On Axially Symmetrical Residual Stresses in Bars with Longitudinally Nonuniform Stress Distribution

New equations for calculations of residual stress distribution are theoretically derived for solid cylinders. The initial distribution of the stresses including the shearing stress is computed from longitudinal distribution of residual stresses measured at a surface after removal of concentric successive layers of material. For an example, the residual stresses of a specimen quenched in iced water form the temperature below the phase transformation point were measured by the X-ray methods. Then initial residual stress distribution was numerically computed. A comparison of the values by the new calculations and by the conventional method, which assumes the longitudinal distribution of the stresses as uniform, is made and the results are discussed. The end effect is taken into account in this paper, so that the residual stress distribution in short cylinders can be determined.