Numerical and Theoretical Studies on Axial Compression Performance of Modular Steel Tubular Columns Grouped with Shear-Key Connectors
Bibliographic record
Abstract
Shear-keyed inter-modular connections (IMCs) are integral components of high-rise modular steel structures (MSSs), providing robust interconnectivity to support grouped tubular columns across modules, thereby introducing column discontinuities and distinctive structural behavior. This study conducted a comprehensive numerical assessment and theoretical analysis of the axial compression behavior of grouped tubular columns based on a validated finite element model (FEM), which captured the member-to-structural level behavior of steel hollow section (SHS) columns and accommodated geometric imperfections. An FEM was initially developed and validated using 28 axial compression tests documented in the literature, comprising 15 tests on cold-formed and 13 on hot-rolled steel hollow section (SHS) columns. The primary parameters explored in tests included material properties (stainless/carbon), processing methods (cold-formed/hot-rolled), cross-section sizes (D/B), cross-sectional or member slenderness ratios (D/tc, B/tc, or Lc/r), and the number of columns (1, 7, and 11). A comprehensive parametric numerical study involving 103 grouped tubular column FEMs then investigated the influence of initial imperfection, shear-key height (Lt), thickness (tt), steel tube length (D), width (B), thickness (tc), and height (Lc) alongside the effects of space between tube and key, and the gap between tubes. The results indicated that the load-shortening behavior of the grouped columns consists of linear elastic, inelastic, and recession stages. The failure modes observed primarily displayed an S-shaped pair of inward and outward local buckling on the outer sides and double S-shaped local buckling on the interior sides. The buckling arose near the shear key or at 1/4 or 1/2 of the column height. None of the considered models experienced global buckling. Increasing tt, Lt, tc, D, or B enhances strength and stiffness, while Lc or Lc/r linearly affects stiffness and ductility. The columns’ nominal axial strength was reduced because of the shear keys, which decreased compression yielding and caused localized elastic buckling. Subsequently, the theoretical analysis revealed that the design codes do not capture this behavior, and thus, their capacity estimate yields inaccurate findings. This discrepancy renders existing code prediction equations, including those from Indian (IS800), New Zealand (NZS400), European (EC3:1-1), Canadian (CSA S16), American (AISC360-16), and Chinese (GB50017) standards, as well as the model proposed by Li et al., non-conservative. To assure conservative results, the paper recommended modification of existing standards and proposed prediction equations based on a fourth-order differential equation that describes the actual behavior of modular steel columns grouped with shear keys. The proposed design approach accurately predicted the axial compression capacity of modular steel-grouped columns, proving conservative yet effective. This provides valuable data that could transform design and construction techniques for MSSs, extending to various column and IMC forms through adaptable design parameters. This enhancement in structural performance and safety significantly contributes to the advancement of modular construction practices.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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) | 0.000 | 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 teacher head, 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".