# What is the stress induced by steel bar of 10 mm heated from 10° C to 30° C which is free to expand?

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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

`Deltatheta=30-10=20`

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:

`alpha=Eepsi=EalphaDeltatheta`

`alpha=(200x10^9)(13x10^-6)(20)=52x10^6`

Therefore, the stress in the bar when it is heated from 10 C to 30 C is 52e6 Pa or 52 MPa

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