INELASTIC SEISMIC RESPONSE OF TORSIONALLY COUPLED MULTISTOREY BUILDINGS

Abstract

In case of buildings with large asymmetry, codes prescribe the response spectrum analysis to assess the design forces in members. Such computations necessarily involve estimation of magnitude of asymmetry, location of centres of rigidity and evaluation of accidental and design eccentricities. The procedures prescribed to implement torsional provisions in building codes were reviewed. Three asymmetric buildings representative of frame shearwall buildings and frame buildings with setbacks were selected. A review of the static and dynamic torsional provisions in National Building Code of Canada (NBCC 1995), Eurocode8 ENV 1998-1-2 1994 (Eurocode 8 1994), draft Indian Standard (IS:1893-1996 Draft), New Zealand Standard NZS 4203:1992 (NZS 1992) and Uniform Building Code (UBC 1994) of the United States of America has been made. Design shears in frames were computed by two Static 2-D methods-storey eccentricity method and floor eccentricity method, the Static 3-D method and two response spectrum methods-Dynamic-1 method and Dynamic-2 method. Of the two response spectrum methods, Dynamic-1 method is appropriate to implement torsional provisions in the case of buildings with irregular configuration along the height in comparison to Dynamic-2 method. Structural eccentricity and uncoupled frequency ratio (UFR) influence elastic response of torsionally unbalanced systems. A three element single storey monosymmetric system is subjected to inelastic dynamic analysis using an ensemble of 10 real earthquakes. Three values of uncoupled natural periods for different values of stiffness eccentricity and torsional stiffness distribution are studied. Ductility index of the edge elements is taken as the response parameter. Nine systems having the same total lateral stiffness but with different first and second moments of stiffness are considered. The uncoupled frequency ratios Q0, Q.m and Qs are related as Qw>Q0>QiS. For D.0=l=Q.m = Cis, the corresponding relation among the torsional stiffnesses is PL > P*o > pL • The effect of these definitions of UFR does not appear to be significant on the ductility indices of the various eccentric systems provided the value is admissible. In order to study the inelastic response of multistorey buildings, three models with 2, 5 and 10 storey are considered, having fundamental natural periods of Ty=0.2, 0.5 and Is, in respectively. The inelastic design base shear is computed using two values ofRequal to 4 and 2. Aseries of equivalent single storey systems are generated for each model having the same R, Ty and strength distribution as the associated multistorey model. The element strength distribution is carried out using the same code torsional provisions as the corresponding multistorey models. The inelastic dynamic response of the systems is carried out by a step-by-step numerical integration procedure. The elements are assumed to possess a bilinear, stiffness degrading moment-rotation relationship. The systems are also subjected to a static monotonically increasing inelastic analysis to determine the yield displacements of the elements. The overstrength is maximum in the case of NBCC 1995 and minimum in the case of UBC 1994, with Eurocode 8 1994 falling in between the two. Ductility demand is most conservative in the case ofNBCC 1995 and least conservative in the case ofUBC 1994. For all codes the peak ductility demand on the REE coincides with the trough in the strength ratio variation corresponding to the value of critical eccentricity. A change in the force reduction factor R from 4 to 2 reduces the ductility demand in a multistorey model with R=2 by a factor of about 3 to 4 compared to the corresponding model with R=4. However, variation of ductility demand on the edge elements is similar for the two values of R. Thus variation of ductility demand is insensitive to the value of R, in the case of buildings with regular configuration along the height. The comparison of the ductility demand on the bottom storey of the multistorey models with the corresponding element in the associated single storey model shows that for multistorey models with regular configuration over the height, the ductility demand on the edge elements of the bottom storey shows the same variation with elb as in the associated single storey model. Effective design eccentricity attempts to distribute the strength amongst the lateral load resisting elements such that the ductility demand on the two edge elements will be nearly the same and at the same time very close to the ductility demand on the corresponding elements in the associated torsionally balanced system. This is sought to be achieved even when the additional strength provided to the structure is zero. A series of single storey models was analysed to arrive at a modified approach to strength for three fundamental natural periods of 0.2, 0.5 and Is. The maximum displacements were used to compute the ductility index for the edge elements. The loci of the effective strength iv eccentricity and effective design eccentricity resulting in equal ductility index for the edge elements were computed. An empirical design eccentricity expression was obtained by a curve fitting technique to closely match the computed effective design eccentricity. The ductility demand on the FEE of the multistorey model with empirical effective design eccentricity strength distribution is consistently larger compared to the other codes and remains fairly constant while the other codes tend to result in lesser ductility demand. This trend increases with increase in stiffness eccentricity and decrease in torsional stiffness. The EDE strength distribution is more equitable resulting in a ductility demand similar to that observed in the REE. The ductility demand on the REE is lesser than that with Eurocode 8 1994 strength distribution while it is greater than those with UBC 1994 and NBCC 1995 strength distribution for systems with high and medium torsional stiffness. But for systems with low torsional stiffness it results in very large ductility demand. The concept of effective design eccentricity has been extended by evaluating it for an ensemble of earthquakes. Its application to' the design of multistorey buildings has been verified by evaluating its performance in comparison with the torsional provisions of current building codes.