【正文】 load applied at the midspan of the interior beam. Verticalponents of these forces tend to cancel each other. However, since the yield strength of thepression brace is assumed to be 10% higher than that of the tension brace, an unbalanced upwardforce remains once both braces have yielded, causing bending moment in the beam. Thus, the interiorbeams were designed as simply supported beams with an axial load and a transverse load applied at thecenter, as shown in Figure 6. The wide flange sections used in the exterior beams were checked againstthis bined loading following the provisions of the AISC steel design manual [6], and were foundadequate for use in the braced frame.P s θ in θPs in θ in θθFigure 6: Forces in braced frame after yieldingDesign of the interior columns was done primarily from axial load consideration (Figure 6). Columns inany story carry the vertical ponents of the brace forces from the stories above. Thus, interior columnsin the 1st story were designed for an axial force which is the sum of the vertical ponents of the braceforces from the 2nd and 3rd stories. Brace forces were calculated at the point when the frame is at itsassumed target drift of %. Also, the higher yield load of the pression brace pared to that of thetensile brace, as mentioned earlier, was considered. However, there are some other factors that affect theload on the interior column. These are:1. Shear force on the exterior beams is transferred through the pinned connection and acts as axial loadon the interior columns. From the deflected shape of the frame, it is seen that this shear force always actsin the opposite direction to the force ing from the braces, thus reducing the net load on the column.2. Shear force on the interior beams adds a small tensile load on both interior columns.P PθPsinθ 3. Interior columns carry some shear and bending moment by virtue of their bent shape.For simplicity of design, the above factors were neglected.COMPARISON OF UM FRAMES WITH TAIWAN FRAMEThe crosssection areas of various members obtained from the two UM designs and from the Taiwandesign are shown in Table 1. It can be seen that the UM Frame 1 had almost identical member sizes asthose in the Taiwan frame. Some differences can be seen in the sizes of the beams at all three floors those in the UM frame being lighter than those in the Taiwan frame. While the difference is small at the1st and 2nd levels, the beams at the 3rd (roof) level in the UM frame were significantly lighter than those inthe Taiwan frame. The UM Frame 2, being designed for a significantly smaller base shear, was muchlighter than the other two frames.Table 1: Member crosssection areas (in2) of frames for Taiwan siteTaiwan Frame UM Frame 1 UM Frame 21st Floor 2nd Floor Braces3rd Floor 1st Floor 2nd Floor ExteriorColumns3rd Floor 1st Floor 2nd Floor InteriorColumns3rd Floor 1st Floor 2nd Floor Beams3rd Floor FRAME DESIGNED FOR . EARTHQUAKESTo further the study on applicability of the energybased approach to calculate design base shear, thesame frame was redesigned for a . location (UMUS). Seattle was chosen as the site for the frame.For design purpose, an increased triangular profile of lateral forces, as specified in IBC 2000 [5], wasused. The frame was designed to meet the performance criterion of % target roof drift in a 2/50 seismicevent. Using a spectral acceleration of for a 2/50 event, the design base shear Vd was puted as680 kips. Table 2 shows the member sizes obtained for this frame.Table 2: Member crosssection areas (in2) of frame for Seattle siteBraces Exterior Columns Interior Columns Beams1st Floor 2nd Floor 3rd Floor PUSHOVER ANALYSISStatic pushover analyses were performed on the first three frames as a first step in evaluating andparing their behavior. SNAP2DX program, developed at the University of Michigan for nonlinearstatic and dynamic analysis of 2D frames (Rai [7]), was used for this purpose. The pushover analysis wasdone under displacementcontrol mode and the frames were pushed to about 3% roof drift with the lateralloads being applied at three floors in the same ratio as the design distribution of the base shear. This ratiowas maintained while the controlling roof displacement applied to the frame was increased. Thedisplacement of the roof was increased in steps of inch. Lateral load at any floor was distributedequally at all five nodes. ., four beamcolumn joints and one bracebeam joint. BRBs were modeledusing a simple truss element with bilinear loaddisplacement relationship. The truss element had apression capacity 10% higher than its tension capacity, and 2% strain hardening. The beams and theCFT columns were modeled using a beamcolumn element. Bilinear momentrotation curves with 4%strain hardening were assumed for these members. Appropriate PM interaction relations for the beamcolumnelements were also used. The resulting pushover curves obtained for the three frames werepared with the loaddisplacement curves originally assumed in the design stage. Locations andsequence of yielding were noted and pared for the three frames.DYNAMIC ANALYSISDynamic analyses were carried out on all the frames by subjecting them to scaled real ground motionsusing the SNAP2DX program. All the ground motions used represented seismic events with 2%probability of occurrence in 50 year intervals. The ground motion time history used to analyze the framesdesigned for the Taiwan site was obtained by appropriate scaling of a record from the ChiChiearthquake. UMUS frame was subjected to three ground motions selected from those remended bySAC for a Seattle site. Some characteristics of the selected ground motions are given in Table 3. Framemembers were modeled as in the pushover analysis. A 5% viscous dampin