【正文】 ode (2020) for the two considered hazard levels. The value of ??was obtained from the ????????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 the frame as it is pushed to the target drift as shown in Figure 4a. For this purpose, a bilinear loaddisplacement behavior (Figure 4a) and a linear distribution of the floor displacements along the height of the frame were assumed. A distribution of floor forces, as mentioned earlier, was also assumed. From this Idealized trilinear curve Simplified bilinear curve Brace yielding Moment frame yielding Base Shear/Vd % Roof Drift 0 1 0 1 2 3 Period (sec) ?s=2 ?s=6 ?s=5 ?s=4 ?s=3 ??energy balance equation, design base shear d V was obtained. As with the Taiwan method, the base shear puted from the second criterion (% drift for 2/50 earthquake) governed and was equal to 340 kips, which is significantly smaller than that obtained from the Taiwan method. (a) (b) Figure 4: (a) Energy input in elastic and inelastic systems, (b) Energy modification factors against period UM PLASTIC DESIGN METHODOLOGY The research team at the University of Michigan adopted a simple plastic design procedure to design the test frame. Designs of the bracing part and the moment frame were done independently from each other with an 8020% sharing of total base shear between the two ponents. Material Properties Material properties used for the design and analysis of the frame were kept the same as those used in the Taiwan design. All steel sections: core member of the braces, wide flange beams and steel tubes of the CFT columns, had nominal yield strength of 50 ksi with bilinear stressstrain curves. Strain hardening ratios of 4% for beams and columns, and 2% for the brace members were considered. Additionally, a 10% overstrength was considered for the expected yield strength of steel for the beams and columns. However, no overstrength was considered for the brace members, because the material for the braces was to be tested before their fabrication in order to get an accurate measure of its strength, and its effect was to be incorporated by adjusting the crosssectional areas of the braces. The concrete used for the CFT columns was assumed to have a strength of 5000 psi. Design of Moment Frame The moment frame was designed for 20% of the total base shear, to be carried by the exterior columns and the exterior beams. The design of the frame was done following the guidelines provided in a related research by Leelataviwat [2] and Lee [3], and using the proposed plastic design methodology. Designs of the columns and beams were done simultaneously to balance the member capacities, so that a desired yield mechanism is achieved. The design steps are described below. As a first step, a desired failure mechanism was selected. The assumed failure mechanism consisted of beamcolumn junctions developing plastic hinges only in the beams at all three floors, and a plastic hinge at the base of each column (Figure 5a). Thus, strong columnweak beam philosophy was followed. It should be mentioned that the design strength of the columns was calculated only from the steel tube section, neglecting the contribution from the concrete core. Δy Δeu Δma Base Shear 2 E ??1 MS Drift Δ CyW CeW EE ??Ep γ Period (sec) An initial required strength of the column section was estimated from the consideration of avoiding the possibility of a story mechanism in the first story. This was done by considering the base shear to be resisted by a story mechanism in the first story, ., the columns in the first story forming plastic hinges at both ends (Figure 5b). Minimum required flexural capacity of the columns was obtained by equating the overturning moment due to the shear carried by the columns to the bined design capacity of the plastic hinges at the ends of the columns. A 10% margin of safety was also considered. A square tubular section with strength greater than the required strength was then assigned to the columns. Since the same column section was continued along the full height, story mechanisms in the upper stories were automatically avoided. Required flexural strengths for the beams were calculated in the next step. Beam strengths were determined by assuming a scenario where the moment frame is acted upon by its full share of base shear, distributed at the three floors as described earlier, and having developed plastic hinges in all three beams and at the base of the columns (Figure 5c). Thus, the total resisting moment provided by the capacity of the plastic hinges in the beams and column bases was equated to the total overturning moment of the applied floor forces. This, however, produced only one equation, whereas three beam strengths needed to be determined. This was dealt with by assuming the flexural capacities of the beams at the three floors to be proportional to the applied story shears (Figure 5c). The required flexural strengths of the beams were then calculated and available wide flange sections with strengths closest to the required strengths were selected. (a) (b) (c) Figure 5: (a) Moment frame yield mechanism, (b) Minimum column strength from story mechanism, and (c) Moment demands on beams As a last step, the expected beam strengths with strain hardening and the applied floor forces were used to calculate the moment demands on the column at the beamcolumn joints to ensure that no plastic hinge formed in the column at any location. ~ ~ ~ ~ ~ ~ h MC MC MC MC Vd Vd MC Mb h MC Mb kips b kips kips () () () Design of Braced Frame As mentioned ea