 1800173 20 " 10 60 " " " 14 6 1.4? 216 20.6015.00 2200208 21 8 4 3214 12 12 1.18139 15.0012.00 900132 22 " (i 48J" 12 10 1.33185 18.0022.00 1800248 23 " 8 64" " " 12 8 1.47215 20.4030.00 2200328 24 "10 80 " tt tt 14 6 1.76265 24.7043.00 3200472 25 10 4 4017 1 51,4 If) 1 15 1.71241 23.3018.00 1400200 26 " 6 60 " " 15 12 1.84266 25.4028.00 2200312 27 " 8 80 " " " 15 12 2 . 07 282 27.9037.00 3200424 28 "ilOlOO " " " IS 10 2.50324 32.9046.00 4000'528 29 "12120 " " " IS 8 2.88381 38.3057.00 5000*656 30 12 4 48 20 1 4'4 IS 15 2.33327 31.8023.00 1800256 31 "6 72 18 12 2.56362 34.9037.00 2800'378 1)2 "8 96 18 12 2.78378 37.3052.00 4000576 33 "10 120 " 20 10 3.00412 40.4068.00 5000 744 34 " 12 144 " 120 8 3.40466 45.80J82.00 6500916 CONCRETE CULVERTS AND TRESTLES. 205 TABLE VII Continued REINFORCED CONCRETE, SINGLE BOX, RAILROAD CULVERTS SLAB CONSTRUCTION TO ACCOMPANY FIGURE 43 10 ft. Bank. 15 ft. Bank. 20 ft. Bank. 30 ft. Bank. 40 ft. Bank. 50 ft. Bank M ~S> j a 1 M J 1| J w I .a 1 3 I -a I I be J 1 39 106 54 145 69 182 99| 254 129 327 159 400 1 36 122 51 175 66 219 96 305 126 392 156 479 2 39 172 54 228 69 283 99 393 129 501 159 611 3 35 189 50 257 65 324 95 458 125 593 155 727 4 32 216 47 296 62 376 92 538 122 696 152 859 5 29 248 44 346 59 444 89 643 119 838 149 1033 6 38 230 52 318 68 386 98 546 128 700 158 861 7 35 230 50 314 65 399 95 564 125 734 155 1004 8 32 267 47 366 62 466 92 664 122 864 152 1064 9 29 291 44 407 59 522 89 756 119 986 149 1216 10 26 330 41 467 56 609 86 884 116 1157 146 1439 11 34 312 49 417 64 524 94 737 124 947 154 1162 12 31 315 46 427 61 547 91 772 121 1050 151 1295 1,3 28 348 43 489 58 630 88 914 118 1194 148 1484 14 25 365 40 532 55 675 85 987 115 1297 145 1607 15 34 598 49 801 79 1206 109 1616 139 2016 16 31 366 46 631 61 806 91 1136 121 1486 151 1816 17 25 470 40 662 55 857 85 1247 115 1637 145 2017 18 34 725 49 762 79 1453 109 1943 139 2433 19 . 28 783 43 1090 73 1708 103 2328 133 2928 20 30 582 45 807 60 1032 90 1482 120 1932 150 2382 21 . 40 968 55 1238 85 1778 115 2318 145 2848 22 . 34 1020 49 1328 79 1938 109 2548 139 3148 23 28 1157 43 1522 73 2262 103 3072 133 3732 24 30 900 45 1250 60 1600 90 2300 120 3000 150 3700 25 39 1297 54 1682 84 2442 L14 3192 144 3962 26 33 1339 48 1754 78 2594 108 3424 138 4244 27 27 1413 42 1908 72 2888 102 3878 132 4849 28 36 2036 66 3176 96 4316 [26 5456 90 29 1166 44 1656 59 2126 89 3076 119 4026 149 4978 ^ J 30 38 1698 53 2218 83 3278 .13 49Q8 4.Q KCMC 01 32 1766 47 2326 77 3436 107 *^fi7o 4536 LrrO 137 OO^o 5676 >i 32 26 1794 41 2394 71 3604 101 4814 131 6024 33 35 2516 65 3886 95 5266 125 6636 34 206 CONCRETE BRIDGES AND CULVERTS. TABLE VIII REINFORCED CONCRETE, DOUBLE BOX, RAILROAD CULVERTS SLAB CONSTRUCTION TO ACCOMPANY FIGURE 44 1 t ~ I e .j O ^4 '- ^ Top and Bottom] Sides. Quantities per ft. 2 Tortals. Concrete, In. 'quareRod: c.c. j Square Rod C. C. Concrete.C.Y. A I 1 Concrete.C.Y. A i OS i 1 2 2 8 6 6 4" 6" 6'W 12" .32 51 4.60 2.6; 20 2 " 3 12 " " e 10 .38 43 4.72 3.9 31 3 3 3 18 9 8 a^ 9 7 3/ 15 .61 76 7.94 4.9 39 4 " 4 24 " " " " 8 12 .72 89 9.30 5.3 200 50 5 " 5 30 " " " " 9 10 .8410410.85 7.0 250 66 6 4 3 24 12 9 34 _7 14 7 15 .82101 10.52 5.5 44 7 " 4 32 " " " " 8 12 .94114 12.05 6.6 250 62 8 " 5 40 " " " " 9 " 10 1.08129 13.65 8.0 300| 76 9 " 6 48 u " " 10 8 1.19152 15.60 10.0 500100 10 5 3 30 12 103^ 7 8 15 1.08123 13.50 6.7 600| 77 11 " 4 40 " " " " 9 12 1.21 135 15.10 8.2 700 89 12 " 5 50 " . " " 10 10 1.35 151 16.81 9.7 800101 13 " 6 60 " " " " 11 8 .51 174 19.0212.6 1000140 14 " 8 80 " " 12 6 .79 232 23.6515.0 1600184 15 6 4 48 12 12% -7 10% -12 .62 206 21.1011.0 900124 16 " 6 72 " " " " 11 10 .89239 24.5018.0 1200192 17 11 8 96 " " " " 12 8 .20285 29.0024.0 1800264 18 " 10 120 " " " " 14 6 .62353 35.5030.0 2400336 19 8 41 64 15 14 7^ 5 1// 12 12 .35 306 30.9014.0 900148 20 " 6 96 " " " " ' 12 10 .65 338 33.7020.0 2000246 21 " 8128 " " " " 12 8 .95 384 38.9027.02700304 22 10160 (1 14 6 .36 457 45.3037.03200424 2310 4 80 15 17 i sms 1 15 3.36 462 45.5015.0 1400176 24 " 6120 " " 15| 12 3.75 498 49.6025.0 2200288 25 " 8160 " " 15 12 4.11 522 53.5037.0 3200424 26 27 28 12 10200 12240 4 96 18 20 1 4^ IS IS IS 10 8 15 4.70577 5.10660 4.62647 60.5047.04000536 66.8062.05000696 62.8020.01800232 29 " 6144 " " " -jis 12 5.08685 67.6035.02800 392 30 31 32 " 8192 1 O OOO !_->*>> " ] '< " IS 2!) 20 12 10 8 5.50708 6.02759 6.55'838 71.7045.04000520 78.0062.05000,696 85.0075.06500'860 CONCRETE CULVERTS AND TRESTLES. 207 TABLE VIII Continued REINFORCED CONCRETE, DOUBLE BOX, RAILROAD CULVERTS SLAB CONSTRUCTION TO ACCOMPANY FIGURE 44 10 ft.B'k!5 ft. Bank. ! 20 ft. Bank 30 ft. Bank 40 ft. Bank. 50 ft. Bank. .d J V* 1 1 & & JS t JS .d a 1 53fi 91 7450 121 9450 ?Q 25 3660 55 5760 85 7860 115 991030 210 CONCRETE BRIDGES AND CULVERTS. TABLE X REINFORCED CONCRETE, DOUBLE BOX, RAILROAD CULVERTS BEAM AND SLAB CONSTRUCTION TO ACCOMPANY FIGURE 45 c Top and Bottom. Sides. Per Lin. ft. 1 ! I J Rods. Rods. 1 & 5 i ?' ^ ail || - 9 8 II S K g^ 2 c ' S O ! -O EH > f- p ^ ^ / y 2 Y* ^ " /. -7 ^/ ^ /. ^ M ^ M ~ ^ / /, ^ / 3 > s / /^ * / s . ^ / / , ^ / > 2 V ^ s S /< / ' t s / ^ / /> / / ^ ,/ . <: P > ' / /> f J ^1 ' / / ~. ^ ^ / / / i / > ^ t > 1 '\ / / s 1 ) S / y j !^ =t ^o*' /oo'' /So'' Tor At. /?*e# of Wfirc'/vw/tY. Fig. '47. 20^ 218 CONCRETE BRIDGES AND CULVERTS. No. 3 are concrete rail top culverts having slabs 15 to 18 inches thick, and reinforced with rails spaced 38 inches apart for a 6-foot span, 10 inches apart for an 8-foot span, and 6 inches apart for a 10-foot span. Xo. 4 are reinforced concrete arches, similar to those in use on the above named railroads. Xo. 5 are concrete arches without reinforcement. Xo. 6 are segmental stone arch culverts as pro- posed by Mr. Baker in his book on Masonry Con- struction. Xo. 7 are reinforced concrete box culverts, similar to Xo. 2, excepting that they are without bottoms 2: Portals Concrete 72 yds. $8.00 == $576 Steel 3450 Ibs. @ .04= 13S *714 Barrel per lln. ft. Concrete 468yds. (& $8.00=$374 Steel 450 Ibs. @ .04= 180 $554 Length for 20 ft. bank = 32. Area = 180 sq. ft. Cost $2490. Fig. 48. CONCRETE CULVERTS AND TRESTLES. 219 and cost proportionately less. They have offset footings under the side walls. No. 8 are rubble stone box culverts, the kind most commonly used by the railroads until recently, for small openings. No. 9 are wooden box culverts, and while they are not permanent, they have the merit of being the least expensive of all. No. 10 are the new standard reinforced concrete box culverts, as shown in Figures 43, 44 and 45, the quantities and cost of which are given in Tables VII, VIII, IX and X. An actual cost record for building a 4-foot con- crete arch culvert under a railroad embankment in Idaho, during the thirty days from June 5th to July llth, 1903, is as follows : Foundations contain 111 yards, and cost $5.00 per yd. Upper part contains 137 yards, and cost 7.00 per yd. Average cost about 6.00 per yd. Cost of whole culvert per cu. yard of concrete. 10. 00 per yd. Portland Cement used, 272 barrels. Cost 2.70 perbbl. Foreman paid $150.00 per month. 1 Finisher paid 3.00 per day Laborers paid 2.00 per day 4 Carpenters paid 3.00 per day Labor cost $1723.00 Material cost 830.00 Total $2553.00 Concrete made entirely from sand and gravel at rail- road company's pit, without any broken stone. Other Common Culvert Forms. Figures 48 to 57 inclusive, show other forms of culverts, and Table 220 CONCRETE BRIDGES AND CULVERTS XI contains their estimated quantities and costs. For the purpose of comparing these with others, the costs have been estimated for lengths required under a 20-foot embankment, and these costs are given in Figure 47, together with their correspond- ing numbers. They vary in cost from 26 to 36 cents per square foot of section area, for each lineal foot of culvert. Figure 48 is a reinforced concrete box culvert 12 feet high and 15 feet wide, with rod reinforcement, similar to the new single box slab culvert. For so large a section area, the slab type is not economical. Figure 49 is a reinforced concrete box culvert of combined beam and slab construction, 12 feet high 2 Portals: Concrete 74 yds.@s8.00 Steel 4720 Ibs. @ .04 Barrel per ft. Concrete5 . 8yds.fr *H.oo Steel 5151bs.@ .04 Length for 20 ft. bank Area = 230 square Cost = $2930. = $592 = 188 $780 =$464 = 20.6 $67.0 = 32 ft. feet. Fig. 4i>. CONCRETE CULVERTS AND TRESTLES. 221 and 20 feet wide. For an area of this size a more economical form is secured by using a double box of the same general type. Figure 50 is a beam top culvert, 12 feet high and 15 feet wide. The culvert top is arched 3 feet and the arch strength is considered when proportioning 2 Portals: Concrete 88yds. @ $8.00=4704 Barrel per lln ft. Concrete 6. lyds. @$8.00=$48.8 Steel 240 Ibs. @ .04= 9.6 $58Ti Length for 20 ft. Bank=32 feet. A rea = 161 sq. ft. Cost = $2570. Fig, 50. the thickness of the culvert top. Culverts similar to this have been used by the Illinois Central Railway Company. Figure 51 is a concrete box culvert with rod rein- forcement similar to Figure 58, excepting that in it offset footings and cobble stone pavement are used instead of a reinforced concrete pavement slab. 222 CONCRETE BRIDGES AND CULVERTS. < 1 2 Portals: Concrete 88 yds. @$8.00=$704 Barrel per lin. ft. Concrete 6. 2 yds. @$8.00=$49.0 Steel 150 Ibs. @ .04= 66 $556 If foundation is depressed as shown dotted, then area = 172 square feet. Length for 20 ft. bank=32ft. Cost =$2480. Fig. 51. Figure 52 is a reinforced concrete box culvert of beam and slab construction, 12 feet high and 20 feet wide. For so large an area, a double box of the same type will be more economical. Figure 53 is a culvert of the same dimensions as Figure 52, with solid concrete side walls, bottom cobblestone pavement, and roof reinforced with dou- ble lines of 60-pound track rails, united with %-inch. Figure 54 is a reinforced concrete arch culvert with buttressed side w r alls and slab pavement. Structures similar to this are used by the Northern Pacific Railroad. CONCRETE CULVERTS AND TRESTLES. 223 '^^^^7^''' QUANTITIES 2 Portals: Concrete 113 yds. fi $8.00=1904 Steel 14500 Ibs. (a, .04= 580 11484 Barrel per lin. ft. Concrete4.fi yds. (ft $8.00=$36.8 Steel 700 Ibs. @ .04= 280 $64.8 Length for 20 ft. bank =25 ft. Ar ea = 240 sq. f t . Cost $3 1 00. Fig. 52. Figure 55 is a beam top culvert 12 feet high and 20 feet wide, similar to Figure 50. It will be seen that neither of these types are economical. Figure 56 is a parabolic arch culvert. Figure 57 is a reinforced concrete arch culvert possessing greater merit than any other form of arch culvert now in use. It contains the least amount of material, the saving being chiefly in the sides. Masonry arch culverts of the old type, whether built of stone or concrete, have the greater part of their material in the side walls or abutments. Figure 57 is designed similar to a tunnel center, or a sewer arch, and its form and light construction 224 CONCRETE BRIDGES AND -CULVERTS. are possible only because of the presence of rein- forcing metal in the arch ring. Culverts of this general form are being used by several of the rail- road companies and are economical. They have a disadvantage, however, in requiring the use of curved forms, but this is overcome to some extent by using collapsible centers. A modification of this form of culvert using a semicircular top, is also shown in Figure 57. Mr. Luten's rules for proportioning such arches under railroad banks, in spans of 50 feet or less, and with a depth of earth filling above of not less than 10 feet, are as follows : Crown Thickness D.= 30 2 Portals: Concrete 88 yds. @ $8.00 $701 Barrel per lin. ft. Concrete 8 yds. @ $8.00 = $64.00 Steel 1015 Ibs. @ .015= 15.22 $7V.22 Length for 20 ft. bank = 30 ft. Area = 250 sq. ft. Cost $30hO. Fig. 53. CONCRETE CULVERTS AND TRESTLES. 225 span : ^o" Back of abutments batter one in four. The number of square inches of steel for one edge per lineal foot of arch is __ 400,000 D. L is the live load in pounds that can be concen- trated on the half arch for one track. 2 Portals: Concrete 47yds. @ $8.00 = $376 Steel 1600 Ibs. @ .04= 64 $140 Barrel per ft. Concrete 3. lyds. @ $8.00=$24.8 Steel 170 Ibs. @ .04= 6.8 $31.6 Area = 92 sq. ft, Length for 20 ft. bank = 42 ft. Cost for 20 ft. bank, $1780. re, Fig. 54. 226 CONCRETE BRIDGES AND CULVERTS. C704 2 Portals: Concrete 88 yds. (&, $8.00 Barrel per ft. Concrete 7.25 yds. n t-^ c s^' oo to cc o lsS - el ^lOW5Ot-COOJOlM ssass^ oo o cj -* SS S a 5 236 I a w H U PC! H I G O 238 CONCRETE BRIDGES AND CULVERTS. Design D. Figure 61. This type is similar to Design B, but differs from it in having a sufficient thickness of concrete, reinforced with steel beams, to carry the entire loads by the bending resistance of the concrete slab. The steel beams are covered on the lower side with a 2-inch layer of concrete. The lower two inches only of the steel beams arc considered effective as tension metal, for concrete reinforcement. Beams are spaced about 18 inches apart on centers. Piers have corbels and in propor- tioning the thickness of the slabs the effective span length is assumed one foot shorter than the actual, because of the presence of these corbels. Design E. Figure 62. This is a reinforced con- crete trestle design, both span and piers having rod reinforcement. In the two previous pier designs, reinforcing steel is omitted, but for Design E one- half inch square rods are placed 18 inches apart both horizontally and vertically. These rods serve not only to prevent cracks from change of tempera- ture, but also resist any tensile stresses which might occur in thin piers, due to the sudden stopping of heavy trains on the bridge. The spans are slab con- struction, with a 10-inch slab for 6-foot span, in- creasing to 36 inches for a 24-foot span. Design F. Figure 63. Like the previous one, this design is reinforced entirely with rods, but is a combination of beam and slab construction. Longi- tudinal concrete beams are placed 10 feet apart in the clear, and to these loads are transmitted by means of 18-inch transverse slabs, carrying the Fl S S \ W S S 3 5S S N P5 a5 r iil 8 * O rt 3 O S I cc o W O> H A o O J* send I OUOQ I 1991S rH ICS O ,H,H,-I 1 1 1 1 1 i 1 1 i isoo OUOQ 8 S3 2 O H U |3 P4 O co |0 Q M s 3f co fM W J H 240 I 1 1 1 1 S 2 s ' "3 B 4 &* s to oo 8* i *. ?o t o (M d W ti 000 g o 1 ^-. 8 S $ 5 ^OQ Hi t 1C <^* | ^ j. Hi 1 H 1 t* S c H P o> *o w tajn'-a- - 1 ! fi *" o j S !.Vi! S '*' 1 f "? ^ ^- -2 - - ^ S ^ ^^ f ' i S \ 2 -d ft H \S' ;! I i!J s ;J - s 3 | -3 o i? // mm*~~m ."MOW O* H w 1 241 242 CONCRETE BRIDGES AND CULVERTS. track and ballast. The side beams are each 2 feet in width, while the center beam is 4 feet. The load per lineal foot on the side beams varies from 8,500 pounds for a 10-foot span to 9,300 pounds for a 2-4- foot span. Designs G and H. Figures 64, 65. These are designs for single track trestles, similar to E and F already described. They differ, however, in that G and H have a 3-foot depth of earth and ballast filling. Comparative Trestle Costs. The comparative costs for the foregoing trestle spans for both single and double track structures is given on the chart, Figure 66. The horizontal ordinates represent clear spans in feet, while the vertical ordinates give the costs in dollars for a complete span, not including piers. This chart clearly shows that reinforced concrete trestles of the types marked E and F with rod reinforcement are more economical than any other form of perma- nent trestle, with solid roadway. The chart shows further that reinforced concrete railroad trestle spans of slab constructions are economical for single track in spans up to 14 feet, and for double track in spans up to 20 feet. Above these lengths the economic form of span is a combination of beam and slab. Comparative Cost of Short Span Bridges. i & /* /S oo 3.. C I 1 ( / OLD X* LJ ,v PLA KooS o# C I > 2 l f *" /a 1 I AS A 2. / 1 / / y A / ~*-\ / / * ^ j I / ? t ifL ? X / > V / |/ ? g ^5(> 1 2 ^. y 1 iy X ^ t u/ 1 ^ 2 5 / ^/ S /^ ' ? ^ ^, X /* ^ r (^ X X // >x ^ x" ix ^ / ^T * K^J I*" 1 * ^ fr & > - ( &' /O' /S' to ZS'Ci** Fig. 66. 243 INDEX. Page Abutments ...55, 57, 148 Movements of 10 Rankine's Rules for 58 Trautwine's Rules for 55 Abutment Piers 11, 54, 70 Trautwine's Rules for 55 Adda River Bridge 80 Adhesion, Concrete to Steel 108, 114, 116, 126, 186 Advantages of Masonry 1 Aisne River Bridge 176 Almendares, Cuba Bridge... 97 Augustus, Bridge of 3, 75, 76 Anthony Kill Bridge 97 Anderson. L. W 169 Approximate Computations.. 32 Aqueduct of Vejus 106 Arcade Spandrels 19 Arch Ring, Thickness of 50, 51 Architectural Design 100 Area of Arch Ring, Required 69 Atlantic Highlands Bridge.. 178 Atlanta, Georgia, Viaduct. . .189 Auckland, New Zealand, Bridge 80 Austell, Georgia, Bridge 178 Austrian Experiments 105 Avranche, France, Bridge.. 174 Backing 52 Baker's Masonry Construc- tion 59, 218 Balustrade 187 Batter of Piers 150 Bearing Power of Soils 59 Bellefield Bridge, Pittsburg. 18 Beam Bridges 181, 183 Advantages of 183 Cost of 185 Design of 185 Bending Moments 133,135 Biddle, Col. John 89 Binnie 96 Big Muddy River Bridge 17, 60, 89, 116 Blome, Rudolph S 163 Block Structures 7 Bond, Mechanical 108 Contractors' 157 Boston, Bridges in 63 Borrodale Bridge 95 Bormida Bridge, Italy 174 Bosnia 176 Boulder, Col 178 Page Boulder Faced Bridge. 166, 168 Brookside Park, Cleveland.. 97 Brick Arches ' 1 Brick, Strength of 34 Brooklyn, Seeley St. Bridge.176 Brunei 30 Brown, Wm. H 98 Building Lintels 5 Burr, Wm. H...80, 147, 159, 179 Bush, Lincoln 96, 98 Buda Pesth 176 Cain, Prof. Wm 128 Carriage Travel Loads 123 Cantilever, Action of 5 Concrete 10 Caius Flavius, Bridge Built by 74 Casey, E. P., Architect. .87, 159 Canada Creek 178 Carter 98 Cartersburg, Ind 176 Canal Dover, Ohio 176 Cedar Rapids, Iowa 176 Centers 7 Chester Bay 176 Charley Creek 178 Chicago Park Bridge. .. .169, 172 Chatellerault, France, Bridge 174 Church, Prof. I. P 42 Cincinnati Park Bridge 104 Cleveland, Rocky River 81, 82, 83, 84, 95 Colfax Ave., So. Bend 176 Columbia Park, Lafayette. . .178 Courtwright, P. A 179 Composition of Arches 1 Concrete 120 Cost of Solid Concrete Bridges 63 Re-Concrete 150 Slab Bridges 183 Beam 185 Piers 183 Concrete Steel Engineering Co 163 Como Park, St. Paul 61, 163, 167, 178 Conjugate Pressures. . .4, 31, 67 Continuity of Arch 7 Colonnade Spandrels 19 Computations, Approximate.. 32 245 246 INDEX. Page Cooper's Engine Loading 49, 197, 229 Connecticut Ave. Bridge 60, 87, 88, 95 Competitive Designing lot Corrugated Bar 118 Cracks 107 Cruft St. Bridge, Indianap- olis 178 Crum Elbow Creek 178 Crittenden, H. M 175 Crown Thrust 39, 40, 43 Crown of Arch., Rise and Fall 10 Thickness 14 Radius 15 Filling Depth of 16. 67 Crushing of Arch Blocks, 33 34 Cut Water on Piers 150 Cunningham, A. O 177 Culverts 189 Required openings for 191 Box 194 Tables of 205, 207, 209, 211 Cost Chart 213 Side Walls 215 Comparative Cost 216 Comparative Cost Chart.. 217 Other Common Forms of.. 219 Curves for 8 Cushion, Filling as 16 Cup Bars 118 Danville Bridge 72, 97 Danube River Bridges 95 Dayton, Ohio 174, 176 Des Moines Bridge 63, 176 Detroit Ave. Bridge, Cleve- land 64 Cost of 81, 82, 83, 84, 95 Development of Concrete Bridges 102 Design, Ultra Refinement in 7 General, of Re-Concrete. . .136 Diversity of 18 Beam and Slab Bridges. . .185 Dean, John 161, 179 Delaware River Bridge 95 Decize, France, Bridge 174 Decatur, 111., Bridge 176 Decorah, Iowa, Bridge 176 Derby, Conn., Bridge 178 De Mollins, M. S 175 De Palo, Michael 175 Deck, Kind of 138 Deck Bridges, Preference for.108 Diversity of Design 18 Diamond Bars 118 Douglas, W. J 81, 89, 166, 177 Drainage of Arches 52 Page Duane, W. M 98, 179 Earth Slopes 5 Eads Bridge, St. Louis 145 Economic Span Lengths 230 Edmonson Ave. Bridge 95 Eden Park, Cincinnati. .104, 178 Elastic Theory 128 Electric Car Loads 123 Ellipse 8 lo Draw 20 Elliptical Intrados 145 Emperor Augustus 4, 76 Embankments, Loads from.. 5, 30 Emperger, Von ....104, 177, 179 Empirical Rules 139 Emerichsville 174 Engine Loading Cooper's E-50 49 Estimating 154 European Practice 10 External Loads and Forces 4, 29 Expansion 60 Expansion Joints 148 Expanded Metal 118 Eyach River Bridge 97 False Work, Removal of 11 Fall Creek 178 Felgate, A. M 85, 96 Filling-Crown 16 Load from 30 Over Elliptical Arches 32 Earth 32 Finish, Surface 60 Five Centered Arch, To Draw 22 Merits of 145 Fire Insurance 157 Floor Renewals 2 Fluid Pressure 8 Flat Arches 107 Floors 107 Fleischman, Eduard 98 Florida 178 Forms 8 Forms, How ti Draw 20 Selection of Most Suitable. 27 Cost of 154 Forces, External 29 Polygon of 39 Foundations 58 Fort, E. J 177 Fort Snelling, Concrete De- sign 80, 153 Frankfort Creek Bridge 97 Friction, Sliding 33 Franklin Bridge, Forest Park 161, 162, 178 Funicular Polygon 67 INDEX. 247 Page Gary, Ind., Bridge 163, 1G5 Galicia Bridge 176 Garfield Park Bridge, Chi- cago 169, 172 General Outline 8 Germantown Bridge 82 General Design of Re-Concr. Bridges 136 Geisel Construction Co 161 Geostatic Arch, To Draw... 24, 29 Glendoin, Cal., Bridge 178 Golden Gate Park Bridge... 61, 104 Granite, Strength of 34 Green Island, Niagara ... .61, 174 Gruenwald 80, 95 Grand Rapids Bridge 166, 169, 170, 176 Grand River 174, 176 Grand Tower. Ill 89, 95 Grand Ave., Milwaukee 119, 126, 143 Green, Prof. Chas. E 128 Guaya River 173 Gwynns River 95 Hawgood. Henry 91, 98 Hammond, A. J 163 Hainsburg Bridge 97 Height of Bridges 12 Headroom Under Bridges... 66 Heyworth J. O 163 Hewett, W. S 166, 179 Herkimer, N. Y 178 Hinges 7 Hinged Arches ..10, 129, 132, 140 History of Concrete Bridges. .102 High Tension Steel Ill Highway Beam Bridges 181 Hilty 179 Hibbard. M. S...., 179 Huntington. Ind 174 Hudson Memorial Bridge 72, 77, 78, 95 Hudscn River Bridge, Sandy Hill 153 Hydrostatic Arch, How to Draw 24, 26, 27 Hyde Park on Hudson 176 Idaho, Bridge in 48 111. Cent. R. R. Bridges.... 17, 60, 89, 116 Standard Culverts 221 Illinois River Bridge, Peoria.149 Illustrations of Bridges 71 lller River Bridge 95, 141 [mpact 127, 229 Imnau, Bavaria 97 Interlaken, Minneapolis ..,.178 Page Intermediate Piers 69 Ingersoll, C. M 80 Intrados Form 145 Inzighofen Bridge 95 Indianapolis, Morris St 174 Meridian St 178 Illinois St 178 Cruft St 178 Northwestern Ave 178 lola. Kansas 178 Irrigation Canal, in Idaho.. 48 Isar River Bridge. 95 Jacksonville, Florida, Bridge. 178 Jacaquas River Bridge 174 Jamestown Exposition Bridge' 59, 160, 161, 174 Jefferson St., South Bend... 161, 164, 174 Jeup, B. J. T 179 Joints, Expansion 148 Tension in 7 Judson 175, 17d Kahn, Julius 179 Bar 118, 120 Kansas River 174 Kalamazoo River . .178 Keepers 175 Kempten Bridge 95, 141 Key West, Florida 97 Kissinger Bridge 140 Kirchheim Bridge 97 Kresno, Galicia 176 Laibach, Austria 174 Lake Park, Milwaukee 174 Law of Lever 131 Larimer Ave., Pittsburg. . . . 97 Lawrenceburg Trestle 190 Lansing, Mich 174 Lautrach, Germany 95 Leffler, B. R 175 Leonard, John B '....117 Length of Span, Economical. 13 Lea, A. B 85 Leibbrand, Max 96, 98 Lindenthal Gustav 177 Lima. Ohio 178 Liquid Pressure 5 Lintels 5 Line of Resistance, Indefinite 7 Determination of 36 Position of 42 For L T niform Load 43 For Partial Load 45, 129 Linear Arch 9, 28 Limestone, Strength of 34 Liability Insurance 157 Logansport, Ind 178 London, Ohio 178 248 INDEX. Page Loire River 174 Local Labor 2 Loads 121 Load, Contour Reduced 41 Adjustment to Form 19 External 29 Uneven 68 On Culverts 195 Long Key Viaduct 97 Luten, D. B 175, 177, 179 Truss 118 Luten's Empirical Formula.. 224 Luxemburg 80, 144 Mary River 178 Maryborough Bridge 178 Maumee River Bridge 176 Marsh Bridge Co 177 Maintenance 2 Masonry, Strength of 6 Mathematical Theory of Arch 32 Materials, Strength of 34 Marachina River, Italy 76 Main River 97 Main Street Bridge, Dayton.. 176 Mclntyre, Charles 179 Melan, Prof. J 103, 175 Merits of Concrete Bridges.. 107, 103 Metal Reinforcement Ill Medium Steel Ill Meyer's Formula 194 Mechanicsville Bridge 97 Mercereau 179 Milwaukee Viaduct 119 Miltenburg 97 Mississippi River 97 Middle Third of Arch Ring. . . 33 Miners Ford 178 Mission Ave., Spokane 178 Miami River 174, 176 Monroe St. Bridge, Spokane. 72 Moisseiff, L, S 80 Morsch, Prof. J 81, 96 Morrison, George S 80, 96 Monier, Jean 103 Morris St.. Indianapolis 174 Monolith Frame 118 Murray, Paul R 177 Multi-Center Curve 9 To Draw 20, 21 Municipal Art League 78 Munderkingen 85 Navier's Principle 24 National Zoological Park 61 New York Bridges 73 New Zealand, Longest Ma- sonry Span 80 Page Neckar River 85 Bridge 95 Nelson St. Viaduct, Atlanta. 189 Newark, N. J 174 New Goshen, Ohio 176 Newton, Ralph E 175 Neckarhausen, Germany .... 95 Niagara Falls, Green Island.. 61, 174 Nimes, Aqueduct, France. . .105 Noise, Absence of 107 Northern Pacific R. R Cul- verts 222 Nobel, Alfred 98 Oconomowoc. "Wis 178 Olive Ave. Bridge, Spokane.. 178 Open Spandrels 17 Ornamental Bridges 99 Osborn. Frank C 17! Outline, General 139 Parkhurst, H. W 91, 96 Park Bridge Design 99 Pantheon, Rome 106 Painting 2 Painting Reinforcing Steel.. 116 Parabolic Arch, To Draw 23, 134, 147 Pavement 16 Pavement Slabs 215 Pavement Ties 56 Paulins Kill 97 Painsville, Ohio 1 7'4 Paterson, N. J 176 Plainwell, Michigan 178 Passaic River 176 Partial Load, Line of Press- ure 45, 68 Peoria Bridge 149 Pelham Bridge 176 Peru, Ind., Bridge 176 Pena River 174 Philadelphia 85, 86, 87, 95 Philadelphia, Tacony Creek. 97 Piney Creek 18, 97. 142 Piers, Thickness of.. 66, 148, 150 Cost of 183 Abutment 11, 54, 70 Intermediate 53, 69 Pier Thrust, To Balance 14 Pine Creek ITS Pittsburg, Pa 9 1 Piles, Batter and Plumb 59 Load on 59 Playa Del Rey 174 Plainfield, Ind 178 Plauen, Germany 80, 85 Potomac Memorial Bridge... 147, 153, 159 River 87 INDEX, 249 Page Portland, Pa., Bridge 95 Porto Rico 174, 178 Portugal 174 PollusKy, Cal 176 Pont Du Gard 105 Ponte Rotto, Rome 3, 73, 74 Pons Aemilius 74 Palatinus 74 Lapideus 74 Polygon, Force 39 Pole 39, 67 Distance 43 Point of Rupture 50 Pressure Curve, To Deter- mine 36 Pressure of Liquid 5 Sand 5 Pressure on Surfaces, To Find 42 Prices, Estimating 155 Preservation of Steel 114 Pyrimont, France 174 Quimby, Henry M 87, 98 Quantities, Approximate 158 Railing 187 Ralston, J. C 179 Rankine's Rules for Crown Thickness 14 Pier Thickness 53, 66 Rankine's Method of Draw- ing Hydrostatic Curve.. 26, 27 Rules for Abutment Thick- ness 58 Railroad Bridges 2, 3 Reinforced Concrete Arches, Costs 150 Table of ..174, 175, 176, 177. 178, 179 Part II 100 Advantages of 106 Reynolds 175 Reduced Load Contour 41 Reilly and Riddle 87 Reinforcing Steel 101, 111 Reinforcing Systems 117 Retaining Walls 122 Rhone River 174 Riverside, Cal, 91, 92, 93, 94, 97 Riboud 177 Richmond, Va., Trestle 154, 188 Rise of Arch 8. 40, 66 Rise and Span 12 Ribbed Arch 129, 142 Rockville Stone Arch 61 Roxborough, Pa 87 Rocky River Bridge, Cost of 64, 95. 80, 81, 82, 83, 84 Rotation of Arch Blocks.. 33 Page Rock Skewbacks 28 Rock Creek 87, 176 Rome, Ponte Rotto 3, 73, 74 Roman Arches 8 Length of Spans 13, 73, 74, 75, 76 Rusche, J. P 169 Rupture, Point of 50 Santa Ana Bridge, Cal 55, 91, 9^, 93, 94, 97 San Gabriel River Bridge.. 178 San Joaquim River 176 San Francisco Bridges 61 Sangamon River 176 Sandy Hill, N. Y 153, 178 Sarajero, Bosnia 176 St. Paul Bridges 174 St. Joseph River 174 St. Louis, Eads Bridge.. .145 Sand Pressure Sandstone, Strength of . . . . 34 Scofield Engineering Co.. 161, 175 Schillinger Bros 85 Seeley St. Bridge, Brooklyn.176 Schenley Park Bridge 18 Schemers Theorem 32 Semi-Circular Arch 8 Senators' Bridge 74 Segmental Arches 8 Culvert Arches 14 Selection of Most Suitable Form 27 Sewer Arch 32 Simpson and Wilson, Engi- neers 96 Sitter River 81 Skewback, Rock 28 Slab Table for Culverts 198 Slabs, Cost of 200 Slab Reinforcing 118 Slab Arches 129 Slab Bridges, Table with Costs 183 Slab and Beam Bridges 198 Slopes, Earth 5 Sliding of Blocks 33 South Bend, Ind 174 Soissoins. France 176 Solid Arches, Tables of 95, 96, 97, 98 Soil, Bearing Power of 59 Spokane, Mission Ave 178 Olive Ave 178 River 178 Monroe St 79. 72, 97 Spandrels 147, 16, 17 Spandrel Columns 138 250 INDEX. Page Spandrels, Arcade or Col- onnade 19 Spandrel Filling 28, 37 Springs, Low 149 Position of 10 Span 12 Spuyten Duyvil Creek ..78, 95 Stony Brook Bridge, Bos- ton 63 Steyr, Austria 145, 174 Stability Requirements. .33, 136 Stockbridge, Mass 176 Stein-Teufen Bridge 173 Steel Reinforcement ..101, 111 Strength of Re-Concrete Arches 107 Stirrups 117 Survey for Bridge 157 Surface Finish 60 Switzerland Bridge 81 Tacony Creek 97 Telephone at Bridge 157 Terre Haute 178 Test Loads 1 Tension in Joints 7 Tension in Concrete 114 Teufen Bridge. Switzerland.173 Temperature Stresses. .124, 150 Thickness of Arch Ring 135 Thebes Bridge 97 Thames River Bridge 95 Thacher, Edwin 18, 119, 177 Thacher Bars 118 Three Centered Arch, To Draw 20 Merits of 145 Theory, Mathematical 32 Theory of Arches 126 Thrust on Piers, Unbal- anced 53 Ties on Bridge Floors 107 Ties, Pavement 56 Tiber River. Rome 74 Topeka Bridge, 10, 31, 149, 174 Trestles 1S9, 228 Economic Spans 200 Rail Tops 230, 231, 232 Beam Tops 233. 235 Steel Beam Decks 234. 23r, Beam Tops 236, 238 Slabs, Rod Reinforcement. 237, 238, 240 Beams, Rod Reinforce- ment 238, 239 Comparative Costs 242 Chart 243 Temporary 48 Trinidad, Col 178 Trim Creek . ..178 Page Truss System 4 Trautwine's Rule for Crown Thickness 14 Abutment Piers 55 Travertine, Used in Rome 74 Trial Method of Design 146 Tubesing, W. F 169 177 Tuscarawas River . 174 Turner, F. M 175 '177 Turner, C. A. P 144, 175 Tunnel Arch 5 Twisted Rods us Twisted Lug Bars llg Tyrrell, H. G., Concrete Bridges Designed by 48, 62, 99, 167 Tyrrell, M. K., Designs by 182, 184 Ultra-Refinement in Design. 7 Ultimate Values 34 Ulm, Germany 95 Uncertainty of Masonry 4, 129 Unit Pressures 33 On Surface. To Find 42 Working 35 Ultimate and Working. . .125 Unit Reinforcing Frame 118 Uneven Loading 68 Unsymmetrical Arch 139 Various Forms, To Draw... 20 Values, Ultimate 34 Varying: Span Lengths 13 Vauxhall, London 95 Vermillion Riv. Bridge, Wakeman 9. 30, 174 Vermillion Riv. Bridge, Dan- ville 72, 97 Vejus. Aqueduct of 106 Venice. Cal 169. 171 Viaducts over Yards 13, 66 Vibration. Absence of 107 Vienne River 174 Von E'mperger 104, 177, 179 Washington, D. C., Rock Creek 176 Connecticut Ave 87, 88, 166, 168 Washington St., Daj'ton. . . .176 Waterloo, Iowa 178 Wabash. Ind 140, 178 Waterville, Ohio 176 Wayne St.. Peru. Ind 176 Walker 177 Wakemen. Ohio 9. 30, 174 Walls. Thickness of Span- drel 19 Loads on 29 Waterproofing 52, 216 INDEX. 251 Page Watersoaking 110, 115 Waterway, Width of 56 Walnut Lane Bridge, Sur- face Finish 60 Cost of ....64, 142, 80, 85, 95 Warren, Whitney, Architect. 80 Watson, Wilber J 85, 175 Waidhofen 174 Wells, W. H 179 Webster, George S..85, 96, 98 Whited, Willis ...; 98 Wildegg. Switzerland 174 Wise, C. R 177 Wilson. George L 179 Widening Concrete Bridges. 3 Page Window Arches, Load on... 6 Wire Net Reinforcement 118 Width of Deck 138 Wing Walls 149 Wissahickon Creek 95 Workmanship 7, 110 Working Units 35, 106 Wood Bridges, Competition with 102 Wunsch, Professor 116, 177 Wyoming Ave., Philadel- phia 97 Yellowstone Park Bridge... 174 Zesiger, A. W 98 Koehring Mixers are built in all sizes and styles with any kind of power. Write for Special Catalogue No. 4. KOEHRING MACHINE CO. MILWAUKEE :: :: :: WISCONSIN "CHICAGO AA" 1,000,000 Barrels Annual Production. Highest Quality Portland Cement 15,000 Barrels Used in CHICAGO'S NEW CITY HALL AND COOK COUNTY COURT HOUSE Specified by the leading Architects, Engineers and Contractors for all work requiring a strictly high grade and absolutely uniform Portland. "WE MAKE ONE BRAND ONLY THE BEST THAT CAN BE MADE." CHICAGO PORTLAND CEMENT CO. 108 La Salle Street, CHICAGO, ILL. (Instructive Booklets on Request.) EUREKA MIXERS A Portable Mixer of Good Capacity For Particular Work. ASK FOR CATALOGUE "C." EUREKA MACHINE CO. LANSING, MICH. DESCRIPTION OF The Longest Simple-Truss Bridge Span in Existence, BY H. G. TYRRELL, CIVIL ENGINEER. FOR SALE BY THE ENGINEERING NEWS NEW YORK CITY 24 Pages. 5 Illustrations. 6x9 inches. Paper Covers. Price, 50 Cents. What is Engineering-Contracting? Engineering-Contracting is a weekly journal for civil engineers and contractors, edited by Halbert P. Gillette, M. Am. Soc. C. E. author of the "Handbook of Cost Data" and other books for Engineers and Contractors. Engineer- ing-Contracting might be termed a serial sequel to this "Handbook," for no issue is printed that does not contain valuable cost data. This feature alone makes the paper one that no civil engineer or contractor can afford to be without. Mr. Gillette has just completed his appraisal of all the rail- ways in the State of Washington, acting as Chief Engineer for the Railroad Commission. Data of cost of all kinds of railway structures, secured from the original records of rail- ways, are now being printed in Engineering-Contracting. The "Methods and Cost" articles that are appearing cover so wide a range that every engineer and contractor should read each issue. Mr. Daniel J. Hauer has recently become one of our associate editors. Mr. Hauer is well known as an authority on earth and rock excavation. The other asso- ciate editors include : Mr. Charles S. Hill, joint author with Mr. A. W. Buel of "Reinforced Concrete," and for eigh- teen years on the Editorial staff of Engineering News ; Mr. C. T. Murray, for many years editor of the construction news department of Engineering News ; Mr. F. A. Smith, author of "Railway Curves," "Maintenance of Way Stan- dards" and " Standard Turnouts. " The entire staff includes fourteen persons formerly with other leading engineering journals, thus placing every department in charge of experi- enced and competent men. Engineering-Contracting is published every Wednes- day and costs only 12.00 for the 52 issues. SAMPLE COPIES FREE. ENGINEERING-CONTRACTING 355 Dearborn Street, Chicago. Concrete Construction Methods and Costs By HALBERT P. GILLETTE and CHARLES S. HILL, This book is unique among all the books on concrete. It is devoted exclusively to the methods and costs of concrete construction, and it gives detailed information regarding every phase of that work. It tells what an engineer or contractor needs in estimating the cost and in reducing the cost of concrete work, both plain and reinforced. The various designs of forms and centers and the layout of plant for mixing, conveying and placing concrete, receive the most complete treatment ever given to these important subjects. The book should be purchased by every con- tractor and by every concrete foreman and super- intendent, for it is the best "correspondence school" on practical concrete construction that has ever appeared in print. 16-page circular FREE. Cloth, 6x9 inches , 700 pages ; 306 illustrations ; price $5.00 net, postpaid. THE MYRON C. CLARK PUBLISHING CO. 355 Dearborn Street, Chicago Concrete and Reinforced Concrete Construction By HOMER A. REID, Assoc. M. Am. Soc. C. E. This is the most complete and comprehensive book ever written on this subject. It is, in fact, a combination of several books in one all original, carefully vvritten and up-to-date. It has 200 working drawings of bridges, bridge piers and culverts; 60 working drawings of sewers, water mains and reser- voirs; 30 working drawings each of retaining walls and dams; 200 working drawings of buildings and foundations, including shops, roundhouses, etc. It has more text pages, more drawings and more tables of test data on concrete and reinforced concrete construction than any other book ever published. No other book on concrete contains one-tenth so much of the very latest data on tests, theory and practice. 9O6 pages, 715 illustrations, 7O tables; $5.OO net, postpaid. 16-page Table of Contents free. The Myron C. Clark Publishing Co. 355 Dearborn St., Chicago Theory and Design OF Reinforced Concrete Arches A Treatise for Engineers and Technical Students. By ARVID REUTERDAHL, Sc. B., A. M. Chief of Bridge Department, Engineering Department, City of Spokane, Wash. The books which have heretofore been published on this subject are either so mathematically abstruse or leave so much to the reader to demonstrate for himself, that they are of little value to the general practitioner or to the tech- nical student whose mathematical ability is not of exceptional order. These objec= tions have been overcome in this book. Every principle is explained thoroughly there are no missing steps in the mathe= matics. The book should be in the hands of every engineer who has concrete bridges to design and of every student of the theory and practice of concrete bridge design. Cloth, 6x9 inches; 132 pages; numerous diagrams and tables; price $2.00 net, postpaid. THE MYRON C. CLARK PUBLISHING CO. 355 Dearborn Street, Chicago Reinforced Concrete A Manual of Practice By ERNEST McCULLOUGH, C. E. This book was written for the practical concrete worker the man on the job who has not the re- quirements of statics and the theories of the mathe- matician at his tongue's tip but who desires, in plain words, the fundamentals of correct design and the practice of sound and economical construction work. Cloth, Sx7f inches; 136 pages; illustrated; price $1.50 net, postpaid. Field System By FRANK B. GILBRETH This book was written by one of the largest general contractors in the world, and contains nearly 200 pages of rules and instructions for the guidance of his foremen and superintendents. It is the out- growth of over twenty years of experience in the contracting business, and embodies scores of sug- gestions for economizing and for increasing the out- put of the men on the job. Mr. Gilbreth is the con- tractor who made the "Cost-plus-a-fixed-sum-con- tract" famous; in doing so, he has likewise made famous Gilbreth's "Field System," only a few ex- cerpts from which have heretofore appeared in print. One thousand copies were sold in the first ten days. In making public his "Field System" Mr. Gilbreth is performing a service to the public that is com- parable with the action of a physician in disclosing the secret of his success in curing a disease. The disease that Gilbreth's "Field System" aims to cure is the hit or miss method of doing contract work. System supplants slovenliness, and makes sloth an absolute impossibility. 200 pages, with illustrations; bound in leather; price $3.00 net, postpaid. THE MYRON C. CLARK PUBLISHING CO. 355 Dearborn Street, Chicago H. G. TYRRELL CIVIL ENGINEER Chicago, Illinois Evanston, Illinois DESIGNER AND ENGINEER FOR ALL KINDS OF Bridges and Structures Special Attention to Selection of Economic Types UNIVERSITY OP CALIFORNIA LIBRARY THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW SEP 13 1915 MAR S 1S27 JAN flPP 2 195. 930 30m-l,'15 194738 r