Generalized force vectors for multi‐mode pushover analysis

Abstract

SUMMARYA generalized pushover analysis (GPA) procedure is developed for estimating the inelastic seismic response of structures under earthquake ground excitations. The procedure comprises applying different generalized force vectors separately to the structure in an incremental form with increasing amplitude until a prescribed seismic demand is attained for each generalized force vector. A generalized force vector is expressed as a combination of modal forces, and simulates the instantaneous force distribution acting on the system when a given response parameter reaches its maximum value during dynamic response to a seismic excitation. While any response parameter can be selected arbitrarily, generalized force vectors in the presented study are derived for maximum interstory drift parameters. The maximum value of any other response parameter is then obtained from the envelope of GPAs results. Each nonlinear static analysis under a generalized force vector activates the entire multi-degree of freedom effects simultaneously. Accordingly, inelastic actions develop in members with the contribution of all 'instantaneous modes' in the nonlinear response range. Target seismic demands for interstory drifts at the selected stories are calculated from the associated drift expressions. The implementation of the proposed GPA is simpler compared with nonlinear response history analysis, whereas it is less demanding in computational effort when compared with several multi-mode adaptive nonlinear static procedures. Moreover, it does not suffer from the statistical combination of inelastic modal responses obtained separately. The results obtained from building frames have demonstrated that GPA is successful in estimating maximum member deformations and member forces with reference to the response history analysis. When the response is linear elastic, GPA and response spectrum analysis produce identical results.

Concept of Risk-Based Seismic Design of Buildings Using Methods of Nonlinear Analysis

“…Over the last two decades, the pushover-based methods become popular among both researchers and engineers, but these methods have several limitations. Many different procedures have been developed [29][30][31][32][33][34][35]. For brevity, the detailed description of these pushover-based methods is omitted in this paper.…”

Seismic Response of Rc Bridges Using Generalised Force Vectors

“…Finally, the GFV can be obtained by replacing Equation (10) into Equation (3), and successively in Equations (2) and (1), leading to Equation (11). Given that the terms in Equation (11) are related to the maximum displacement of the j 'th pier or the maximum displacement of the j 'th deck node, it is associated with the subscript of the j 'th pier or deck node.…”

“…In the alternative approach, employing relative displacement, analogous to inter-storey drift in buildings, may improve the NSP predictions with respect to NTHA results [11] in bridges. One reason is related to the fact that higher order seismic response parameters, such as plastic rotations and curvatures, are closely related to the inter-storey drift and not to floor displacements.…”

“…This approach will thus be referred to as relative-displacement (RD) based generalized force vectors. For this alternative, the formulation presented in [11] for GFV is used, although the physical interpretation is different. For convenience and completeness, the formulation is summarized in the following.…”

“…Some of the most commonly employed procedures include the N2 Method [1]; Capacity Spectrum Method (CSM) [2,3], Modal Pushover Analysis (MPA) and its variant, the Modified Modal Pushover Analysis (MMPA) [4,5]; Incremental Response Spectrum Analysis (IRSA) [6]; Adaptive Capacity Spectrum Method (ACSM) [7][8][9]; Modified Adaptive Modal Combination Method (M-AMC) [10]; and Multi-Mode Pushover Analysis using Generalized Force Vectors, or Generalized Pushover Analysis (GPA) [11]. All these procedures can be distinguished based on: (i) the use of single-mode based conventional pushover analysis, such as N2 and CSM; (ii) the use of multi-mode based conventional pushover analysis, such as MPA, MMPA, IRSA and GPA; and (iii) the use of multi-mode adaptive pushover analysis, such as ACSM and M-AMC.…”