A cantilever I-Beam needs to support a distributed load of 300 lb/ft for the last 2 feet, as shown in the diagram on the left. The beam is a standard I-Beam S18x70. What is the maximum shear stress in the web section at location a-a? Account for the weight of the beam.

The actual shear load at the specified location, a-a, needs to be determined before the shear stress can be calculated. Both the applied load, 600 lb, and the beam weight need to considered. Using the appendix Structural Shapes, the beam weight is 70 lb/ft.

Cutting the beam at a-a, and summing forces in the vertical gives,

     V = 300(2) + 70(7)
        = 1,090 lb

Recall, the shear stress at any location can be calculated from

     τ = VQ / It

Using the appendix, the moment of inertia, web thickness, and flange thickness are given as,
     I = 926 in⁴
     t_w = 0.711 in
     t_f = 0.691 in

All that is missing is Q. Since the maximum shear is needed, the largest Q is required. The largest Q of most symmetrical cross sections occurs at the middle. Thus, determining Q for top half of cross section is

     Q_max = A₁ y₁ +A₂ y₂
        = 0.691 (6.251) [(9 - 0.691 / 2)]
            + (9 - 0.691) (0.711) [(9 - 0.691)/2]
        = 37.38 + 24.54 = 61.92 in²

This gives the final shear stress as

     τ = VQ / It
       = (1,090)(61.93) / [(926)(0.711)]

     τ = 102.5 psi