Sequential Plastic Method for 2D frames limit analysis

Abstract

This work focuses on the limit analysis or plastic calculation of slender beam planar frames using a new method. Sufficient static equilibrium equations are proposed by the Principle of Virtual Displacements (PVD) and kinematic compatibility equations are proposed by the Principle of Virtual Forces (PVF). The load level is increased and the structure is solved step by step until the plastic collapse. Equilibrium equations are posed by virtual problems in displacements and compatibility equations are posed by simple virtual problems in equilibrium. The method provides the following results: the collapse load factor, the final collapse mechanism, the bending moments and the accumulated rotations in the plastic hinges in each load step of the structure. This method has advantages over the classical methods; first, with respect to the step-by-step method based on matrix formulation, especially in the case of beams and/or columns with uniform distributed load, and secondly, with respect to the kinematic direct method, since the sequential method provides more information on the quantities involved in the plasticization process of the structure and also goes directly to the calculation of the collapse mechanism without the need to test or combine possible mechanisms.