Effect of second-order forces on seismic response
Bibliographic record
Abstract
In a building structure subjected to seismic forces, the gravity loads acting through the lateral displacements lead to additional shears and moments. This is generally referred to as the P–Δ effect; it tends to reduce the capacity of the structure to resist the seismic forces and may lead to instability. It has been suggested that an increase in structural strength, in stiffness, or in both would mitigate the P–Δ effect and ensure stability of the structure. It is shown here that instability results when the P–Δ effect causes the stiffness of the structure to become negative in the post-yield range, in which case increasing the strength, the stiffness, or both does not ensure stability. In a single-storey structure, stability can be ensured if there is sufficient strain hardening that the post-yield stiffness is positive even in the presence of the P–Δ effect. For a multistorey building the vulnerability of the structure to P–Δ instability can be judged by obtaining a pushover curve. It is shown that as long as the maximum displacement produced by the design earthquake lies in the region of positive slope of the pushover curve, the structure will remain stable.Key words: seismic response, P–Δ effect, dynamic instability, stability coefficient, amplification factor, pushover analysis, nonlinear analysis.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.006 | 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".