Equivalent Moment of Inertia Based on Integration of Curvature
Bibliographic record
Abstract
This paper evaluates the benefits of computing deflection with an equivalent moment of inertia based on integration of curvature to account for changes in member stiffness along the span. Results are evaluated for steel and fiber-reinforced polymer reinforced (FRP-reinforced) concrete flexural members with different loading arrangements and support conditions. Closed-form solutions of integrated expressions for deflection are expressed in terms of an equivalent moment of inertia Ie′ and compared to deflection computed with an effective moment of inertia Ie based on the stiffness at the critical section. Results from this comparison are validated with measured deflections from an experimental database for FRP-reinforced concrete. Current code-related approaches are also compared to the experimental database. It is shown herein that the use of an integration-based expression for the moment of inertia can lead to improved prediction of deflection, though the use of an effective moment of inertia based on member stiffness at the critical section gives a reasonably conservative estimate of deflection in many cases. The benefits of taking account of changes in stiffness along the member span are more evident when low reinforcing ratios are used in combination with FRP reinforcement, and use of the integration-based expression Ie′ may be warranted when deflection control is critical in such cases.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".