Summary: | 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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