Elastoplastic Collapse of Tubes Under External Pressure

R. J. FRITZ. The authors' paper proposes a modification in the ASME Code criteria for the strength of tubes subjected to external pressure. The discusser agrees that these criteria should be modified and makes these comments on the paper. The authors could have emphasized that the plastic tangent and reduced moduli used by them apply to uniaxially loaded rings, and that using these moduli in their collapse equation is inconsistent for two reasons: (a) plastic moduli should not be used with the elastic Poisson's ratio, and (b) plastic moduli for uniaxially loaded rings should not be used in the biaxial stress relationship implied by the use of the Poisson's ratio in the collapse equation. Also, the authors could better have called the reduced modulus an effective modulus rather than an average modulus. The reduced modulus is based on a consideration of equilibrium and compatibility and is associated with a shift in the neutral axis as the section is bent in the plastic range. In such a case the local modulus is considered to be the plastic modulus on the side with increasing compressive stress and the elastic modulus on the side being unloaded by bending. The reduced modulus is the effective bending modulus.