Simplified 3‐D dynamic analysis of structures with flexible diaphragms

Abstract

AbstractA simplified method of 3‐D dynamic analysis, named 3‐D quasi‐dynamic analysis, is presented. This method has been primarily used to evaluate stress states at identified times of peak dynamic responses of structures with flexible diaphragms. The quasi‐dynamic analysis consists of extracting the accelerations predicted by the time‐step integration analyses of two 2‐D discrete MDOF dynamic models of a given structure (each discrete model corresponding to one of the principal orthogonal directions of the structure) at given times of interest. These accelerations are imposed on a 3‐D representation of the structure (for example, a finite element mesh) as equivalent static forces. Accelerations at the diaphragms are assumed to act over the same tributary areas of the diaphragms considered in the 2‐D discrete dynamic models.The study of the firehouse of Gilroy (an unreinforced masonry structure with flexible diaphragms) during the Loma Prieta Earthquake is presented to illustrate the 3‐D quasi‐dynamic seismic analysis. This method was compared to the more traditional 3‐D modal time‐step integration and 3‐D response spectra analyses. The quasi‐dynamic analysis had a general good agreement with the more formal, complex and computationally extensive modal time‐step integration analysis. The 3‐D response spectra analysis was very conservative and had a poor correlation with both the quasi‐dynamic and the modal time‐step integration analyses. The case study of the firehouse of Gilroy suggested that if 3‐D effects have to be considered in the evaluation of a given structure, the quasi‐dynamic analysis constitutes a reliable and computationally cheaper alternative to the more traditional methods of 3‐D dynamic analysis.