Analysis of Arch Dams by the Trial Load Method

This paper presents a method of arch dam analysis that has been gradually developed in the Designing Office of the United States Bureau of Reclamation. It has also been used by the Salt River Valley Water Users Association, the Middle Rio Grande Conservancy District, and by one of the writers for a high arch dam in Mexico. It is base d on the assumption that an arch dam is composed of systems of horizontal arches and vertical cantilevers, that each system carries a proportion of the total load, and that the deflections of the two systems are equal.The method consists in applying a series of assumed proportional loads to each system and computing their deflections. When a proportionate loading has been found that gives equal deflections at all points for both systems, the stresses are computed and are considered to be those which will obtain in the dam.The mathematical treatment of the problem has been gradually developed and improved. The final form is given in the Appendix. If applied to the earlier designs, the numerical results would be slightly different, but the stresses and the shape of the loads would not be greatly changed.