True Collapse Mechanisms of Two Dimensional Frames Determined from True Nonlinear Yield Surfaces

Abstract

In this work, collapse mechanisms and collapse load factors of two-dimensional frames which are subject to point loads and uniformly distributed loads are determined by employing new elastoplastic analysis method. In this new iterative method as the applied loads on frames are gradually increased, plastic hinges begin to develop at frame member sections and this continues until the partial or total collapse occurrence. If a plastic hinge develops at a section of a frame member, then a mechanical hinge is defined at this location and at each iteration reduced plastic moments are also applied as external loads. This is a new approach to search for the next plastic hinge where a series of linear elastoplastic analyses are executed. For each analysis the revised reduced plastic moments are used in the calculations. For elastoplastic calculations of two-dimensional frames, yield surface definitions of frame member sections are needed, and for I sections, yield surfaces are defined by two curves. In order to simplify collapse load factor calculations these yield surfaces are generally approximated by two lines. In this work the influences of the approximations on the elastoplastic behaviour of two-dimensional frames are examined by comparing the solutions of four example frames. When their solutions are compared, it is observed that almost equal collapse load factors are determined when true and approximate yield surfaces are used in the elastoplastic calculations but true collapse mechanisms are obtained only when true nonlinear yield surfaces are used.