In composite bars made of materials with different rates of thermal expansion, internal stresses can be set up by temperature changes; these
stresses occur independently of those due to external restraints.
Consider, for example, a simple composite bar consisting of two members-a solid circular bar, 1, contained inside a circular tube, 2, Fig:1, The materials of the bar and tube have Different coefficients of linear expansion, a, and q, respectively. If the ends of the bar and tube are attached rigidly to each other, longitudinal stresses are set up by a change of temperature.
If A, and E, are the cross-sectional area and Young's modulus, respectively, of the inner bar, and A, and E, refer to the outer tube, then the contraction of the inner bar to P is
and the extension of the outer tube due to P is
Then from compatibility considerations, the difference in lengths (a, - %) OL, is eliminated completely when;
On substituting for e1 e2, we have;
The force P is induced by the temperature change 8 if the ends of the two members are attached rigidly to each other; from equation (1.22), P has the value;
An internal load is only set up if alpha 1is different from alpha 2.