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is linear and elastic under small loads. The total deflection of 0.8 in. is obtained by multiplying the deflection of 0.02 in. by the scaling factor of 40. The deflection ratio over the span length is 1/1200, which meets the limitation 1/360. The deflection at the service load will be smaller than that above since the factored load is used for the calculation of deflection above.

### 5.6.1.2 Comparison of Results

The advanced analysis and LRFD methods predict the same member size of steel pipe with 6 in. diameter and 0.28 in. thickness. The load-carrying capacities of element 10 predicted by these two methods are the same, 80.5 kip. This is because the truss system is statically determinant, rendering inelastic moment redistribution of little or no benefit.

### 5.6.2 Unbraced Eight-Story Frame

Figure 5.37 shows an unbraced eight-story, one-bay frame with hinged supports. All beams are rigidly connected to the columns. The column and beam sizes are the same. All beams are continuously braced about their weak axis. Bending is primarily about the strong axis at the column. A36 steel is used for all members.

### 5.6.2.1 Design by Advanced Analysis

Step 1: Load condition and preliminary member sizing. The uniform gravity loads are converted to equivalent concentrated loads, as shown in Figure 5.41. The preliminary column and beam sizes are selected as W33 x 130 and W21 x 50.

Step 2: Structural modeling. Each column is modeled with one element since the frame is unbraced and the maximum moment in the member occurs at the ends. Each beam is modeled with two elements.

The explicit imperfection and the further reduced tangent modulus models are used in this example, since they are easier in preparing the input data compared to equivalent notional load models. Figure 5.42 shows the model for the eight-story frame. The explicit imperfection model uses an out-of-plumbness of 0.2%, and in the further reduced tangent modulus model, 0.85Et is used.

Herein, a scaling factor of 10 is used due to the high indeterminacy. The load increment is automatically reduced if the element stiffness parameter, z, exceeds the predefined value 0.1. The 54 load steps required to converge on the solution are given in P.OUT2.

Step 3: Analysis. The input data may be easily generated, as listed in Table 5.9. Programs are executed in sequence by typing the batch file command RUN.

Step 4: Check of load-carrying capacity. From the output file P.OUT, the ultimate load-carrying capacity of the structure is obtained as 5.24 and 5.18 kip with respect to the lateral load at roof in load combination 2 by the imperfection method and the reduced tangent modulus method, respectively. This load-carrying capacity is 3 and 2% greater, respectively, than the applied factored load of 5.12 kip. As a result, the preliminary member sizes are satisfactory.

kip kip)

25 ft

FIGURE 5.41 Concentrated load condition converted from the distributed load for the two-story frame.

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