Torques T = 5.7 kN . m are applied to a hollow aluminum shaft (G = 27 GPa and $d_{1}=52 \mathrm{~mm}$ . The allowable shear stress is 45 MPa
And the allowable normal strain is $8.0 \times 10^{-4}$ . The required outside
Diameter $d_{2}$ of the shaft is approximately:

Question

Quizplus · Accepted Answer

To find the required outside diameter $d_2$, we use the torsion formula $\tau = \frac{T \cdot c}{J}$, where $\tau$ is the shear stress, $T$ is the torque, $c$ is the outer radius, and $J$ is the polar moment of inertia for a hollow shaft. Given the allowable shear stress and the torque, we solve for $d_2$ ensuring it does not exceed the allowable stress. Calculations show that $d_2 \approx 91 \, \text{mm}$ satisfies the conditions.

Torques T = 5 d1=52 mmd_{1}=52 \mathrm{~mm}d1​=52 mm the Allowable Shear Stress Is 45 MPa and the a Hollow

Torques T = 5 $d_{1}=52 \mathrm{~mm}$ the Allowable Shear Stress Is 45 MPa
and the a Hollow