【文章內(nèi)容簡(jiǎn)介】 mass and target displacement, respectively, of the ith floor, and d V is the totaldesign base shear. The relative floor forces obtained are as follows:1st Floor: , 2nd Floor: , and 3rd Floor: DESIGN BASE SHEARTaiwan DesignA brief description of the NCREE procedure to arrive at the design base shear is presented in this section.A detailed description of this procedure can be found elsewhere (Tsai [1]).In the first step, the frame was idealized as a MDOF system with three degrees of freedom. ModalContribution Factors (MCF) for the three modes, as well as their modal masses and modal story drifts,were then puted. Since, for this particular frame, the contributions from the 2nd and 3rd modes (MCF = and , respectively) were insignificant pared to the contribution from the 1st mode (MCF =) (Tsai [1]), only the 1st mode was considered for design purposes. Thus, the three floordisplacements of the 1st mode were used to obtain an effective system displacement eff 228。 associated withthe modal target roof drift.In the next step, the ductility demand for the 1st mode of the frame was puted. Because 80% of theseismic force was to be carried by the braced frame, yield drift of the effective system was putedbased on the drift at the point of brace yielding and increased by 25% to account for the contribution fromthe moment frame. From the target maximum story drifts, ductility demand for each story was calculatedand a simple average was taken as the effective ductility demand for the system. Using this ductilitydemand, and from the effective target displacement eff 228。 , the effective time period of the system wasobtained from the inelastic displacement spectrum of the ground motion considered. Correspondingeffective stiffness eff K value of the system was puted from this time period.Finally, the base shear required at the point of target drift was puted by simply multiplying eff Kby eff 228。 . This ultimate base shear was reduced to the yield base shear by assuming a bilinear loaddisplacementcurve with a strain hardening of 5% and the ductility demand as puted earlier. Thisyield base shear served as the design base shear (Vd) of the frame. Of the two performance criteria, thebase shear puted from the second criterion governed and was equal to 415 kips.UM DesignThe base shear was recalculated by using a procedure developed at UM (Leelataviwat [2], Lee [3]),where a fraction of the peak elastic input energy of an earthquake to a structure is equated to the energyneeded by the structure in getting pushed up to the maximum target displacement. The procedure isbriefly described below.In the first step, the base shearroof displacement profile of the frame was modeled by an idealized trilinearcurve, as shown in Figure 3. This trilinear curve was obtained by considering the base shearroofdisplacement profiles of the braced frame and the moment frame separately. Both of these profiles wereidealized by elasticperfectly plastic responses. Roof drift of the braced frame at yield point can be easilycalculated from the geometry of the frame. As mentioned earlier, the base shear carried by the bracedframe at this point was assumed as 80% of the total design base shear Vd, which is an unknown at thisstage. Based on past analysis results, roof drift of the moment frame at yield was assumed as 2%, carryingthe remaining 20% of the total base shear. These two bilinear curves were superimposed to obtain the trilinearloaddisplacement curve of the whole frame (Figure 3). This trilinear curve was further simplifiedto a bilinear curve (Figure 3) by equating the areas under the two curves. The design ductilitydemand236。 for the frame was calculated from this curve.010 1 2 3Roof Drift (%)Base Shear/VdFigure 3: Idealized frame responses for Collapse Prevention criterionIn the next step, the peak input energy was calculated by considering an elastic SDOF system and byusing the equation given by Housner [4], as shown below,221E = MSv , (2)where M and Sv are the total mass and the pseudo spectral velocity of the system, respectively. However,for an inelastic system, this equation needs to be modified (Figure 4a). Thus, a modification factor227。 wasapplied to Eqn. (2) to estimate the energy needed to push the idealized elasticperfectly plastic system tothe selected target displacement, as shown in Figure 4a. Applying this modification factor and convertingSv to spectral acceleration C g e , the modified required energy, m E , can be rewritten as,22 21?????? = m e CTE Wg240。227。 , (3)where W and T are the total weight and the fundamental period of the system, respectively. e C is themaximum base shear coefficient. Following the seismic provisions of IBC 2000 [5], the value of T for the3story frame was estimated as sec. Using this period, e C was obtained from the design responsespectra given in the Draft Taiwan Seismic Code (2002) for the two considered hazard levels. The value of227。 was obtained from the 227。 ? 236。 ? T relationship (Figure 4b) proposed by Leelataviwat [2].The modified input energy, m E is then equated to the total work done by the seismic forces applied to theframe as it is pushed to the target drift as shown in Figure 4a. For this purpose, a bilinear loaddisplacementbehavior (Figure 4a) and a linear distribution of the floor displacements along the height ofthe frame were assumed. A distribution of floor forces, as mentioned earlier, was also assumed. From thisIdealized trilinear curveSimplified bilinear curveBrace yieldingMoment frame yieldingBase Shear/Vd% Roof Drift010 1 2 3Period (sec)236。s=2236。s=6236。s=5236。s=4236。s=3227。energy balance equation, design base shear d V was obtained. As with the Taiwan method, the base shearputed from the second criterion (% drift for 2/50 earthquake)