Approximate elastic stress estimates for elbows under internal pressure

This paper presents closed-form approximations to elastic stresses in thick- and thin-walled elbows with attached straight pipes under internal pressure, based on three-dimensional elastic finite element analysis. Elastic stresses in the centre of an elbow are found to be close to an existing closed-form solution, suggesting that the hoop stress varies with the longitudinal position. The FE results indicate that the hoop stress varies linearly with the longitudinal position. Moreover, stresses in the junction of an elbow and straight pipe are shown to be the average of those in the centre of the elbow and in the straight pipe.

► We propose closed-form approximations to elastic stresses in thick- and thin-walled elbows under internal pressure, based on 3-D elastic FE analyses.
► We first extend existing analytical solution by Goodall [1] to thick-walled elbows.
► We find that elastic stresses in the centre of an elbow with an attached straight pipe are close to those without an attached straight pipe.
► We find that the hoop stress is shown to vary linearly with the longitudinal direction from the centre of the elbow to the straight pipe.
► We find that stresses in the junction of an elbow and straight pipe are shown to be the average of those in the centre of the elbow and in the straight pipe.