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Investigation of effective stiffness of high-rise concrete shear walls

University of British Columbia

High-rise concrete shear walls are expected to crack during an earthquake. To account for cracking when conducting linear seismic analysis an effective moment of inertia I[subscript]e; recommendations for I[subscript]e vary widely. Expressions for the upper and lower bound effective stiffness were previously developed using bilinear curves with equal area-under-the-curve as the actual nonlinear force-displacement curves determined by numerically integrating a trilinear moment-curvature model. In this thesis, the analysis tools required to study the transition between an uncracked and a severely cracked response are developed. These tools include a simplified force-displacement relationship that approximates the theoretical response better than numerical integration of a trilinear moment-curvature model. A hysteretic force-displacement model is also developed through using experimental data obtained f rom large scale wall specimen. The hysteretic model is implemented into OpenSees to allow for nonlinear time history analysis of high-rise concrete shear walls as a single-degree-of-freedom system that accounts for the effects of cracking. The maximum nonlinear displacement is used to find the effective elastic stiffness. The factor α quantifies the amount the initial stiffness of the wall needs to be reduced for an elastic system to have the same maximum displacement. A range of R values are studied by scaling the ground motions so the elastic demand is R times greater than the strength of the wall. This scaling method is verified as part of the thesis work. A suite of unmodified ground motions and a suite of modified spectrum matched ground motions are used in this study. A set of generalized walls are developed to represent the range of wall shapes, re- inforcement and axial load o f typical high-rise concrete shear walls. A preliminary nonlinear time history analysis is conducted for nineteen generalized walls using two suites of ground motions at initial periods of 2 and 4 seconds with nineteen R values ranging from 0.5 to 5.0. The results of the analysis suggest that determining effective stiffness from equal area bilinear curves has limited success. The trends in stiffness effective stiffness are remarkably similar considering the wide range of generalized walls studied. T h e initial period has greater influence on effective stiffness than the shape of the force-displacement curve. T h e effective stiffness dropped sharply for higher R values for the 2 second initial period while remain constant for the 4 second initial period.

Text

2011-03-24

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http://hdl.handle.net/2429/32856

Civil Engineering

University of British Columbia

Graduate