Plastic Interaction Relationships for Square Hollow Structural Sections: Lower Bound Solution
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Bibliographic record
Abstract
General interaction relationships for hollow structural square sections subjected to general combinations of normal force, twisting moments, biaxial bending moments, and biaxial shearing forces are developed. The lower bound theorem of plasticity is employed to obtain the fully plastic resistance of the section as determined by the maximum distortional energy density criterion. Previously established interaction relationships for hollow structural sections subjected to bending moments, axial force, and twisting moments are recovered as a special case of the general solution. The developments are expressed as universal, nondimensional relationships suitable for limit state design. Consideration is given to the limits of applicability of the interaction relations. Simplifying assumptions are made and their effects are discussed. A stress resultant transformation scheme is developed in order to reduce the number of interaction relations to be developed from 20 cases to only three fundamental cases.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it