Two-phase model to predict the inelastic, seismic response of a steel frame

Abstract

Previous papers reported on the use of a nonlinear differential equation (containing a Ramberg-Osgood term) to represent the inelastic, seismic behavior of a single-story steel frame. The structure was tested on the shaking table at the Earthquake Engineering Research Center at the University of California, Berkeley. The correlation between the predicted and measured acceleration time histories was exceptionally good. However, the computed displacement time histories did not predict the permanent offset experienced by the structure. The reason for this shortcoming is that the hysteretic behavior of virgin steel is different in the first inelastic excursion than it is in subsequent excursions. The Ramberg-Osgood model can represent only the subsequent hysteretic behavior. To alleviate this deficiency, the present paper presents a two-phase model. One set of parameters is established for the initial phase of the response, in which hysteretic behavior is approximately elastic, perfectly plastic; and another set is established for the second phase, in which the hysteretic behavior has a more rounded transformation from elastic to plastic deformation. The importance of this work lies not so much in its application to steel, as in its potential for application to degrading materials like reinforced concrete and masonry.