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. — Formulae 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

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 bents when cantilevers are employed. — Elevated railroads. — Best span lengths therefor. — Plate-girders versus open-webbed girders. — Best sections for columns. — Paper by Mr. Greist. ............... 250

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