dead load, the two adjacent arch spans of different lengths (or, still more important, if there be only one arch), and the substructure work expensive or the foundation of low bearing-value, the ratio of rise to span length should be large.

Frequently an arch abutment retains a fill, in which case a very low rise is likely to be economic, in order that the larger thrust of the rib may oppose the earth-thrust on the abutment. In such an event it may be economic to make the springing higher. This is the only exception to the general rule that, for maximum economy, the springing should be placed as low as clearances, waterway requirements, or due consideration of aesthetics will permit.

Economic Span-Length with Rise Unchanged

In most instances there is little chance to vary either the grade or the elevations of the springings to any great extent; hence the principal economic problem is the determination of the best span-length. The principal factors to be considered are the following:

A. The rise of the arch.

B. The distance from springing to bottom of base.

C. The character of the substructure work.

D. The massiveness or lightness of the piers, determined from the
        aesthetic viewpoint.

E. The ratio of live load to dead load.

F. The type of arch-ring-whether solid-barrel or two or more
        separate ribs.

G. The equality or inequality of lengths of adjacent spans.

H. Arbitrary requirements fixing clearances of ribs or positions of
        piers.

I. Other special conditions.

The rise of the arch is evidently of paramount importance; because the greater it is the greater will be the economic length of span.

The distance from springing to bottom of base is another very important factor. In general, it may be stated that, for ribbed arches, when the adjoining spans are of equal length and when the springings are but a short distance above the bottom of the base, a ratio of rise to span-length of one-third or even less will be quite economic; while, if the said springings are a considerable distance above the said bottom, a ratio of one-half will be better. Generally speaking, it may be said that low ratios of rise to span are more pleasing to the eye than higher ones, so that the adoption of longer spans is preferable from the aesthetic standpoint. Also longer spans involve larger members, and consequently lower unit costs, so that the economic span-length is somewhat greater than that which gives minimum quantities of materials.