deck; whereas for the former type it will be satisfactory to carry a part of the deck on cantilevers. The consequent narrowing of the arch-rings and shortening of the piers involve quite a saving in cost.

Comparing, in open-spandrel structures, the solid-barrel type and the ribbed type, it will be found that the latter is cheaper, except in the case of very low ratios of rise to span-length. In the solid-barrel type there is one wide, rather-thin ring carried on a wide, comparatively-thin pier; while in the ribbed type there are two or more thicker and rather-narrow ribs, carried on piers which must be somewhat wide as seen in side elevation, there usually being a separate shaft for each line of ribs. For arches of considerable rise in which the live load moments are the only ones of importance, the thick, narrow rib is much the cheaper; but, as the rise is reduced, temperature and arch-shortening stresses increase in importance, and it becomes more economical to reduce the thickness and make each rib wider, until eventually the solid-barrel rib is reached. For any special case, comparison can be made by means of the curves on pages 1332 and 1333 of "Bridge Engineering." It must not be forgotten that, with the ribbed type, cross-braces between the ribs are generally necessary. The type of pier required is also important. If a separate shaft can be used for each line of ribs, the ribbed type will usually be the more economical; but in many cases, as in most rivers, solid pier-shafts must be employed in any event. Frequently, in river crossings, the springings are located below the high-water line; and the adoption of solid barrels then becomes almost imperative.

Hingeless and Three-Hinged Arches

Comparing the hingeless and the three-hinged types for reinforced-concrete arch-bridges, it will be found that the latter is cheaper for low rises, and the former for high ones. The principal objection to the three-hinged type is its awkward appearance, due to the fact that it is thicker in the haunch than at the springing line; and since the concrete-arch bridge is often selected from aesthetic considerations, this is an important matter. If the three-hinged rib be thickened at the springing, in order to make its appearance satisfactory, it will rarely, if ever, prove to be cheaper than the hingeless type.

Arch with Steel Bottom Chords

An unusual economic problem arose in the design of the author's Twelfth Street Trafficway Viaduct in Kansas City, Mo. This is a double-deck, reinforced-concrete-girder structure; but there was one portion of it where a 134-foot span was required over some railroad tracks. An arch span was adopted; but the springings were high above the foundations, which were on piles; and the area allowable for the piers was restricted by other tracks. The  question  of  what  to  do  was  finally  solved  by  putting  in