| Abstract: | A 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. |
