Multiobjective Optimization for Performance-Based Design of Reinforced Concrete Frames

In order to meet the emerging trend of performance-based design of structural systems, attempts have been made to develop a multiobjective optimization technique that incorporates the performance-based seismic design methodology of concrete building structures. Specifically, the life-cycle cost of a reinforced concrete building frame is minimized subject to multiple levels of seismic performance design criteria. In formulating the total life-cycle cost, the initial material cost can be expressed in terms of the design variables, and the expected damage loss can be stated as a function of seismic performance levels and their associated failure probability by the means of a statistical model. Explicit formulation of design constraints involving inelastic drift response performance caused by pushover loading is expressed with the consideration of the occurrence of reinforced concrete plasticity and the formation of plastic hinges. Due to the fact that the initial material cost and the expected damage loss are conflicting by nature, the life-cycle cost of a building structure can be posed as a multiobjective optimization problem and solved by the $\epsilon$ –constraint method to produce a Pareto optimal set, from which the best compromise solution can be selected. The methodology for each Pareto optimal solution is fundamentally based on the Optimality Criteria approach. A ten-story planar framework example is presented to illustrate the effectiveness of the proposed optimal design method.