Deflection of elastic-plastic frames at finite spread of yielding zones.

In elastic-perfectly plastic beams and frames finite zones of yielding develop under the collapse load. The classical deflection analysis assumes that the elastic rigidity reduces locally to zero at the yield hinges only. Such an approach underestimates the deflections at collapse. A method is proposed in order to evaluate the displacements of elastic-plastic frames when the actual spread of plastic zones is included in the analysis. In comparison with the classical method the developed technique accounts for the flexural stiffness variation between the hinges and due to the partial yielding of cross-sections. The actual extent of plastic zones depends on the bending moment distribution in the structure. The method contains both the algorithms and program for the deflection evaluation, specified for I-shape cross-sections. The elastic-plastic moment-curvature relations are derived and integrated to obtain additional rotations due to the flexural stiffness variation when the structure transforms in a mechanism. A linear programming program developed earlier is modified to account for the supplementary rotations. The essential features of the method and those of the program application are illustrated purposely in simple examples, showing the order of magnitude of the actual displacements in comparison with the results of the classical deflection analysis of elastic-plastic beams and frames.