Question

A 50 mm diameter soild shaft is welded to a flat plate as shown in figure. If the size of the weld is 15 mm, what is the maximum shear stress in the weld?

• A. 6 MPa
• B. 96.05 MPa
• C. 90 MPa
• D. 48.4 MPa

Answer 1

The correct option is D 48.4 MPa


Let, t = Throat thickness

h = Size of the weld

t = 0.707 h

Direct transverse stress, $\tau =\frac{10\times {10}^3}{\pi \times D\times t}=\frac{10\times {10}^3}{\pi \times 0.05\times 0.707\times 15\times {10}^{-3}\times {10}^6}$

$\tau =6MPa$

Bending stress, $\sigma =\frac{M\times y}{I}$ (Where, M = 10 $\times$ 0.2 $\times$ ${10}^3$ = 2000 N-m)

$I=\frac{\pi D^{3}t}{8}=\frac{\pi (0.05{)}^3\times 0.707\times (0.015)}{8}=5.2057\times {10}^{-7}{m}^4$

$y=\frac{D}{2}=\frac{0.05}{2}=0.025m$

$\sigma =\frac{10\times {10}^3\times 0.2\times 0.025}{5.2057\times {10}^{-7}\times {10}^6}=96.05MPa$

Maximum shear stress, ${\tau }_{max}=\frac{1}{2}\sqrt{{\sigma }^2+4{\tau }^2}=\frac{1}{2}\sqrt{(96.05{)}^2+4\times 6^2}$

${\tau }_{max}=48.4MPa$