What is the stress induced by steel bar of 10 mm heated from 10° C to 30° C which is free to expand?
First we need to know some information about steel, namely its modulus of elasticity (E) and the coefficient of linear expansion (`alpha`).
E = 200 GPa and `alpha=13 x 10^-6 ` per Kelvin
The equation for stress (`sigma`) is:
`alpha=Eepsi` , where `epsi` is equal to strain
The equation for strain is:
`epsi=DeltaL/L=alphaDeltatheta` , where `Deltatheta` is equal to the change in temperature of the bar
If we substitute the equation for strain into the equation for strees, and sub in the values that we know, we can calcualte the stress in the steel bar:
Therefore, the stress in the bar when it is heated from 10 C to 30 C is 52e6 Pa or 52 MPa