Cantilever Beam with Loads

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.


Shear Load at Section a-a

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


I-Beam Cross Section

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

     Qmax = 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

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