elastic stresses for 90° elbows under in-plane bending

using finite element analysis, this paper extends elastic stress solutions for 90° pipe elbows under in-plane bending, given in marie et al. (2007), to cases of mean pipe radius-to-thickness ratio up to 50. it is found that for 90° elbows an in-plane bending moment produces not only an axial membrane stress component but also axial and hoop bending stress components. furthermore, the magnitudes of these stress components depend strongly on the mean radius-to-thickness ratio, the circumferential location and the longitudinal location. maximum stresses tend to occur in the centre of the elbow at or near the crown.