GATE 2021 ME (ME1) – Question 65

Machine Design · Bolted, riveted and welded joints · 2 marks · Numerical answer

A cantilever beam of rectangular cross-section is welded to a support by means of two fillet welds as shown in figure. A vertical load of 2 kN acts at free end of the beam. Considering that the allowable shear stress in weld is 60 N/mm², the minimum size (leg) of the weld required is _____ mm (round off to one decimal place).

Two vertical fillet welds each 40 mm long and 50 mm apart; a 2 kN downward force acts 150 mm from the support. See the attached source image.

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Correct answer: 6.67 to 6.73

Explanation

Let throat t=0.707 s. Direct shear is $\tau=2000/(80t)=25/t$. Weld-group second moment about the horizontal axis is $I=2t(40)^3/12$, giving extreme bending normal stress $\sigma=M(20)/I=562.5/t$.

Using maximum shear stress, $\tau_{max}=\sqrt{(\sigma/2)^2+\tau^2}=282.359/t$. Equating to 60 gives t=4.70598 mm and **s=6.7 mm**.