A cantilever beam analogy for quantifying higher mode effects in multistorey buildings
Bibliographic record
Abstract
Summary This paper examines higher mode effects in systems where the ductile mechanism for seismic design is the base moment‐rotation response. The modal properties of flexural and shear beams with uniform mass and elasticity and with a variable amount of base rotational restraint are derived. As the base fixity is released, the first mode becomes the rigid body rotation of the beam about the base, but the higher modes change much less, particularly for the shear beam model. Most response quantities that are of interest in the seismic design of typical mid‐rise buildings are controlled by the first two lateral modes, except at locations along the height where the second mode contributes little. However, the third and higher lateral modes are more significant for high‐rise buildings. Based on the theory of uniform cantilever shear beams, expressions are developed to avoid the need for a modal analysis to estimate the overturning moment, storey shear, and floor acceleration envelopes. Considering the measured response from the shake table testing of a large‐scale eight‐storey controlled rocking steel braced frame, the proposed expressions are shown to be of similar or better accuracy to a modified modal superposition technique, which combines the higher mode response from an elastic modal analysis with the response associated with achieving the maximum base overturning moment according to an inverted triangular load distribution. Because the proposed method uses only parameters that are available at the initial design stage, avoiding the analysis of a structural model, it is likely to be especially useful for preliminary design. Copyright © 2015 John Wiley & Sons, Ltd.
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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) | 0.000 | 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".