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Effective Net Area With Shear Lag

Module by: Michael Terk. E-mail the author

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Summary: (Blank Abstract)

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Why use the factor U?

"Shear lag occurs when some elements of the cross section are not connected, as when only one leg of an angle is bolted to a gusset plate. The consequence of this partial connection is that the connected element becomes overloaded and the unconnected part is not fully stressed. Lengthening the connected region will reduce this effect. Research by Munse and Chesson (1963) suggests that shear lag be accounted for by using a reduced, or effective, net area. Because shear lag affects both bolted and welded connections, the effective net area concept applies to both types of connections." LRFD Steel Design Second Edition -- William T. Segui

Figure 1: An L-shaped member that is only bolted on one side. This type of member will have shear lag.
Figure 1 (shearlagpic.bmp)

Bolted Sections

The equation for the effective net area is:

A e = A n U A e A n U (1)
U=1−x¯ℓ≤0.9 U 1 x ℓ 0.9 (2)

where:

  • A e A e = effective area, in. 2 in. 2
  • A n A n = net area, in. 2 in. 2
  • U U = reduction coefficient
  • x¯ x = connection eccentricity, in.
Figure 2: An example of the connection eccentricity for an L-shaped member.
Figure 2 (x.bmp)
  • ℓ ℓ = length of the connection in the direction of loading, in.

Welded sections

The equation for the effective net area depends on the type of weld

  1. When the tension is transmitted only by a longitudinal weld connecting the member to something other than a plate, or the weld is both longitudinal and transverse:
    A e = A g U A e A g U (3)
    U=1−x¯ℓ≤0.9 U 1 x ℓ 0.9 (4)
  2. When the tension is transmitted only by a transverse weld:
    A e =AU A e A U (5)
    U=1.0 U 1.0 (6)
  3. When the tension is transmitted to a plate only by longitudinal welds along both edges at the end of the plate:
    A e = A g U A e A g U (7)

    where

    • For ℓ≥2w ℓ 2 w ........................... U=1.00 U 1.00
    • For 2w>ℓ>1.5w 2 w ℓ 1.5 w .................. U=0.87 U 0.87
    • For 1.5w>ℓ>w 1.5 w ℓ w .................... U=0.75 U 0.75

where:

  • A e A e = effective area, in. 2 in. 2
  • A g A g = gross area, in. 2 in. 2
  • A A = area of directly connected elements, in. 2 in. 2
  • U U = reduction coefficient
  • x¯ x = connection eccentricity, in.
  • ℓ ℓ = length of the longest weld, in.

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