Report - PEER - University of California, Berkeley

that the SRSS combination of the two separate orthogonal inputs is a conservativeestimate of the response. More recently Rutenberg et al. (2002) demonstrated the hightorsional stiffness and strength of perimeter frame structures on the SAC 9-storeybuildings modelled as mass eccentric structures and excited bidirectionally. They alsoconcluded that corner columns could be quite vulnerable, as noted earlier by, e.g.,Cruz and Cominetti (2000). The recent study of Stathopoulos and Anagnostopoulos(2002) on 3 and 5 storey frame structures designed per EC8 concluded that even morecaution should be exercised when extrapolating from one-storey models. Forexample, they found that whereas in some cases code-designs lead to large ductilitydemands on the stiff side elements, the opposite results were obtained for thecorresponding multistorey structure. They also concluded that the amplification ofeccentricity as required by SEAOC/UBC has relatively small effect on the response,and hence does not appear to justify the additional computational effort involved.Finally, they found, as also some other researchers did, that code-design did notadequately protect the flexible edge elements. Very recently De la Colina (2003)presented a parameter study on code-designed 5-storey eccentric stiffness shearbuildings excited by the two components of the 1940 El Centro record. The resultsconfirm those obtained from 1-storey models, namely that a design eccentricity of1.5e for elements located on the flexible side of the floor deck and of 0.5e for therigid side elements recommended by several seismic codes lead to ductility demandslower or equal to those obtained for similar elements in similar but torsionallybalanced systems. He also concluded that an eccentricity not lesser than 0.2e forstoreys with very small or zero eccentricity should be stipulated in order to avoidexcessive ductility demand, again in line with some codes.The application of pushover analysis to asymmetric structures has becomepopular since the mid 1990s. However, assigning a shape to the loading vector is amuch more difficult problem than for the corresponding 2-D problem, (while thechoice of the target displacement is probably not). Several approaches have beenproposed. The simplest one is to apply the code loading shape along the mass axis ofthe building, or at a prescribed offset (the design eccentricity) until the targetdisplacement is reached. Indeed many earlier studies took this approach (seeRutenberg 2002). More recent studies by Fajfar and coworkers (e.g., Fajfar et al.2002) extended the N2 method to bidirectionally excited multistorey structures byevaluating the performance point separately for each direction and then combining theresults by means of the SRSS formula. Again, they concluded that for torsionally stiffstructures the approach leads to acceptable results. Ayala and Tavera (2002) proposea pushover procedure in which the shapes of the lateral loads in the two orthogonaldirections and of the torques about CM are obtained from 3-D modal analysis usingaccepted modal combination rules. The resulting 2 base shear and the base torqueversus roof displacement/rotation curves are converted into the 1st mode behaviourcurves and further transformed into the 1-DOF behaviour curve. Good prediction ofthe response is shown for the example 8-storey frame building. Chopra and Goel(2003) extended their modal pushover analysis procedure to asymmetric structures.372