Plastic calculation of slender beam frames systematic method based on mechanism theory

Abstract

This work focuses on the limit analysis or plastic calculation of slender beam planar frames using a direct method based on the Virtual Works Principle (VWP). The method consists in looking for the structure’s collapse mechanism from the equilibrium equations posed by means of virtual problems in displacements. This approach, in its classic formulation, is very unsystematic and requires a convenient choice of virtual problems.

In this work, it has been possible to systematize the plastic calculation of the structure by applying the theory of mechanisms to obtain, fully automatically, the equilibrium equations necessary to completely solve the structure. Also, the compatibility equations necessary to know the accumulated rotations in the plastic hinges at the instant of collapse are presented. Finally, the search for the collapse mechanism is not carried out by trial and error, but is posed by optimization based on energy criteria.