Fragility of a Structure, System, or Component for Seismic Performance

Structural engineers, researchers, code committees, and regulatory bodies have become increasingly interested in performance-based design of structures, systems, and components (SSCs) in the past few years. This has been demonstrated by the publication of codes for the performance-based design of traditional buildings, and by publication of a consensus standard for evaluating the seismic performance of nuclear facilities. Performance-based design is an engineering approach, where the design process is structured to achieve performance requirements (limit states) specified by the owners for asset protection, and/or to meet a risk level, specified in regulations, to ensure adequate protection of public health and safety. The probability of unacceptable performance of an SSC, or of exceeding a given limit state, is determined by convolving the seismic hazard curve for the site of the proposed facility with the fragility curve of the SSC, defined as a conditional limitstate probability of occurrence, expressed in terms of a given earthquake ground motion demand quantity (e.g., spectral acceleration, spectral velocity). This paper examines a Monte-Carlo method of analysis to develop a fragility curve for a low-rise concrete shear-wall component of a building structure, using empirical equations based on tests, and theoretical equations based on the truss and arch mechanisms for shear failure. Results of the analyses are compared with the analytical results available in the literature, and the capacity based on the consensus building code standard, to gain insight into the potential safety margins. INTRODUCTION Structural engineers, researchers, code committees, and regulatory bodies have become increasingly interested in performance-based design of structures, systems, and components (SSCs) in the past few years. This has been demonstrated by the publication of codes for the performance-based design of traditional buildings [1], and by publication of a consensus standard for evaluating the seismic performance of nuclear facilities [2]. Performance-based design is an engineering approach, where the design process is structured to achieve performance requirements (limit states) specified by the owners for asset protection, and/or to meet a risk level, specified in regulations, to ensure adequate protection of public health and safety. Performance of an SSC is its ability to perform its function, within tolerable limits of damage, for specifiedmagnitudes loads resulting from man-made and natural events. Functional requirements of an SSC may be specified in terms of structural stability, life safety, protection of property, and building system or component function. Loads can be considered as a range of magnitude of events or loads for various performance levels [1], or as events varying in magnitudes at different values of probability of occurrence (e.g., seismic hazard curve) [2]. A seismic hazard curve is defined as a graph of the ground motion parameter of interest, such as peak ground acceleration, peak ground velocity, or spectral acceleration at a given frequency, plotted as a function of its annual probability of exceedance. Probability of unacceptable performance of an SSC, or exceeding a given limit state, during a seismic event, is determined by convolving the seismic hazard curve for the site of the proposed facility with the fragility curve of the SSC, defined as a conditional limit-state probability of occurrence, expressed in terms of a given earthquake ground motion demand quantity (e.g., spectral acceleration, spectral velocity). Thus, the probability of unacceptable performance of an SSC during a seismic event would depend on the seismic hazard curve and the fragility curve of the SSC. This paper examines a Monte-Carlo method of analysis to develop a fragility curve for a low-rise concrete shear-wall component of a building structure, using empirical equations based on tests [3], and theoretical equations based on the truss and arch mechanisms for shear failure [4]. Results of the analyses are compared with the analytical results available in the literature [5], and the capacity based on the consensus building code standard [6], to gain insight into potential safety margins from a probabilistic perspective against the unacceptable performance of a concrete shear-wall during a seismic event. Effects of various parameters on the probability of unacceptable performance of an SSC, considering the seismic hazard curve and the fragility curve, have been examined in a separate paper [7]. DEVELOPMENT OF A FRAGILITY CURVE Fragility curves for the low-rise concrete shear-wall component of a building structure were developed using the methodology described below: