Question
A solid cube of side 1 m is kept at a room temperature of 32°C. The coefficient of linear Q.4 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, then the magnitude of volumetric (mean) stress induced due to heating is __________MPa.
Answer :
Since block is constrained in all direction and heated uniformly. So it is the case of hydrostatic state of stress
As we know, For hydrostatic state of stress,
Volumetric strain, εv = σv /K= 3αΔT
σv = 3KαΔT
σv = 3•200 •103•10–5•(42 – 32)
σv = 60 MPa
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