 In this problem we have two concentric shafts, the shaft B which is hollow, and the shaft A which is solid. They are both clamped at this end, at this wall, and they are rigidly connected at this end. Also at this point at this end we are applying the torque T. And the problem is asking to determine what is the angle of rotation of the overall system. Then we have to calculate basically what is the angle of rotation of this structure at this point. Then we can start as usually drawing the free body diagram. So we have cut the structure at this point, then we have here the applied torque T, and we have here the internal torques T A and of course T B. Then now from the equilibrium equations we know that the sum of torques at any point of the structure must be equal to zero. Then from this equation we have that T A plus T B is equal to T. Then we have two unknowns on one equation and we need to look for one additional equation. In this case of course we are looking for the displacement compatibility equation. So if we look at the geometry of the problem you can see here that both shafts are connected rigidly at this point, at this end. So then the rotation angle of this structure theta will be equal to the rotation angle of the inner shaft theta A and will be equal to the rotation angle of the outer shaft theta B. So this is the compatibility equation that we were looking for, theta is equal to theta A is equal to theta B. So we have now one additional equation, but what we are really looking for is for an equation which relates the torques T A and T B. And this is a relationship between angles so we can use the force displacement relationship in order to find that equation. So from the torsion formula we have that the rotation angle due to the torque is equal to T L divided by J times G. Then we can start calculating what is the rotation angle of the shaft A. So we can first determine what is the internal torque. So if this is shaft A we have that the internal torque is equal to T A and it is constant. Then the rotation angle of this point with respect to the wall is equal to T A times L divided by G and J. And we have something similar for the shaft B. We have the torsion diagram so we have that the torque is also constant and the magnitude is equal to T B. Then the rotation angle theta B is equal to T B times L divided by J and G B. So now if we use these two relationships and we substitute them into the compatibility equation we find that then this is the second equation that we were looking for and if we combine this equation with equation one so we have that T is equal to T A plus T B. We have a set of two equations with two unknowns that we can easily solve. So from equation two we have for example that T B is equal to then if we substitute this result into equation one we have that and if we solve this equation we find that T A is equal to then we already know the first reaction torque and of course it's very easy to calculate the second one T B but actually we don't need to do it because what the problem is asking is to calculate what is the rotation angle of the whole structure and if you remember the rotation angle theta is equal to theta A is equal to theta B. So it's enough to know what is the torque T A to calculate what is this angle because it will be equal to theta B and equal to the total rotation angle of the structure so from here we have that theta A if you remember this is equal to T A times L divided by J G A so this is equal to we can rearrange this equation in a more beautiful way so this is equal to then this is the final result as I said before this is the angle of rotation of the shaft A which is equal to the angle of rotation shaft B which is equal to the total rotation angle of the whole structure