thermal stress(Tensile or compressive stress)

thermal stress(Tensile or compressive stress)

is  a tensile or compressive stress that occur when a solid is prevented from expansion after a change in temperature, if the end of a rod are rigidly fixed so as to prevent expansion or contraction when change of temperature occur thermal stresses will be set up in the rod.  the stress may become very large and even stress the rod beyond its elastic limit or beyond its breaking strength.

 we can compute the thermal stress set up in a rod which is not free to expand or contract , suppose that a rod at a temperature of T, has its end rigidly fastened and that while they are thus held the temperature is reduced to a lower value T.

  THE FRACTIONAL change in length, if the rod were free to contract would be

∆L/L₀ =α(T-T₀) =α∆T

since te rod is not free to contract , the tension must increase by a sufficient amount to produce the same fractional change in length , but  from the distribution of young’s modulus

Y= (F/A)/(∆L/L₀) , F= AY ∆L/L₀

= F=AYα∆T

Which gives  the tension F, in the rod . the stress in the rod is F/A =Yα∆T