Asolid long cylinder of radius b is heated such that there is a uniform temperature change t. the cylinder is encased in a rigid material such that the displacement at the outer surface u(r = b) 0. the young's modulus, poisson's ratio, thermal expansion coefficient and yield stress of the cylinder are denoted by e, v, a, and oyp, respectively background: we are always looking for where the stresses are the largest, so pay attention to whether the stresses in part c) are constants or functions or r
a) assuming the cylinder has fixed ends (in z direction), determine u, ar, aa, and oz [roadmap: you can use equations 8.47b-e]. verify that the stress state is hydrostatic and oz
b) assuming the ends of the cylinder were unconstrained, determine o,, oe,
c) using the stresses in part-(b), determine the tresca equivalent stress oeg. find the temperature t for yield.