The equations of thermal stresses and displacements in anisotropic hollow cylinders subjected to various selected temperature boundary conditions have been derived. The hollow cylinder is assumed to be made of transversely isotropic material. Several numerical examples are treated and the effects of the degree of anisotropy on the magnitudes of the critical stress and maximum permissible gas temperature for various sizes of grades ATJ and ZTA graphite hollow cylinders are examined. The errors which could result from the assumption of isotropic material are calculated.

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