Project ForgeStrength of Materials
Stress & Strain
GATE 2016
Hard
A horizontal bar of constant cross-section, fixed at A, is loaded as follows: section AB (length L) has Young's modulus 3E, section BC (length L) has Young's modulus E. A force P pushes inward at B (toward A) and a force F pulls outward at the free end C. For the deflection at C to be zero, the ratio P/F is __________.
4(± 0.1 accepted)
Explanation
Internal force in BC = F (tension). Internal force in AB = F-P (by sectioning to the right of any cut in AB). Total elongation at C = (F-P)L/(3AE) + FL/(AE) = 0 → (F-P)/3 + F = 0 → 4F = P → P/F = 4.
Source: GATE ME 2016 Set-1 (2016)
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