Modal pushover analysis for degrading structures

Abstract

While Non-Linear Response History Analysis (NL-RHA) is the most rigorous procedure to estimate seismic demands for buildings, it is not quite practical for use by regular engineers. Thus, the static pushover analysis, a simple and approximate method, has been improved, and a Modal Pushover Analysis (MPA) has recently been proposed with an assumption that structural responses can be estimated by superposition of modes. Several researchers evaluated MPA procedure by using simple material model, i.e. bi-linear relation, which did not explicitly account for degradation behavior representing the moment-rotation relation of plastic hinge. Therefore, conventional MPA procedure may not be suitable for use with the type of building that takes account degrading behaviour such as reinforced-concrete (RC) buildings. This study aims to develop MPA procedure for degrading structures by utilizing the degrading equivalent SDF systems to improve the step for calculating the target roof displacement of multi-degree-of-freedom (MDF) system. The next step is to evaluate the accuracy of proposed procedure by comparing the floor displacement and the story drift demands estimated by proposed procedure to those computed by NL-RHA, which is regarded as the reference value. The bias is shown by the ratio of floor displacement and story drifts computed by proposed procedure, and dispersion of the story drift ratios were also examined. The evaluation has been performed on a real RC 8-story building and a wide range of frame buildings with heights varying from 3, 6, 9, 12, 15, to 18 stories, designed by strong-column weak-beam concept, and having different strength levels corresponding to systems with reduction factors (R) equal to 2, 4, and 6. The structures were subjected to ground motions: 20 large-magnitude small-distance (LMSR). The following results have been found: (1) using the degrading equivalent SDF systems can predict the peak roof displacement more accurate than using non-degrading, or bi-linear, equivalent SDF systems, (2) the proposed procedure provides less bias of floor displacements and story drift demands than the conventional MPA procedure, (3) the proposed procedure generally provides floor displacements that are quite similar to NL-RHA's results while story drift demands tend to overestimate at lower-half, and underestimate at upper-half of building, (4) the bias and dispersion of both floor displacements and story drift demands tend to increase when the building is subjected to high intensity ground motion and/or the building components are designed with low strength level (5) the bias of seismic demands in the mild-degrading structure estimated by proposed procedure is less than that of the severe-degrading structure.