If the outer radius is halved while torque and the polar moment of inertia remain constant, how does the shear stress change?

If the outer radius is halved while torque and the polar moment of inertia remain constant, how does the shear stress change?

• A. Tau doubles.
• B. Tau quadruples.
• C. Tau halves.
• D. Tau remains the same.

Answer: (C)

When a shaft is under torsion, the shear stress at the outer surface is given by tau = T * c / J, where c is the outer radius and J is the polar moment of inertia. If torque and J stay the same but the outer radius is halved, the only change is c, which halves. Therefore tau becomes (T * (c/2)) / J = (1/2) * (T * c / J). So the shear stress is reduced by half.

When a shaft is under torsion, the shear stress at the outer surface is given by tau = T * c / J, where c is the outer radius and J is the polar moment of inertia. If torque and J stay the same but the outer radius is halved, the only change is c, which halves. Therefore tau becomes (T * (c/2)) / J = (1/2) * (T * c / J). So the shear stress is reduced by half.