Project ForgeStrength of Materials
Stress & Strain
GATE 2009
Hard
A solid shaft of diameter d and length L is fixed at both the ends. A torque T₀ is applied at a distance L/4 from the left end (so the shaft is split into a segment of length L/4 and a segment of length 3L/4). The maximum shear stress in the shaft is
- A16T₀/πd³
- 12T₀/πd³
- C8T₀/πd³
- D4T₀/πd³
Explanation
Statically indeterminate: let TA (in the L/4 segment) and TB (in the 3L/4 segment) be the fixed-end reaction torques, TA+TB=T0. Twist compatibility at the load point requires TA(L/4)=TB(3L/4) ⟹ TA=3TB, so TA=3T0/4, TB=T0/4. The larger torque (3T0/4) governs: τmax=16(3T0/4)/(πd³)=12T0/(πd³).
Source: GATE ME 2009 (2009)
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