GATE 2020 ME (ME1) – Question 49
A rectangular steel bar of length 500 mm, width 100 mm and thickness 15 mm is cantilevered to a 200 mm steel channel using four bolts as shown. For a 10 kN tip load, find resultant shear load on bolt B (kN), to one decimal. Dimensions in the figure are in mm; drawing is not to scale.
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Correct answer: 15.9 to 16.1
Explanation
Direct shear is 10/4=2.5 kN downward per bolt. Moment is 10×400=4000 kN·mm and Σr²=4(50²+50²)=20000 mm². Secondary components at B are 4000(50)/20000=10 kN horizontally and 10 kN downward. Resultant is $\sqrt{10^2+12.5^2}=16.0078$, or **16.0 kN**.