Report - PEER - University of California, Berkeley

3.2 Strength Allocation for Systems with Strength Dependent StiffnessElementsMost analytical studies in past and current codified torsional provisions are based onthe assumption that the stiffness of lateral force resisting elements (LFRE) can beestimated with some degree of accuracy prior to strength allocation, and will not beaffected by the subsequent strength allocation process. Using elastic-plasticmodelling, the force-displacement relationship of two elements of similar sizedesigned to have different strengths is assumed to take the form as shown in Fig. 3a.Recent studies (Paulay 1997, 2001; Priestley 1998; Priestley and Kowalsky 1998; andAschheim 2002) have shown that for most ductile LFRE, the stiffness and strengthare related. A more realistic representation of the force-displacement relationship fortwo elements of similar dimensions but different strengths would appear as shown inFig. 3b.Figure 3: Force-displacement relationships.An increase of strength will lead to an increase of stiffness, while the yielddisplacement stays essentially the same. This interdependence between strength andstiffness of LFRE gives rise to a number of issues in the seismic design process. First,the process of strength allocation to LFRE would change both the strength andstiffness distributions of a structure. What would be a desirable strength/stiffnessdistribution combination to reduce torsional response? Second, contrary to most codeprocedures, the final stiffness distribution cannot be considered known prior tostrength assignment. What strength allocation procedure is available to achieve thedesirable strength/stiffness distribution combination target? Finally, how effective arethe current torsional provisions for structural systems with LFRE having strengthdependent stiffness?376