Temperature stresses

When temperature of body increased or decreased, due to application of heat or any other causes like due to summer seassion, due to wintter, etc. Then change in dimentions of body is take place. Many materials are expands due to increase in temperature and contract due to decrease in temperature. When body is free to contract and expand due to temperature variation no stresses are induced in it, but this expansion and contraction is privented then it is subjected to internal stresses. Such stresses are called as "Temperature Stresses".
And strain developed in materials due to temperature variations is called as "Temperature Stains".
Let a consider a body of uniform cross section A, having length L, heated upto temp. t^oC. Increase in length of body depends upon its coefficient of linear expansion α (expressed in /^oC). Therefore increase in lenght due to increase in temperature when body is free to expansion is given by

δL = α.t.L

Now, when expansion prevented it results in development of internal stresses and strains, in which strain e,

Compressive strain,

e = ^{Change in length}/_{Original length}
e = ^δL/_L
e = ^α.t.L/_L
∴ Temperature strain e is,= ^α.t.L/_L

∴ Temperature strain = compressive strain =

e = α.t

From Hook's law,

E = ^σ/_e
σ = E.e
σ = E.compressive strain
σ = E.α.t

∴ Temperature stress,

σ = α.t.E