Seismic collapse capacity and dispersion spectra for self‐centering braced frames considering uncertainty propagation

Abstract

This paper presents the development and application of seismic collapse capacity and dispersion spectra for self‐centering (SC) systems considering uncertainty propagation. A methodology for uncertainty evaluation is proposed to investigate the influence of material‐to‐system uncertainty on the collapse capacity of SC systems. The probability distributions and the correlation of SC system parameters are derived from statistical data obtained via generating non‐deterministic structural models and performing static push‐over and push‐pull analysis. Based on the uncertainty analysis, the influences of system hysteretic parameters, P‐Δ effect and near‐fault ground motions on the collapse capacity of SC systems are comprehensively investigated. Aided by an extensive parametric study on single‐degree‐of‐freedom (SDOF) systems, predominant factors controlling the collapse capacity of SC systems are revealed. The total dispersion of collapse capacity stemming from various sources including the record‐to‐record (RTR) variability and uncertainty in hysteretic parameters is subsequently quantified. Different definitions of RTR variability are discussed, highlighting the necessity of utilizing the RTR variability involving collapse state. The contribution of RTR variability and the uncertainty in hysteretic parameters are then evaluated by the first‐order second‐moment (FOSM) approach. Furthermore, the design collapse capacity spectra and design dispersion spectra, are developed. The results indicate that the design spectra are capable of estimating the collapse capacity of SC systems, and provide an easy‐to‐use quantification tool for probabilistic seismic assessment.

Risk‐targeted seismic design for collapse safety of SMA‐based structures considering temperature effect

“…To comprehensively assess the collapse capacity of SMA‐based systems with different fundamental periods, equivalent single‐degree‐of‐freedom (SDOF) systems are utilized as an efficient and effective substitute of a multiple‐degree‐of‐freedom structural system to identify the system parameters which may have dominant influence on the structures with relatively small computational efforts 31,43,44 . A dimensionless index, that is, CC is utilized to symbolize the collapse capacity of structures 31,43,44 .…”

“…To comprehensively assess the collapse capacity of SMA‐based systems with different fundamental periods, equivalent single‐degree‐of‐freedom (SDOF) systems are utilized as an efficient and effective substitute of a multiple‐degree‐of‐freedom structural system to identify the system parameters which may have dominant influence on the structures with relatively small computational efforts 31,43,44 . A dimensionless index, that is, CC is utilized to symbolize the collapse capacity of structures 31,43,44 . CC is estimated by incremental dynamic analysis (IDA), as expressed by: $$$$\begin{equation} CC = \frac{{M \cdot {S_{a,c}}({T_1},5\% )}}{{{V_y}}} = \frac{{{S_{a,c}}({T_1},5\% )}}{{g\eta }} \end{equation}$$$$where S a,c ( T 1 ,5%) is the 5% damped spectral acceleration at the fundamental period of the SDOF system inducing structural collapse, in which the collapse state is indicated by the point of dynamic instability.…”

“…A more significant difference in the collapse capacity can be found in the systems at higher environment temperature θ T (e.g., θ T = 35°C). Since a higher energy‐dissipation capacity is expected for systems with a larger β , which may have a positive effect in controlling the peak dynamic response, 31,46 the result seems counterintuitive. In other words, the observed tendency is in contradiction with the performance of conventional SC systems combining FRP tendons and friction ED devices 31 …”

“…Different ground motions may lead to various seismic responses due to the record‐to‐record (RTR) variability, which further results in the dispersion of collapse capacity. The level of RTR variability corresponding to collapse state, 31 that is, σ lnCC|RTR , is adopted to estimate the dispersion of collapse capacity in this study, as expressed by: $$$$\begin{equation}{\sigma _{\ln CC|RTR}} = \sqrt {\frac{1}{{N - 1}}\sum_{j = 1}^N {{{(\ln (C{C_j}) - \ln (C{C^{50\% }}))}^2}} } \end{equation}$$$$where N is the sample size, CC j is the seismic collapse capacity under j th ground motion.…”

“…Utilizing the above results, the temperature‐modified collapse capacity CC θ 50% can be calculated, where CC θ 50% against the fundamental period T are represented in Figure 12. The following empirical formula 26,31,51 is adopted to construct the design collapse capacity spectra of CC θ 50% , as expressed by: $$$$\begin{equation}CC_\theta ^{50\% } = {b_1}^{\exp ({b_2}/{T^{{b_3}}})}\end{equation}$$$$where b 1 , b 2 , and b 3 are the regression coefficients. The fitted curves against the fundamental period are exhibited in Figure 12.…”