Ellipsoidal Head Rules: A Comparison Between ASME Section VIII, Divisions 1 and 2
Bibliographic record
Abstract
In ASME Section VIII, Division 1, rules are provided for calculating the thickness of 2:1 ellipsoidal heads in UG-32. UG-32(c) also states that “an acceptable approximation of a 2:1 ellipsoidal head is a torispherical head with a spherical radius of 0.9D and a knuckle radius of 0.17D”. However, calculating the thickness of a torispherical head with those “equivalent” dimensions results in a thicker head. This result is inherently inconsistent, which starts to bring into question the so-called equivalency. Code Case 2260 further perpetuates this equivalency by providing alternative rules for calculating the thickness of torispherical heads, and then permitting the engineer to calculate 2:1 ellipsoidal heads implementing this 90-17 equivalency. Additionally, the calculation methodology for a 2:1 ellipsoidal head in ASME Section VIII, Division 2 uses the torispherical head calculation methodologies and directly implements this 90-17 equivalency. However, this calculation method results, for the same allowable stress basis, in a completely different thickness from the above three methods. This paper reviews the past 90+ years of work on this topic, and presents some theoretical treatment of the different head geometries. A review of the current Code rules is presented, with a comparison of results for several sizes. A survey of head fabricators is presented to show the actual geometries produced for use in ASME pressure vessels. Finally, conclusions regarding whether or not the 2:1 ellipsoidal head is in fact equivalent to the 90-17 torispherical head are presented, and recommendations for future revisions to both ASME Section VIII, Division1 and Division 2 are provided.
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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 | 0.005 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 0.006 |
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".