The Influence of the Bourdon Effect on Pipe Elbow

Abstract

Pipe elbows are frequently used in a pipeline system to change the directions. Thermal expansion and internal pressure results in bending moments on the bends causing ovalization of the initial circular cross-section. The ability of the bend to ovalize will result in an increase in the bend flexibility when compared to straight pipes [1]. In case of bends subjected to internal pressure, the pipe will start to straighten out due to the difference between the intrados and extrados surface areas. The internal pressure causes unbalanced thrust forces tending to open up the elbow depending on its stiffness and surrounding constraints. These forces tending to cause ovalization of the cross section and causing the tendency of pipe bends to open up are termed the “Bourdon effect”. If these unbalanced thrust forces are not taken into consideration, unanticipated deformations and high stress levels could occur at the elbow location that may not be accounted for in traditional stress analysis [2]. A better understanding of the influence of the Bourdon effect on the elbow design parameters is required. Past studies have investigated the behaviour of pipe elbows under closing bending moment and proposed factors that account for the increased flexibility and high stress levels resulted from ovalization. These factors are used in the current design codes [3],[4] &[5] and known as the flexibility factor and stress intensification factor. In this investigation, pipe elbows with different nominal pipe size and various bend radiuses to internal pipe radius ratios (R/r) are studied to get a better understanding of the Bourdon effect and its influence on the pipe stresses and deformations. Differential equilibrium equations are solved to derive a mathematical model to evaluate the unbalanced thrust forces resulted from the Bourdon effect on a pipe elbow. The forces evaluated from the derived model are compared to finite element model results and showed excellent agreement. A comparison between the CSA-Z662 code and the FEA results is conducted to investigate the applicability of the stress intensification factors used in the current design code for different loading cases. The study showed that the external bending moment direction acting on the pipe has a significant effect on the distribution of stresses on the pipe elbow and significantly depending on the level of applied internal pressure.

A methodology for flexibility analysis of pipeline systems

“…It is expected that higher sustained stresses will occur in such region due to the bourdon effect influence on pipeline elbow. 66 Possibility of bend ovalization can lead to higher induced stresses on the nearby straight piping due to the difference between the inner and outer pipe crosssection. It is therefore necessary to specifically pinpoint such locations to ensure pipeline functionality with respect to primary stresses.…”