GATE 2020 CE (CE1) – Question 52
The doubly symmetric built-up section shown has flange/web plates joined by continuous 10 mm fillet welds. About X–X, $I=7.73\times10^6$ mm⁴. Permissible weld shear stress is 100 N/mm²; weld capacity governs. Find maximum section shear force (kN), to one decimal place.
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Correct answer: 393.5 to 399.1
Explanation
Flange area is $100(10)=1000$ mm² and centroid offset 55 mm, so $Q=55000$ mm³. Four longitudinal welds provide capacity per length $4(10/\sqrt2)(100)=2828.427$ N/mm. Equate this to shear flow VQ/I: $V=2828.427(7.73\times10^6)/55000=\mathbf{397.5}$ kN.