Minimum failure cost-based energy dissipation system designs for buildings in three seismic regions – Part I: Elements of failure cost analysis

• Framework to calculate the expected failure cost under seismic events is developed.
• All response limit states are used to evaluate performance-based seismic designs.
• Random characteristics of seismic motions included in failure cost estimations.
• Response spectrum method is an acceptable approach to calculate failure cost.

This and the companion papers are focused on the optimal utilization of viscous dampers for performance improvement of building structures by minimizing the failure/life-cycle costs. The cost minimization is a natural choice as the primary motivation for introducing the multi-objective performance based design concept in the earthquake engineering community was to reduce the observed unacceptable levels of damage costs in buildings for moderate intensity but more frequent earthquakes. This paper describes an approach to calculate the failure and life-cycle costs associated with different levels of damage and their consequences considering the random occurrences of seismic events and uncertainties in the calculated response. The inter-story drift is used as an effective response variable to define fragilities and failure costs, although it is realized that damage of some components may be better expressed in terms of the acceleration response. Since a life-cycle cost-based optimization methodology could be computationally demanding especially for yielding structures, the use a response spectrum method of analysis is considered for the response and failure cost calculations. Comparison of the numerical results, for three example buildings in Los Angeles, Seattle and Boston, obtained by the approximate response spectrum method and accurate time-stepping method utilizing an ensemble of base motions indicates that the response spectrum methods can provide a good estimate of the failure cost for a quick performance-based evaluation of different design alternatives. The companion paper utilizes this failure cost and performance evaluation approach to determine optimal designs of damping systems.