Example Problem 3.2.1

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: What is 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

This value (5%) is very much larger than desired in engineering situations.

Example Problem 3.2.2

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

Req'd: Estimate the shear stress in the thin-walled pipe due ONLY the Torque. Hint: Area = pDt = 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 in-lb)] / [p(1 in)²(0.05 in)]

t = 255 psi = 260 psi (2 significant digits)