UBC Theses and Dissertations
Seismic demand in high-rise concrete walls White, Timothy Watkins
In order to understand the behaviour of concrete walls concerning the inelastic rotational demand, the results of the dynamic analysis at the time of maximum base rotation and maximum displacement were studied. The results indicate that, due to the influence of higher modes and the "pull-back" of the coupling beams, the maximum inelastic rotations of tall cantilever walls and of coupled walls usually do not result from the maximum displacement demand. However, it is reasonable to estimate the maximum plastic hinge rotation from the difference between the maximum total displacement and an elastic displacement that has a fictitious value for tall cantilever walls and coupled walls. For cantilever walls with T< 2 seconds, the elastic displacements are equal to the first-mode yield displacements. Alternatively, for any height cantilever wall, the ratio of elastic to total displacement can be estimated from the ratio of actual wall strength to elastic demand (1/R). Due to "pull-back" of the coupling beams on the top of coupled walls, the "elastic displacements" of coupled walls are much smaller than for cantilever walls, and this must be accounted for when estimating inelastic rotation of coupled walls. The simplified approach of assuming the inelastic drift is equal to total global drift gives good results for coupled walls. Due to the variability of top wall displacements, the most accurate method for estimating inelastic rotation of tall cantilever walls and coupled walls involves using the maximum mid-height displacement, and equations are presented to facilitate this approach accounting for the initial fundamental period and degree of coupling. From the same analysis program, the results at the time of maximum coupling beam chord rotation and maximum top displacement were studied to examine the wall behaviour associated with the rotational demand of coupling beams. The maximum coupling beam rotation depends on the critical wall slope and critical floor slope. The critical wall slope and critical floor slope occur at the same time arid level as the maximum coupling beam rotation. The critical level usually corresponds with the location of the maximum wall slope, as wall slopes are typically much larger than floor slopes. However, there are cases where the floor slope is significant enough to shift the critical level down. Short cantilever walls usually have the maximum coupling beam chord rotation occur near the top of the wall, while for tall cantilever and coupled walls it tends to be in the bottom half. The critical wall slope can be estimated as the product of the maximum global drift, which can be estimated from a linear dynamic analysis, and a correction factor that accounts for the initial fundamental period. The critical floor slope can be estimated from the coupling beam shear strengths, the axial stiffnesses of the walls, and a correction factor that depends on the initial fundamental period and degree of coupling. A simplified procedure that gives reasonable results is to assume that the critical wall slope is equal to the maximum global drift, and the critical floor slope is equal zero. Based on the results of the analysis program, the axial response of coupled walls was studied. The results show that the axial demand of coupled walls decreases as the period of the wall increases, and that a good approximation is given in the Commentary to the Canadian Concrete Code, A23.3-94. Walls that are allowed to yielding in axial tension have lower coupling beam rotations and energy dissipation, and consequently show an increase in the displacement demand and maximum tensile strain in the wall. The increases are proportional to the amount by which the axial demand exceeded the capacity, and in general were more extreme for first-mode dominated walls than walls subjected to a significant higher mode influence.
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