Thermal stresses

 Content  Thermal stresses. Thermal Stresses on Tapering Section.

Whenever there is some increase or decrease in the temperature of a body, it causes the body to expand or contract. A little consideration will show that if the body is allowed to expand or contract freely, with the rise or fall of the temperature, no stresses are induced in the body. Such stresses are the deformation of the body is prevented, some stresses are induced in the body. Such stresses are known as Thermal Stresses or temperature stresses and corresponding strains are called Thermal strain or temperature strains.

When a bar of length (l) is subjected to an increase in temperature (t), then the increase in length when the bar is free to expand is given by…

δl = l . α . t            [α= Coefficient of linear expansion]

If, the ends of the bar are fixed to rigid support so that expansion is prevented, then compressive thermal strain is induced in the bar,

ε = δl / l  = l . α . t/l  = α . t

and thermal stress,                           = ε . E = α . t . E

*** If the support yields an amount equal to δ, then the actual expansion that has taken place is given by,…

δl = l . α . t-δ

Thermal Stresses on Tapering Section:- When a circular bar of uniformly tapering section fixed at its ends is subjected to an increase in temperature (t) as shown fig.

induced thermal stresses,

= α . t . E . d/ d2