Figure 6 Confidence level curves for structural and NSD components.
Related Figures (13)
Table 1. Confidence evaluation parameters for spe- cial moment frames (SAC 2000) Table 2. Fragility curve parameters for nonstructural components for S1L building type and high-code seismic design level (FEMA 2003) The conditional probability of being in, or exceeding, a particular damage state, ds, given any engineering demand parameter, EDP, is computed using the normal cumula- tive distribution function, ®, given by Equation 4: Table 3. Interstory drift and floor acceleration limits corresponding to 50%, 75%, and 95% confidence PERFORMANCE-BASED OPTIMIZATION CONSIDERING STRUCTURAL AND NONSTRUCTURAL COMPONENTS 695 Figure 1. Two-story frame topology used in design example. Figure 2. Yield surfaces assumed in the nonlinear response-history analysis: (a) beam member, and (b) beam-column member. Seven pairs of strong ground motion records representing 2% and 50% probabilities of exceedance in 50 years for the city of Los Angeles were chosen from the records de- veloped in the SAC steel project (Somerville et al. 1997). The selected records represent Figure 3. Input strong ground motion record sets used in the analyses (Somerville et al. 1997) Table 4. Probabilistic optimal design problem statements * Target damage state for evaluating the performance of nonstructural components. ° 7 stands for inactive, meaning that such objective does not contribute to the fitness of the individual because the design is controlled by another performance. “ NA=Does not apply (e.g., an objective is not included in a given case, so the weight coefficient is zero). Notes: (i) All cases have a constant limit for confidence level at CP performance, Ung 0.95. (ii) All cases have a constant limit for SCWB criteria, (2M, co//2My beam) imir= 1-20. (ili) Case 3 does not include performance of nonstructural components in the design. (iv) In Case 5, maximization of confidence level for performance of NSA components is intended so the ds = QNSA,limit= 1.00. Table 5. GA-generated designs for the different cases in study the relative plastic moment capacity of girders and columns at every joint, to validate that the strong column-weak beam constraints are active. These columns of plastic mo- ment capacity ratios also allow the impact of the problem formulation on column sizing to be evaluated. Table 6. Performance information of structural and NSD components extensive, and complete damage states remain very high. It appears that the slight dam- age states for NSD components can lead to improved IO performance as well. This was expected. Case 2 illustrates that while elevating levels of confidence in not exceeding the moderate damage state result in virtual assurance of not exceeding extensive and com- plete damage, there remain significant probabilities that slight damage will take place (i.e., 92% for Case 2A, 76% for Case 2B, and 40% for Case 2C). Case 3 illustrates that elevating levels of confidence in meeting IO performance does not guarantee acceptable confidence levels for not exceeding damage states for NSD components. Table 7. Performance information of structural and NSA components Table 7 summarizes the weight of the structure, the confidence levels for IO and CP performance of structural components, the median PFA under a set of seven ground mo- tions with 50% probability of exceedance in 50 years, and the corresponding confidence levels for not exceeding each damage state for NSA components. As can be seen in the table, the final designs satisfy the constraints that were formulated in order to achieve the confidence required in the performance of every case in study. The results in the table indicate that constraints on CP and IO performance have relatively little bearing on confidence in not exceeding NSA component damage states. Figure 4. Performance of structural and NSD components: Cases | through 5. Figure 5. Performance of NSA components: Cases | through 5. As expected, Figure 4 and Table 6 illustrate that the weight of the structure increases as the confidence level in meeting performance increases. This is seen by considering the weight moving from Case 1A to 1C, Case 2A to 2C, and Case 3A to 3C. For the NSD components, the high variability of each damage state (@,,=0.5) results in small PERFORMANCE-BASED OPTIMIZATION CONSIDERING STRUCTURAL AND NONSTRUCTURAL COMPONENTS 705 Figure 7. Pareto front for floor acceleration and interstory drift for SOPOESO.
