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

Abstract

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.

Closed-Form Dynamic Stability Criterion for Elastic–Plastic Structures under Near-Fault Ground Motions

“…The phenomenon of dynamic instability or dynamic collapse is of principal concern in the field of earthquake and structural engineering (Jennings and Husid, 1968;Sun et al, 1973;Tanabashi et al, 1973;Bertero et al, 1978;Takizawa and Jennings, 1980;Bernal, 1987Bernal, , 1998Nakajima et al, 1990;Ger et al, 1993;Challa and Hall, 1994;Hall, 1998;Hjelmstad and Williamson, 1998;Uetani and Tagawa, 1998;Araki and Hjelmstad, 2000;Sasani and Bertero, 2000;Ibarra and Krawinkler, 2005;Adam and Jager, 2012). The theoretical investigations from the viewpoint of applied mechanics have also been conducted (Herrmann, 1965;Ishida and Morisako, 1985;Maier and Perego, 1992;Araki and Hjelmstad, 2000;Williamson and Hjelmstad, 2001).…”

“…Sun et al (1973) derived a similar condition by studying the free vibration of the system under an initial impact and demonstrated the stability boundary in terms of initial velocity and displacement. Extension of the SDOF criterion to multi-degree-of-freedom (MDOF) systems has been tried (Takizawa and Jennings, 1980;Nakajima et al, 1990).…”

Parametric Investigation of Plane Frame Structure Using Excel Vba And Sap2000 oapi Based Programming

“…The single-degree-of-freedom idealization emanate from linking the actual structure to an auxiliary rigid frame that makes the structure follow a specified deformation pattern [12]. Takizawa and Jennings [13]employed an equivalent single-degree-offreedom system to examine the ultimate capacity of ductile reinforced concrete frame structures under the combined action of strong ground shaking and gravity loads. In conjunction with derivation of statistical expressions, Bernal [14] reduced a multistory structure to an equivalent single-degreeof-freedom system to help correlate the minimum base shear coefficient needed to avert instability.…”

Seismic Induced Global Collapse of Non-deteriorating Frame Structures

“…the normalized median intensity of earthquake excitation at collapse, is subsequently determined from, compare with Eq. 13, (16) This outcome represents an approximation of the collapse capacity CC MDOF of the actual MDOF building, CC MDOF CC ESDOF (17) …”

“…Takizawa and Jennings [16], Bernal [17], Adam et al [18], it is proposed to assess the global P-delta effect in frame structures by means of equivalent single-degree-of-freedom (ESDOF) systems. If the story drifts remain rather uniformly distributed over the height, regardless of the extent of inelastic deformation, a global assessment of the P-delta effect by means of ESDOF systems is not difficult.…”