Keywords: probabilistic assessment, limit states, stochastic analysis, seismic vulnerability, fragility, steel buildings, strength degrading, non-linear analysis.

Seismic regulations and building codes experienced major advances in recent decades. Nevertheless, current trends in earthquake engineering are the assessment of the computational procedures provided by such design rules, by using probabilistic techniques, in order to test the anticipated levels of reliability and performance of the structures. While some consideration is given in codes to the uncertainties associated with seismic action, no probabilistic requirements are posed on the responses, which determine the final design. Consequently, the risk associated with the design formulas remains unknown. The objective of this chapter is to study whether steel buildings designed and constructed according to the load and resistance factor design (LRFD) specification for structural steel buildings, reasonably meet the probabilistic requirements on structural member safety applying non-linear dynamic analyses and Monte-Carlo techniques. Starting from a specific low-rise braced frame steel building existing in Manizales, Colombia, also we analyze mid-rise and high-rise braced frame buildings. Similar low- mid- and high-rise Moment-resisting frame buildings also are studied. For each building we performed more than ten thousand dynamic simulations, covering a wide range of combinations on demand and strength. In this way, we determine the exceedance probability of the construction capacity and we verify the safety and reliability of the structural members of the buildings. In the analysis of demand, we consider the probabilistic variation of the vertical gravity loads as well as of the seismic horizontal ones. The analyses of the strength of the buildings studied take into account the uncertainties and probability distributions of several parameters such as: the yielding strain, the elasticity modulus, the cross-sectional area and their inertia moments. The analysis shows that in the cases analyzed here, but especially in moment-resisting frame buildings, the uncertainties in the input parameters may lead to significant failure probabilities. We conclude that braced frame steel buildings fulfil the seismic safety requirements while moment-resisting frame buildings would require a safety factor of about 2.7 for the column anchorages to the foundations.

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