At a point in a stressed body, the state of stress can be expressed in a polar (cylindrical) coordinate system using radial normal stress, circumferential (tangential) normal stress, and shear stress, related by two differential equilibrium equations derived from force balance on an infinitesimal polar element (neglecting body forces). For axisymmetric bodies — those symmetric about a central axis and symmetrically loaded — the stress state is independent of the circumferential angle and shear stress components vanish, reducing the equilibrium equations to a single relation between the radial and circumferential normal stresses. This belongs to the theory of stress analysis within strength of materials/solid mechanics, extending the earlier Cartesian stress equilibrium formulation to curved-boundary and axisymmetric structural elements, and connects to principal stress, Mohr's circle, and octahedral stress theory covered elsewhere in stress analysis.
At a point in a stressed body, the state of stress can be expressed in a polar (cylindrical) coordinate system using radial normal stress, circumferential (tangential) normal stress, and shear stress…