3b-ex. Shear Stress Examples
Ex. 3b.1Ex. 3b.2
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Example 3b.1

Given: A rectangular piece of Jello™, h=2 inches tall by L=6 inches wide, sits on a plate with a piece of aluminum foil on top. The foil is moved to the right by w=0.1 inch, with the Jello sticking to it.

Req'd: Determine the shear strain in the Jello™.

Sol'n: The shear strain is the reduction in right angle (in radians):

g = w/h= (0.1 in.)/(2 in.) = g = 0.05 = 5.0%

This value of strain (5%) is much larger than that in typical engineering systems.

Example 3b.2

Given: A pipe of average diameter D=1.0 in. and thickness t=0.050 in. is twisted by a wrench with a torque of T = Pd = 20 lb-in.

Req'd: Estimate the shear stress in the thin-walled pipe due only to the torque.
Hint: Area = 2pRt = circumference times thickness.

Sol'n: Shear stress for the thin-walled pipe is:

t = (T/R)/A = T/[R·2pRt] = [2T]/[pD2t]
    = [(2)(20 lb-in.)] / [p(1 in.)2(0.05 in.)]

t = 255 psi

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Updated: 05/24/2009 DJD