Bending stresses in out-of-round uni- and multi-axial internally pressurized strength specimens

A derivation is presented for the bending stresses in internally pressurized slightly elliptical tubular or ring specimens used in the testing of uni- and multiaxial strength. The solution obtained shows that the bending stresses are directly proportional to Young's modulus of elasticity of the material being tested. A numerical example applicable to strength testing of aluminum oxide demonstrates, that a slight out-of-round-ness can result in bending stresses which are an appreciable percentage of the observed values of the fracture strength. It is concluded that strength testing by means of the internal pressurization of tubular or ring specimens requires close dimensional control in specimen manufacture.