Elastic-Plastic Analysis of Rectangular Frames

For a ductile material such as steel, the stressstrain curve may be taken as linear up to the yield point and then indefinitely horizontal. Under this assumption, the first-named author has shown in 1963 that the response of a continuous beam or rigid frame under increasing loads may be traced from the beginning to collapse by a stepwise elastic analysis procedure. This procedure requires that the structure is subjected to concentrated loads only so that plastic hinges can form only at the ends of the elements which are themselves unloaded. In this paper, this restriction is removed by allowing uniform and concentrated loads to act on the elements. Consequently, a plastic hinge may form anywhere on an element, and the fixed-end moments and the stiffness coefficients of that element must then be modified for the next stage of elastic analysis. The advantage gained is enormous because previously a uniform load has to be replaced by a number of concentrated loads and a node placed at any point where there is a concentrated load.