Collapse of a model for ductile reinforced concrete frames under extreme earthquake motions

A mathematical formulation is presented for modelling the dynamic process of failure of a class of ductile, moment-resisting, reinforced concrete (R/C) frame buildings when subjected to intense earthquake motion. The formulation includes the geometrically non-linear term that accounts for the destabilizing action of gravity. In many cases of practical interest, in which the structures have strong columns and weak girders, the employed method of synthesizing the restoring force properties can provide a satisfactory description of the structural deformation at large deflections. By modelling approximately the effects of gravity, cracking, yielding and degradation of stiffness, the study is intended to aid the understanding of the process of failure in this type of ductile R/C structure, and to relate the mechanics of collapse to characteristics of the excitation. The collapse of R/C frames having strong girders and weak columns, which can develop sway mechanisms at a single storey, is not considered in this study. Special examination is made of the capacity to resist short-duration motions consisting of a few pulses versus the capacity to resist motions of longer duration. For the class of structures modelled, the results indicate an extremely low destructive capability associated with short-duration motions, even when they have very high accelerations. The application in research of a two-parameter characterization of the severity of ground motion in terms of intensity and duration is also examined.