Shakedown of Frames with Semirigid Connections

Abstract

The shakedown analysis of elastoplastic plane frames with semirigid connections is considered within a framework of discrete models and piecewise linear yield surfaces. The formulation adopted is based on the classical Bleich‐Melan static theorem, and leads to a linear programming problem. A simple linear elastic perfectly plastic connection element is used to account for the reduced flexibility and partial strength of semirigid beam‐to‐column connections. The necessary conditions of equilibrium and of yield conformity are expressed compactly in matrix form, and the calculation of the elastic locus for the cyclic‐load domain is clarified. A means of identifying whether incremental collapse or alternating plasticity governs failure under repeated loading is also mentioned. Finally, three examples are presented primarily as a preliminary assessment of the shakedown behavior of semirigid frames. In particular, it is shown that the shakedown limit of such structures can be significantly lower than the corresponding plastic collapse limit. The importance of considering axial effects on plasticity and of using the correct elastic stiffness in shakedown calculations are also highlighted.