Abstract: Dependencies between diverse factors involved in probabilistic seismic loss evaluation are recognized to be an imperative issue in acquiring accurate loss estimates. Dependencies among component damage costs could be taken into account considering two partial distinct states of independent or perfectly-dependent for component damage states; however, in our best knowledge, there is no available procedure to take account of loss dependencies in story level. This paper attempts to present a method called "modal cost superposition method" for decoupling story damage costs subjected to earthquake ground motions dealt with closed form differential equations between damage cost and engineering demand parameters which should be solved in complex system considering all stories' cost equations by the means of the introduced "substituted matrixes of mass and stiffness". Costs are treated as probabilistic variables with definite statistic factors of median and standard deviation amounts and a presumed probability distribution. To supplement the proposed procedure and also to display straightforwardness of its application, one benchmark study has been conducted. Acceptable compatibility has been proven for the estimated damage costs evaluated by the new proposed modal and also frequently used stochastic approaches for entire building; however, in story level, insufficiency of employing modification factor for incorporating occurrence probability dependencies between stories has been revealed due to discrepant amounts of dependency between damage costs of different stories. Also, more dependency contribution in occurrence probability of loss could be concluded regarding more compatibility of loss results in higher stories than the lower ones, whereas reduction in incorporation portion of cost modes provides acceptable level of accuracy and gets away from time consuming calculations including some limited number of cost modes in high mode situation.
Abstract: Buildings vulnerability due to seismic activity has been highly studied since the middle of last century. As a solution to the structural and non-structural damage caused by intense ground motions, several seismic energy dissipating devices, such as buckling-restrained braces (BRB), have been proposed. BRB have shown to be effective in concentrating a large portion of the energy transmitted to the structure by the seismic ground motion. A design approach for buildings with BRB elements, which is based on a seismic Displacement-Based formulation, has recently been proposed by the coauthors in this paper. It is a practical and easy design method which simplifies the work of structural engineers. The method is used here for the design of the structure-BRB damper system. The objective of the present study is to extend and apply a methodology to find the best combination of design parameters on multiple-degree-of-freedom (MDOF) structural frame – BRB systems, taking into account simultaneously: 1) initial costs and 2) an adequate engineering demand parameter. The design parameters considered here are: the stiffness ratio (α = Kframe/Ktotal), and the strength ratio (γ = Vdamper/Vtotal); where K represents structural stiffness and V structural strength; and the subscripts "frame", "damper" and "total" represent: the structure without dampers, the BRB dampers and the total frame-damper system, respectively. The selection of the best combination of design parameters α and γ is based on an initial costs analysis and on the structural dynamic response of the structural frame-damper system. The methodology is applied to a 12-story 5-bay steel building with BRB, which is located on the intermediate soil of Mexico City. It is found the best combination of design parameters α and γ for the building with BRB under study.