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.

Recent studies reveal that R/C structural members subjected to biaxial flexure due to two‐dimensional earthquake excitation can deform much more than would be predicted by conventional one‐dimensional response analysis. The biaxial flexure may therefore have a significant effect on the dynamic collapse process of structures subjected to intense ground motions. The present paper is intended to develop a new formulation of the two‐dimensional restoring force model of R/C columns acted upon by biaxial bending moments, and to discuss the dynamic response properties of R/C structures. The model considered is a two‐dimensional extension of various non‐linear models for one‐dimensional response analysis, including the degrading trilinear stiffness model which is one of the simpler idealizations of the restoring force characteristics of flexural‐failure‐type R/C structures. The modelling validity is then examined by comparison with experimental data on the biaxial bending behaviour of R/C columns. Calculations are made to study the role of different system properties on the influence of inelastic biaxial bending on the dynamic structural response. It is shown that the inelastic biaxial effect is generally significant and, in some cases, critical in the case of R/C structures with stiffness‐degrading properties, while the effect is not so important for the non‐degrading inelastic cases.