Multicriteria Capacity Envelopes for Biaxial Bending of Concrete Hydraulic Structures
Bibliographic record
Abstract
Envelopes for biaxial bending capacity of reinforced concrete elements are used extensively in design or in structural safety evaluation to verify the adequacy of internal force resultants from series of axial P and bending moments Mx and My loading pairs computed for prescribed load combinations. However, existing methods to construct P-Mx-My (PMM) interaction curves are not appropriate for concrete hydraulic structures because (1) pressurized water could penetrate in cracks leading to a coupled hydromechanical problem and (2) the structural performance is assessed using several criteria related to the allowable cracked area as well as allowable compressive (tensile) stresses for usual, unusual, and extreme load combinations. This paper presents a methodology to construct PMM interaction curves for arbitrary cross sections of hydraulic structures considering multiperformance criteria, water penetration in cracks, as well as the presence of reinforcing steel. The computations are based on a robust and efficient isogonic approach based on strength of materials where the position of the neutral axis is systematically varied over the cross section to find PMM equilibrium solutions. Four application examples of the proposed approach are presented (1) to illustrate its versatility, (2) to validate the results, and (3) to show its convergence properties. In some cases, PMM capacity envelopes are formed by distinct closed surfaces where equilibrium solutions are possible. This type of PMM capacity envelope, which the proposed algorithm is able to construct, is not found for classical reinforced concrete elements.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".