Performance-~Based Economical Seismic Design of Multistory Reinforced Concrete Frame Buildings and Reliability Assessment
As the next generation of seismic design methodology, performance-based seismic design (PBSD) method requires a structure satisfy multiple preselected performance levels under different hazard levels. Optimal PBSD methods provide different strategies to design the numerous variables, including strength, stiffness and ductility of each structural component. The overall goal of this study is to develop a new optimal PBSD method for multi-story RC moment frames. This method is capable of overcoming the deficiencies of existing optimal PBSD methods and can be implemented by the U.S. design practice. The proposed method minimizes construction cost and takes the limit of member plastic rotation and optionally inter-story drift as optimization constraints. Other seismic design requirements reflecting successful design practice are also incorporated. Simplification is made by reducing design variables into two, one for the overall system stiffness and the other for the overall system strength. The optimization contains two stages, the determination of feasible region boundary in normalized strength and stiffness domain and optimization in the material consumption domain. Capacity spectrum method, which jointly considers nonlinear static analysis and inelastic design spectrum, is used to estimate the global and local deformation demands at the peak dynamic response.
The proposed optimization approach is applied to the design of a six-story four-bay reinforced concrete frame. The optimal design results indicate that 30% of needed flexural strength and 26% of the cross-sectional area can be reduced from the initial strength-based design of this prototype structure. Nonlinear time-history analyses are conducted on the optimized structure using ten historical ground motions scaled to represent three levels of seismic hazard. In general, the average peak dynamic response meets the target performance requirements under the three levels of seismic hazard. Structural reliability analyses are applied on the optimal structure, the original structure and other 26 structures with different overall system stiffness and strength. The effects on nonperformance probability are determined based on the nonperformance contours, which is generated based on the reliability analyses results of all the 28 structures. To ensure the probabilities of nonperformance due to either plastic hinge or inter-story drift rotation is lower than the limits of all three preselected performance levels, the prototype structure should be design based on the relative overall system stiffness larger than 0.84 and the relative overall system strength larger than 0.4. To ensure that the probabilities of nonperformance only due to plastic hinge is lower than the limits of all three preselected performance levels, the prototype structure should be design based on two cases of relative strength and relative stiffness: (1) the relative overall system stiffness is larger than 0.75 and the relative overall system strength is larger than 0.4, and (2) the relative overall system stiffness is larger than 0.65 and the relative overall system strength is larger than 0.45. To ensure that the probabilities of nonperformance only due to inter-story drift rotation is lower than the limits of all three preselected performance levels, a structure should be design based on the relative overall system stiffness larger than 0.85 and the relative overall system strength larger than 0.6.