Bibliographic record
Abstract
The tangent modulus or reduced modulus are used instead of the modulus of elasticity in the Euler formula for inelastic buckling of columns. Theories are given to derive these moduli. Shanley's theory of inelastic columns is described where it recommends the use of tangent modulus rather than reduced modulus. Effective lengths can be used to find the critical load for columns having different boundary conditions. Procedure to find the critical load for eccentrically loaded inelastic columns is shown by solving a problem. U.S., Canadian, and Australian codes are mentioned to find critical load for aluminum columns. The graph of slenderness ratio versus critical stress known as column strength curve is plotted using Ramberg-Osgood formula for aluminum columns. Formulas are given to find the critical stress for different aluminum alloy elastic and inelastic columns. Residual stresses are discussed in steel columns. Column strength curves given by Column Research Council, Structural Stability Research Council, and Eurocode3 are shown for steel columns. The American Institute of Steel Construction (AISC) criteria of allowable stress design (ASD) and the load resistance factor design (LRFD) are used to solve a column problem. Three practice problems, and forty-five references are given at the end of the chapter.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.065 | 0.013 |
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".