Project ForgeA bolted joint has 3 holes (M10 bolts) equally spaced 40 mm apart (bolts A, B, C from bottom to top), with a 10 kN force applied 150 mm horizontally from the bolt line (at bolt B's height, the group centroid). The maximum shear stress, in MPa, in the bolts at A and B, respectively, are
- 242.6, 42.5
- B42.5, 242.6
- C42.5, 42.5
- D242.6, 242.6
Explanation
Primary (direct) shear per bolt = 10000/3=3333.3N, over nominal bolt area π/4(10)²=78.54mm²: τp=42.44≈42.5 MPa (this alone is the stress at centroidal bolt B, whose secondary shear is zero). Moment M=10000×150=1.5×10⁶ N·mm; with r_A=r_C=40mm and Σr²=3200mm², secondary force at A = M·r_A/Σr²=18750N, giving τ_secondary≈238.7 MPa (perpendicular to the primary shear direction). Resultant at A = √(42.44²+238.7²)≈242.6 MPa.
Source: GATE ME 2007 (2007)
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