Question

The maximum and minimum shear stresses in a hollow circular shaft of outer diameter 20 mm and thickness 2 mm, subjected to a torque of 92.7 N.m will be

• A. 59 MPa and 47.2 MPa
• B. 100 MPa and 80 MPa
• C. 118 MPa and 160 MPa
• D. 200 MPa and 160 MPa

Answer 1

The correct option is B 100 MPa and 80 MPa

Outer dia,
$D_0=20$ mm
thickness,
t = 2mm
Inner dia,
$D_i=D_0-2t$
$=20-2\times 2$
$=16$mm
Torque,
$T=92.7$N.m
$=92.7\times {10}^3$Nmm
Polar moment of inertia
$J=\frac{\pi (D_0^4-D_i^4)}{32}=\frac{\pi ({20}^4-{16}^4)}{32}$
$=9273.982m{m}^4$
$\frac{\tau }{r}=\frac{T}{J}$
Maximum shear stress,
$\tau =\frac{T{r}_0}{J}=\frac{92.7\times {10}^3\times 10}{9273.982}$
$=99.957$ MPa
Minimum shear stress,
$\tau =\frac{T{r}_i}{J}=\frac{92.7\times {10}^3\times 8}{{9273.98}^2}$
$=79.966$ MPa