Analytical Description of Pinching, Degrading Hysteretic Systems

Abstract

Physically based analytical models capable of describing the behavior of general hysteretic systems are formulated. The formulation includes the effects of pinching, stiffness degradation, and load deterioration. Two types of pinching, one due to the system encountering additional stiffness and one due to unequalness of strengths for loading in opposite directions, are considered. The latter pinching is represented in terms of strength ratios. Both stiffness degradation and load deterioration are described in terms of functions of total adsorbed hysteretic energy. Two possible forms for each of these functions are presented. All of the system parameters are in terms of definite physical materials or system properties that can be measured through tests. To show that the proposed analytical models provide realistic descriptions of the resistance-deformation behavior for general hysteretic systems, examples of bilinear and quatrolinear systems are presented, using harmonic excitations as examples of the applied forcing functions.