Question

A solid shaft with a 30 mm diameter will substitute a hollow one with an outside diameter of 44 mm and an inside diameter of 22 mm. What is the ratio of the maximum resistible torque in the hollow to that of the solid shaft if the maximum shear stresses produced in the two shafts are to be equal?

Answer 1

The ratio of the maximum resistible torque in the hollow shaft to the solid shaft depends on the ratio of their polar moments of inertia.

Step-by-step explanation:

The ratio of the maximum resistible torque in the hollow shaft to the solid shaft is given by the ratio of their polar moments of inertia.

To find the polar moments of inertia, we need to use the formula:

Ih = π/32 * (Dh4 - dh4) (for the hollow shaft)

Is = π/32 * Ds4 (for the solid shaft)

Where Dh is the outside diameter of the hollow shaft, dh is the inside diameter of the hollow shaft, and Ds is the diameter of the solid shaft.

Substituting the given values, we have:

Ih = π/32 * (444 - 224)

Is = π/32 * 304

Finally, we can calculate the ratio by dividing the polar moment of inertia for the hollow shaft by the polar moment of inertia for the solid shaft.