Report - PEER - University of California, Berkeley

limit states, the suggestions given by Calvi (1999) have been followed (see Crowleyet al., 2004). The non-structural components will again fall within one of four bandsof damage: undamaged, moderate, extensive or complete.2.3 Displacement Capacity as a Function of HeightThe demand in this methodology is represented by a displacement spectrum whichcan be described as providing the expected displacement induced by an earthquake ona single degree of freedom (SDOF) oscillator of given period and damping.Therefore, the displacement capacity equations that are derived must describe thecapacity of a SDOF substitute structure and hence must give the displacementcapacity, both structural and non-structural, at the centre of seismic force of theoriginal structure. In the following sub-sections, structural displacement capacityformulae for moment-resistant reinforced concrete frames exhibiting a beam- orcolumn-sway failure mechanisms are presented.2.3.1 Structural Displacement CapacityBy considering the yield strain of the reinforcing steel and the geometry of the beamand column sections used in a building class, yield section curvatures can be definedusing the relationships suggested by Priestley (2003). These beam and column yieldcurvatures are then multiplied by empirical coefficients to account for shear and jointdeformation to obtain a formula for the yield chord rotation. This chord rotation isequated to base rotation and multiplied by an effective height to produce thedisplacement at the centre of seismic force of the building.The effective height is calculated by multiplying the total height of the structureby an effective height coefficient (ef h ), defined as the ratio of the height to the centreof mass of a SDOF substitute structure (H SDOF ), that has the same displacementcapacity as the original structure at its centre of seismic force (H CSF ), and the totalheight of the original structure (H T ), as explicitly described in the work by Glaisterand Pinho (2003).The yield displacement capacity formulae for beam- and column-sway frames arepresented in Equations (1) and (2) respectively; these are used to define the firststructural limit state.lb∆Sy= 0.5efhHTεyhh∆Sy= 0.43efhHTεyhbsc(1)(2)Post-yield displacement capacity formulae are obtained by adding a post-yielddisplacement component to the yield displacement, calculated by multiplying togetherthe limit state plastic section curvature, the plastic hinge length, and the height/lengthof the yielding member. The post-yield displacement capacity formulae for RC beam-176