Shear Stress Based on Circular Bar Theory
Shear stress based on circular bar theory is considered exact for circular bars and shafts. It will be interesting to see how well thin-walled theory compares.
The shear stress for a circular bar is given by
τ = Tro/J
where J is the polar moment of inertia and ro is the outside radius. For this example, the polar moment of inertia is
J = π ro4/2 - π ri4/2 = π [(1+0.2/2)4 - (1-0.2/2)4]/2
= 1.269 in4
Thus, the shear stress is
τ = (5 kip-ft)(12 in/ft)(1.1 in) / (1.269 in4)
= 52.01 ksi
This is about 9% higher than the value calculated from thin-walled theory. Thus, for thin-walled theory to be accurate, the tube thickness should be less than 10% of the overall dimension.