Developing a method for multi-modal shear-based pushover analysis
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ORIGINAL PAPER
Developing a method for multi‑modal shear‑based pushover analysis Farhad Behnamfar1 · Behzad Tavakoli2 Received: 21 April 2020 / Accepted: 11 September 2020 © Springer Nature Switzerland AG 2020
Abstract The nonlinear static seismic analysis has become the focus of many research works because of its simplicity compared with dynamic time history analysis. Procedures have been proposed to include the effect of higher modes in pushover analysis. In this study, a combinatory procedure of two independent modal pushover analyses is presented. The proposed method uses the story shear force. Essentially, the elastic relative stiffness of each story along with the story drifts are used to calculate the story shear force. Two different ways are utilized to estimate the contributions of higher modes to the story shear force. As confirmed by representative examples, it is shown that a combinatory approach of picking up the maximum values of responses between the two presented pushover procedures results in minimum RMS errors in comparison to the exact nonlinear dynamic analysis. In other words, always the maximum response between the two methods is nearest to the exact value calculated as the average of nonlinear time history analysis with earthquakes. Moreover, the combinatory method is shown to be considerably more accurate than previous methods including the modal pushover (MPA) and a recent method of pushover analysis (SSAP) on the basis of story shear force. This is true while the proposed method is much easier to carry out than both MPA and SSAP approaches. Keywords Nonlinear static analysis · Story shear force · Higher modes · Modal pushover · Adaptive
Introduction Seismic design based on performance, i.e., seismic behavior or damage extent, has been introduced as a promising alternative for the traditional strength-based procedure of the current building codes. Meanwhile, a very effective analysis procedure for the same purpose has been developed that is called the nonlinear static or the pushover analysis. In this method, the structure is pushed in successive static steps with a known pattern of lateral forces toward a target displacement at its roof. This procedure, which is called the conventional pushover analysis (CPA), benefits from the simplicity of the linear methods and accuracy of the nonlinear approaches. The pushover analysis developed by Freeman, has been enhanced by taking the effects of the higher modes in several methods proposed by different researchers
* Farhad Behnamfar [email protected] 1
Department of Civil Engineering, Isfahan University of Technology, Isfahan 84156‑83111, Iran
Isfahan, Iran
2
(Sasaki et al. 1998; Bracci et al. 1997; Bertero 1997; Priestley 2000; Yön and Calay 2015). In the well-known modal pushover analysis (MPA) procedure (Chopra and Goel 2001; Ashoory et al. 2013), a number of independent pushover analyses are implemented using loading patterns consistent with the few lower modal shapes of structure. Then the total responses are calculated as a
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