Project ForgeStrength of Materials
Stress & Strain
GATE 2019
Medium
A solid cube of side 1 m is kept at a room temperature of 32°C. The coefficient of linear thermal expansion of the cube material is 1×10⁻⁵/°C and the bulk modulus is 200 GPa. If the cube is constrained all around and heated uniformly to 42°C, the magnitude of volumetric (mean) stress (in MPa) induced due to heating is ___
60 MPa(± 0.5 accepted)
Explanation
Free volumetric thermal strain = 3αΔT = 3×10⁻⁵×10 = 3×10⁻⁴. Since the cube is fully constrained, this strain is entirely suppressed, developing a volumetric stress σ = K×(3αΔT) = 200,000 MPa × 3×10⁻⁴ = 60 MPa.
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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