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.