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A solid cube of side 1 m is kept at a room temperature of 32C. The coefficient of linear thermal expansion of the cube material is 1 × 10-5/° and the bulk modulus is 200 GPa. If the cube is constrained all around and heated uniformly t o 42°C, t hen t he magnit ude of volumetric (mean) stress (in MPa) induced due to heating is _____.
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- 60 MPa
- 59 MPa
- 58 MPa
- 61 MPa
Correct Option: A
a = 1 m
Ta = 32°C
α = 1 × 10-5/°C
K = 200 GPa
∆T = 10°C
| εv = | (3σ) = 3αT | E |
As σ1 = σ2 = σ3 = σ (mean volumetric stress)
σ = 3Kα∆T
= 3 × 200 × 103 × 1 × 10-5 × 10
σ = 60 MPa
