Inelastic interactions in the dynamic response of structures

Abstract

The dynamic response of structures is examined under a general condition of loading. It is shown that the inelastic response of structures depends on the interaction between forces and displacements existing at a section during yielding. A theory of yielding is developed in terms of forces and displacements incorporating the effects of such interactions. Based on this theory, a force-displacement relationship is derived under a general condition of loading. The use of this relationship to study the response of structures is discussed and equations of motion are derived for a simple frame subjected to simultaneous base excitation along its principal directions. To study the inelastic response of structures, under a general condition of loading, it is necessary to derive the equation of the yield surface in terms of forces acting at a section. For the special case of bending about the principal axes of a section, equations of yield surfaces are derived for various structural sections. The response of a simple frame, subjected to sinusoidal base excitation, is obtained for elastic behavior, elasto-plastic behavior and elasto-plastic behavior with interaction. The response for these behaviors is compared and it is shown that interaction causes significant changes in the response. The response of the frame is also investigated for earthquake type excitation and a series of curves are presented to show the effect of interaction on various response parameters. Use of these curves for inelastic design of structures is indicated and the implications of the effects of interaction are examined.