Predicting the Distribution of Hysteretic Energy Demand in Frame Members

A simple analytical procedure is developed for predicting the distribution of hysteretic energy demand from the building frame into frame members. The frame systems considered are code-designed frames conforming to capacity design principles where the formation of plastic hinges are permitted at member ends. Total hysteretic energy demand is obtained from attenuation relations developed for input energy, by employing response spectrum analysis. Energy dissipated by damping is conservatively ignored in estimating total hysteretic energy demand. Empirical relations are derived first for the ratio of energy dissipated at the maximum displacement cycle to total input energy for elasto-plastic SDOF systems under several ground motions, and expressed in spectral form. Then, hysteretic energy is distributed to the plastic hinges at member ends in accordance with their maximum chord rotations, which are estimated by a modified equivalent linear analysis. Verification of the proposed procedure is demonstrated on a five-story frame subjected to a recorded strong ground motion. The basic advantage of the developed procedure is estimating hysteretic energy dissipation demands in plastic hinges without conducting nonlinear dynamic analysis, which is also a notable advantage for energy-based design.