Report - PEER - University of California, Berkeley

(3) Calculate cumulative scale factor from Eq.8 and check if it exceeded unity. If(p)exceeded, calculate the incremental scale factor, ∆F % , from Eq.15 for the finalpushover step. If not, continue with the next stage.(4) Calculate all response quantities of interest developed at the end of thepushover step from the generic expression of Eq.14. If the final pushover step hasbeen reached, terminate the analysis. If not, continue with the next stage.(5) Modify the current second-order stiffness matrix by considering the lastyielded hinge identified at Stage (2) and return to Stage (1) for the next pushover step.3. ILLUSTRATIVE EXAMPLES3.1 3-D Pushover Analysis of a 9-Story Building with Mass EccentricityThe first example is the 9-story benchmark steel building with basement designed forthe Los Angeles area as part of the SAC project (Gupta and Krawinkler 1999). It hasfour identical moment resisting perimeter frames on each side as shown in Fig. 2a.Other details of modeling are given elsewhere (Aydinoglu, 2004). In order to create a3-D mono-symmetrical response, mass centers of all floors are shifted eastward by anon-dimensional eccentricity of e=0.15. Earthquake ground motion is applied in N-Sdirection and defined through a standard response spectrum (ASCE 2000) with shortperiodand one-second spectral accelerations being 1.375 g and 0.80 g, respectively.Taking P-delta effects into account, 8 vibration modes are considered to adequatelyrepresent the coupled lateral-torsional response using CQC modal combination rule.Fig. 2b shows modal capacity diagrams with implementation of equal displacementrule. Fig. 2c, 2d, 2e show variations of peak floor displacements, story drift ratios andright-end beam plastic hinge rotations at central spans, respectively. Peak flooraccelerations are shown in Fig. 2f. Response quantities are given for each perimeterframe and centre of mass (CM) where applicable. Intensity/demand curves are plottedin Fig. 2g in terms of maximum story drift ratios where the vertical axis indicates theseismic intensity measure (IM) defined as first-mode elastic spectral acceleration.(a)West(b)eSouthCMNorthEastFigure 2. (a) Plan of 9-story steel building, (b) modal capacity diagrams,353