gear shaft transmits torques $T _ { A } = 975 \mathrm {~N} \cdot \mathrm { m } , T _ { B } = 1500 \mathrm {~N} \cdot \mathrm { m } , T _ { C } = 650 \mathrm {~N} \cdot \mathrm { m } \text {, and } T _ { D } = 825 \mathrm {~N} \cdot \mathrm { m } . \text { If }$ the allowable shear stress is 50 MPa, the required shaft diameter is approximately:

Question

Quizplus · Accepted Answer

The maximum torque among the four is 1500 N·m.
Using the torsion formula,
T/J = τ/R = Gθ/L
J = πd⁴/32
τ = (T/J)R = (T/πd⁴/32)(d/2) = 16T/πd³
d = (16T/πτ)^⅓
τ = 50 MPa = 50 N/mm² (given)
For T = 1500 N·m at section B,
d = (16×1500/π×50)^⅓ = 45.6 mm
Therefore, the required shaft diameter is approximately 46 mm.

Gear Shaft Transmits Torques The Allowable Shear Stress Is 50 MPa, the Required Shaft