THe-purpose of this paper is to describe a reliable method of finding the most economical general dimensions of long-span ordinary truss and cantilever bridges, and incidentally to give formulas which express their weight as a function of the loads, the unit stresses, and the general dimensions.
In the course of twenty-six years spent in designing bridges, among which were numerous long-span truss, cantilever, and suspension bridges, many rules for finding approximately the most economical dimensions and the weights of details were developed. This paper combines these rules into a logically connected whole and gives, where practicable, the mathematical reasons for them. The formulas are all given with their proofs, so that their truth can be easily tested.
Though many of the formulas appear, on first inspection, complicated, they permit the calculation of the weight of the longest cantilever bridge within a few days with reasonable accuracy, and make it thereby possible "to compare the weights of designs with different general dimensions and to select the most economical shape of the trusses in a very short time.
Without such formulas the only practicable way to exactly compare the economy of different designs is by means of stress sheets and estimates which require often more time and labor than is available, and these estimates give very little indication how the general dimensions should be changed to secure the most economical design. The wri,ter, therefore, believes that the method given in this paper is the only explicit method to attain this end, which is not based on mere trained feelings. These latter are only acquired after a lifetime of bridge calcuIatjon and are even * Communicated by the author. 645 646 JOSEPH ~'IAYER.
[J. F. I. then only roughly approximate guides, reliable only within the range of the experience on which they are based.
MO~TR~^L, July, 19x3. ORDINARY TRUSSES
For the purpose of giving in a compact form the general course of the argument and its useful results the proofs for the formulas used are given in an appendix. The general method followed is to express the weight of the trusses and bracing as functions of the general dimensions of the trusses, the loads, and U~I == IT,Soo --7 O~--O'b r