Shear Stress in Beams

Example: * (continued)

The maximum shear force is P throughout the beam. The maximum bending moment is PL.

PL = P(3)(12) lb in = - 36P lbin.

Now τ = VQ/It and σ = Mc/I

For a glued section Q = A’Ybar = (2)(4)(2) = 16 in³

I = (1/12)bh3 = (1/12)(4)6³) = 72 in⁴ t 4 in, V = P

τ = (P)(16)/(72)(4) = (1/18)P = 50 So P = 900 lb

The maximum bending stress occurs at the support on the top and bottom fibers of the beam.

So σ = Mc/I = (36P)(3)/72 = 1.5P = 1600 psi So P = 1067 lb

To not exceed the allowable stress, P must be the smaller value. P = 900 lb (result)

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