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Static and dynamic inelastic P-Δ effect for seismic design

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Abstract

Seismic influence of P-Δ effect is the subject of this study. First, it is pointed out that the elastic static amplification factor shall be isolated in formulating the dynamic inelastic second order effect. An amplification factor for the static inelastic P-Δ effect is derived. Seismic force reduction factors (SFRF) for given ductility and stability coefficients are computed for one-story, one-span frames. The P-Δ amplification factors for seismic base shears are obtained by dividing SFRFs with and without P-Δ effect. Both P-Δ amplification factors and SFRFs are presented separately with two kinds of period abscissas. The P-Δ amplification factors are dependent on periods with the maximum occurring at about 0.75 s for site type C and approach to the static inelastic counterpart at long periods. Post-yield stiffness cannot fully counteract the adverse impact of the P-Δ effect. Formulas for seismic P-Δ amplification factors are proposed and compared to results of others. Collapse capacity spectra (CCS) are reviewed and their application in codes discussed. Available CCSs are compared with SFRFs with finite ductility computed for two ensembles of seismic records. A comparison reveals that the SFRFs are affected by seismic records, and available CCSs do not always provide upper limits for the SFRFs when stability coefficients are greater than 0.1 for frame models.

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Authors and Affiliations

  1. Department of Civil Engineering, Zhejiang University, Hangzhou, 310058, China

    Li Xiao & Tong Genshu

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  1. Li Xiao
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  2. Tong Genshu
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Correspondence to Tong Genshu.

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Xiao, L., Genshu, T. Static and dynamic inelastic P-Δ effect for seismic design. Earthq. Eng. Eng. Vib. 20, 645–660 (2021). https://doi.org/10.1007/s11803-021-2044-5

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