MecMovies 4.0 : M1.5: Shear Stress in Pin Support

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The figure shows a L shaped rigid bar B C D. Segment B C has a height of 0.4 meters and segment C D has a height of 0.6 meters. The bar is pinned at C and supported at B by a 2 meter long horizontal rod A B with a diameter of 25 millimeters. The rod is pinned to a bracket on a wall at the point A. A 50 kilo newton load acts at the midpoint between C and D and a 15 kilo newton load acts at point D. The reaction force at C is F subscript C directed to the top right. The reaction force at B is F subscript A B directed to the left along the rod.

The shear stress in the pin is given by:

$τ = \frac{F_{C}}{A_{V}} where A_{V} = area subjected to shear force$

$∴ A_{V} = \frac{F_{C}}{τ} = \frac{(88.46 kN) (1, 000 N / kN)}{(50 N / {mm}^{2})} = 1, 769.2 {mm}^{2}$