Elastic-Plastic Beams and Frames with Unilateral Boundary Conditions*

Abstract

ABSTRACT Elastic-plastic beam elements joined by hinges with constrained mutual rotations are considered. The problem belongs to mechanics of systems with unilateral boundary conditions. In the pure elastic range, one can observe effects such as nonlinear response of the structure and concavity of the elastic surface in the load space. It appears that there exists an optimum value of the limit mutual rotation associated with the maximum elastic strength. Free elastic vibrations of a portal frame at unilateral boundary conditions are also considered. An important feature of such a structure is the fact that the amplitude may be a double-valued function of the natural frequency. The method of reaching the ultimate load is not unique. In particular cases, one can observe changes in the plastic flow mechanism, even in the range of small displacements. In case of optimum value of limit mutual rotation, the ultimate load is reached in a purely elastic way. The work presented may explain some effects that occur in real strutures when connection slackening is induced by the exploitation process.