Parabolic Arches of Variable Thickness

Tabulations for aid in designing parabolic arches of variable depth are presented. Design coefficients usually given for these arches are restricted to a single abutment to crown thickness ratio for various rise to chord ratios. Even in the instance in which various abutment to crown thickness ratios are considered, only a few cases are treated because of the extensive tables needed to fully cover the case involving two parameters. To overcome this a variation in thickness was derived that permits the tabulation of the resistance of the arch to loads and end movements in terms of a single parameter, K_A. Fixed end moment and reactions are given for four loading conditions. In addition, elastic constants are tabulated so that any degree of end restraint can be considered. The arch that will attain the optimum ratio of abutment to crown depth can thus be obtained without any extensive calculations. Furthermore, unusual and complex boundary conditions can be investigated.