Rational model for calculating deflection of reinforced concrete beams and slabs
Bibliographic record
Abstract
Deflection control is an important performance criterion that needs to be satisfied to ensure serviceability of the structure for its intended use. The extent of cracking and amount of reinforcement affects the flexural rigidity, EI, of a reinforced concrete member and both the Canadian concrete design standard (CSA A23.3-04) and ACI Building Code (ACI 318-05) use an effective moment of inertia, Ie, that was originally proposed by Branson to compute beam deflection. This is an empirically derived equation that works well within a narrow range of limits corresponding to steel-reinforced concrete beams with a reinforcing ratio between 1% and 2%. However, the equation underestimates deflection for steel-reinforced concrete beams and slabs with a reinforcing ratio less than 1% and for most beams reinforced with low-modulus, fibre-reinforced-polymer (FRP) bars. Deflection of slender tilt-up wall panels can also be underestimated with Branson's equation. This paper provides an explanation of why the Branson equation does not always work well in predicting deflection, and presents a rational approach to develop an alternative expression for the effective moment of inertia that works equally well for both steel- and FRP-reinforced concrete at all reinforcing ratios. A rational expression is also introduced for continuous beams that uses an averaged moment of inertia, Ie,avg, to calculate beam deflection. Changes are included in a proposed revision to deflection prediction requirements specified in clause 9.8 of CSA A23.3-04.Key words: reinforced concrete, deflection, effective moment of inertia, serviceability.
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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 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".