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80 k

Figure 7.49a. Composite diaphragm design example: (1) floor plan; (2) equivalent lateral load; (3) shear force diagram; (4) bending moment diagram.

80 k

Figure 7.49a. Composite diaphragm design example: (1) floor plan; (2) equivalent lateral load; (3) shear force diagram; (4) bending moment diagram.

system (see Fig. 7.49a1). Solid arrows indicate the values of shear below the diaphragm while dashed arrows are for values above the diaphragm. All values are in WSD format calculated by dividing the ultimate values by a factor of 1.4. The loads are for seismic forces in the north-south direction.

Figure 7.49a. (Continued.) Bending moment diagram.

It should be noted that a three-dimensional analysis that includes torsional effects always generates shear forces in a direction perpendicular to the applied load. However, these forces in the E-W direction do not affect our analysis performed for the N-S direction.

Required. Verification of shear capacity and design of the diaphragm chord and collector elements.

Solution. For analytical purposes, consider the diaphragm as a continuous beam spanning between grids A and G. Calculate the net shear forces in the frames by taking the difference in shears above and below diaphragm level. For example, the shear at grid A is equal to 185 - 125 = 60 kips. Similarly, calculate the shears in other frames. The resulting shear forces, shown in Fig. 7.49a1, may be considered, for design purposes, as reactions to the diaphragm inertial loads.

Equivalent Loads. Because the shear in the frame on line G is larger than at A, by inception, the equivalent load distribution is trapezoidal as shown in Fig. 7.49a2. If w1 and w2 are the unit values of shear at A and G, by the force equilibrium:

Summing the moments about G due to w1 and w2 and the reactions at A, C, and E, we get

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