Under the caption of this chapter there was delivered by the author on September 15, 1919, before the Western Society of Engineers a paper based upon some two hundred bona fide special estimates of cost and illustrated by thirty-six diagrams. These illustrations are interesting in that they show graphically how the economics for various types of structure vary with the depth of the foundation; but it has not been thought necesary to reproduce here more than a single set (four) of them and one additional diagram (Fig. 18h) in which all the results have been combined in a general way by ignoring certain small, abnormal variations caused by slight irregularities due to the employment of special instead of general data in making the calculations.

The paper reads as follows:

Up to the present time the general knowledge possessed by the engineering profession concerning economic span lengths for bridges has been rather crude and unsatisfactory. Until three decades ago the only data available on this subject were covered by the broad statement that the greatest economy in a bridge layout exists when the cost of a span is equal to the cost of a pier. In his pamphlet on "General Specifications for Highway Bridges of Iron and Steel," issued in 1888, the author pointed out the fact that the then popular impression concerning this question was incorrect, because the cost of the floor is constant, and hence the adjustment is one between cost of substructure and cost of metal in trusses and laterals; Three years later he gave, in a paper published by "Indian Engineering," a mathematical demonstration of the theory of the economics of bridge layouts, showing that the greatest economy will exist when the cost of a pier is equal to one-half of that of the trusses and laterals of the two spans which it helps to support. This demonstration was based upon the assumptions that the piers rest on hard material at moderate depth and that, in most cases being of minimum size, they would not vary in dimensions or total cost for small changes in the span-lengths.

This principle, though, is not applicable to the case of piers resting on sand or on piles, because the cost per lineal foot for substructure is often nearly constant for all moderate span-lengths, while that for the superstructure augments; and this fact is not at all generally recognized by bridge designers. It has become evident of late to the author by reason of

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