ELASTOPLASTIC DEFLECTIONS FOR PRISMATIC AND NONPRISMATIC BEAMS

Analytical solutions are presented for deflections beyond the elastic limit for prismatic and nonprismatic beams (beams with linearly varyin g depth) restrained and loaded in any way. The analytical solutions pr ovide by differentiation the rotation, curvature, moment, and the shea ring force. Simply supported and built-in beams with uniform cross sec tion and with linear variations in depth symmetrically with respect to midspan, loaded at midspan, are analyzed; and the results are given i n a dimensionless form. The displacement occurring just prior to the c ollapse mechanism is 2.243 of that occurring at the limit clastic beha vior for simple and built-in uniform beams. For ratios between the min imum and the maximum depths of the beam less than 0.41, the collapse m echanism occurs with plastic hinges located at midspan and along the b eam. Five elastoplastic behaviors for built-in beams with linearly var ying depth arc established, and the limit ratios between the maximum a nd the minimum depths of the beam separating these behaviors are deter mined.