And so here I'm going to have a fixed end on the right-hand side.

I'm going to have an angle of twist of C with respect to A.

And then I'm going to have an angle of twist, of D with respect to C,

that angle of twist is going to be in this direction because of my applied torque.

Then I'm going to have to have an angular twist of C with respect to D,

excuse me, D with respect to C in the other direction,

to bring it back to a total of zero displacement.

because I got zero displacement on either end.

So I've got the angle of twist of C

with respect to A minus the angle of twist of D with respect to A has to equal zero.

So here's my equilibrium equation, equation one,

here's my deformation equation but they're in terms of different unknowns so

I need to have them in terms of the same unknowns.

To do that,

let's start by saying we're going to use the elastoplastic assumption and

assume that the steel and the monel shafts remain in the linear elastic region.

And we'll assume that the steel has a torsional yield strength of 18 ksi and

the monel has a torsional yield strength of 25 ksi.

Here's a plot of an idealized elasto plastic material.

And we're saying okay let's assume we're continuing to operate for

all these situations in the linear elastic range.

Can we find a relationship between the torque and the angle of twist?

And the answer is yes.

We've done that before.

The angle of twist if we assume linear elastic is equal to the torque,

the length of this section divided by the module of this rigidity

times the polar moment of inertia of this section.

And, so let's go ahead and do that for my deformation equation and

I've got the angle of twist, the C with respect to A, which is my steel section.

So, that's T of Steel, times its length, which is 11 feet,

and we're going to convert everything to inches,

that's 12 inches per foot, and we're going to divide then by G.

I said at the beginning I'm going to change this to,

instead of 11.6, I'm going to say 11.0 times 10 to the third or

11,000 Ksi times J, solid circular cylinder.

So J is pi over 2 times the radius,

which is 3 to the fourth, 3 inches to the fourth.