Formulation of Inelastic Bar Under Repeated Axial And Thermal Loadings

Abstract

A theoretical study is made of the inelastic hysteretic behavior of an axially loaded bar member. Variable repeated loading is applied by axial load, axial displacement, change in temperature, or a combination of these actions. Elastic‐perfectly plastic constitutive relations in the use of stress resultants lead to a closed‐form solution to determine the planar deformation characteristics of the bar. This formulation allows for the reduction of yield stress due to a rise in temperature and is done in a form convenient to take viscous effect into consideration. Both lateral deflection and elongation or shortening cause the axial displacement of one bar end relative to the other; the two causes are additive. The concept of an extensible yield hinge is used. It is pointed out that the plastic axial deformation at a yield hinge plays an important role in the hysteretic behavior of bars of moderate length. This governs the behavioral deterioration, and stabilization or convergence of hysteretic loops for cyclic loading.