Report - PEER - University of California, Berkeley

∆NSLsi= SϑH(5)iTFor column-sway frames, the potential for concentration of non-structuraldamage at the ground floor should be considered. Thus it is assumed that once thefirst floor reaches the limit state interstorey drift capacity, then the non-structuraldamage limit state has been attained. Therefore it should be ascertained whether thedisplacement at the first floor (∆ NS1st ), obtained by multiplying the interstorey driftwith the storey height, is greater than the first floor structural yield displacement(∆ Sy1st ), found by multiplying the yield base rotation by the height of the first storey.As shown by Crowley et al. (2004), the above effectively means that the nonstructuraldisplacement capacity of column-sway frames for limit states beforestructural yielding, ascertained at the first floor, may be found using Equation (6)whilst for limit states occurring after structural yielding at the first floor, Equation (7)applies.∆NSLsi= 0.67ϑiHT(6)hs∆NSLsi= ϑihs+ 0.43( efhHT− hs) εyh(7)c2.4 Period of Vibration of Buildings as a Function of HeightSimple empirical relationships are available in many design codes to relate thefundamental period of vibration of a building to its height. However, theserelationships have been realised for force-based design and so produce lower boundestimates of period such that the base shear force becomes conservatively predicted.The use of a reliable relationship between period and height is a fundamentalrequirement in this methodology, so that the displacement capacity formulae can beaccurately defined in terms of period and directly compared with the displacementdemand; however with a conservative period-height relationship the displacementdemand would generally be under-predicted. Therefore, Crowley and Pinho (2004)carried out an extensive parametric study to derive a suitable relationship betweenyield period and height, which is given in Equation (8). For post-yield limit states, onthe other hand, the limit state period of the substitute structure can be obtained by thesecant stiffness to the point of maximum deflection on an idealised bi-linear forcedisplacementcurve, which, as demonstrated by Glaister and Pinho (2003), leads to anexpression (Equation (9)) that depends on elastic period (T y ) and ductility (µ Lsi ) alone.Ty= 0.1H T(8)T = (9)LsiTyµLsi178