Project ForgeA rectangular steel bar of length 500 mm, width 100 mm, and thickness 15 mm is cantilevered to a 200 mm steel channel using 4 bolts arranged in a square pattern (A, B top row; C, D bottom row), each bolt 50 mm from the pattern's centroid O in both the horizontal and vertical directions, with the centroid located 100 mm from the fixed end. For an external load of 10 kN applied at the tip of the steel bar (400 mm from the bolt-group centroid), the resultant shear load on the bolt at B is __________ kN (round off to one decimal place).
Explanation
Primary (direct) shear per bolt = F/n = 10,000/4 = 2500 N, in the direction of F. Moment about centroid, M=F×e=10,000×0.4=4000 N·m. Secondary shear per bolt = M·r/Σr², with r=√(50²+50²)=70.71mm and Σr²=4×5000=20,000mm² for all 4 bolts, giving secondary shear magnitude ≈12,374 N with components ±8750 N in x and y. For bolt B, the secondary-shear y-component adds to the primary shear (both downward): resultant = √(8750² + (2500+8750)²) = √(8750²+11250²) ≈ 16.0 kN.
Source: GATE ME 2020 Session 1 (ME-1) (2020)
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