FIGURE 21.16 Prescribed force-deformation behavior of members and monotonic behavior identifying different performance limit states.

computed assuming a yield stress of 414 MPa (60 ksi). Using nominal dimensions for the floor slab and standard weights for nonstructural elements, the floor weights are estimated as 6227 kN (1400 kip) at the first level, 5338 kN (1200 kip) at the second through fifth level, and 7562 kN (1700 kip) at the roof level, resulting in a total building weight of approximately 33,805 kN (7600 kip). A 2D model of the frame was developed to estimate seismic demands. The computer program OpenSees (2003) was used for the analytical simulations since it provided the capability to carry out nonlinear static and dynamic analyses.

Nonlinearity in members is modeled using a bilinear force-deformation behavior in view of the fact that fully restrained connections are used and no brittle fracture is expected. The performance regime of the components will, therefore, lie in the ascending slope of the force-deformation envelope, and softening behavior need not be considered. The expected cyclic behavior of the each yielding section and the monotonic envelope identifying the different performance limit states is qualitatively displayed in Figure 21.16.

Beginning with the trial design (Figure 21.14), the performance of the building is evaluated by determining the demands in each component and comparing these demands to performance-based acceptance criteria. However, as discussed in previous sections of this chapter, there are different approaches to estimating demands and consequently, different assessment criteria to evaluate the performance of the structure. Different methods will be presented in the following sections so as to make readers aware of the predicament that will face engineers when making a decision on which method to use in a given situation. Hopefully, some of the observations and comments offered in this example will assist in clarifying some of these issues. Method I: Deterministic Assessment — LSP (FEMA-356)

The so-called ''pseudo'' lateral load to be applied on the frame is determined from Equation 21.10. The fundamental period of the building (established from an eigenvalue analysis of the frame model) is 1.45 s. The coefficients needed to evaluate the total lateral load V are

C2 = 1.0 for linear procedures

C3 = 1.0 (assuming P-D effects can be ignored)

This results in a total lateral force of V = 6672 kN (1500 kip) to be applied on each perimeter frame in each direction. The lateral load is distributed over the building height using the expression given in Equation 21.12. The resulting moments on the structural components are recorded, and the peak m-factors are evaluated. Recall that the m-factor is the ratio of the peak moment to the moment capacity

(defined here as the yield moment and computed by taking the product of the yield stress of the material and the plastic section modulus) of the beam. A typical summary of such an evaluation is shown in Table 21.13 for all the beam elements on the first level of the building.

This process is carried through all the beams and columns in the structure. The resulting m-factors for the entire frame are exhibited in Figure 21.17.

These m-factors are then compared to the acceptance criteria listed in FEMA-356 to check if the desired performance level has been satisfied. The limits on m-factors for different performance levels are a function of certain section characteristics as identified previously in Table 21.5. For the beams on the first level for which m-factor computations were listed in Table 21.13, the following section characteristics are established:

bf = 267 mm(10.5 in.), tf = 21.6 mm (0.85 in.), t„ = 14.5 mm (0.57 in.), h = 762 mm (30 in.)

bf 52 h 418

2tf Vfe tw Vfe

The above numbers, using Table 21.5, require that for IO performance the m-factors be less than 2.0. Since this is true for all beams in the first-story level, they satisfy IO criteria. This performance limit is summarized in Figure 21.18 along with the performance limit states for all elements in the building. As displayed in Figure 21.18, several columns fail LS performance level at the third and fifth floor levels. The notation CP indicates that the element meets the criteria for CP but fails LS performance levels. Since the objective of the design was to ensure LS performance, the result of this evaluation indicates that the

TABLE 21.13 Peak Demands in Beams on First Floor Using LSP
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