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Shear Stress

Example: The rocker-arm linkage, ABCD, is supported by a vertical post CF with smooth

pins at A, B, C, and D. A force, P, shown in the figure below is 500 lb. The pin at C has

a diameter, e, of ½ in. The following data apply: a = 2 in. , b = 8 in., c = 4 in., d = 7 in.,

θ = 20^o, and α = 75^o . Find the average shear stress in the pin.

Strategy: Construct a free body diagram of the link, BCD, recognizing that link AB is

a two-force member (from statics). Use the equations of equilibrium ΣM_C = 0, ΣF_x = 0,

and ΣF_y = 0 to find the resultant force acting on the pin. The average shear stress in the

pin is then this resultant force carried by the pin divided by its cross-sectional area.

A free body diagram of link BCD is:

Here tan β = 2/8 so β = 14 ^o

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