Inelastic interactions in the dynamic response of structures

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

Digital calculation of response spectra from strong-motion earthquake records

This report presents a numerical method for computing response spectra from strong-motion earthquake records. The method is based on the exact solution to the governing differential equation and gives a three to four-fold saving in computing time compared to a third order Runge-Kutta method of comparable accuracy. An analysis was made of the errors introduced at various stages in the calculation of spectra so that allowable errors could be prescribed for the numerical integration. Using the proposed method of computing or other methods of comparable accuracy, example calculations show that the errors introduced by the numerical procedures are much less than the errors inherent in the digitization of the acceleration record. Included as appendices to the report are computer programs in Fortran IV, with instructions for their use, for computing spectra, for correction of the baseline of the digitized record, and for the computation of ground velocity and displacement