Single-Run Adaptive Pushover Procedure for Shear Wall Structures

Introduction

Nonlinear static procedures or pushover analyses constitute an efficient tool to assess the seismic demand of structures. They constitute a reliable alternative of nonlinear time-history analysis of structures. For tall buildings, the effect of higher modes is not negligible, that's why ignoring their effect is one of the main limitations of pushover analyses. Furthermore, the modes of vibration of the structure can significantly change during strong seismic motion.

In recent years, several techniques have been proposed to integrate the effect of higher modes in pushover analyses and to incorporate the variation in dynamic properties associated to structural damages. Gupta and Kunnath (2000) updated the applied load at each increment. The eigenvalue analysis is carried out at each load increment, then a static analysis is carried out for each mode independently. The calculated effects are combined with SRSS and added to the corresponding values from the previous step. Similarly, Aydinoǧlu (2003, 2004, 2007) developed and extended this method to estimate the peak demand quantities. These adaptive procedures provide good estimates of seismic demands, however:

• 1.

  They are computationally complicated (Chopra and Goel 2002; Baros and Anagnastopoulos 2008). This is mainly due to the absence of a structural equilibrium at the end of each step as the result of using SRSS to combine the responses (Antoniou and Pinho 2004a), so a routine application has to be made to impose the stiffness of the structure at the beginning of each step.

• 2.

  In the inelastic domain, the structural system could not be decomposed into several independent systems (corresponding to the desirable number of modes), consequently the application of the modal combination rule in the inelastic domain is no longer valid. To overcome this difficulty, small steps should be taken where the system can be considered linear (Gupta and Kunnath 2000) or the modal response increments in each mode must be scaled in such a way that the response spectrum analysis (RSA) is implemented in a piecewise linear fashion at each pushover step (Aydinoǧlu 2003), but it increases the computational demands.

In an attempt to avoid the previous computational complexity (the absence of structural equilibrium) and based on the work of Chopra and Goel (2002), Kalkan and Kunnath (2006) developed an adaptive modal combination procedure that accounts for higher mode effects. They combine the response of individual modal pushover analyses and incorporate the effects of progressive variation in dynamic characteristics during the inelastic response via its adaptive feature. The lateral load distribution used in the progressive pushover analysis is based on instantaneous inertia force distribution across the height of the building for each mode. However, these multi-run methods do not reflect the yielding effect of one mode on other modes and on the interaction between modes in the nonlinear range. On the other hand, this method, as the method of Chopra and Goel (2002), is not applicable to estimating member forces because forces computed by this procedure may exceed the specified member capacity. Therefore, there is a need to recompute the member force from the member deformation(s) determined by this procedure to have member forces consistent with their specified capacity (Goel and Chopra 2005). That needs additional computational effort. A variant of modal pushover analysis (VMPA) has been presented by Surmeli and Yuksel (2015) in order to evaluate the seismic performance of the structures.