What will happen of a rod is tied with fixed supports rigidly at both ends and temperature is increased ?

Explanation

If a rod is tied with fixed supports rigidly at both ends, then it will have expansion with increase with increase in temperature.
At both ends, forces are applied due to rigid supports hence compressive strain is produced. And corresponding thermal stress is produced in rod. As result rod can be banded.
E.g. length of track of steel is 5 m and cross sectional area is `40" cm"^(2)`. Thermal expansion is prevented by decrease of `10^(@)C` in temp. Coefficient of linear expansion is
`alpha_(l"(Steel)")=1.2xx10^(-5)K^(-1)`
There will be slight change in length due to temperature change (it is compressive strain).
`:.` Compressive strain `=(Deltal)/(l)`
`:.` Compressive strain `=(alpha_(l)lDeltaT)/(l)`
`:.(Deltal)/(l)=alpha_(l"(Steel)")Delta T`
`=1.2xx10^(-5)xx10`
`=1.2xx10^(-4)`
Now, Young.s modulus `"Y = "("Compressive stress")/("Compressive strain")`
`:.` Compressive stress = Y `xx` Compressive strain
`(DeltaF)/(A)=Yxx(Deltal)/(l)`
`:.DeltaF=AYxx1.2xx10^(-4)`
`=40xx10^(-4)xx2xx10^(11)xx1.2xx10^(-4)`
`=96xx10^(3)N`
`~~10^(5)N`
Thus, by this value of force with two rigid supports, tracks can be banded.