Constructing approximate yield loci of notched members under complex loading states

For pipe beams with a stable crack under bending only, Petroski proposed that the cracked section yields at a reduced bending moment Mp=γM0 with γ<1 being a reduction factor. A Reduction Factor Approach is defined in this paper to approximately construct the yield loci of notched/cracked members under various complex generalized loading states. By introducing a reduction factor γ into the yield functions of the perfect member, the interactive yield loci for a V-shape notched/cracked member under interactions between bending and tension, between bending and shear, or amongst bending, tension and shear, are straightforwardly constructed. When tension n is involved, a term (i.e. 2cn) arising from the effect of ligament eccentricity should be added to the bending moment m. The approximate yield loci can be expressed in analytical forms, facilitating applications in engineering analyses when complex generalized loading states are involved. The yield surfaces tabulated in Lee and Parks [7] are consistently fitted by a concise analytical expression whose form is suggested by the present approach.