Economics of bridgework, a sequel to Bridge engineering

Front matter

/ Gl- /. 9}cUJuJl.

A SEQUEL TO BEIDGE ENGINEERING

BY

Preface

The author's object in foisting still another bridge book upon his longsuffering brother engineers is twofold, viz.:

First. A desire to leave behind him for the benefit of the next generation of bridge speciahsts, in shape readily available for use, a solution of all the major economic problems in bridge work and an extensive treatment of most of the minor ones. He has endeavored to cover every possible economic question of importance; and, if any such be omitted, it is because he did not recognize their existence. To what extent he has succeeded in this endeavor can be determined only by the reception which the book meets from the engineering profession.

Second. To show to specialists in all branches of the engineering profession the type of book on economics which, in his opinion, each specialty needs and how broad and thorough, if possible, should be the treatment of the subject.

The author feels that he is the logical person to write a book upon the economics of bridgework, because he has been investigating the matter for thirty-seven years, and has dealt at length, upon more than twenty different occasions, in books, pamphlets, and memoirs, with various economic topics on the subject of bridge designing, as can be seen by referring to the list of the said writings given in the Appendix.

An explanation but not an apology is needed for the fact that certain portions of "Bridge Engineering" have been copied in a few of the chapters. As that work from start to finish is impregnated with the fundamental idea of economy, and as this book is intended to cover the entire field of bridge economics, it was necessary to include herein the gist of all that appears on the matter in that work, as well as the substance of all the author's economic writings that are subsequent to its publication. Wherever an3^hing previously written on the subject could advantageously be modified or enlarged, this has been done; but where it could not be improved upon or augmented, the only thing to do was to copy it verbatim. Hence, should any reader see any portion of "Economics of Bridgework," which appears familiar to him, if he has read this preface he will understand the reason therefor and will, the author trusts, excuse the occurrence.

V

VI PREFACE

In proof of the previous statement that the treatment throughout "Bridge Engineering" is based on the conception of economics, there is offered the following extract from a review of that work written by Albert Reichmann, Mem. Am. Soc. C.E., and pubHshed in the October, 1916, issue of the Journal of the Western Society of Engineers.

"In a larger sense, this work is a treatise on the subject of 'Economics of Bridge Engineering.' This train of thought can be traced throughout the entire work, all subjects being treated fully and in a broad way, and with the idea of value constantly brought out."

There is a salient feature of the present book to which attention should be called, and that is the scarcity of treatment of economic problems by pure mathematics, nearly all the form_ulse given being semi-rational, semi-empirical. The reason for this is that the conditions affecting most of the economic questions in bridge designing are far too complicated to lend themselves to solution by mathematical manipulations. This fact has not always been recognized by engineering writers; for, during the last three or four decades, numerous attempts have been made to settle important economic bridge-problems mathematically, with the result that the conclusions thus drawn have proved to be erroneous and generally totally useless.

It is prognosticated that, in the future, there will be no such fundamental changes in methods of bridge design and construction as to render really incorrect the numerous economic conclusions reached herein; because bridge building has now become fairly well systematized. About the only important change in sight is the adoption of high-alloy steel for long-span superstructures; and the effects of this have been duly anticipated. The reasons for this belief are that the investigations upon which the book is based were in general predicated upon fundamental engineering principles that do not vary; and that the effects of possible changes in unit prices of materials in place and in other general conditions affecting design have been indicated. While it is true that an abnormal variation of a temporary nature in the unit price of some important material of bridge construction, some pecuhar feature of structure-location affecting erection, or possibly some other cause, may change somewhat the findings stated herein, it must be remembered that, as pointed out in several places, up to a certain limit a considerable divergence from the exact economic condition will usually cause no serious augmentation of total cost. This is the saving clause which Hinders the author's economic conclusions sufficiently dependable for th(; future as well as for the present.

The story of the writing of this treatise is as follows:

In the summer of 1916, when "Bridge Engineering" was issued, the author recognized that there was one very important bridge subject that he had not completely covered, viz., economics; and he thereupon listed ten major e(;onomic pro])loms at tliat time unsolved, and came to the determination that they should no longer be left in that condition, if he could prevent it. After repeatedly failing to interest any other investigator in

PREFACE Vll

the matter, he himself undertook the task and accomphshed it, at least to his own satisfaction, in four years of hard work.

The following is a hst of the said economic questions arranged in the order of their final solution:

2. Comparative Economics of Cantilever and Suspension Bridges.

3. Economic Span-Lengths for Simple-Truss Bridges on Various Types of Foundation.

5. Comparative Economics of Continuous and Non-Continuous Trusses.

6. Comparative Economics of Wire Cables and High-Alloy-Steel Eye-bar-Cables for Long-Span Suspension-Bridges.

7. Economics of Reinforced-Concrete, Steam-Railway Bridges.

8. De VEmploi Economique des Alliages d.Acier dans la Construction des Fonts.

9. Bridge Versus Tunnel for the Proposed Hudson River Crossing at New York City.

As fast as these economic investigations were finished, they were separately incorporated in chapters of this book, occasionally in toto but generally with slight modifications or omissions.

In the preparation of a few portions of the manuscript, the author has received valuable assistance from the following engineers, to whom he herewith tenders his hearty thanks: Messrs. Thomas E. Brown, Leon L. Clarke, Watson Vredenburgh, Thomas Earle, C. M. Canady, Harry K. Seltzer, Joseph J. Yates, Frank W. Skinner, Charles F. Loweth, Carl S. Heritage, J. G. Chalfant, Vernon R. Covell, Edward A. Byrne, J. B. W. Gardiner, L. H. Beach, P. S. Bond, A. H. Sabin, and Shortridge Hardesty.

The special portions of the book whereon these gentlemen have aided are indicated throughout the text, excepting in the case of the author's assistant engineer, Mr. Hardesty, who helped with certain of the calculations and gave the entire treatise a general check.

It may be of interest to some readers to learn how Chapter XLIV on "Economics of Military Bridging" happened to be included in the book; for it is a subject concerning which, before the said chapter was written, the author knew practically nothing. Incidentally it came to the attention of Major R. W. Lewis — a young engineer who served with distinction in the American Army on the battle fields of France, and a son of Col. I. N. Lewis, the famous inventor of the machine gun which bears his name, and which so greatly aided the Allies in winning the war — that this book was in course of preparation. He thereupon called on the author and asked if he would consider favorably a suggestion to insert in the treatise a chapter prepared officially by the Engineer Corps of the Army on the subject of

VIU PREFACE

economics of military bridgework. Upon receiving an acquiescent reply, Major Lewis proceeded to the Capital, consulted Major General Beach, the Chief of Engineers, and made a Uke suggestion to him. The result was that the General agreed to write a "Foreword" for the chapter, and detailed Col. P. S. Bond, in consultation with some of his brother officers, to do the writing. The author deems the outcome an exceedingly valuable addition to his book; and he hopes that many of his readers, in consequence of its perusal, will be induced to take such an interest in mihtary bridge engineering as to ensure that they shall be better prepared to serve our country in case of war than were most of the civilian engineers when the call to arms came in 1917.

It is intended that this shall be the last technical book which the author will ever write, for reasons explained in the concluding chapter; and he hopes that it and its immediate predecessor, "Bridge Engineering," wiU, for many a year to come, prove of real service to the engineers of his specialty, in the advancement of which, almost ever since graduation forty-five years ago, he has taken an intense and absorbing interest.

Contents

PAGE

Preface • v

Table op Contents . ix

List of Illustkations xxvii

List of Tables xxxi

Introduction

Necessity for general application of principles of economics. — Labor a blessing — not a curse. — Love for one's work a requisite. — ^Business opportunity of U. S. A. being lost. — Necessity for Americans to work harder and more efficiently. — Increasing national efficiency through application of economic principles. — Importance of the work of the engineer and increasing his efficiency. — Teaching economics in technical schools. — Report of Committee of S.P.E.E. on "The Study of Economics in Technical Schools." — Suggested treatise on "Economics of Engineering." — Author's lectures on "Engineering Economics" at University of Kansas. — -Author's failure to interest others in proposed treatise on "Economics of Engineering." — Presentation of this book as a sample of what is needed in all engineering specialties.

Chapter II

Literature on Engineering Economics very meagre. — Definition of "Economics." — General economic principle. — Economics of proposed enterprises. — Experience requisite for making economic investigations. — -Complication of economic investigations. — Example of economic study for proposed bridge across San Francisco Harbor. — Short-sightedness of promoters. — ^Glaring example of failure for want of economic study. — ^Economic study for proposed bridge over Mississippi River near New Orleans. — Economic study for replacement of a bridge over the Mississippi River. — Method for comparing the economics of several methods of accomplishing the same result. — Method of contrasting several differing types of construction. — ^Mathematical treatment of economic comparison. — Special conditions precluding adoption of most economic method of procedure. — Anticipating the future. — First cost. — Systemization. — Time versus materials. — Labor versus materials. — Compensating factors in economic comparisons and frequent wide range of economic limits. — Economic variation with live loads. — Recording diagrams. — Economics of mental effort. — Labor 6

X CONTENTS

Chapter III Economics Of The Promotion Of Bridge Projects Page

Promoter's inflated ideas. — Keeping down first cost. — -Traffic investigation. — Revenue investigation. — Maintenance and repairs. — Determination re undertaking the proposed venture. — Pedestrian traffic. — Initial temporary economic expedients. — Constructions part permanent part temporary. —East Omaha Bridge, — Growing scarcity of timber 20

Chapter IV

EFFECT ON ECONOMICS FROM VARIATIONS IN MARIvET PRICES OF LABOR AND MATERIALS

Comparative unimportance of market price variations. — Structural metal price variations. — Cement price variations. — Monograph on "Economic Span-lengths for Simple-truss Bridges on Various Types of Foundation." — Suspension-bridge price- variations. — Location affecting economic layout. . . 23

Three fundamental conditions affecting economic question. — Economic criterion for rods or bars. — Economic criterion for plate-girder spans. — Economic criterion for long spans. — Examples computed. — How economic curves were established. — Extension of economic curves into "speculative zone." — Cutting out carbon steel entirely in very-long-span bridges. — Accuracy of the curves. — General applicability of curves for all cases. — Use of alloy steel for bridgework in its infancy. — ^Author's investigation on "Nickel Steel for Bridges." — -Present great demand for nickel prohibits use in bridges. — Other alloys of steel for bridgework. — High-carbon steel not advisable for bridges. — Mayarl Steel. — Vanadium steel. — Silicon steel. — "Purffied steel." — Aluminum steel. — Molybdenum steel. — Nichromol steel. — Improvement by French scientists on Bessemer process. — Study on economics of molybdenum steel for bridgework. — Catalogue re " Molybdenum Commercial Steels." — Proposed nomenclature for various molybdenum-steel alloys. — Legitimate working intensities for molybdenum steel alloys. — Moa^reness of data. — Heat-treated chrome steel with and without molybdenum. — Heat-treated chrome-nickel steel with and without molybdenum. — Ileat-troated chrome-vanadium steel with and without molybdenum. — Heat-treated nickel steel with and without molybdenum. — Heat-treated carbon steel with molybdenum. — Untreated and treated chrome steel with molybdenum. — Assumed unit prices erected for alloy steels. — Best drawing temperature for alloy steels in bridgework. — Carmol steel versus carbon steel. — Chromol steel versus vhromo, steel. Nicmol steel versus nickel steel. — Nichromol steel versus nichro steel. — Chrovanmol steel versus chrovan steel. Best percentage of molybdenum for alloy steels in bridgework. — Comi)ilation of results. — Most i)romisiiig molybdenum alloy for bridge steel 26

CONTENTS XI

Chapter VI Page

Difficulty of comparison. — Must be between one bridge and several tunnels. — ■ Traffic in tunnels. — Ventilation of traffic tunnels. — Comparative agreeableness of passage by bridge and tunnel. — Comparative extents of climbing ia bridges and tunnels. — Comparative costs. — Bridge versus Tunnel for the Proposed Hudson River Crossing at New York City. — Desirability of methods of handUng traffic across the river. — Cost of operation. — Time expenditures. — ^Agreeableness. — Sanitation. — Ventilation. — Carbon monoxide danger.— Approach grades used in the comparison. — Tunnel estimates. — Variation of cost of tubes with diameter. — Comparative cost of a double- track tube and two single-track tubes. — Unit prices for bridge materials in place. — Limitation of cost by efficiency instead of aesthetics. — Cost diagram for bridges and tunnels. — Description of contrasted structures. — Fairness of comparison.— Cost of right-of-way and property damages. — Spiral approaches. — Table of total costs of bridges and tunnels. — Conclusion as to the comparative economics. — Temporary combination of bridge and tunnels. — Suggestion for further study of proposed crossing before committing the pubUc to the present policy 53

Chapter VII Comparative Economics Of High-level And Low-level

CROSSINGS

Definition of terms. — Comparison generally a matter of expediency instead of one of economics. — Using one through span over channel and making all other spans deck structures. — Advantages and disadvantages of the two types. — Approximate average figures of comparative costs. — Capitalization of various aimual expenditures. — Power-cost capitaHzation unnecessary 61

Chapter VIII Comparative Economics Of Steel And Reinforced- Concrete Structures

Difficulty in making comparison. — Variation in market prices an important factor. — Must consider factors of maintenance and repairs. — Greater popularity of concrete structures among non-technical, iminitiated people. — -Comparative limits of life. — Personal equation. — Science of reinforced-concrete-bridge designing not yet so highly developed as that of steel-bridge designing. — ^Esthetics affects costs of reinforced-concrete bridges. — Live load affects the economic comparison. — Designing by inexperienced computers. — Variation in costs of excavation for foundations. — Quick method of settling this economic question. — Practicable limit of span-length for reinforced-concrete bridges. — Settlement of arches during construction. — Effect of height of crossing upon the economic comparison. — Unavoidable generality of treatment of subject and reasons therefor. — Impracticable to reach any fixed or reliable conclusion 64

XIV CONTENTS

PAGE

emment requirements. — Rules somewhat elastic. — Location of movable span. — Grade and alignment. — Curvature on approaches. — Skew crossings. — Geographical conditions. — Commercial influences. — Proposed bridge at Second Narrows, Vancouver, B, C. — ^Property considerations. — General features of structure. — Character of movable span. — Shore protection.— Future enlargement.— Time considerations. — Stream conditions. — Passing drift and ice. — Clear waterway for probable maximum flood. — Shifting of channel. — Foundation considerations. — Navigation influences. — Construction facilities. — ^Erection considerations. — ^Esthetics. — Maintenance and repairs. — Theoretical economics. — Conclusion .,,,.. 116

CHAPTER XVI

Importance of economic determination of live load. — Occasional excess live loadings.— Modern truck loadings. — ^Decrease of live load with span-length. — Electric-railway car loads. — Standard steam-railway loadings. — Electric-railway loadings. — Highway loadings. — Loadings for cantilevers. — Impact loadings.— Widths for roadways. — Three-line-travel decks are unsatisfactory. — Footwalk widths. — Pedestrian trafiic. — Gauntleted tracks. — Economic arrangement of decks to accommodate several kinds of traffic. — Combined-railway-and-highway-bridge traffic. — Screens. — Division of combined bridges into six classes and dissertation concerning economics of each class. — Author's Sioux City Bridge. — Author's East Omaha Bridge. — Author's Eraser River Bridge at New Westminster, B. C. — Design for Second Narrows Bridge over Burrard Inlet at Vancouver, B. C. — Author's Fratt Bridge at Kansas City. — Keeping live loads down to least legitimate limits. — ^Extreme and illegitimate reduction of live loads. — Determination of unit stresses. — High-carbon steel not good for reinforcing bars. — In frequent loadings permit live-load reduction. — Fallacy of abnormally high live loads and correspondingly greater unit stresses. — Selection of live load important for very-long- span bridges. — Forced increase in unit stresses. — Skimping of details. — Combination of stresses in trestles. — Increments of intensities for various combinations of stresses, and dissertation on the economics involved. — Impracticability of eliminating entirely the personal equation in trestle designing. — Combination of stresses in cantilever bridges and arches. — Caution against inadvertently adding stresses of opposite kinds. — Combination of stresses of opposite kinds. — Conclusion re best policy for combining reversing stresses. — Combinations of live and dead-load stresses with secondary stresses. — Proper relation between intensities of working stresses in tension and compression. — Report of the Committee on Column Tests of the A.S.C.E. and author's comment thereon in Engineering News Record. — Suggested tests of members when actually in full-size bridges. . . 125

CHAPTER XVII

ECONOMICS OF TIME AND MONEY IN MAKING COST ESTIMATES

FOR BRIDGES

Value of data in "Bridge Engineering" for making bridge estimates expeditiously. — Four problems in economic estimating set for solution in a competition

CONTENTS XV

PAGE

between students of technical schools. — Tests made by the author of the "B. E. " methods of making quick cost-computations in bridgework. — Eleven examples solved in the making of quick estimates. — Quick estimates for suspension bridges. — Statement of the student problems 141

ECONOMIC SPAN-LENGTHS FOR SIMPLE-TRUSS BRIDGES ON VARIOUS TYPES OF FOUNDATION

But little known previously concerning true economic span-lengths for varying substructure conditions. — Author's mathematical solution of three decades ago and its limitations. — Special investigation made by actual estimates of cost of over two hundred piers with their spans. — -Instigation of the investigation was the series of studies for the proposed New Orleans bridge. — ■ Assumptions and conditions for investigation. — -Character of structures. — ■ Methods of pier sinking. — ^Specifications for designing. — -Loads. — Permissible pressures on soil and piles. — Unit prices of materials in place. — Method of determining the economic span-length. — Recording-diagrams and table. — Resume of results of computations. — Deductions. — Check on old method of determining economic span-lengths. — -Relative weights of metal in equal-truss, three-span bridges and structures of the same kind, same total length, and same loading, but having the central span lengthened and the other two equally shortened , 150

CHAPTER XIX

Old method of designing masonry piers. — Author's experience in designing piers for Red Rock Cantilever bridge. — Day of cut-stone-masonry piers is past. — ■ Copings. — Economics of reinforcing for traction effects. — Dumb-bell piers. — Hollow shafts to reduce load on foundations. — Piers composed of two cylinders.— Mattresses. — Temporary piers. — Cocked hat. — -Cutting down and rebuilding of main piers of the Fratt Bridge at Kansas City. — Ice-breakers. — Reinforced-concrete versus timber for cribs and caissons of bridge piers. — Steel versus timber for concrete forms. — Best depth to carry pier-shaft below low-water mark. — Reduction of pier size to avoid lessening the area of Avaterway. — Clearance in crib around base of shaft. — Pneumatic process versus open-dredging. — Coffer-dam method versus open-dredging. — Comparative economics of open-dredging caisson and pile-filled crib. — Economics of employing both the pneumatic and the open-dredging processes on the piers for same bridge. — Economics of hastening pier sinking. — -Comparative economics of stepping off plain-concrete bases or spreading suddenly by using reinforcing bars. — Reinforced concrete piles versus wooden ones. . 167

CHAPTER XX

This problem cannot be solved by complicated mathematics, but only by making actual competitive designs and estimates of cost. — Mathematical solution of economic truss-depths. — Economic depths of plate-girder spans and

XVI CONTENTS beams. — True economic investigation for plate-girders. — Considerations tending to offset the advantage of employing economic web-depth. — Old rule of making weight of flanges equal to that of web and its stiffening is just about right. — Economic panel-lengths. — Comparative economics of Warren with Pratt and Petit trusses. — Economic limiting span-lengths for polygonal chords 175

CHAPTER XXI

Possible types of deck for railway bridges. — -Open-floor. — Trough floor. — Ballasted decks. — Ballast resting directly on steel plate. — Ballast resting on reinforced-con Crete slab. — Resting ties on bottom-flange angles or on special shelf-angles. — Depth and number of beams and stringers. — Encasing the said beams in concrete. — Floor systems. — Standard floor system. — Jack-stringers versus fom- lines of carrying stringers per track. — Economic panel length. — Cut-away ends of floor-beams. — Economic depths for stringers. — Economic depths for floor-beams. — -Effect on economics of under-clearance requirements. — Floors for half-through, plate-girder spans. — -Economic spacing of deck trusses for double-track bridges. — Electric-raU^^ay bridges. — Highway-bridge decks. — Timber deck versus concrete deck. — Danger to timber deck from fire. — Deck for bascule bridges. — Pavings for roadways. — Plank floors. — Creosoted planks. — ^Concrete base. — Wooden block pavement.— Brick pavement. — Asphalt and bituminous pavements. — Concrete wearing surface. — -Sidewalks. — ^Sub-paving or base. — Curbs. — Handrails. — • Electric-railway tracks. — Floor systems. — Spaqing of I-beams. — Omission of floor-system in deck spans.— Economic number of girders in deck, plate-girder spans. — Standard floor-system in deck, plate-girder spans. — Stringer spacing. — Sidewalk slabs. — Number of girders in half-through spans. — Stringerless floor vers^ls floor with stringers. — Cantilever brackets. — Floor of minimum weight. — Stiffened-buckle-plate floor. — Haydite concrete. . 182

CHAPTER XXn

GENERAL ECONOMICS OF DESIGNING AND DETAILING

Simple details are economic. — Carry stresses by shortest route. — Reduction of number of rivet holes in a section to a minimum. — Largest practicable radii of gyration for compression members. — H sections for posts. — Compression members carrying shear. — Non-use of cover plates in railway, deck, plate-girder spans. — Batten plates. — Turning flanges of post channels in. — Must consider all panels of compression chord simultaneously when designing any length thereof. — Use metal to best advantage in detailing. — False economy to skimp details. — Details and joints frequently defy exact analysis. — Consider i)ossiblc rusting when detailing. — All parts to be easily accessible to paint brush. 199

CHAPTER XXni

Designs to be made so as to facilitate shopwork. — Sub-i)imcliiiig ;\ii(l reaming versus imiiching full size. — Drilling solid. — Sheared edges. — End stiffencrs

CONTENTS XVll

PAGE

must not be omitted. — Turning in flanges of channels. — Batten plates inside of the gussets. — Girders of constant or varying depths for viaducts. — Location of pedestal pins. — Non-omission of end floor-beams. — Single angles not to be used in tension.— Exact location of top-chord pins. — Cast iron in bridges. — Insertion of casting between foot of column and the masonry. — Variation in pound prices for different sections of metal. — Avoid special material. — Adhere to standard sizes. — Design to avoid all unnecessary shopwork. — ^Reaming to templates. — Avoid side plates and doubling of web plates. — Cheaper to use heavy flange angles in stringers rather than lighter angles with cover-plates. — Avoid beveled cuts. — Design so as to use multiple punches. — -Do not crimp stiffeners for ordinary work. — Solid web versus lacing. — Avoid hand-riveting. — Duplication in skew spans. — Use very few sizes of pins in same bridge. — In riveted tension members use tie plates instead of lacing. — ^AUow ample clearance. — When metal is drilled from the solid use as few pieces as possible in make-up of sections. Mr. Canady's contribution to chapter: Duplicate spans. — Avoidance of light and heavj^ trusses in same span. — Long panels. — Symmeliry. — Squaring small skews. — -Treatment of skewed spaiis. — Unnecessary completeness of many engineers' drawings. — Freedom to be allowed shops in rivet spacing. — • Duties of shop designing-engineer. — Full-punched work. — Sub-punching. — •' Forge and machine-shop work to be a minimum. — Curving ends of girders. — Staggering rivets. — Variety of rivet diameters. — Web-plate versus lacing for I-shaped sections of struts. — -Thickening of stringer webs. — Allowing sufficient difference between gross and net sectional areas. — Fitting of fillers beneath stiffeners. — -Avoiding bevel cuts. — ^Thickening of base plates to avoid shop-work. — Coordination of different parts of a design 202

CHAPTER XXIV

Design so that metal will go together easily in field. — Furnish sufficient clearance. — Wolf el's general instructions. — Allow one-half inch clearance for sheared ends. — Allow for "growth of steel." — Allow ample space in pockets. — Allow ample width for packing. — Begin erection at center panel. — Arrange for putting floor in place either before or after trusses are erected. — Detail through plate-girders so as to avoid spreading them in field. — Half pin-holes undesirable. — Entering connections to be avoided. — Clearance for packing.— Avoid necessity for notching timber ties to clear rivet-heads. — ^Minimize number of field rivets. — Most important points to facilitate and cheapen erection. — Viaducts. — Make two bents of tower alike. — Proper lengths for sections of columns. — Swinging-in of cross-frames 214

CHAPTER XXV

ECONOMICS OF REINFORCED-CONCRETE BRIDGES

Economics of this type not yet so highly developed as that of older types. — Intensity of stress for reinforcing bars. — Objections to high-carbon steel therefor. — Intensity of working stress for concrete. — Pavings. — Hand rails. — Designs. — Economics of design rather difficult to determine. — Slabs. — Girders. — Simple-span girders versus continuous girders. — Character of foundations. — Balanced-cantilever type of girder. — Columns. — Footings. —

XVIU CONTENTS

Highway girder-bridges. — Panel length. — Girder spacing. — Best number of columns per bent. — Economic span-lengths. — Pile foundations. — Arch bridges. — -Ratio of rise to span. — Abutment reaction affects ratio of rise to span. — Economic span-length with rise unchanged. — Factors to be considered.— Distance from springing to bottom of base. — Substructure effects. — Massiveness of piers. — Ratio of live load to dead load. — Type of arch-ring. — Equality or inequality of adjacent spans. — Arbitrary requirements. — Other special conditions. — Solid spandrel versus open-spandrel. — Solid barrel versus ribbed structures. — Hingeless and three-hinged arches. — Arch with steel bottom chords. — Reinforced-concrete trestles for steam-railways. — Slabs therefor. — Special economic investigation. — Retaining walls. . . 218

Great lack of reliable information thereon prior to 1918. — Failure to build many steel arch-bridges in America. — Author's appeal to the profession for investigation on arches.— Relation between metal weights in arch bridges and corresponding truss bridges. — Paper on "Economics of Steel Arch Bridges" for A. S. C. E. — Invitation to discuss same. — Effect of discussion. — Fowler's arch-dimension compilation. — Economic ratio of rise to span-length. — Economic rib-depths. — Percentage effects of using uneconomic rib-depths. — Location for crown hinge. — Solid-rib versus braced-rib versus spandrel-braced arches. — Three-hinged versus two-hinged versus hingeless arches. — Combination of three hinges for dead load and two hinges for live load. — Cantilever arches. — Ratio of metal weights in arch-bridges and corresponding truss-bridges. — Other 'economic factors than weight of metal. — Side issues of investigation. — Percentage equations for metal weights in arches and trusses. — Arches more economic for highway than for railway bridges. — Formulaj for weights of metal in arches alone. — Limiting span-length for three-hinged arches of carbon steel. — Economic or practicable limit of arch spans. — Influence of substructure on economics — Suitable foundations for arch bridges. — Conclusion 232

CHAPTER XXVn

ECONOMICS OF STEEL TRESTLES, VIADUCTS, AND ELEVATED

RAILROADS

Economic factors for high steel-railway-trestles. — Distance from center to center of towers. — Modifications necessary for three diagrams of "Bridge Engineering."— Economic span-lengths for low railway-trestles. — Double-track-railway trestles. — Pedestal costs to be included. — Highway trestles. — Column spacing for h(!nts when cantilevers are employed. — Elevated railroads. — Best span lengths therefor. — Plate-girders versus open-webbed girders. — Best sections for columns. — Paper by Mr. Grcist 250

CHAPTER XXVni

ECONOMICS OF CANTILEVER BRIDGES

Division of cantilevers into types. — Comparison of Types A and B. — Comparison of Types A and C. — Comparison of Type D with other types. — Economic

CONTENTS XIX

PAGE

division of span-lengths. — Economic truss depths. — Legitimate economies in cantilever designing. — Wind stresses during erection. — Splaying the trusses. —Reducing weight during erection. — Solitary piers or pedestals are economic. — Adoption of intermediate trusses. — Division of stress on members meeting over main pier. — Choice between riveted and pin-connected construction. — Box-section chords. — Merriman and Jacoby's treatment of cantilevers. — Truss-depth constant for cantilevers: the practice is absurd. — Simple trusses and cantilevers compared 257