End Thermal Stresses in a Long Circular Rod

Abstract

The title problem is solved by the method of collocation utilizing complex nonorthogonal characteristic functions. It is shown that the characteristic values can be obtained by repeated linear interpolation without much difficulty. Ten roots are given for the case of Poisson’s ratio equaling 0.3. For large temperature gradients, an example is given which shows high end stresses. The general solution due to the end effect dies down at the rate of exp (–2.722 z/a) or faster, but its magnitude depends on the steepness of the temperature gradient. This paper also shows that the Saint-Venant principle may not always be sufficient, that the end stress could be critical, and that, therefore, it should be calculated.