Report - PEER - University of California, Berkeley

and column-sway frames are presented here in Equations (3) and (4), respectively. Inthis formulation, the soft-storey of the column-sway mechanism is assumed to form atthe ground floor. Straightforward adaptation of the equations could easily beintroduced in the cases where the soft-storey is expected to form at storeys other thanthe ground floor, but this is not dealt with herein.lb∆ = 0.5ef H ε + 0.5( ε( )+ ε( )− 1.7 ε ) ef Hh∆SLsi h T y C Lsi S Lsi y h TbSLsi=hs0.43efhHTεy+ 0.5( εC( Lsi )+ εS( Lsi )− 2.14εyhc) hs(3)(4)A detailed account of the derivation of Equations (1) through to (4) can beobtained from the work of Glaister and Pinho (2003). These equations employ thefollowing parameters:∆ Sy∆ SLsief hH Tε yl bh bh sh cε C(Lsi)ε S(Lsi)structural yield (limit state 1) displacement capacitystructural limit state i (2 or 3) displacement capacityeffective height coefficienttotal height of the original structureyield strain of the reinforcementlength of beamdepth of beam sectionheight of storeydepth of column sectionmaximum allowable concrete strain for limit state imaximum allowable steel strain for limit state i2.3.2 Non-Structural Displacement CapacityIn the derivation of the non-structural displacement capacity equations for beam-swayframes, the effective height coefficient cannot be used directly because, rather thanmechanically deriving a base rotation capacity, as in the structural displacementcapacity formulation, it is the roof deformation capacity that is directly obtained (seeCrowley et al., 2004). Hence a relationship between the deformation at the roof andthe deformation at the centre of seismic force is required. The factor relating thesetwo displacements is named a shape factor (S) and it can be found from thedisplacement profiles suggested by Priestley (2003) for beam-sway frames of variousheights. The non-structural displacement capacity of the SDOF substitute structure(∆ NSLsi ) for a given limit state i can thus be found by multiplying the roofdisplacement by the shape factor to give the displacement at the centre of seismicforce of the structure, as presented in Equation (5), where ϑ i stands for the drift ratiocapacity at limit state i (Crowley et al., 2004).177