Indeterminate Bars:

With reference to thermal stresses, bars whose thermal expansion is not restrained in any manner are known as determinate bars and the bars whose thermal expansion is restrained in any manner are known as indeterminate bars. As in the case of several of the other indeterminate problems thermal stress analysis of indeterminate bars might be carried out simply through the method of compatibility or consistent deformations.

Consider the prismatic bar of length 'L' display in Figure. The bar is linked to a rigid support at LHS and free at the other end. But at a little distance 'd' from the free end of the bar there is a rigid body that would avoid any expansion of the bar beyond the small gap of that 'd'. If the thermal expansion of the bar is less than or even equal to'd' no stresses will be induced in the bar and the problem remains determinate. If the bar is heated additional, then temperature stresses will be generates. As the bar is heated it will push against the rigid support that will restrain the expansion through exerting a compressive force on the bar that must generates elastic shortening equal to the excess thermal expansion.

Figure