## 319 Latticed and BuiltUp Members

The main difference of behavior between solid-webbed members and latticed members and built-up members is the effect of shear deformation on their buckling strength. For solid-webbed members, shear deformation has a negligible effect on their buckling strength, while for latticed structural members using lacing bars and batten plates, shear deformation has a significant effect on their buckling strength. It is common practice that when the buckling model involves relative deformation produced by shear forces in the connectors, such as lacing bars and batten plates, between individual components, a modified effective length factor Km is defined as follows:

where Kis the usual effective length factor of a latticed member acting as a unit obtained from a structural analysis and av is the shear factor to account for shear deformation on the buckling strength, or the modified effective slenderness ratio (KL/r)m should be used in the determination of the compressive strength. Details of the development of the shear factor av can be found in textbooks by Bleich (1952) and Timoshenko and Gere (1961). The following section briefly summarizes av formulas for various latticed members.

### 31.9.1 Laced Columns

For laced members as shown in Figure 31.18, by considering shear deformation due to the lengthening of diagonal lacing bars in each panel and assuming hinges at joints, the shear factor av has the form

FIGURE 31.18 Typical configurations of laced members: (a) single lacing and (b) double lacing. Copyright 2005 by CRC Press

where Ed is the modulus of elasticity of materials for lacing bars, Ad is the cross-sectional area of all diagonals in one panel, and f is the angle between the lacing diagonal and the axis that is perpendicular to the member axis.

If the lengths of the lacing bars are given (Figure 31.18), Equation 31.108 can be rewritten as

where a, b, and d are height of the panel, depth of the member, and length of the diagonal, respectively.

The SSRC (Galambos 1988) suggested that a conservative estimate of the influence of 60 or 45° lacing, as generally specified in bridge design practice, can be made by modifying the overall effective length factor K by multiplying a factor av, originally developed by Bleich (1952) as follows:

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