The Influence of the Bourdon Effect on Pipe Elbow
Bibliographic record
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".