Consider the thermal stress problem in a circular ring as shown in the figure. Assuming the temperature

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Consider the thermal stress problem in a circular ring as shown in the figure. Assuming the temperature and stress fields depend only on the radial coordinate r, the general solution is given by (12.7.4). If the surfaces r = a and r = b are to be stress free, show that the solution can be written as:

Ea o=4+4 (2 10g +1)+24 / Tror Or a a

for appropriate constants Ai. Note for this type of problem the logarithmic term is retained as long as the ring is only a segment and not a full ring. For this case the displacements at each end section need not be continuous.

a b

Equation 12.7.4

Ea or=++(2 logr-1) - Fa [Trdr

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