Elasto-Plastic Dynamic Behaviors of the Building Frames Subjected to Bi-Directional Earthquake Motion

In building frames designed to resist earthquakes, the girders usually have a lower yield moment than the columns. This arrangement distributes the inelastic action among many frame members, leading to good overall energy dissipation. By contrast, the damage in a weak-column structure is concentrated in particular story, with potentially disastrous results. Studies on the column/girder strength ratio required for creating a weak-girder frame subjected to one-directional seismic motion have been carried out by many researchers. But there are few studies of the behavior of frames subjected to bi-directional ground motion. In this paper, a simplified frame model is used to study the inelastic dynamic behavior of a 10-story frame subjected to bi-directional horizontal ground seismic motion. By changing the column/girder bending strength ratio, the column strength required to create a weak-girder frame and the energy input to the structure are examined. The effects of bi-directionality and orientation of the input motions on the behavior are also examined. The girder flexibilities are represented by elasto-plastic rotational springs. The columns are modeled as rigid members, joined by springs at mid story height. The force-deflection relationships governing relative rotation and relative horizontal displacement of two contiguous column segments were derived independently. The story drift, which includes the displacements caused by both reversed curvature bending and shear, is modeled by a multiple shear spring (MSS) system. The purpose of the MSS model is to simulate a bi-directional inelastic spring, including interaction between the two directions. It consists of N displacement springs arranged radially around a circle.