## Y FIGURE 31.20 Typical configurations of members with battens and with perforated cover plates: (a) battens, (b) lacing-battens, and (c) perforated cover plates.

f = 1.98 in.4 (8.24 x 105mm4) a = 15 in. (381 mm) b = 9 in. (229 mm) Ib = 9 in.4 (3.75 x 106 mm4)

Solution

1. Calculate the shear factor av by Equation 31.112

2. Calculate (Ky)m by Equation 31.107

31.9.3 Laced-Battened Columns

For the laced-battened columns as shown in Figure 31.20b, considering the shortening of the battens and the lengthening of the diagonal lacing bars in each panel, the shear factor av can be expressed as i p2 ei f d3 tt

where Eb is the modulus of elasticity of materials for battens and Ab is the cross-sectional area of all battens in one panel.  FIGURE 31.21 A battened column.

### 31.9.4 Columns with Perforated Cover Plates

For members with perforated cover plates shown in Figure 31.20c, considering the horizontal cross-member as infinitely rigid, the shear factor av has the form

where c is the length of a perforation.

It should be pointed out that the usual K-factor based on a solid member analysis is included in Equations 31.108 to 31.114. However, since the latticed members studied previously have pin-ended conditions, the K-factor of the member in the frame was not included in the second terms of the square root of the above equations in their original derivations (Bleich 1952; Timoshenko and Gere 1961).

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