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Strength of Materials
Stress & Strain
GATE 2007
Easy

A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of ΔT. The Young's modulus is E and the coefficient of linear expansion is α. The thermal stress in the rod is

  • A0
  • BαΔT
  • EαΔT
  • DEαΔTL

Explanation

Since both ends are fixed, the free thermal expansion αΔT is entirely prevented, producing a compressive strain of magnitude αΔT and hence stress σ=EαΔT.

Source: GATE ME 2007 (2007)

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