In order to meet the emerging trend of the performance-based design approach and to improve the design efficiency, this chapter presents a numerical optimization technique for both minimum material cost and life-cycle cost design of building structures subject to multiple levels of linear elastic and nonlinear elastic seismic drift performance design constraints. This chapter firstly introduces an elastic seismic drift design of reinforced concrete (RC) building structures based on elastic response spectrum analysis method; and then presents the inelastic design optimization based on the nonlinear pushover analysis method. Finally, the optimal seismic performance-based design of RC buildings is posed as a multi-objective optimization problem in which the life-cycle cost of a building is to be minimised subject to multiple levels of seismic performance design criteria. The computer based optimization methodology developed provides a powerful numerical design tool for performance-based design of RC building structures.
Top1. Introduction
The concept of performance-based design appears to be the future direction of seismic design codes (SEAOC 1995; ATC-40 1996; FEMA 356 2000; FEMA 440 2005; FEMA 445 2006; ASCE41 2007). According to the newly developed performance-based seismic design approach, an acceptability analysis needs to be conducted at various design load levels in order to ensure that the corresponding performance objectives are satisfactory. The acceptability checking procedures may employ various linear or nonlinear analysis methods to assess the seismic responses of structures in relation to the acceptable design criteria. Response spectrum analysis, which is one of the most common linear elastic methods, provides designers with a simple but rational basis for determining the responses of structures under minor or moderate earthquake loading. In the advent of advanced computational techniques, nonlinear analysis procedures become significantly necessary to identify the pattern and level of damage and to understand the modes of failure of structures during severe seismic events. In assessing the nonlinear seismic behaviour of framework structures, pushover analysis has provided an effective means for distinguishing between good and bad seismic performance of structures (Krawinker 1994).
It has been recognized that the displacement or lateral drift performance of a multi-story building can be a good measure of structural and non-structural damage of the building under various levels of earthquake motions (Moehle and Mahin 1991). The performance-based seismic design provisions for multi-story buildings can be based upon controlling story drifts to prescribed limit states under different design levels of earthquakes. Lateral drift design requires the consideration of a proper distribution of the stiffness of all structural elements and, in a severe seismic event, also the occurrence and redistribution of plasticity in structure elements.
Numerous studies on structural optimization in the seismic design of structures have been published in the past two decades, including Cheng and Botkin (1976), Feng et al. (1977), Bhatti and Pister (1981), Balling et al. (1983), Cheng and Truman (1982), Arora (1999). However, most of these previous research efforts were concerned with optimization through prescriptive-based design concepts. Recently, Beck and his associates (1998) developed an optimization methodology for performance-based design of structural systems operating in an uncertain dynamic environment. Foley (2002) provided a comprehensive literature review of current state-of-the-art seismic performance-based design procedures and presented a vision for the development of performance-based design optimization. It has been recognized that there is a pressing need for developing optimized performance-based design procedures for seismic engineering of structures (Charney 2000; Foley 2002). Zou (2002), Chan and Zou (2004), Zou and Chan (2001, 2005a, b), Zou et al (2007a, b), Zou (2008), Wang et al (2010) and Zou et al (2010) had been working at the performance-based seismic design optimization of RC building structure and developed an effective method for design optimization of buildings subject to seismic elastic and inelastic seismic drift performance criteria.