Project ForgeStrength of Materials
Stress & Strain
GATE 2018
Hard
A bar of circular cross section is clamped at ends P and Q. A torsional moment T=150 Nm is applied at a distance of 100 mm from end P (200 mm from end Q). The torsional reactions (TP, TQ) in Nm at the ends P and Q respectively are
- A(50, 100)
- B(75, 75)
- (100, 50)
- D(120, 30)
Explanation
For a uniform shaft (same GJ throughout) clamped at both ends with a torque applied at an interior point, compatibility (equal twist through both segments back to the load point) gives reactions proportional to the opposite segment length: TP = T×L2/(L1+L2) = 150×200/300 = 100 Nm, TQ = T×L1/(L1+L2) = 150×100/300 = 50 Nm.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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