The text has expressions for the yield torque as a function of the yield shear stress for a thin-walled object. Assume you have a thin-walled cylinder of radius r0 and wall thickness t. You also have a cylindrical pipe of inner radius r2, and outer radius r1. Here, r1 and r2 are similar in magnitude such that r1-r2=t, and r2=ro. You also have an expression for the torque shear stress relationship for a cylindrical objects. Assume the thickness is such that the whole wall of thickness t yields at a single torque, the yield torque. (part a) Find the relationship between the yield torque and yield shear stress and the geometric parameters given for the thin-walled cylinder.

part b) Find the relationship between the yield torque and yield shear stress and the geometric parameters given for the pipe.

b1) Let r2=r0=1 and make a table that looks like you cared with t as a parameter between 0.5 and 0.001 that compares the two expressions. Discuss the results. This just normalizes the results.

b2) In your answer to part b let r2= r1-t, do an expansion, and show to first order in t you get the same answer as part a).

b3) Part of the difference in part i) is in the loose way we defined our parameters. For example, in the thin-walled cylinder is t located so the outside radius is r0+t, or r0+t/2, or somewhere else? Thus, better approximations can be made. Ignoring this, based on the above, what is a reasonable value of t/ ro for the thin-walled approximation to be considered good? Explain your reasoning.