Mechanics - Torsion theory help!?

Question

Determine the diameter of a solid steel shaft which can trasmit 45kW at 400rev/min if the maximum shear stress is not to exceed 45MN/m^2.

If the wright of this shaft is reduced by 50% by drilling and axial hole through the centre, what will be the maximum stress is the power and speed remain unchanged?

Answer 1

I won't work it out for you, but I'll explain what you need to do.  You are given the power (45 kW) and the shaft speed (400 rpm), so you can calculate the torque applied to the shaft.  Shear stress in the shaft is given by

tau = Torque * r / J

where tau is the shear stress, r is the radius to the location where you want to calculate the stress (in your case the outer radius of the shaft), and J is the polar moment of inertia.  So, you know tau & torque and can reduce the remainder of the equation to be in terms of shaft radius.

Next, weight of the shaft will be a function of radius squared so just calculate what the inner diameter would have to be for a 50% weight reduction.  Then, recalculate the shear stress.