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UBC Theses and Dissertations

Linear and nonlinear flexural stiffness models for concrete walls in high-rise buildings Ibrahim, Ahmed M. M.

Abstract

In the seismic design of high-rise wall buildings, the fundamental period of the building and the building drift are usually determined using linear elastic dynamic analysis. To carry out this analysis, designers need to assume a linear flexural stiffness of the wall sections that account for cracking. The commentary to the 1994 Canadian concrete code (CPCA 1995) suggests a stiffness value of 70% of the gross moment of inertia (Ig) of the wall section. The commentary to the 1995 New Zealand Standard (NZS 3101 1995) suggests much lower stiffness values. A wall subjected to axial compression of 10% of fc’ Ag is suggested to have half what is recommended in the CPCA Handbook (i.e. 0.35 Ig). The NEHRP Guidelines for the Seismic Rehabilitation of Buildings (FEMA 273) suggests stiffness values of 0.8 Ig and 0.5 Ig for uncracked and cracked concrete walls, respectively. While it is not clear which of the recommended stiffness values should be used, it is certainly clear that the choice of stiffness value will have a significant influence on the predicted period and drift of the building. The actual influence of cracking on the flexural stiffness of a concrete wall subjected to seismic loading is nonlinear. Nonlinear static analysis is increasingly used to capture this influence provided that an appropriate nonlinear model is used for the material. In this thesis, a simple nonlinear flexural (bending moment-curvature) model for concrete walls in high-rise buildings is proposed. To validate the model, a 40 ft high slender concrete wall was constructed and tested under simulated earthquake loading. Results from the test were compared with the proposed model and showed good agreement. Based on the proposed piece-wise linear model, a general method to determine the linear "effective" flexural stiffness of concrete walls was developed. Results from the general method for the effective flexural stiffness showed that the large variation in effective stiffness that is recommended by various design guidelines does actually exist for different wall configurations under certain conditions. The general method presented in this thesis gives the appropriate stiffness for a particular wall considering all important parameters that influence the stiffness. A study was conducted to examine the influence of a variety of parameters on the stiffness of concrete walls and a set of simplified expressions are proposed for the effective flexural stiffness of concrete walls. The piece-wise flexural model is implemented into a nonlinear static (pushover) analysis computer program to demonstrate the use of the model in predicting the nonlinear static response of concrete walls. Two example applications are presented, including the analysis of a 450 ft high coupled wall structure currently being constructed. The results from the analysis showed the importance of accurately modeling the nonlinear flexural stiffness of concrete walls.

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