Increase or decrease of temperature of a free body causes the body to expand or contract and no stresses are induced. However, if the deformation of the body is constrained, some stresses are induced in the body, and such developed stresses are called temperature stresses which may be tensile or compressive based on either the contraction is prevented or extension is prevented.
A bar whose ends are fixed to rigid supports, so that the expansion is prevented, is considered. Let the length of the bar be l subjected to an increase in temperature T°. The expansion of the bar will be
where α is the coefficient of thermal expansion of the material of the bar.
Because of the end conditions the bar is not allowed ...