Question

A 1.1 m long and 50 mm thick mild steel plate is welded to another plate of the same size at a right angle as shown in the figure. The size of the weld is 16 mm and permissible shear stress intensity in the weld material is not to exceed 90 MPa. What will be the maximum torque that the welded joint can bear?

• A. 385 kN-mm
• B. 411 kN-m
• C. 411 kN-mm
• D. 385 kN-m

Answer 1

The correct option is B 411 kN-m

Polar moment of inertia of load section

$J=2\times \frac{t\times L^3}{12}=\frac{2\times 0.707h\times l^3}{12}$

$J=\frac{2\times 0.707\times 16\times {1.1}^3\times {10}^9}{12}=2.51\times {10}^{9}m{m}^4$

Torque is resisted by shearing stress developed between the fillet welds and the horizontal plate.

Shear stress, $\tau =\frac{T\times \frac{l}{2}}{J}=\frac{T\times \frac{1.1}{2}\times {10}^3}{2.51\times {10}^9}=0.2191\times {10}^{-6}T$

Maximum shear stress occurs at the throat,

${\tau }_{max}=90N/m{m}^2=0.2191\times {10}^{-6}T$

$T=410.7272\times {10}^{6}N-mm$

$T=\mathrm{410.7272.}kN-m$