Report - PEER - University of California, Berkeley

The following is a summary of two studies carried out recently to address thesequestions in the context of single storey asymmetric structures (Tso and Myslimaj2003 and Myslimaj and Tso 2004). The studies start with the premise that the yielddisplacements of LFRE along different column lines can be determined, and hencethe yield displacement distribution is known. The asymmetry of such distribution ischaracterized by the yield displacement centroidal location in relation to center ofmass CM, or equivalently, the yield displacement eccentricity (YDE). Using theforce-displacement relation as shown in Fig.3b, the stiffness of each individualelement is determined once its strength is specified. In terms of distributions, it isshown that the distance D between the center of strength (plastic centroid) CV and thecenter of rigidity CR is approximately equal to YDE. For design purpose, one canconsider the distance D equal to YDE. Another important observation is that thedistance D is insensitive to the details of the strength distribution. Therefore, differentstrength allocation strategies result in pair-wise shift of CV and CR in relation to CM.The studies showed that in order to reduce torsional responses, a preferredstrength allocation strategy is to have both small strength and stiffness eccentricities.This will minimize the occurrence of large torques on the floor deck and reduce itsrotation. Such consideration will lead to CR located on one side and CV located onthe opposite side of CM, a condition labeled as a “balanced CV-CR location”criterion to reduce torsional response. One can arrive at this balanced CV-CRcondition strategy using the following heuristic argument. Subjected to a major pulsefrom the ground, the elements experience one of the following states. First, they are inthe elastic state. Then some elements yield while other remains in the elastic state.Then all of them yield and enter the plastic state. This is followed by the unloading ofsome elements while other elements remain yielded. Finally, unloading of allelements occurs and all elements are in the “elastic state” again. When all elementsare in the elastic state, the resultant of the element resisting forces passes through CR.When all elements are in the plastic state, the resultant of resisting forces passesthrough CV. To reduce torsional response, one should therefore arrange the strengthand stiffness distributions with as small stiffness and strength eccentricities aspossible. If both CV and CR were on the same side of CM, the system would haveeither stiffness or strength eccentricity larger than the YDE, since the distancebetween CV and CR is equal to the YDE. However, if one adjusts the strengthdistribution such that CR is, say, on the left and CV on the right of CM, the systemwould have strength and stiffness eccentricity values lesser than YDE. There isanother advantage to arrange CV and CR on opposite sides of CM. With CR locatedon the left of CM, an anti-clockwise torque will be generated when the elements arein the elastic state. With CV located on the right of CM, a clockwise torque will begenerated when the elements are in the yield state. The deck rotations generated bythese anti-clockwise and clockwise torques would tend to cancel out, ending in asystem with small deck rotation when a system has a balanced CV-CR location.Two strength allocation procedures are presented to achieve the desired balancedCV-CR location criterion. Both procedures involve steps to create a strength377