Report - PEER - University of California, Berkeley

Yield Strength Coefficient, Cy*1.61.4Elastic Design Spectrum1.2Ductility = 21.0Ductility = 40.8Ductility = 80.60.40.380.2µ=2.30.0*∆ y = 0.1040.0 0.1 0.2 0.3 0.4 0.5Base Shear/Weight0.40.350.30.250.20.150.10.05Cy = 0.329Yield Drift = 1.11%00 1 2 3 4(b) Roof Displacement/Height (%)(a) Yield Displacement, mFigure 5. (a) YPS for design of 3-story frame, and (b) capacity curve obtainedfrom pushover analysis.where g= the acceleration of gravity. (If the capacity curve exhibits early softening,formulas such as those in ATC-40 can be used to relate the initial and effectiveperiods of vibration.)As an example, the design of steel moment-resistant frames is typicallycontrolled by drift. Suppose that the roof drift of a 3-story frame is to be limited to2.5% of the building height and that story heights are 4 m. Assuming that the roofdrift at yield is 1.1% of the height, the system displacement ductility limit is µ =2.5/1.1= 2.3. The roof drift at yield is estimated to be ∆ y = (1.1%)(4 m)(3) = 0.132 m.The ESDOF yield displacement is estimated to be ∆ y * = 0.132/1.27 = 0.104 m, basedon an estimate of Γ 1 from Table 1.Using the YPS of Figure 5a, the required yield strength coefficient, C y * , is 0.38.The corresponding base shear coefficient (at yield) is C y = 0.38(0.90) = 0.34, based onan estimate of α 1 from Table 1. The corresponding period, T, is 1.05 s according toEquation (4).A design nominally satisfying these requirements is the 3-story moment-resistantframe designed for Los Angeles in the SAC steel project. The capacity curve for thisframe, corresponding to the “M1” model in which beam-column elements extendbetween nodes located at the intersections of member centerlines, is given in Figure5b. The base shear coefficient is 0.329 and fundamental period is 1.01 sec, making theframe slightly stiffer than is needed on the basis of the estimated properties. Theactual values of Γ 1 and α 1 (1.27 and 0.83, respectively) can be used to refine the yielddisplacement estimate to ∆ y * = (1.11%)(4 m)(3)/1.27 = 0.104 m and the required baseshear coefficient to 0.38(0.83) = 0.32. The actual base shear coefficient slightlyexceeds the required base shear coefficient, resulting in a slightly lower period ofvibration and a smaller displacement ductility demand, indicating acceptableperformance. Further refinement of the design is not warranted at this stage.The preceding illustrates that in a single step the strength can be selected tosatisfy limits on roof drift and system ductility. This is simpler than other proposalsfor performance-based design and current design procedures, which often requireseveral design cycles to satisfy code drift limits. This simplicity is possible when487