Elastic-plastic finite element analysis has been carried out to evaluate collapse moments of six elbows with elbow factors varying from 0.24 to 0.6. The loading conditions of combined in-plane closing/opening bending moment and varying degree of internal pressure are considered in the analysis. For each case, collapse moment is obtained by twice elastic slope method from the moment versus end-rotation curve. Based on these results, two closed-form equations are proposed to evaluate the collapse moments of elbows under combined internal pressure and in-plane closing and opening bending moment. [S0094-9930(00)00103-7]
A large throughwall circumferential crack in an elbow subjected to in-plane bending moment can significantly reduce its collapse load. Therefore, it is very important to know the collapse moment of an elbow in the presence of a throughwall circumferential crack. The existing closed-form collapse moment equations of throughwall circumferentially cracked elbows are either too conservative or inadequate to correctly quantify the weakening effect due to the presence of the crack, especially for opening mode of bending moment. Therefore, the present study has been carried out to investigate through elastic-plastic finite element analysis the effect of a throughwall circumferential crack on the collapse moment of an elbow under in-plane bending moment. A total of 72 cases of elbows with various sizes of circumferential cracks (2θ=0–150 deg), different wall thickness (R/t=5–20), different elbow bend radii Rb/R=2,3 and two different bending modes, namely closing and opening have been considered in the analysis. Elastic-perfectly plastic stress-strain response of material has been assumed. Collapse moments have been evaluated from moment-end rotation curves by twice-elastic slope method. From these results, closed-form expressions have been proposed to evaluate collapse moments of elbows under closing and opening mode of bending moment. The predictions of these proposed equations have been compared with 8 published elbow test data and are found to be within ±11% variation except for one case.
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