Simplified 3-D dynamic analysis of structures with flexible diaphragms

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.     

Behavior of ductile steel X-braced RC frames in seismic zones

A satisfactory ductile performance of moment-resisting reinforced concrete concentric braced frame structures (RC-MRCBFs) is not warranted by only following the provisions proposed in Mexico’s Federal District Code (MFDC-04). The nonlinear behavior of low to medium rise ductile RC-MRCBFs using steel X-bracing susceptible to buckling is evaluated in this study. The height of the studied structures ranges from 4 to 20 stories and they were located for design in the lake-bed zone of Mexico City. The design of RC-MRCBFs was carried out considering variable contribution of the two main lines of defense of the dual system (RC columns and steel braces). In order to observe the principal elements responsible for dissipating the earthquake input energy, yielding mappings for different load-steps were obtained using both nonlinear static and dynamic analyses. Some design parameters currently proposed in MFDC-04 as global ductility capacities, overstrength reduction factors and story drifts corresponding to different limit states were assessed as a function of both the considered shear strength and slenderness ratios for the studied RC-MRCBFs using pushover analyses. Additionally, envelopes of response maxima of dynamic parameters were obtained from the story and global hysteresis curves. Finally, a brief discussion regarding residual drifts, residual drift ratios, mappings of residual deformations in steel braces and residual rotations in RC beams and columns is presented. From the analysis of the obtained results, it is concluded that when a suitable design criterion is considered, good structural behavior of RC-MRCBFs with steel-X bracing can be obtained. It is also observed that the shear strength balance has an impact in the height-wise distribution of residual drifts, and an important “shake-down” effect is obtained for all cases. There is a need to improve design parameters currently proposed in MFDC to promote an adequate seismic performance of RC-MRCBFs.