Torsion — Worked Examples

A solid shaft with diameter $40\text{ mm}$ carries $T=500\text{ N}\cdot\text{m}$. Determine maximum torsional shear stress.

A hollow shaft has $D=60\text{ mm}$, $d=40\text{ mm}$, and carries $1.50\text{ kN}\cdot\text{m}$. Determine shear stress at the outer and inner surfaces.

A $50\text{ mm}$ diameter steel shaft is $2.00\text{ m}$ long and carries $1.00\text{ kN}\cdot\text{m}$. Take $G=80\text{ GPa}$. Determine the elastic twist.

A solid shaft must carry $800\text{ N}\cdot\text{m}$ while keeping $\tau_{\max}\le50\text{ MPa}$. Determine the theoretical minimum diameter.

A shaft transmits $60\text{ kW}$ at $600\text{ rpm}$. Determine the torque.

Two solid shafts carry the same torque. Shaft B has diameter $50\text{ mm}$ while Shaft A has diameter $40\text{ mm}$. Find $\tau_B/\tau_A$.

Two steel shaft segments carry the same torque $T=600\text{ N}\cdot\text{m}$. Segment 1 has $L_1=1.0\text{ m}$ and $J_1=5.0\times10^5\text{ mm}^4$; Segment 2 has $L_2=1.5\text{ m}$ and $J_2=8.0\times10^5\text{ mm}^4$. Take $G=80\text{ GPa}$. Determine total twist.

A shaft satisfies its allowable shear-stress limit but twists $3.0^\circ$ over a machine span where the service limit is $1.0^\circ$. Is the shaft acceptable under the stated criteria?

A uniform shaft is fixed at both ends. A torque of $9.0\text{ kN}\cdot\text{m}$ is applied at a junction located $1.0\text{ m}$ from the left support and $2.0\text{ m}$ from the right support. The shaft has constant $GJ$. Determine the reaction-torque magnitudes.

A machine transmits constant mechanical power. Its shaft speed doubles while power remains unchanged. Determine the ratio of new torque to original torque.