Alright, so anything that deals with torque is my weakness in this class.

I'm given the following question:

A stepped shaft is subjected to three torques: 3000 N*m, 2000 N*m, and 800 N*m -- in between each shaft member. The first member has a diameter of 80mm, the second is 60mm, and the third is 40 mm with each member being 0.5m long where the first member is welded to a wall. The modulus of elasticity, G, is 80 GPa. Calculate the maximum shear stress in the shaft, then the angle of twist (phi) in degrees at the free end.

I set up by drawing my diagram with the welded end on the left being point A, then the first torque point as B, the second C, then the free end on the right with the 800 N*m as D.

Now, my question from there is how to solve for the maximum shear stress. I considered two different ways: calculating it as a whole piece or calculating the shear stress for each member (T_ab, T_bc, T_cd) then using the smallest value as my maximum. I'm just not sure which way is correct (I'm aware that there's multiple techniques, but these are the two I was able to come up with).

My second question is how to calculate the torque of the welded segment. I'm used to there not being any free ends, so both sides are welded. Would I set up my moment equation as,

Code:

T_a + 3000 + 2000 + 800 = 0

Then I'm not exactly sure what to do from there. My instinct tells me to start working from the free end towards the closed, calculating the max shear stress each segment can handle. Or should I start from the closed and work towards the free?

Thanks in advance!