Shaojun Zhu
Assistant Professor, Distinguished Research Fellow
Department of Structural Engineering, College of Civil Engineering
Tongji University, Shanghai, China
Tongji University, Shanghai, China
Shaojun Zhu, Doctor of Engineering, Shanghai High-Level Scholar, Shanghai Pujiang Scholar, Assistant Professor and Distinguished Research Fellow of Department of Structural Engineering, College of Civil Engineering, Tongji University. He also serves as a council member of the Engineering Fire Protection Technology Branch of the China Society of Civil Engineering and a member of the Structural Fire Resistance Committee of the Earthquake Resistance and Disaster Prevention Branch of the Architectural Society of China. He majors in the research on smart firefighting and smart structural design. Specific research topics include real-time early warning of fire-induced collapse of large steel structures, shape and topology optimization of skeleton structures, and reinforcement learning-driven automatic design of structures. He hosted 1 project sponsored by the National Science Foundation of China, 1 project sponsored by the Shanghai Pujiang Program, and 2 secondary projects sponsored by the National Key Research and Development Program of China, participated in the revision of 1 standard, published 68 journal papers indexed by SCI, published 16 Chinese journal papers indexed by EI, and got 3 patents granted. During his Ph.D. period, he was awarded by the National Scholarship of China 3 times, and he visited Kyoto University as a guest research associate for 2 years funded by the Chinese Scholarship Council (supervised by Prof. Makoto Ohsaki). The achievements won the First Prize for Scientific and Technological Progress from the China Steel Structure Society and the First Prize for Science and Technology from the China Railway Society. His E-mail is: zhushaojun@tongji.edu.cn
Last update of this page: February 14th, 2026
Note: * denotes corresponding author. Each row includes a research visual distilled from the paper.
The paper starts from a scaled gridshell test: m=2, L=0.9 m, f/L=1/3, 5 mm joint-coordinate tolerance and ±2 mm member-length tolerance, measured by 3D laser scanning.
The core contribution is not merely random imperfection generation. CSIMM is validated against 50 physical assemblies, then 800 imperfect models per K6 gridshell type are used across 24 structures and 5 uncertainty groups to derive buckling-capacity distributions and design recommendations: L/1500 imperfection amplitude and safety factors of 1.44/1.30.
| Metric | Measured | RIM | CSIMM |
|---|---|---|---|
| Joint deviation ||ΔP|| mean/std | 1.564 / 1.157 mm | 4.729 / 1.327 mm; KL=1.538 | 1.704 / 1.243 mm; KL=0.006 |
| Member-length deviation Δl mean/std | 0.068 / 1.492 mm | 0.093 / 3.714 mm; KL=0.125 | 0.012 / 1.601 mm; KL=0.002 |
| Error relative to measurement | benchmark | ||ΔP|| mean +202.37%; Δl std +148.93% | ||ΔP|| mean +8.95%; Δl std +7.31% |
Data source: abstract, Tables 1-2, Sections 3.2 and 4, and conclusions.
The paper combines fire temperatures, structural responses, and geometry to train a structural deep-learning model that forecasts key displacement histories.
REACT-Net turns fixed three-level warning into continuously updated remaining-safe-time prediction. The model is trained on 540 FE samples and validated by a real fire test that collapsed at 5.5 min. At 241 s of fire exposure, the DL model predicted 101 s remaining time, only +12 s from the actual remaining time and closer than the traditional method.
| Alert time | Actual remaining time | Three-level P=50% | Three-level P=80% | DL P=50% | DL P=80% |
|---|---|---|---|---|---|
| 1st alert / 117 s | 213 s | 333 s (+120) | 199 s (-14) | 328 s (+115) | 309 s (+96) |
| 2nd alert / 210 s | 120 s | 113 s (-7) | 63 s (-57) | 171 s (+51) | 129 s (+9) |
| 3rd alert / 241 s | 89 s | 68 s (-21) | 42 s (-47) | 101 s (+12) | 97 s (+8) |
Data source: abstract, Sections 4.1-4.3 and 6.2-6.3, and Table 5.
The target is 3 h standard fire exposure, with a 250 ? limit for the CFRP cable and anchor filler, tied to the epoxy glass-transition temperature.
The paper separates the CFRP cable, anchor, and adapter because the original system reaches 593.8 ? at the adapter after 3 h, much hotter than the anchor and cable surface. Single-cable tests, a full-scale cable-anchor test, and FE parametric analysis lead to a combined strategy: 5 blanket layers, 65 mm anchor coating, and 85 mm adapter coating.
| Part | Key data from the paper | Design reading |
|---|---|---|
| Original full-scale cable-anchor system | 3 h: adapter 593.8 ?; anchor 316.9 ?; cable surface 375.9 ? | Adapter is the critical hotspot |
| Ceramic fiber blanket | 4/5/6 layers: 324.3/247.8/179.2 ? | At least 5 layers meet the 250 ? limit |
| Anchor coating | 50/60/65/70/80 mm: 298.4/255.9/237.1/223.2/196.9 ? | Minimum recommendation: 65 mm |
| Adapter coating | 70/80/85/90/100 mm: 307.6/269.6/250.3/229.9/200.8 ? | Minimum recommendation: 85 mm |
Data source: abstract, Sections 2.1, 3.2 and 4.3, Table 6, and conclusions.
The Q235B trusses are 1.7 m long, 0.26 m high, and 1.68 m in span, with 6 mm and 12 mm thickness groups; they are heated linearly to 900 ? over 120 min under sustained load.
The paper moves member critical-temperature design into an indeterminate truss system. Six localized-fire tests and ABAQUS models reveal arching, restoring, collapse, and force redistribution; then upper-chord and diagonal-web failure temperatures are redefined so a simplified component method can predict them with calibrated effective length factors of 0.65 and 0.60.
| Evidence | Paper data | Research meaning |
|---|---|---|
| Specimens and heating | Six Q235B planar trusses; 1.7 m × 0.26 m, span 1.68 m; 6/12 mm groups; 900 ? over 120 min | Calibrates critical temperatures from a real system, not isolated members |
| Key temperatures and failure criterion | L/30 = 56 mm; in a-3, M2 buckles at 198.6 ? and M1/M2/truss fail at about 618.0/619.1/619.1 ? | After local member failure, system redundancy can still redistribute force briefly |
| Parametric study | t-12-r-I fire resistance at n=0.4/0.5/0.6/0.7/0.8: 103.2/97.0/90.6/84.8/77.4 min | Higher load ratio nearly linearly reduces fire resistance |
| Component-method correction | PF boundary errors are 6.97%/7.80%; optimized effective lengths 0.65/0.60 reduce them to 6.68%/6.37% | Folds system restraint and redundancy into simplified critical-temperature design |
Data source: abstract, Tables 1-7, Sections 3.2-4.4, Sections 5-6, and conclusions.
Parametric analysis identifies A1-A4. A1 is progressive buckling of compression web members with almost no warning; A2-A4 have post-peak descending stages that can serve as warning windows.
The paper designs for warning reliability, not only fire resistance duration. Under adverse near-support fires such as F1/F5, adjacent compression web members must fail later than tension web members; t2,min = t1 + tn is used to back-calculate the required compression-member critical temperature. Numerical examples increase available escape time from 0 s to 129 s and 159 s, i.e., over 2 min.
| Case | Critical temperature and time | Collapse-mode reading |
|---|---|---|
| Tension-web baseline | 50×3, load ratio 0.72, Tcr,t=492 ?, t1=591 s | The ductile trigger point that compression webs must outlast |
| Compression web 104×3 / 114×4 | Tcr,c=145/313 ?; t2=324/547 s; tp=0/0 s | Compression webs buckle first: still brittle A1 |
| Compression web 126×4 | Tcr,c=496 ?; t2=630 s; tp=39 s | Tension web yields first, but the warning window remains short |
| Compression web 150×5 | Tcr,c=549 ?; t2=1008 s; tp=129 s | Typical ductile A2 mode, with escape time over 2 min |
| Compression web 170×7 | Tcr,c=647 ?; t2>1500 s; tp=159 s | Additional section increase has diminishing returns; Case 5 adds only 30 s over Case 4 |
Data source: abstract, Tables 1-4, Sections 2.3, 3.1-3.3, Section 4, and conclusions.
The paper first tests one ambient and three post-fire push-out specimens to obtain stud shear capacity and load-slip models, then tests four composite beams through constant-load heating, natural cooling, and constant-amplitude fatigue.
The paper asks how long a visually intact bridge/floor composite beam can survive cyclic loading after fire. Around 443.8 ?, stud shear capacity drops to about 83% of ambient; in post-fire fatigue, interface slip and mid-span displacement increase. CB-2 fails at only 295,000 cycles after 383 ? under a 40 kN amplitude, while CB-1 and CB-3 exceed two million cycles under their tested conditions before static failure.
| Item | Paper data | Meaning |
|---|---|---|
| Stud shear capacity | PUSH-0: 236.0 kN; PUSH-1: 220.3 kN; PUSH-2/3 average 195.2 kN; QUT/QU=1.00/0.93/0.83 | Higher post-fire temperature reduces connector strength and ductility |
| Composite-beam setup | Span 3750 mm; shear span 1475 mm; 27 Φ16×70 studs; shear connection degree 0.82; C30 concrete; I20a Q235B steel beam | Fatigue response is governed by interface-connection degradation |
| Fatigue loading | CB-S0/1/2: 75-35 kN, amplitude 40 kN; CB-3: 75-45 kN, amplitude 30 kN; frequency 4 Hz; benchmark 2 million cycles | CB-3 has high post-fire temperature but lower amplitude improves fatigue outcome |
| Fatigue results | CB-S0: 235×10^4 cycles/120 kN; CB-1: 207×10^4 cycles/125 kN; CB-2: failure at 29.5×10^4 cycles; CB-3: 208×10^4 cycles/129 kN | Post-fire fatigue cannot be read from peak temperature alone; load amplitude and interface slip matter |
Data source: abstract, Tables 1-5, Sections 3-5, and conclusions.
The paper collects real in-service steel coating images and labels corrosion, cracks, flaking, and blistering; 1200×1200 sliding-window crops produce 6554 training samples and 1639 validation samples.
SAFE-Net is not a simple detector swap. It modifies Backbone, Head, and Loss for small, slender, low-contrast, imbalanced coating defects: DA_C2f captures small targets, Dynamic Head improves multi-scale recall, Slide Loss handles rare classes, and Shape IoU improves irregular boxes. It reaches P=88.94%, R=75.38%, mAP=78.02%, and 221 FPS, improving over YOLOv8m by 5.82, 5.01, and 4.78 percentage points.
| Item | Paper data | Meaning |
|---|---|---|
| Dataset | 961 high-resolution images; 8193 crops; 6554 training / 1639 validation; 640×640 training input | Dedicated dataset for in-service steel coating defects |
| Class distribution | Peeling/flaking 7445 (23.99%); blistering 2629 (8.47%); cracking 3275 (10.55%); corrosion 17684 (56.98%) | Class imbalance motivates Slide Loss |
| Model comparison | YOLOv8m: 83.12/70.37/73.24/208 FPS; SAFE-Net: 88.94/75.38/78.02/221 FPS | Compared with baseline, P/R/mAP improve by 5.82/5.01/4.78 percentage points |
| Generalization and errors | 5-fold CV: 86.64±1.3 / 73.54±1.4 / 77.32±0.9; MR=10.9%, FR=15.9% | Stable across splits, with remaining room to reduce missed and false detections |
Data source: abstract, Tables 1-4, Sections 4-6, and conclusions.
The paper fabricates cement- and gypsum-based non-intumescent coatings and tests dry density, compressive strength, and thermal conductivity; density becomes the fast assessment input.
The key move is to bring both thermal and mechanical coating performance back to one field-friendly parameter: dry density. Tests show that lower density generally reduces both thermal conductivity and compressive strength; at the same density, cement-based coatings have higher compressive strength and lower conductivity than gypsum-based ones. Image processing and random FEMs then model the coating as a two-phase substrate-insulation composite. FEM thermal predictions average below 7% error for cement-based coatings and mostly below 15% for gypsum-based coatings, and the density-only thermal model reaches a 7.67% average relative error.
| Item | Paper data | Meaning |
|---|---|---|
| Cement-based density gradient | CB800: 811.62 kg/m3, 3.88 MPa, 0.233 W/(m·K); CB500: 495.10 kg/m3, 0.70 MPa, 0.144 W/(m·K) | Lower density reduces conductivity while sacrificing compressive strength |
| Gypsum-based density gradient | GB800: 699.19 kg/m3, 2.12 MPa, 0.312 W/(m·K); GB500: 496.34 kg/m3, 0.55 MPa, 0.181 W/(m·K) | Gypsum-based coatings conduct more heat at comparable density and need calibrated parameters |
| Commercial coating comparison | CA: 529.27 kg/m3, 0.79 MPa, 0.122 W/(m·K); GE: 308.68 kg/m3, 0.20 MPa, 0.145 W/(m·K); GZ: 408.09 kg/m3, 0.32 MPa, 0.167 W/(m·K) | Commercial materials show density is not the only physical factor, but it is a practical first input |
| Model accuracy | FEM: cement average error <=7%, gypsum mostly <=15%; density-based TC model average relative error 7.67% | Density models support first-pass assessment; calibrated material parameters control the accuracy ceiling |
Data source: abstract, Table 2, Section 3.1, Sections 4.1-4.2, and conclusions.
The paper reduces a 5×5 B-spline control net to 6 independent shape variables and simultaneously optimizes 45 tube-radius variables, minimizing volume under stress and displacement constraints.
The paper proposes LSOLA, placing free-form single-layer gridshell shape and section optimization inside one local online-learning framework. LHS and K-means partition the high-dimensional space, DNNs are trained per subregion, local search generates informative query points, and query assignment, cluster merging, and data removal exchange information. In the 30 m by 30 m, 320-member example, LSOLA reaches a best volume of 1.753 m3; for seed 200, LSOLA-NIX is 1.983 m3, GSOLA is 2.687 m3, GA is 2.230 m3, and SA is 6.107 m3. Compared with GA, LSOLA is about three times more efficient near the same volume level.
| Item | Paper data | Meaning |
|---|---|---|
| Table 2, seed 200 | LSOLA: 1.753 m3, 31,760 FEA; LSOLA-NIX: 1.983 m3, 44,000 FEA; GSOLA: 2.687 m3, 44,000 FEA; GA: 2.230 m3, 40,000 FEA; SA: 6.107 m3, 45,500 FEA | Local online learning finds a lighter design with fewer FEA calls |
| Information exchange | LSOLA-NIX best volumes are 2.5%-13.1% larger than LSOLA; for seed 200, the ten best LSOLA-NIX designs average 2.215 m3, 21.64% larger than LSOLA | Information exchange improves efficiency and quality but reduces shape diversity |
| Local DNN accuracy | Volume-prediction R2 reaches 0.933 at Iteration 69 and drops to 0.450 after the first merge | Merging expands the dataset coverage, improving search while reducing local prediction accuracy |
| Efficiency versus GA | Near 2.330 m3, LSOLA uses 7600/9800/8400 FEA calls, while GA uses 38200/27800/17600; DNN training and query generation take about 3% of FEA time | LSOLA is about three times as efficient as GA |
Data source: abstract, Sections 4.1-4.7, Tables 2 and 6-8, and conclusions.
The paper targets edge devices in fire-collapse warning, optimizing an LSTM model to predict hard-to-measure key displacements while reducing sensor inputs, parameter count, and training cost.
The paper turns a fire-collapse warning model into an edge-deployable pipeline. It first compares uniform sampling with a normal-distribution strategy closer to engineering reality and selects the better-generalizing Model-nor. SHAP ranks 34 input features; removing 16 temperature inputs keeps high accuracy and cuts thermocouple layout cost by 50%. GA-LSTM then optimizes layer count, neuron count, and learning rate, reducing total parameters by 78% and training time by 52%. For vertex displacement across 100 test sets, the optimized model has 100% of r values in 0.9-1 and 84% of R2 values in 0.9-1, with per-sample inference under 1 s, below the 10 s recording interval.
| Item | Paper data | Meaning |
|---|---|---|
| Key physical parameters | Five displacements in the fourth bay: VvL and VhL are easy to measure; Vp, VvR, and VhR are hard to measure; temperature inputs come from 32 thermocouples in the 5th-8th bays | The model uses measurable data to infer hard-to-measure collapse-state quantities |
| Sampling comparison | Share of test sets with r>0.95: Model-nor 99%, Model-uni 94%, cross-distribution models about 92%; Model-nor generalizes better | Normal sampling of engineering random variables better reflects real physical conditions |
| SHAP feature deletion | After deleting 16 input features, Vp prediction has 98% of test sets with r=0.95-1, 79% with R2=0.95-1, and 38% with RMSE=0-5; thermocouple layout cost drops 50% | Explainability reduces model input and guides onsite sensor placement |
| GA-LSTM and warning | Parameters down 78%, training time down 52%; for Vp, 100% of test sets have r=0.9-1 and 84% have R2=0.9-1; level-3 warning at 570 s predicts 71 s remaining versus 90 s real | The model is small and fast enough for edge-side real-time warning |
Data source: abstract, Sections 3.1-3.4, Sections 4.2-4.8, Tables 4-6, and conclusions.
The paper decomposes CFST axial-force prediction into two modules: CNN-LSTM reconstructs the section temperature field from surface temperatures, then a skip-connected LSTM predicts axial-force ratio from the temperature field and axial deformation.
The paper addresses the fact that axial force in a CFST column cannot be directly measured during fire. The temperature module uses 585 heat-transfer cases and generates 10 by 10 temperature matrices every 5 min; the axial-force module uses 180 thermo-mechanical cases and forms 10,440 samples with a 20 min sliding window. The final MAI reaches R2=0.9884 and RMSE=0.2539 on the noisy test set; the comparable integrated model has RMSE=2.3854, so MAI's RMSE is only 10.46% of it, with inference under 1 s on an i3 CPU.
| Item | Paper data | Meaning |
|---|---|---|
| Temperature-field database | 585 cases; each has 8 h duration, 5 min interval, 97 slices, and 10×10 temperature matrices; TFPM2 training/testing data: 90,792/22,698 | The temperature field is reconstructed before the axial-force module receives internal concrete temperatures |
| Axial-force database | 180 cases; 61 slices per case at 5 min interval; Nt=4 sliding windows produce 58 segments per case, 10,440 samples total | The 20 min window lets the LSTM learn the history linking temperature, deformation, and axial force |
| Module ablation | TFPM2 testing R2=0.9719; AFPM1 testing R2=0.9711; AFPM2 testing R2=0.9569 | The temperature module is noise-robust, and the axial-force skip connection is effective |
| MAI versus IDLM | MAI testing MAE=0.0377, RMSE=0.2539, R2=0.9884; IDLM testing MAE=0.4651, RMSE=2.3854 | Modular training avoids coupled multitask error; RMSE is only 10.46% of IDLM |
Data source: abstract, Sections 4.2-4.4, Tables 2-6, application case, and conclusions.
The paper tests protected PEC beams and columns under ISO 834 fire, recording temperature fields, mid-span deflection, and fire resistance, then builds ABAQUS thermal-mechanical models.
The paper uses fire tests on 3 PEC beams and 6 PEC columns to show that the gypsum-based non-intumescent coating remains generally stable despite cracking and local peeling, and practical coating thickness meets the 2 h ISO 834 requirement. All beams show high-temperature flexural deformation and tensile concrete cracking; PEC-B2 has 207 min fire resistance and PEC-B3 has 154 min. Columns PEC-C5 and PEC-C6 fail by peak-temperature criteria at 121 and 105 min. Parametric analysis shows that increasing coating thickness from 7 mm to 11 mm reduces 3 h peak temperature by about 150 ?, and increasing beam load ratio from 0.4 to 0.7 can reduce fire resistance by up to 142 min.
| Item | Paper data | Meaning |
|---|---|---|
| Specimen configuration | PEC-B1/B2/B3: L=5500 mm, H400×180×6×10; PEC-C1-C6: L=1000 mm; Q355B plate average yield strength 462.5 MPa | Specimens cover flexural beams and thermally exposed columns without applied load |
| Table 5 fire tests | PEC-B2: 3 h max temp 501.9/598.6 ?, deflection -137 mm, tR=207 min; PEC-B3: 503.3/645.1 ?, deflection -175 mm, tR=154 min; PEC-C5/C6: 824.8/711.6 ?, tR=121/105 min, failed | Beams are deflection-controlled, while columns are judged by peak temperature |
| Table 7 load ratio | GL1 fire resistance decreases from 198.22 min at n=0.4 to 99.55 min at n=0.7; across models the maximum reduction reaches 142 min | Load ratio is a governing variable for PEC beam fire-resistance design |
| Parametric conclusion | Coating thickness 7.0->11.0 mm reduces 3 h peak temperature by about 150 ?; temperature decreases into encased concrete, and beam longitudinal temperature gradient reaches 142.4 ? | Temperature distribution is the basis for high-temperature capacity-zone calculation |
Data source: abstract, Tables 1-7, Sections 3-6, and conclusions.
The paper uses CSIMM to generate reliable imperfect samples, encodes nodes, members, and global structural parameters as graph inputs, and uses GRIDSNET as a surrogate for expensive nonlinear FE buckling analysis.
The paper reformulates single-layer gridshell stability prediction as graph learning. The Kiewitt-6 dataset covers 486 parameter combinations: ring number m=8/10/12, span 40/50/60 m, rise-to-span ratio 1/4/1/5/1/6, imperfection amplitude L/500/L/1500/L/3000, three sections, and two boundaries. CSIMM generates 100 imperfect samples per type, giving 48,600 samples split into 32,400/8,100/8,100. GNN B has the best K6 sample accuracy with R2=0.9237 and RMSE=0.0592, but GNN D is selected for engineering use because it is more robust for K8 universality and 95% confidence-interval quantiles, reaching 0.52% and 7.30% quantile errors. GNN D takes 0.0007 s per sample, compared with 55.6 s for FE analysis.
| Item | Paper data | Meaning |
|---|---|---|
| Training database | m=8/10/12; L=40/50/60 m; f/L=1/4,1/5,1/6; alpha=L/500,L/1500,L/3000; 3 sections; Pinned/Fixed; 486 types ×100 = 48,600 samples | CSIMM provides topology-constrained realistic imperfection samples |
| K6 test set | GNN A: R2=0.9034, RMSE=0.0671; GNN B: 0.9237, 0.0592; GNN C: 0.9017, 0.0673; GNN D: 0.8580, 0.0809 | GNN B is best for single-sample capacity prediction |
| Probability distribution prediction | In Type 1, GNN D mean error is 0.29% and right quantile error is 2.43%; in K8 UT2, GNN D quantile errors are 0.52% and 7.30% | Composite loss strongly improves capacity-distribution and quantile prediction |
| K8 universality and speed | UT1: GNN D R2=0.8566, RMSE=0.0524; GNN D 0.0007 s/sample, FE 55.6 s/sample | No retraining is needed as topology changes, and computation is orders faster than FE |
Data source: abstract, Sections 2-4.7, Tables 2, 4, 5, 7, 9, 11, and conclusions.
The study is not a component furnace test. It instruments a real truss-roof building with temperature, rotation, and displacement sensing, then streams data to a cloud warning system.
This paper validates a fire-induced collapse warning system in a real building rather than an idealized model. The test building is a triangular truss roof from the 1950s with an 11.6 m span, an 8 m x 3 m x 2.7 m fire platform, 60 thermocouples, inclinometers, and radar for comparison. Gas and steel temperatures approach 900 ?. Significant deformation and partial collapse occur 4134 s after ignition, followed by total roof collapse at 4253 s. The system issues warnings at 642 s, 948 s, and 3504 s; the third warning predicts 596 s remaining versus 759 s actual, giving a conservative and actionable warning in a complex real fire.
| Event | Relative time | Paper data |
|---|---|---|
| Ignition | 130 s | Ignition at 10:09:16 after cloud monitoring has started |
| 1st / 2nd warning | 642 s / 948 s | Predicted remaining time 1972 s / 1327 s versus actual 3621 s / 3315 s |
| 3rd warning | 3504 s | Predicted 596 s remaining versus 759 s actual to partial collapse |
| Collapse | 4134 s / 4253 s | Significant deformation and partial collapse / total roof collapse; peak temperature near 900 ? |
Data source: abstract, Tables 1, 3, and 4, test observations, sensor layout, and conclusions.
The paper addresses a practical fire-scene problem: displacement sensors fail easily, so protected inclinometers measure rotations and infer key displacements.
This paper develops a high-temperature resistant inclinometer and validates it through a furnace steel-beam test and a real building fire. The device combines electronics, aerogel, and fireproof panels, with a 180 ? electronics limit. During roughly 70 min of ISO 834 heating, 30 mm aerogel keeps the furnace-test device below 100 ?. In the real fire, 40 mm aerogel keeps the device mostly below 180 ? while gas temperature approaches 900 ? for more than one hour. Rotations R1-R6 are then converted to displacements D1-D3 through polynomial and deep-learning models; during large deformation, the DL model is closer when boundary displacement is unavailable.
| Step | Paper data | Meaning |
|---|---|---|
| Device thermal resistance | Electronics limit 180 ?; 30 mm aerogel keeps the device below about 100 ? for 70 min in furnace; 40 mm aerogel keeps it below 180 ? in real fire | The sensor can provide usable rotations through early and middle fire stages |
| Furnace displacement validation | HW100x100x6x8 beam, 50 kg concentrated load, ISO 834 heating for about 70 min; difference below 2 mm at 40-55 min | Rotation-derived displacement can be checked against direct displacement during high-temperature bending |
| DL training | 900 samples, 4:1:1 split, MSE loss, Adam, batch=128, 10000 epochs, stabilizing after 5000 epochs | R1-R6 or R3-missing rotation inputs predict D1-D3 displacement |
| D1 accuracy | DL1 RMSE=12.7, R2=0.82; DL2 RMSE=37.5, R2=0.94, covering until 11:16:36 | With partial monitoring loss, deep learning still extends usable warning time |
Data source: abstract, Sections 2-4, Tables 2 and 3, furnace beam test, real building fire test, and conclusions.
The paper pretrains an LSTM on large-scale parametric fire models, then uses a small FDS field-simulation set for transfer learning so the model can serve real large-space buildings.
This paper builds a machine-learning framework for real-time identification and temperature forecasting in large-space fires. The LSTM is pretrained on 5000 classical fire samples split into 3000/1000/1000, with 60 min heating histories cut into 153,000 input-output pairs using 5 min input/output windows. Transfer learning then uses 50 FDS samples, augmented to 120/40/40 train/validation/test sets. The transfer model keeps roughly above 90% average temperature prediction accuracy for a 20 min lead time and reaches about 89.6%/91.8% average accuracy for fire location coordinates. In real fire validation, the LSTM identifies fire location above 92%, predicts temperatures 20 min ahead above 89%, and runs in about 1.83 s; damaged thermocouple detection exceeds 96% when the damage ratio is below 30%.
| Module | Paper data | Meaning |
|---|---|---|
| Pretraining | 5000 classical fire samples, 3000/1000/1000 split; 60 min histories cut into 153,000 training pairs | Low-cost generation of fire time-series prior knowledge |
| Transfer learning | 50 FDS samples split 30/10/10 and augmented to 120/40/40 | A small high-fidelity field-simulation set calibrates the model to large-space fires |
| 20 min temperature forecast | Table 6: for 5-40 min exposure, 20 min-ahead accuracy is about 90.64%-96.89% | Provides long-lead temperature prediction for real-time warning |
| Real-fire validation | Location identification above 92%, 20 min temperature forecast above 89%, inference 1.83 s; damaged thermocouple detection above 96% | The model can maintain fire identification and temperature forecasting with partial sensor failure |
Data source: abstract, Sections 2-5, Tables 6, 9, and 10, damaged-thermocouple analysis, and conclusions.
The paper converts a steel frame into a graph and uses component temperatures plus easy-to-measure joint displacements to predict hard-to-measure top and internal displacements in real time.
This paper proposes FRAME-Net, combining GNN spatial representation with RNN/LSTM temporal modeling to predict hard-to-measure key displacements in multi-story planar steel frames under fire. The training data come from FE models validated by real fire tests: 600 samples split into 350/150/100, with time-series length 72 and about 4.2 h per training cycle. In the test set, over 95% of hard-to-measure displacements reach the 3rd accuracy level, over 90% reach the 2nd, and over 85% reach the 1st. The trained model transfers to different frame topologies without retraining and predicts one case in about 0.01-0.02 s, far below the 72 s sampling interval. In a real steel-frame fire test, pre-collapse prediction errors remain within about 5 mm. The predicted displacements are then used in early-warning calculations: warnings at 403/490/778 s have actual remaining times of 518/431/143 s and predicted remaining times of 190/88/62 s, all conservative.
| Item | Paper data | Meaning |
|---|---|---|
| Training setup | 600 samples; 350/150/100 split; tmax=72; 8000 epochs; RTX4090; about 4.2 h per training cycle, stable test loss after 5000 epochs | Offline training enables fast online fire-scene prediction |
| Test-set performance | Over 95% reach level 3, over 90% reach level 2, and over 85% reach level 1 | Meets early-warning needs for trend and order-of-magnitude accuracy |
| Real-fire generalization | Two-story four-span frame; columns 50x30x3 mm, beams 60x40x3.5 mm; J6/J11 as easy-to-measure joints; errors mostly within 5 mm | Topology, sizes, load case, and fire type absent from training are still predicted |
| Warning remaining time | tγ=403/490/778 s; actual remaining 518/431/143 s; predicted remaining 190/88/62 s | Predictions are conservative, with the third level closest to actual collapse |
Data source: abstract, Tables 1, 8, and 13, Sections 5.5-7, real-fire validation, and conclusions.
This paper does not only predict capacity; it studies why the capacity probability distribution changes with imperfection amplitude, ring number, and rise-to-span ratio.
This paper uses CSIMM for probabilistic nonlinear buckling analysis of Kiewitt-6 single-layer spherical gridshells. Parameters cover ring number m=8/10/12, rise-to-span ratios 1/6, 1/5, and 1/4, and imperfection amplitudes from L/300 to L/3000, giving 63 cases with 1000 initial-imperfection samples per case and 63,000 gridshell models in total. Compared with the traditional random imperfection method (RIM), CSIMM captures bimodal distributions while RIM tends to give unimodal ones. In cases C4/C5, CSIMM gives maximum capacities 8.60%/5.16% lower and minimum capacities 42.29%/52.49% lower. The paper introduces joint well-formedness as a local-stiffness indicator to explain why the capacity distribution evolves from skewed at small imperfections, to bimodal at intermediate imperfections, and to approximately normal at large imperfections. It recommends L/1500 as an imperfection-amplitude acceptance limit and highlights primary-rib and inner-ring joints as critical inspection targets.
| Evidence | Paper data | Meaning |
|---|---|---|
| Parameter cases | m=8/10/12; f/L=1/6, 1/5, 1/4; amplitudes L/300, L/500, L/800, L/1000, L/1200, L/1500, L/3000 | Systematic sweep of form, stiffness, and imperfection amplitude |
| C4 method comparison | RIM max/min/mean/std=7.206/4.987/6.251/0.367; CSIMM=6.586/2.878/4.461/0.761 | CSIMM is more conservative and more dispersed |
| C5 method comparison | RIM max/min/mean/std=7.366/5.407/6.561/0.315; CSIMM=6.986/2.569/4.510/0.877 | RIM can overestimate the minimum capacity by 52.49% |
| Mechanism | Five buckling patterns: primary-rib inner-ring, non-primary-rib inner-ring, primary-rib outer-ring, non-primary-rib outer-ring local indentation, and global indentation | Distribution shape arises from changing proportions of buckling modes |
Data source: abstract, Sections 2.1-2.2, Tables 1 and 2, Section 3.5, Sections 4.3-4.7, and conclusions.
The paper uses an ABAQUS/Explicit model validated by real fire-collapse tests and systematically varies topology, fire scenarios, load, member size, fire protection, temperature gradient, and wind load.
This paper studies collapse modes and mechanisms of multi-story large-span planar steel frames under fire. The study includes 13 frames: S0 is a five-story five-span regular frame, while S1-S12 cover large-span regions at central, edge, eccentric, single-floor, and multi-floor locations. Regular spans are 9 m, large spans are 18 m, the first floor is 6 m high, and other floors are 5.4 m. The parametric study also includes 12 fire-scenario types, six load ratios from 0.2 to 0.7, four fire-protection levels, three section temperature gradients of 300/600/900 ?/m, and six wind-pressure levels. Eight finite collapse modes are identified: A general inward, B rebalancing, C partial lateral, D heated large-span beam-induced inward, E restraint failure-induced, F overall downward, G unheated large-span beam-induced inward, and H overall lateral collapse. Mechanistically, local collapse is reduced to R1 material degradation of heated columns, R2 column-top lateral displacement driven by heated-beam midspan deformation, and R3 loss of column lateral restraint after beam failure; modes F and G also involve unheated lower floors and are therefore more dangerous.
| Dimension | Paper data | Meaning |
|---|---|---|
| Parametric scheme | 13 frames; regular span 9 m, large span 18 m; 12 fire-scenario types; load ratios 0.2-0.7; 4 fire-protection levels; 300/600/900 ?/m temperature gradients; +/-0.3/0.5/0.7 kN/m2 wind pressure | Covers topology, fire, load, and environmental disturbance |
| Large-span-only modes | D heated large-span beam-induced inward collapse; G unheated large-span beam-induced inward collapse, both only in large-span regions | The large-span beam is the key member governing mode transition |
| Local-collapse triggers | A/B/H: R1; C/D: R2; E: R3; F/G: R1 or R2 or R3 | Three mechanisms explain eight macroscopic collapse modes |
| Parameter influence | Temperature gradient usually does not change multi-story-frame collapse mode; wind promotes overall lateral collapse; fire protection can change A to C | Early-warning algorithms can identify modes from key displacement and velocity evolution |
Data source: abstract, Sections 2-6, Tables 1 and 2, Appendix B/C parameter tables, and conclusions.
The paper focuses on making the test reusable: temperatures, mass loss, HRR, rotations, displacements, videos, and geometry are standardized into an open dataset.
This data paper publishes an open dataset from a fire-induced collapse test of an in-service truss-roof building. The test building is a triangular truss factory from the late 1950s with an approximately 12 m span, 1.5 kN/m2 dead load, and about 3.5 kN/m line load over the half-span above the fire source. The steel yield and ultimate strengths are 426 MPa and 553 MPa, and concrete strength is 24.2 MPa. The dataset includes nondestructive and destructive fire tests; the destructive test ignites at 10:09:16 on 2023-11-01 and ends at 11:20:09. Nearly 141 GB of data include Temperatures.csv, Rotations.csv, Displacements.csv, Mass.csv, HRR.csv, videos, photos, geometry files, and metadata. The acquisition system includes 1 Hz thermocouples, 5 Hz mass/HRR data, 1 Hz high-temperature inclinometers, 50 Hz three-radar displacements, and multi-view videos, providing a real-building benchmark for CFD/FE/DL, collapse warning, and computer vision.
| Data type | Paper data | Meaning |
|---|---|---|
| Test timing | Nondestructive 2023-10-29 16:55:18-17:33:56; destructive 2023-11-01 10:09:16-11:20:09 | Data cover both temperature-only and full-collapse tests |
| Sensors | K-type thermocouples 1 Hz; weighbridges 5 Hz; LoRa inclinometers 1 Hz; microwave radar displacement 50 Hz; seven video views | Provides synchronized bases for temperature, HRR, rotation, displacement, and video analysis |
| Displacement coordinates | D1=(3.71,0,-1.867), D2=(0,0,0), D3=(-3.71,0,-1.867); A/B/C radar coordinates enable conversion | Line-of-sight radar displacement is recovered as x/y/z displacement |
| File structure | Temperatures.csv, Rotations.csv, Displacements.csv, Mass.csv, HRR.csv, videos, photos, geometric features, metadata | Turns a non-repeatable real fire test into a reusable data asset |
Data source: abstract, test building, fire scenarios, monitoring equipment, Data Format/Data Processing, Tables 1-3, and reuse discussion.
The paper defines collapse as axial contraction reaching H/100 or column axial force reaching 0, then maps mode boundaries in beta_a and load ratio mu.
This paper uses an experimentally calibrated ABAQUS sequential thermo-mechanical model to study restrained square CFST columns under ISO 834 fire. The model uses DC3D8/S4R/T3D2 elements, allows concrete-steel tube slip with friction coefficient 0.25, and represents axial restraint with an end spring. Validation shows unrestrained fire-resistance times matching tests and restrained critical-time errors within 10%. Collapse is defined by axial contraction reaching H/100 or column axial force P reaching 0. Three modes are identified: expansion-deformation collapse, contraction-deformation collapse, and load-bearing-capacity-loss collapse. At low load ratio, all three modes may occur; at high load ratio, only contraction-deformation and capacity-loss modes appear. For a typical low load ratio mu=0.1, beta_a from 0 to 0.01 reduces collapse time from 86.5 min to 63.5 min, while beta_a >=0.02 gives collapse time above 120 min. At mu=0.5, increasing beta_a raises collapse time from 21.8 min to above 120 min. The paper provides a mode-identification workflow using b, H/b, beta_a, and mu.
| Evidence | Paper data | Meaning |
|---|---|---|
| Model validation | SP-2/SP-3 fire-resistance times 140/109 min; restrained SC150/SC220 critical-time errors below 10% | Heat transfer and mechanical response are adequate for parametric analysis |
| mu=0.1 | Collapse time for beta_a=0/0.01/0.02/0.03/0.1 is 86.5/63.5/>120/>120/>120 min | Weak restraint can advance collapse, while strong restraint can form a new equilibrium |
| mu=0.5 | Collapse time for beta_a=0/0.01/0.03/0.05/0.1 is 21.8/22.9/24.0/30.1/>120 min | At high load ratio, axial restraint is generally beneficial |
| General boundary | Common square CFST columns b=0.3-0.5 m, H/b=7.5-15; max mu for expansion mode about 0.3, max beta_a about 0.11-0.22 | Geometry shifts the beta_a-mu mode boundary |
Data source: abstract, Sections 2-5, Tables 1-5, Figs. 8-18, and conclusions.
The paper uses non-contact DIC to obtain strain during high-temperature tensile tests, avoiding contact-gauge problems in fire-like temperatures.
This paper performs steady-state high-temperature uniaxial tensile tests on galvanized parallel wire strands made of nineteen 5.4 mm wires. The strand has a 27 mm nominal diameter, 435.14 mm2 area, and 1000 mm effective length. Twelve temperature levels from 20 ? to 700 ? are tested with two specimens per level, for 24 specimens total. Heating rate is 10 ?/min, soaking time is 30 min, and both DIC and testing-machine acquisition rates are 10 Hz. The stress at 1.5% strain is recommended as nominal yield strength. Room-temperature ultimate strength is 2553.5 MPa; at 400 ? it is about 1320.7 MPa, only 51.7% of room temperature; at 700 ? it is 63.9 MPa, about 2.5%. Mechanical properties decline rapidly from 200-550 ?. The paper fits elastic-modulus, proportional-limit, yield-strength, and ultimate-strength reduction factors with Boltzmann curves and builds a full-process constitutive model through elastic, plastic-hardening, and necking stages.
| Item | Paper data | Meaning |
|---|---|---|
| Test protocol | 20, 100, 200, 250, 300, 350, 400, 450, 500, 550, 600, 700 ?; two specimens each; 10 ?/min; 30 min soak; DIC 10 Hz | Steady-state tensile curves cover fire-temperature range |
| Nominal yield | Stress at 1.5% strain f1.5%,theta is selected as fpy,theta | Balances strength utilization and safety margin |
| Ultimate strength | 20/400/700 ?: 2553.5 / 1320.7 / 63.9 MPa; reduction factors 1.000 / 0.517 / 0.025 | Strength reserve rapidly vanishes after 400 ? |
| Fitted model | Boltzmann curve fits reduction factors; full constitutive model has elastic, plastic-hardening, and necking stages | Supports fire deformation and capacity analysis of prestressed steel structures |
Data source: abstract, Sections 2-4, Tables 2-5, Figs. 3-8, and conclusions.
The paper builds a 1:3 portal frame, creates a fire compartment in the left span, and uses wood cribs plus gasoline to trigger local collapse while measuring temperature, displacement, and rotation.
This paper connects a natural-fire test, field measurement, and numerical prediction for a double-span steel portal frame. The specimen is a 16 m x 6 m frame with two 8 m spans, and the fire lasts about 22 min. Gas temperature exceeds 700 ? about 2 min after ignition and reaches about 1200 ? around 15 min after roof damage improves ventilation. The heated column and rafter show key displacement peaks near 600 ? and local collapse after exceeding about 800 ?. Thermocouples, LVDTs, microwave radar, and protected inclinometers are compared, and the event is reproduced with FDS and ABAQUS. Parametric analysis shows the collapse process can be regarded as quasi-static; if the peak horizontal or vertical displacement temperature of the heated column is known, collapse temperature can be estimated as 1.2Tx or 1.1Tz.
| Link | Paper data | Meaning |
|---|---|---|
| Natural fire | 16 m x 6 m double-span frame; left-span fire compartment; 8 wood cribs; maximum HRR about 20 MW | Observes local collapse directly rather than relying only on member furnace tests |
| Measurement system | Thermocouples, LVDTs, microwave radar, and protected inclinometers | Compares contact and remote structural-response measurement in fire |
| Collapse process | Gas exceeds 700 ? at 2 min; roof damage and heated-span collapse begin around 15 min; total duration about 22 min | Heated span collapses while the other span remains standing |
| Warning criterion | Peak-displacement temperatures Tx/Tz; collapse temperature estimated as 1.2Tx or 1.1Tz | Turns measurable field displacement into an evacuation temperature threshold |
Data source: abstract, Sections 2-6, Figs. 10-29, Tables 1-2, and conclusions.
The paper uses steady isothermal loading to obtain slip resistance at each temperature, then transient constant-thrust ISO-834 tests to obtain safe working time.
This paper studies the anti-sliding performance of parallel wire strand clamps at elevated temperatures. The 270 mm x 230 mm x 45 mm clamp grips a 46 mm, 1670 MPa parallel wire strand composed of sixty-one 5 mm galvanized wires. Each bolt is pretensioned in three rounds of 51/103/155 kN, and the strand is pretensioned to 600 kN. Steady-state tests cover 8 temperature levels from 20-400 ?; at 400 ?, ultimate anti-sliding resistance drops from 417.8 kN to 86.8 kN, only 20.8% of room temperature. Transient tests use the ISO-834 curve and five thrust levels from 0.30-0.90Ffc,20; at 0.90Ffc,20 the safe time is 531.3 s, only 38.1% of the 1395.9 s at 0.30Ffc,20. FE analysis explains bolt pretension loss: at 400 ? the bolt pretension is 67.3% of that at 20 ?.
| Metric | Paper data | Meaning |
|---|---|---|
| Specimen and loading | Clamp 270 x 230 x 45 mm; strand diameter 46 mm; strand pretension 600 kN; each bolt 155 kN | Represents clamp slip risk under unbalanced thrust |
| Steady resistance | Ffc: 417.8 kN at 20 ?, 270.5 kN at 300 ?, 86.8 kN at 400 ? | Only 20.8% of slip resistance remains at 400 ? |
| Transient safe time | 0.90/0.75/0.60/0.45/0.30Ffc,20: 531.3/915.0/1145.6/1294.2/1395.9 s | High thrust sharply narrows the safe fire-time window |
| Numerical explanation | At 400 ? bolt pretension is 67.3% of the 20 ? value; FE resistance matches tests | Thermal softening, friction reduction, and pretension loss jointly trigger slip |
Data source: abstract, Sections 2-5, Tables 1-5, Figs. 8-19, and conclusions.
The paper parameterizes the surface with LSCM, adjusts a 2D base mesh using an area map and virtual interaction forces, then clips, maps back to 3D, and smooths.
This paper proposes a structured triangular mesh generation method for free-form single-layer reticulated shells. It first uses LSCM conformal mapping to transform a complex 3D surface into a 2D parametric plane, constructs a continuous area map from area compression ratios, and adjusts target member lengths according to local area compression. A structured triangular base mesh is then modeled as a particle-spring system and moved by virtual interaction forces. The paper identifies topology locking in regular triangular meshes and relaxes it using boundary stiffness reduction and internal force redistribution. The mesh is then clipped by triangle centroids, repaired at the boundary, optimized by golden-section search, inversely mapped to 3D with barycentric interpolation, and smoothed by VIFs. Four cases show controllable mesh size and direction; in Case 2 the CPU time is about 13.8 s at the same target length, faster than 46.5-54.0 s in the reference method; in Case 4 the coefficient of variation is about 10.68% versus 24.74% for an isoparametric mesh.
| Step | Paper data | Meaning |
|---|---|---|
| Framework | Six steps: conformal mapping, area map, VIF adjustment of 2D base mesh, clipping, inverse mapping, and 3D smoothing | Reduces difficult 3D meshing to a controllable 2D process |
| Topology locking | Internal nodes have degree 6, so opposite spring forces can cancel | Explains why plain VIF may stop before target lengths are reached |
| Case 2 efficiency | At ltar = 2.30 m, tCPU = 13.8 s; reference method 46.5-54.0 s | 2D adjustment avoids costly 3D projection and topology optimization |
| Case 4 ringed surface | Proposed mesh coefficient of variation about 10.68%; isoparametric mesh 24.74% | More uniform and smooth, reducing short members and fabrication difficulty |
Data source: abstract, Sections 2-9, Tables 1-3, Figs. 1-23, and conclusions.
The paper uses true low-resolution simulations rather than simple down-sampling, with SDF and flow-region channels to recover shock-wave spatial information.
This paper proposes a deep-learning super-resolution framework for 2D explosion pressure fields. The LS-DYNA axisymmetric blast-flow dataset covers a 2 m x 2 m field, 9 scenarios, and 1800 pressure fields per resolution; 20/10/5/2.5 mm meshes correspond to r=8/4/2/1 and about 4/50/465/4200 s per scenario. Multi-resolution concatenation combines low-resolution pressure, an SDF channel, and 6 flow-region channels. UNet performs best among three networks with 31.13 M parameters, 1.52 GFLOPs, and 41.79 dB PSNR. SDF/FR channels improve mean PSNR by 0.66%-5.32% and reduce standard deviation by 18.3%-77.6%. Compared with bilinear interpolation, the model improves PSNR by 28.4%-48.4%, MSSIM by 0.8%-1.5%, and reduces pressure-history RMSE by up to 85.9%.
| Link | Paper data | Meaning |
|---|---|---|
| Dataset | r=8/4/2/1; 100x100 to 800x800; 1800 pressure fields per resolution | Supports multi-ratio super-resolution training |
| Network | UNet / Attention UNet / Swin UNet: 41.79 / 40.39 / 38.99 dB | UNet gives the best accuracy-complexity balance |
| Geometry channels | Mean PSNR +0.66%-5.32%, standard deviation -18.3%-77.6% | Spatial information improves and stabilizes the model |
| Pressure history | Sensor 1, r=8: RMSE 0.0475 -> 0.0067 MPa | Extends pressure-map reconstruction to blast-load histories |
Data source: abstract, Sections 2-7, Tables 4 and 6-9, Figs. 17-27, and conclusions.
A 5000 kN testing machine, 1200 ? furnace, and non-contact DIC obtain full curves at 9 temperature levels.
This paper performs steady high-temperature tensile tests on 1670 MPa Galfan-coated steel cables and 1570 MPa full-locked steel cables. The Galfan cable has a 38 mm nominal and 41.4 mm measured diameter; the full-locked cable has a 48 mm nominal and 51.4 mm measured diameter; both are 1000 mm effective length. Temperatures are 20, 100, 200, 300, 400, 450, 500, 600, and 700 ? with 10 ?/min heating, 30 min soaking, and 0.003 min^-1 strain rate. Stress at 1.25% strain is recommended as nominal yield strength. Room-temperature ultimate strengths are 1681.7 MPa and 1588.5 MPa; at 400 ? about half remains; at 700 ? only 2.36% remains for Galfan and 3.56% for full-locked cables. Full-locked cables are more ductile, and the paper proposes piecewise constitutive and reduction-factor models for elastic, yielding, hardening, and necking stages.
| Metric | Paper data | Meaning |
|---|---|---|
| Test protocol | 9 temperature levels; 10 ?/min; 30 min soak; strain rate 0.003 min^-1 | Steady tests obtain material constitutive curves |
| Room-temperature ultimate | GCSC 1681.7 MPa; FLR 1588.5 MPa | Baseline for high-temperature reductions |
| Elevated ultimate | 400 ?: 830.1 / 841.0 MPa; 700 ?: 39.7 / 56.5 MPa | Capacity is nearly exhausted at 700 ? |
| Model | 1.25% strain nominal yield; elastic, yielding, hardening, necking segments | Describes the full high-temperature cable tensile process |
Data source: abstract, Sections 2-5, Tables 2-8, Figs. 4-13, and conclusions.
The paper uses embedded thermocouples and inclinometers instead of hard-to-measure fire-scene displacements, then FAST-AlertNet predicts KMPP displacement curves.
This paper proposes FAST-AlertNet to predict key displacements of large-span steel trusses in fire from real-time temperatures and rotations, then issue three-level collapse warnings and remaining-time estimates. The example has 8 planar trusses spaced at 6 m, each spanning 24 m, made of Q235 steel. The pre-training dataset has 500 parametric large-space fire scenarios with ABAQUS thermal-structural analysis; the transfer-learning dataset has 60 FDS/PyroSim real-temperature-field scenarios. The model has two LSTM and two FC layers with dimensions 11x64, 64x32, 32x128, and 128x3; dynamic weighted loss outperforms MSE. TL2 freezes LSTM1 and reaches R2=0.92 and RMSE=3.59 mm for uyP. In the application case, the system activates at 203 s, warns at 292/926/1106 s, and collapses at 1198 s; Level 3 predicts 90 s remaining versus the real 92 s.
| Link | Paper data | Meaning |
|---|---|---|
| Inputs/outputs | R1-R6 rotations + G1-G5 temperatures -> uyP, uyR, uyL | Recovers hard-to-measure displacements from measurable data |
| Network | LSTM1 11x64, LSTM2 64x32, FC1 32x128, FC2 128x3 | Outputs synchronous displacement curves |
| Transfer learning | TL2: R2=0.92, RMSE=3.59 mm; Model 2: R2=0.69, RMSE=7.63 mm | FDS temperature fields greatly improve real-fire adaptation |
| Application | 203 s activation; 292/926/1106 s warnings; 1198 s collapse; Level 3: 90 s vs 92 s | Remaining-time estimates improve as collapse approaches |
Data source: abstract, Sections 2-6, Tables 2-9, Figs. 8-27, and conclusions.
The paper proposes an assembled self-centering buckling-restrained brace: BRB core plates dissipate energy, strands provide restoring force, and disc springs add deformability and post-yield stiffness.
This paper proposes an assembled self-centering buckling-restrained brace (ASC-BRB) by combining a BRB system with a self-centering system. The self-centering system connects two strand groups and disc-spring groups in series; in either tension or compression, the device length change stretches the strands and compresses the disc springs, so unloading produces a restoring force that overcomes core-plate yielding and leaves very small residual deformation. In the tests, the BRB theoretical ultimate tensile force was 108.77 kN and the self-centering pretension was 110 kN. Under 36.84 mm cyclic displacement, equivalent to 4% interstory drift, the ASC-BRB showed flag-shaped hysteresis and significant post-hardening; residual displacement was about 1 mm, only 2.91% of maximum displacement, and the maximum ductility was 25.58. The paper also proposes an improved configuration replacing two 1-shaped cores with four angle-steel cores, increasing yield force by 9.4 times while reducing maximum inner-tube stress from 277 MPa to no more than 41 MPa.
| Link | Paper data | Meaning |
|---|---|---|
| Self-centering activation | target pretension 110 kN; SCB activation about 109 kN | measured activation matches the design target |
| Flag-shaped hysteresis | maximum displacement 36.84 mm; residual displacement about 1 mm | the brace recenters after dissipating energy |
| Replaceability | after testing, major damage occurred in core plates while other components stayed intact | post-event repair can focus on replacing the dissipating cores |
| Improved configuration | angle-core yield force is 9.4 times that of the 1-shaped core; inner-tube stress 277 -> <=41 MPa | stronger cores with lower local-instability risk in restraint tubes |
Data source: abstract, Sections 2-6, Tables 3-5, Figs. 23-32, and conclusions.
The paper uses a non-contact video strain measurement system to test full-locked and Galfan-coated cables at 350-500 ? under different stress ratios.
This paper studies high-temperature creep and postfire strength of 1560 MPa full-locked cables and 1670 MPa Galfan-coated cables. Specimens were heated to target temperature, held for 30 min, loaded to a stress ratio, and maintained for 3 h while a non-contact video system recorded strain. Temperature and stress ratio both strongly amplify creep, and Galfan-coated cables creep faster and fail earlier. At 500 ? and stress ratio 0.7, the Galfan cable ruptured after 116 min with 24.36% fracture strain, while the full-locked cable survived 180 min with 8.19% maximum creep strain. At 450 ? and stress ratio 0.9, the Galfan cable ruptured after 46 min and the full-locked cable after 148 min. The fitted composite time-hardening model reached R2 above 0.9, and existing code models substantially underestimated creep. The maximum postfire ultimate-strength reduction was 49% for full-locked cables and 55% for Galfan-coated cables.
| Link | Paper data | Meaning |
|---|---|---|
| Creep matrix | 350/400/450/500 ?, multiple stress ratios, 3 h constant load | separates the coupled effects of temperature and stress ratio |
| Critical comparison | 500 ?, 0.7: Galfan 24.36% and ruptured at 116 min; full-locked 8.19% without rupture | fabrication differences control fire creep resistance |
| Model fit | composite time-hardening model with R2 > 0.9 | code creep models underestimate strain for these cable types |
| Postfire strength | 500 ?: full-locked 0.61/0.51; Galfan 0.54/0.45 | residual capacity must account for temperature and stress history |
Data source: abstract, test program, Tables 3-4, Table 11, creep analysis, and conclusions.
The paper turns sensor placement for single-layer reticulated shells from empirical selection into performance-based optimization: minimize modal confusion while maximizing damage sensitivity.
This paper proposes a performance-based optimal sensor placement method for single-layer reticulated shells (SLRSs), considering both modal observability and damage identifiability. It first reduces the candidate space using a frequency damage sensitivity matrix, then uses a genetic algorithm for multi-objective optimization, and finally fits two performance curves: sensor placement proportion curves for x/y/z direction ratios and a placement effect curve for total sensor count. In the first spherical-shell example, the structure has 600 members and the first 20 modes are used; after screening, 143 joints and 429 DOFs become optimization variables, with GA population 200 and 100 iterations. Compared with the equal-allocation multi-objective method, the performance-based method reduces the z-direction modal observability index by 50.0% and increases the damage identifiability index by 32.3%. The paper also divides the placement effect curve into rapid-growth, transition, and slow-growth stages, recommending Stage II for practical balance between performance and economy.
| Link | Paper data | Meaning |
|---|---|---|
| Mode selection | SLRS modes are dense, so the first 20 modes are selected | avoids missing structural information with too few low-order modes |
| Space reduction | 600 members -> 518 sensitive members -> L2=180 -> 143 joints/429 DOFs | reduces optimization dimension and local-optimum risk |
| Method 4 | 23/23/35 sensors in x/y/z; z-direction f1 decreases 50.0% and f2 increases 32.3% | performance curves outperform empirical equal direction allocation |
| Design guidance | placement effect curve has Stage I/II/III; total count is recommended in Stage II | balances sensor-system performance and economy |
Data source: Sections 2-8, Tables 1-8, Figs. 5-17, and conclusions.
The paper transforms time-domain vibration responses into frequency, amplitude, and phase tensor channels, then uses DCGAN to learn an implicit parameter model of the SLRS.
This paper proposes a fast response-generation method for SLRSs. Monitored time-domain vibration responses are transformed by Fourier transform into frequency, amplitude, and phase, then packed into GAN tensors so a DCGAN can directly learn the structural frequency-domain response distribution. After training, inverse Fourier transform reconstructs time-domain responses. In the numerical spherical SLRS, 10,000 groups of 20 s responses at 50 Hz are generated, and 1DOF, 4DOF, and 9DOF DCGANs are built; the 9DOF dataset is [10000,84,84,3]. JSD ranges 0.010-0.071 and FID 2.321-6.211, satisfying the quality thresholds of 0.5 and 10. Training takes 3.18/4.21/5.72 h, while generating one response takes 35 ms versus about 3 min for ANSYS transient analysis. For a real 45 m x 45 m aluminum SLRS, four accelerometers collect 48 h data; the first 24 h train and the last 24 h validate, giving JSD/FID of 0.018-0.072 and 3.041-4.767, with 4320 generated responses in 151 s.
| Link | Paper data | Meaning |
|---|---|---|
| Tensor construction | 9DOF: [10000,84,84,3]; 4DOF: [10000,60,60,3] | turns responses into image-like frequency-domain data for GAN learning |
| Quality evaluation | numerical SLRS JSD 0.010-0.071, FID 2.321-6.211 | generated samples have both similarity and diversity |
| Speed | GAN 35 ms/group; ANSYS about 3 min/group; 10000 groups 350 s vs 500 h | after training, response libraries can be expanded rapidly |
| Field validation | 45 m x 45 m aluminum SLRS, 4 sensors, 48 h data, 4320 validation groups | the method is not limited to numerical models |
Data source: abstract, Sections 2-6, Tables 1-6, Figs. 7-22, and conclusions.
The paper uses a validated ABAQUS model for parametric analysis and summarizes trapezoid-truss collapse into A1, A2, B1, and B2 modes.
This paper proposes an early-warning method for fire-induced collapse of planar steel trapezoid trusses. The model is validated against an existing full-scale steel roof-truss fire test: the workshop is 8 m in diameter and 4.02 m high, with three 600 mm-high planar trusses; B31 beam elements use 0.05 m mesh, with global imperfection L/300 and local imperfection l/350. A 24 m-span, 1.5-2.7 m-high, 6 m-spaced basic trapezoid truss is then analyzed under six fire locations, weak/strong supports, spans, spacings, load ratios, fire protection, sections, and tie-bar arrangements. Four collapse modes are summarized: weak-constraint A1/A2 and strong-constraint B1/B2, corresponding to rotation-pin or slide-surface mechanisms. Based on key-node displacements and velocities, three-level warning methods are proposed. Normalized warning-time ranges are about 0.2-0.5, 0.5-0.8, 0.7-0.9 for mode A and 0.06-0.3, 0.6-0.8, 0.7-0.9 for mode B. Monte Carlo analysis gives reliability-based remaining safety time, and an existing fire test validates the method: activation at 276 s, warnings at 418/689/734 s, and collapse time set as 836 s.
| Link | Paper data | Meaning |
|---|---|---|
| Modes | A1/A2/B1/B2: weak/strong supports + rotation pin/slide surface | warning criteria depend on identifying the potential mode |
| KMPPs | A: uxL, uyP and velocities; B: uyP, uyL, uzL and velocities | displacement and velocity track collapse state better than temperature alone |
| Warning windows | A: 0.2-0.5 / 0.5-0.8 / 0.7-0.9; B: 0.06-0.3 / 0.6-0.8 / 0.7-0.9 | levels map to continue rescue, prepare evacuation, and immediate evacuation |
| Validation | activated at 276 s; warnings at 418/689/734 s; collapse at 836 s | real fire test supports the three-level warning logic |
Data source: abstract, Sections 2-5, Tables 1-10, Figs. 14-36, and conclusions.
The paper combines measurable side-column displacements with beam and column rotations, using function fitting to infer roof and internal-column key displacements synchronously.
This paper solves a prerequisite for fire-collapse warning: many roof and internal-column displacements among the key monitoring physical parameters (KMPPs) are hard to measure directly with radars in fire scenes. The method embeds inclinometers during construction; in a fire, microwave radars near the two side columns measure easy KMPPs, and rotations plus polynomial deflection functions recover hard KMPPs. Single-span analysis compares 1, 2, and 3 inclinometer arrangements; three-point arrangements are generally satisfactory, and five inclinometer positions make most cases reach R2>0.9. The multi-span scheme uses 5 inclinometers per span and 3 per internal column, totaling 7n-2, plus slope-based weights between left and right predictions. When a weight is below the threshold 0.2, it is reset to 0 to prevent severely fire-affected side errors from contaminating the result. In three-span and parametric analyses, all cases satisfy R2>0.9 or displacement error d<10 mm. In the real single-span fire test that collapsed at about 330 s, warnings occur at 112/214/241 s; under 50% reliability, Level 2 remaining time is 115 s versus real 116 s, and Level 3 is 68 s versus 89 s. A numerical double-span frame collapses at about 15 min, with warning states at 330/570/720 s.
| Link | Paper data | Meaning |
|---|---|---|
| Layout | n-span portal frame: 2 radars and 7n-2 inclinometers | fire-scene setup uses low-position radars while embedded sensors recover hard displacements |
| Single-span accuracy | three-point layouts are often satisfactory; five positions make most R2>0.9 | gives a practical sensor-count basis |
| Robustness | three-span parametric analysis: R2>0.9 or d<10 mm; threshold b=0.2 | works across fire scenarios, spans, load ratios, and column-base conditions |
| Warning validation | test: 112/214/241 s warnings, 330 s collapse; numerical: 330/570/720 s warnings, about 15 min collapse | recovered displacements directly support collapse-risk judgment |
Data source: abstract, Sections 2-6, Tables 2-6, Figs. 10-27, and conclusions.
The paper performs cube compression and cylinder uniaxial compression tests from 20-800 ? to obtain complete stress-strain curves.
This paper tests material properties and a constitutive model of C120 hybrid-fiber UHPC with 0.5% steel fibers and 0.15% PP fibers at elevated temperatures. Tests cover 20, 100, 200, 300, 400, 600, and 800 ?, using a rigid-element-assisted loading system to stably capture the post-peak branch in cylinder uniaxial compression. Cube compressive strength rises from 136 MPa at 20 ? to 152 MPa at 200 ?, then drops to 61 MPa at 800 ?. Cylinder strength rises from 113 MPa to 133 MPa at 200 ?, then drops to 37 MPa at 800 ?. Initial elastic modulus decreases monotonically from 46.40 GPa to 2.17 GPa, while peak strain rises from 0.31e-2 to 1.80e-2. The paper fits strength, modulus, and peak-strain factors and proposes an elevated-temperature stress-strain constitutive model that better captures C120 HF-UHPC pre-peak and post-peak behavior than EC2 and existing models.
| Link | Paper data | Meaning |
|---|---|---|
| Temperature matrix | 20/100/200/300/400/600/800 ? | covers the degradation range under common fires |
| Strength | cube 136 -> 152 -> 61 MPa; cylinder 113 -> 133 -> 37 MPa | strength increases near 200 ? then degrades strongly |
| Deformation | Ec 46.40 -> 2.17 GPa; peak strain 0.31e-2 -> 1.80e-2 | capacity drops while deformation capacity increases |
| Model | strength, modulus, peak-strain functions and stress-strain model proposed | provides direct inputs for fire structural analysis |
Data source: abstract, Sections 2-6, Tables 4-6, Figs. 10-20, and conclusions.
The paper tests 36 PWS specimens in 350-500 ?, three stress levels per temperature, and 2 h steady-state elevated-temperature creep.
This paper studies elevated-temperature creep modeling of 1670 MPa parallel wire strands (PWSs). A CCD non-contact video strain system is used. Target temperatures are 350, 400, 450, and 500 ?, with three stress levels at each temperature, for 12 conditions and 36 specimens. The specimen is heated at 10 ?/min, soaked for 1 h, loaded to target stress within 10 min, then held for 2 h or until failure. Temperature controls creep more strongly than stress level: at 350 ?, 2 h creep strains under 511/617/734 MPa are 0.0863/0.1689/0.2692%; at 400 ? and 511 MPa it reaches 0.4861%; at 500 ? and 238 MPa it reaches 0.9332%. At 442 MPa, creep strain from 400 ? to 450 ? increases 5.74 times, so 450 ? is taken as the segment point. PWS creep strain is lower than steel strands at the same temperature and stress. The paper compares a general empirical formula, Bailey-Norton, and composite time-hardening model, recommending the composite model because it considers temperature, stress, and time simultaneously; the two segments have R2=0.997 and 0.995.
| Link | Paper data | Meaning |
|---|---|---|
| Test matrix | 350/400/450/500 ?; three stress levels per temperature; 36 specimens | covers the key creep range for PWSs in fire |
| Lower temperature | 350 ?: 0.0863/0.1689/0.2692% at 511/617/734 MPa | creep is relatively small below 350 ? |
| Critical change | 442 MPa: 400 ? 0.1572% -> 450 ? 0.9026% | 450 ? is the model segment point |
| Model | composite time-hardening R2=0.997/0.995, valid for 20-500 ? | usable for fire-resistance analysis of pretensioned structures |
Data source: abstract, Sections 2-5, Tables 2-7, Figs. 7-14, and conclusions.
For arbitrary free-form SLRSs, the paper turns an unstructured initial mesh into a uniform, fluent, structured triangular mesh.
This paper proposes a self-adaptive triangular mesh-generation framework for free-form SLRSs. It starts with a constrained Delaunay triangular mesh in the parameter plane, maps it onto the 3D free-form surface, then uses nonlinear virtual interaction forces (VIFs) and forward Euler updates to move joints while projecting them back onto the surface. A mesh-energy function adaptively adds/removes joints and adjusts their distribution according to the desired member length, with a stopping criterion based on low energy and irregularity. Connectivity optimization uses edge collapse, edge split, edge drift, and irregular-joint operations, with distance-based priority and direction rules, followed by VIF smoothing that considers global and local quality. Four free-form surface case studies verify robustness. In Case 1 on a 16.4 x 15.1 x 3.9 m surface, denser/sparser initial meshes end with COVm of 0.091/0.112 and CPU times of 34.4/22.9 s; VIF smoothing reduces COVm by 28.9% and 18.8%, outperforming Laplacian smoothing. Case 3 with a hole and Case 4 ringed surface also produce structured meshes; after Loop subdivision, COVm reaches 0.086-0.104 and the fluency index is about 0.015-0.018.
| Link | Paper data | Meaning |
|---|---|---|
| Self-adaptation | Case 1 converges from denser/sparser starts, COVm 0.091/0.112 | incorrect initial joint density can be corrected |
| Smoothing | VIF smoothing reduces COVm 28.9%/18.8%; Laplacian increases sparse-mesh COVm by 10.7% | global force-based smoothing outperforms local Laplacian smoothing |
| Complex boundary | Case 3 with a hole: final l0 about 2% shorter than lopt, COVm about 0.112 | structured meshes work on multi-boundary free-form surfaces |
| Ringed surface | Case 4 initial energy about 300,000 m2, after adjustment 11.9/0.5 m2 | large radius variation still preserves surface shape and mesh quality |
Data source: abstract, Sections 2-5, Tables 1-5, Figs. 11-17, and conclusions.
The starting imperfection field is stochastic, but many connected members violate the manufacturable length tolerance.
This paper proposes CSIMM, which uses virtual interaction forces to modify MRIMM-generated stochastic initial geometric imperfections into fields that are both random and topology-feasible. The numerical example is a Kiewitt-6 single-layer reticulated shell with L=40 m, f/L=1/4, 8 rings, and 169 internal joints; 1000 random imperfection fields are generated by both MRIMM and CSIMM. MRIMM gives member-length deviations as high as 46.330 mm and as low as -49.325 mm, with 62.939% of members exceeding the 3.5 mm manufacturing tolerance. CSIMM strictly keeps member-length deviations within +/-3.5 mm. For resultant joint deviation, CSIMM has mean 6.174 mm and standard deviation 4.500 mm, reductions of 36.021% and 32.554% from MRIMM values of 9.650 mm and 6.672 mm. A second nonlinear buckling study generates 1000 imperfections for each K6 shell at f/L=1/6, 1/5, and 1/4. The minimum load factors from CSIMM are 3.622, 4.613, and 5.599, all lower than MRIMM, showing that topology constraints do not simply shrink imperfections but help search realistic and more unfavorable imperfection patterns.
| Link | Paper data | Meaning |
|---|---|---|
| K6 shell example | L=40 m, f/L=1/4, 8 rings, 169 internal joints; 1000 IGIs per method | Compares MRIMM and CSIMM imperfection distributions on the same structure |
| Resultant joint deviation ||Delta P|| | MRIMM max/min/mean/std = 26.667/0.000/9.650/6.672 mm; CSIMM = 26.667/0.071/6.174/4.500 mm | CSIMM preserves randomness while removing unrealistic large deviations caused by length violations |
| Member-length deviation Delta l | MRIMM max/min/mean/std = 46.330/-49.325/0.027/9.180 mm; CSIMM = 3.500/-3.500/0.011/1.251 mm | CSIMM keeps every member within the +/-3.5 mm manufacturing tolerance |
| Nonlinear buckling effect | f/L=1/6: MRIMM 5.486/3.863/4.665/0.291; CSIMM 5.279/3.622/4.568/0.296 | Topology-feasible imperfections can locate a lower buckling-load boundary |
Data source: CSIMM framework in Section 2, Sections 3.1-3.3, Tables 1-3, Figs. 8-17, and conclusions.
The paper uses the MPC184 pin sub-element in ANSYS to represent nonlinear moment-rotation behavior of gusset joints, then validates it against room-temperature and destructive fire tests.
This paper studies fire-induced capacity reduction of K6 aluminum alloy reticulated shells with semi-rigid gusset joints. The model embeds 6061-T6 aluminum degradation and temperature-dependent joint bending stiffness into thermal-structural coupling analysis, and is calibrated against room-temperature static tests and destructive fire tests D-1/D-2 for displacement curves, thermal expansion, stiffness degradation, and collapse shapes. The parametric study covers spans of 25/30/40 m, height-to-span ratios of 1/3, 1/4, and 1/5, 10/12/14 rings, three H sections, pinned/fixed perimeter supports, 2/8/25 MW fires, support heights of 0/5/10 m, and center/corner fire locations; fire duration is 2400 s with 240 s capacity-evaluation intervals. The paper defines kΛ(t)=Λ(t)/Λ(0), showing that capacity reduction is governed by span, height-to-span ratio, support height, fire power, and fire location, but is essentially independent of member divisions, ring number, span-to-thickness ratio, and support condition. The mechanism is the ferrule-effect compressive force and relative stiffness change of the outer ring. The paper then uses 324 thermal-structural coupling results to build explicit ML-assisted design formulae and gives distance criteria for ignoring capacity analysis or radiative heat flux.
| Link | Paper data | Meaning |
|---|---|---|
| Parameter matrix | L=25/30/40 m; f/L=1/3, 1/4, 1/5; Q=2/8/25 MW; H=0/5/10 m | covers the most sensitive geometry and fire variables in concept design |
| Reduction mechanism | depends on L, f/L, H, Q, and fire location; mostly independent of rings, span-to-thickness ratio, and support condition | outer-ring ferrule effect governs relative stiffness and failure location under fire |
| Ignore capacity analysis | 5%: f/L=1/5, Q<=8 MW, distance>20 m; 10%: f/L=1/3 or 1/5, Q<=15 MW, distance>20 m, while f/L=1/4 requires Q<=8 MW | defines when coupled analysis may be skipped in early design |
| Radiative heat flux | roof fire 8 MW, df=1 m: tr 132 s vs tnr 216 s; support fire 25 MW, df=1 m: tr 20 s vs tnr 2400 s | ignoring radiation near the structure can severely overestimate fire-resistance time |
Data source: abstract, Sections 2-6, Tables 1-3, Figs. 10-26, and conclusions.
Specimen BT1.5-BH120-2B-Tt has 1.5 mm beam thickness, 120 mm beam height, and two bolts; temperatures cover 20-700 ?.
This paper investigates the flexural behavior of clad-rack beam-to-column bolted connections (CRBCs) at high temperatures. Tests use the EN15512 single-cantilever method with a 400 mm column, 1000 mm beam, and loading point 350 mm from the column edge; one specimen is tested at 20 ? and two parallel specimens at each of 300/400/500/600/700 ?. Nine LVDTs calculate connection rotation and six thermocouples check temperature uniformity. Specimens are heated at about 10 ?/min, held for 30 min at target temperature, then loaded until the load falls to 85% of the peak. Table 5 shows moment capacity dropping from 4.00 to 0.65 kN m and initial rotational stiffness from 146 to 24 kN m/rad. Failure modes at 300-600 ? match ambient behavior: residual top-tab distortion, cracking near the upper weld area of the beam end, local buckling in the lower beam end, and connector squeeze deformation. At 700 ?, beam-end tension cracking disappears while connector-web residual deformation becomes severe. The paper builds an ABAQUS fracture FE model with 2 mm solid and 5 mm shell meshes and friction coefficient 0.3, validated by Table 8 moment-rotation comparisons. Forty-five parametric models show that increasing beam height significantly improves stiffness and capacity, while increasing beam thickness mainly improves capacity and eventually shifts failure to top-tab fracture. Upper bolts matter; lower bolts contribute little to positive moment resistance. Component-method theoretical models give average ratios of 0.98 for capacity and 1.04 for stiffness.
| Link | Paper data | Meaning |
|---|---|---|
| Test setup | 20/300/400/500/600/700 ?; 10 ?/min heating; 30 min soak; 9 LVDTs and 6 thermocouples | captures full moment-rotation response under steady-state high temperature |
| Temperature degradation | Mue: 4.00/4.00/3.64/2.26/1.36/0.65 kN m; K0e: 146/108/90/64/40/24 kN m/rad | capacity and stiffness fall rapidly after 500 ? |
| Parametric analysis | beam height 105->145 mm: +56% capacity at 500 ?; +84%/+94% stiffness at 300/400 ? | beam height improves both stiffness and capacity more effectively than thickness |
| Theoretical model | capacity Mu/Mue average 0.98, std 0.12; stiffness K0/K0e average 1.04, std 0.12 | component method is usable for engineering calculation |
Data source: abstract, Sections 2-8, Tables 1-15, Figs. 8-32, and conclusions.
The paper uses measurable left-side displacements and temperatures as inputs to predict apex and right-side displacements, then feeds them into existing three-stage collapse warning theory.
This paper proposes an LSTM-based real-time prediction method for key monitoring physical parameters (KMPPs) used in fire-induced collapse warning. The example is a single-span steel portal frame with 12 bays, 6 m bay spacing, and 24 m span. ABAQUS thermal-structural coupling generates the dataset; B31 beam elements use 0.15 m mesh for rafters and columns and 0.3 m for secondary members. Randomness includes vertical loads U(0.3qu,0.5qu), Q235 steel fy/fu within 0.9-1.1 times design values, fire parameter C=U(0.5,5), and 39 fire scenarios; heated members can reach 800-1200 ?. Model 1 inputs left-eave horizontal/vertical displacements VhL and VvL plus 32 thermocouple temperatures, and outputs hard-to-measure Vp, VhR, and VvR. Model 2 uses only temperatures. Each model has 500 samples split into 300/100/100 training/validation/test subsets, with 3600 s duration and 10 s interval, trained for 50000 epochs at batch size 128. Model 1 has more than 90% of unknown test samples meeting high-accuracy requirements, and a single-case prediction takes 0.621 s, below the 10 s recording interval. Model 2 performs much worse because it ignores implicit identification of load and material uncertainties. In a typical case, Level 1 warning occurs at 860 s, Level 2 at 1140 s, Level 3 at 1200 s, and collapse at about 1400 s; at 80% reliability, Level 3 remaining-time prediction is 211 s versus 200 s actual.
| Link | Paper data | Meaning |
|---|---|---|
| Structure and fire | 12 bays, 6 m spacing, 24 m span; 39 fire scenarios; C=U(0.5,5), heated members 800-1200 ? | training set covers realistic fire and structural uncertainty |
| Model input | Model 1: VhL, VvL + 32 temperatures -> Vp, VhR, VvR; Model 2: 32 temperatures -> all KMPPs | easy displacements implicitly identify load and material states |
| Training and runtime | 500 samples; 300/100/100 split; 50000 epochs; 31.4 h training; 0.621 s prediction < 10 s | offline training and fast online inference suit fire-scene updating |
| Warning timeline | 860/1140/1200 s for Levels 1/2/3; collapse about 1400 s; TR: 1465/341/211 s vs 540/260/200 s | remaining-time prediction becomes closer at higher warning levels |
Data source: abstract, Sections 2-5, Tables 1-6, Figs. 5-24, and conclusions.
The paper combines 23 spanwise fire locations and two baywise heating ranges into 46 base fire scenarios, then varies protection level, span, bay spacing, supports, and load ratio.
This paper proposes an early-warning method for fire-induced collapse of double-span steel portal frames. ABAQUS thermal-structural coupling is used for a two-span frame with 24 m spans; out-of-plane rotations are restrained to represent adjacent cold bays, B31 beam elements use 0.15 m meshes for rafters/columns and 0.3 m meshes for secondary members, dead load is applied first, and then parametric heating continues until collapse. The study covers 46 base fire scenarios from 23 spanwise heating locations and two baywise heating ranges, then varies nine fire-protection levels, 0-600 ?/m cross-section temperature gradient, 18-30 m spans, 6-9 m bay spacing, column base and middle-column top connections, and load ratios of 0.3-0.6. Six collapse modes are identified: A side-column lateral collapse, B side-column buckling, C overall inward collapse, D overall outward collapse, E side-span collapse, and F middle-column collapse. Compared with single-span frames, the double-span system adds side-span and middle-column behavior because of the middle column and restraint from the cold span. The warning method first identifies the collapse mode from displacement and velocity trends of KMPPs at the apex, eaves, and rafter mid-span, then applies mode-specific ratios for Level 1, 2, and 3 warning and remaining time. Monte Carlo analysis gives recommended 70%-80% reliability values. In the full-scale validation, the frame collapsed at about 16 min, while Levels 1, 2, and 3 warnings occurred at about 7.5, 11.5, and 15 min, matching Mode C overall inward collapse.
| Link | Paper data | Meaning |
|---|---|---|
| FE and fire cases | 24 m double-span frame; B31; 0.15 m rafter/column mesh and 0.3 m secondary mesh; 23 x 2 = 46 fire cases | builds a collapse database covering heating location and extent |
| Parameter range | nine protection levels; gradient 0-600 ?/m; span 18-30 m; bay spacing 6-9 m; load ratio 0.3-0.6 | Monte Carlo covers engineering variability rather than one deterministic example |
| Modes and warning | six modes A/B/C/D/E/F; KMPPs include uhL, uvL, up, uhM, uvM, uq, uhR, uvR and velocities | identifies collapse mechanism before applying mode-specific three-stage warning |
| Validation | Mode C overall inward; Levels 1/2/3 at about 7.5/11.5/15 min; collapse at about 16 min | higher-level warning is close to collapse and supports evacuation decisions |
Data source: abstract, Sections 2-5, Tables 3, 16-17, Figs. 13-19, and conclusions.
The paper describes the K6 spherical shell by a rotated cubic spline; the design variables are three vertical control-point increments bounded by -0.3 to 0.3 m.
This paper proposes a shape-optimization method for aluminum-alloy spherical reticulated shells considering geometric nonlinearity, material nonlinearity, and nonlinear semi-rigid gusset joints. ANSYS BEAM188 elements model members and joint zones, with four elements per member and one element per joint zone; the joint-zone elastic modulus is set to 100E to represent gusset strengthening, and COMBIN39 nonlinear springs simulate out-of-plane joint bending stiffness. The FE model is validated against a five-ring K6 spherical-shell test. The objective is to maximize nonlinear buckling capacity Pc with initial imperfection, where the imperfection combines the lowest symmetric and antisymmetric linear buckling modes and Pc is obtained by the arc-length method. The shell surface is controlled by a rotated cubic spline; symmetry leaves only three independent control points, and Delta Z1-Delta Z3 are bounded by -0.3 to 0.3 m. The genetic algorithm uses 50 generations, 50 individuals, 80% crossover, Gaussian mutation, elitism, and reuse of repeated individuals' prior fitness values. In the 40 m span, f/L=1/4, 12-ring, H400x200x10x16 example, Pc increases from 28.33 to 47.52 kN/m2, a 67.74% gain. At 28 kN/m2, maximum joint displacement falls from 93.7 to 51.0 mm, and compression and strong-axis bending become more uniformly distributed. Parametric design tables are given for different rise-span ratios and load distributions; the paper concludes that optimization considering material nonlinearity better improves the real structure, though at higher computational cost.
| Link | Paper data | Meaning |
|---|---|---|
| FE modeling | BEAM188; four elements per member and one joint-zone element; joint zone 100E; COMBIN39 nonlinear spring | includes semi-rigid joint, material, and geometric nonlinearities in the optimization evaluation |
| Optimization algorithm | three Delta Z variables; +/-0.3 m bounds; 50 generations, 50 individuals, 80% crossover, Gaussian mutation, elitism | searches a complex implicit nonlinear objective with few geometry variables |
| Benchmark case | L=40 m, f/L=1/4, m=12, H400x200x10x16; Pc 28.33 -> 47.52 kN/m2 | small shape tuning substantially delays nonlinear buckling |
| Design tables | f/L=1/4, 1/5, 1/6; gamma=0, 1/4, 1/2, 1; improvement up to about 84% | turns high-cost optimization into engineering lookup coefficients |
Data source: abstract, Sections 2-5, Tables 1-5, Figs. 1-16, and conclusions.
The paper defines each action as removing one removable element; the state integrates node coordinates, supports, loads, member properties, existence, and strain-energy features through edge embedding.
This paper proposes a deep reinforcement-learning framework for critical element identification (CEI) and demolition planning (DP) of frame structures. Conventional sensitivity indices require reanalysis for every removal candidate and are short-sighted, so they cannot directly determine the most expected collapse path after multiple removals. The paper formulates multi-element removal as a Markov decision process: each action removes one element, and the state combines joint and element features. Joint features include normalized coordinates, distance to nearest support, and concentrated load; element features include length, existence, load, yield strength, area, strong-axis moment of inertia, strain energy, and strain-energy ratio. Edge embedding iteratively aggregates these features into a comprehensive vector for each element, making DQN weight sizes independent of the numbers of nodes and elements. The reward function considers ultimate collapse severity, strain-energy sensitivity, demolition cost, and safety preference: lambda_R is near zero for CEI and 100% for DP, while lambda4=10 or 5 represents high or low demolition cost. The example is a 4 x 5 planar steel frame with 4 x 8 m span, 5 x 4 m height, 32 kN/m vertical beam load, fixed supports, BEAM188 elements, geometric and material nonlinearities, and arc-length analysis. Training uses Python 3.8.8 with PyMAPDL/ANSYS, nep=5000, nf=100, Tmax=4, batch size 64, and gamma=1. Task 1 and 2 take about 14.8 and 37.9 h; reward converges after about 2000 episodes and loss is almost zero after about 400 episodes. The trained agent applies without retraining to a 3 x 4 frame and a larger irregular frame. For the 4 x 5 frame, conventional ALP needs 26 nonlinear analyses and 26.61 s, while the trained method outputs all Q values after one state analysis in about 1.37 s and avoids treating locally collapsing, high one-step-sensitivity top-corner columns as the best decision.
| Link | Paper data | Meaning |
|---|---|---|
| State definition | joints: coordinates, support distance, loads; elements: length, existence, load, fy, A, Iz, strain energy, strain-energy ratio | lets topology, loads, and current damage jointly determine action values |
| Training setup | Python 3.8.8 + PyMAPDL/ANSYS; nep=5000, nf=100, Tmax=4, batch=64, gamma=1 | offline training turns expensive nonlinear reanalysis into fast online decisions |
| Generalization test | trained on a 4 x 5 frame; tested on a 3 x 4 frame and a larger irregular frame without retraining | edge embedding lets the network adapt to different action-space sizes |
| Efficiency comparison | 4 x 5: ne=25, training 14.8 h, proposed 1.37 s, conventional 26.61 s; irregular frame 1.63 s vs 76.65 s | online efficiency increases on the order of ne x 100% |
Data source: abstract, Sections 2-5, Tables 1-5, Figs. 1-15, and conclusions.
The paper formulates member addition as reinforcement learning: the action selects the first and second nodes rather than directly selecting a member, greatly reducing the action space.
This paper proposes machine-specified ground structures (MGSs) for binary-truss topology optimization. Fully connected ground structures grow quadratically with node count and do not necessarily perform better for singular optima with stress constraints, while human-specified ground structures require designer experience. The paper formulates generation of a stable sparse ground structure from a node set as an RL task. Step 1 uses a stochastic policy to add m0 favorable members until a stable structure is obtained under three translational constraints; Step 2 randomly adds members until the specified member count m is reached. Graph embedding extracts a comprehensive feature matrix as the state, the policy network uses Softmax to output node-selection probabilities, and REINFORCE trains the policy. Training uses a randomized 4 x 4 node set with Tmax=4, nf=100, RMSprop, learning rate 1e-4, discount factor 0.99, batch size 20, and 10000 batches, i.e. 200000 episodes, taking about 34.2 h. All three random-seed histories converge after about 4000 batches, and the best average reward of 1123.5 occurs at batch 9708 with seed 100. The trained agent handles regular 4 x 4, 5 x 4, and 6 x 3 node sets without retraining, producing stable structures with mostly favorable members. The paper then connects MGSs to binary-truss topology optimization with stress and displacement constraints. In 4 x 4, 5 x 4, and 6 x 6 examples, MGSs with m=65/90/200 produce diverse local optima; in the 6 x 6 case, seed 5 gives 0.01123 m3, better than 0.01291 m3 from the fully connected ground structure. In the L-shaped truss, MGSs improve on the human-specified ground structure at allowable stresses of 170/130/90 MPa, and strict displacement and member-buckling examples show transferability.
| Link | Paper data | Meaning |
|---|---|---|
| RL training | randomized 4 x 4 node set; Tmax=4, nf=100; batch=20, 10000 batches; 200000 episodes; 34.2 h | learns ground-structure generation offline |
| Convergence and transfer | converges near 4000 batches; best average reward 1123.5; stable on 4 x 4, 5 x 4, and 6 x 3 tests | graph embedding avoids binding the policy to the training node count |
| Ground-structure size | Examples 1/2/3: mmin/mmax/m = 28/90/65, 56/190/90, 68/630/200; 20 MGSs each | uses sparse controlled ground structures instead of fully connected explosion |
| Optimization results | 6 x 6: MGS 0.01123 m3 vs fully connected 0.01291 m3; L-shape 170/130/90 MPa: 0.0432/0.0519/0.0564 m3 | MGS diversity increases the chance of approaching the global optimum |
Data source: abstract, Sections 2-5, Tables 3-8, Figs. 4-29, and conclusions.
The paper uses B-splines for architectural surfaces and equal-chord/isoparametric division to maintain member and grid quality.
This paper proposes NSGA-II-FSD for multi-objective shape and size optimization of large-scale free-form spatial latticed structures. B-spline curves or surfaces describe the free-form geometry, and shape parameters V are optimized by NSGA-II. Cross-sections are not searched member by member as genetic variables; instead, fully stressed design (FSD) rapidly selects circular hollow sections T for each candidate shape. The objective functions are total mass m and strain energy C, representing material consumption and global stiffness; constraints include member strength, compression stability, and architectural shape requirements. In FSD, each individual receives a randomly selected stress-ratio limit eta_lim between eta_lb and eta_ub, and the maximum stress ratio over all load cases is pushed into eta_lim-0.1 to eta_lim. To avoid iteration divergence, the maximum section-number change is limited to Delta Ti,max=5. A significant mutation strategy expands the search boundary: special generations use half the variable range as mutation scale, while other generations use one quarter. Example 1 is a double-layer cylindrical latticed shell for a thermal-power-plant coal shed. Load cases are dead load 1 kN/m2 and dead plus 0.8 kN/m2 snow, with weights 0.8/0.2; seven shape parameters control the bottom-chord B-spline and thickness. With 100 individuals, 50 generations, and stress-ratio bounds 0.6-1.0, the Pareto front becomes stable after about 30 generations. Example 2 is a double-layer free-form station-roof truss with an 80 m square projection and 13 tree-column supports. Twenty-five B-spline control points define the surface; eight edge/corner points are fixed at z=15 m and the others vary from 0 to 30 m. With the same 100 individuals, 50 generations, and 0.6-1.0 stress-ratio bounds, the Pareto front stabilizes after about 40 generations. The method provides a Pareto choice set across mass, stiffness, reliability, and architectural aesthetics rather than a single final shape.
| Link | Paper data | Meaning |
|---|---|---|
| Objectives and constraints | objectives: total mass m and strain energy C; constraints: tensile/compressive strength, buckling, architectural g(V)<0 | places material use and global stiffness in one Pareto framework |
| FSD setup | eta_lim in [0.6,1.0]; target band [eta_lim-0.1, eta_lim]; Delta Ti,max=5; numerical test uses 8 FSD iterations | generates section sets with different safety margins |
| Cylindrical shell | dead load 1 kN/m2; snow 0.8 kN/m2; load weights 0.8/0.2; seven shape parameters; 100 individuals, 50 generations | Pareto front becomes stable after about 30 generations |
| Free-form roof | 80 m square projection; 13 supports; 25 control points, eight fixed at z=15 m and others z=0-30 m; stable near 40 generations | shape, aesthetics, and mechanics can be compared together |
Data source: abstract, Sections 2-5, Tables 1-2, Figs. 1-29, and conclusions.
The paper separates compartment and large-space fires: member temperature in large spaces must include hot-smoke convection/radiation and direct flame radiation.
This paper studies temperature development of aluminum alloy members in fire, focusing on direct flame radiation in large-space fires and thermal-parameter calibration. Because aluminum alloys have high thermal conductivity, the cross-section temperature can be treated as uniform when the Biot number is below 0.01; this corresponds to plate thickness below 80 mm for open sections and below 40 mm for closed sections, which practical aluminum alloy members usually satisfy. The theory separates compartment fires and large-space fires: flame radiation is mostly absorbed by smoke in compartments, but direct flame radiation must be added in large-space localized fires. The paper reviews a surface-assumption method, a point-assumption method, and the EC9 method. EC9 uses the surface assumption with conservative parameters, so it is safe but overly conservative. The test uses a model with 4 m radius and 3.7 m total height; fireproof cloth blocks smoke escape, windows are closed, doors are open, and the ventilation factor is 0.0599 m1/2, below 0.07, giving a ventilation-controlled fire. Two 6063-T5 specimens, I100x50x4x5 and Phi32x3.5, are placed near a 2 MW diesel fire, 1.5 m from the fire center and at about +1.900 m height. The fire lasts 706 s, with ignition 0-24 s, growth 24-65 s, stable combustion 65-685 s, and decay 685-706 s. The test shows member temperatures are close to surrounding gas temperatures and cross-section temperatures are nearly uniform, validating the uniform-temperature assumption. Ignoring flame radiation underestimates member temperature and is unsafe. The paper modifies EC9 by adding smoke absorption, then calibrates hc, epsilon_al, and a using MATLAB R2020a genetic algorithm with 50 generations, 100 individuals, 80% crossover, Gaussian mutation, and elitism. The optimal parameters are hc=50.00 W/m2K, epsilon_al=0.2422, and a=-0.00061, i.e. alpha_g(Tg)= -0.00061(Tg-T0)+1.
| Link | Paper data | Meaning |
|---|---|---|
| Theory assumption | Bi=0.01; open section t<80 mm, closed section t<40 mm; aluminum conductivity much higher than steel | member temperature can be calculated by a lumped model |
| Test scenario | 4 m radius, 3.7 m total height; ventilation factor 0.0599 m1/2; 2 MW diesel fire; 1.5 m from fire center; 706 s combustion | creates a temperature field with localized fire and smoke-layer effects |
| Method comparison | neglecting flame radiation underestimates temperature; point assumption agrees well; EC9 surface method is much higher | large-space aluminum temperature prediction must explicitly include flame radiation |
| GA calibration | initial hc=35, epsilon=0.8, a=-0.001; 50 generations, 100 individuals, 80% crossover; optimum 50.00, 0.2422, -0.00061 | replaces conservative EC9 parameters with 6063-T5 test-calibrated values |
Data source: abstract, Sections 2-5, Table 1, Figs. 1-22, and conclusions.
The paper optimizes vertical control-point coordinates, then uses equal-chord isoparametric division to keep the architectural surface smooth and the grid regular.
This paper proposes a form-finding method for free-form aluminum alloy reticulated shells with semi-rigid gusset joints. It describes the surface with a clamped tensor-product B-spline and generates the grid by equal-chord isoparametric-curve division, avoiding a design variable at every joint. Because aluminum gusset plates are stamped into curved plates and different member directions around a free-form joint create nonuniform curvature and gaps, the paper proposes a joint gap index I based on the dispersion of angle residuals between the joint normal and connected member directions. In the FE model, members and rigid joint zones use BEAM188, the joint-zone modulus is set to 100 times that of the member, and semi-rigidity is represented by COMBIN39 nonlinear rotational springs with a four-linear moment-rotation model. The objectives are to minimize joint gap I, minimize strain energy C under a small surface load, and maximize safety factor K under short-term half-span snow load. NSGA-II is implemented by MATLAB R2020a gamultiobj with population 50 and 30 generations. The numerical example is a 30 m x 30 m free-form aluminum reticulated shell with height bounded from 5 to 20 m, 25 control points of which 21 can move and symmetry reduces them to 5 independent variables; isoparametric curves are divided into 10 segments each way, boundary joints are pinned, and members use I300x150x8x12. The semi-rigid-jointed structure obtains 10 Pareto compromise solutions, with range ratios of 85.87%, 83.34%, and 75.84% for I, C, and -K. The key conclusion is that rigid-jointed and semi-rigid-jointed optimal forms are not interchangeable. Semi-rigid structures transfer more load through axial force, while rigid-jointed structures have larger strong-axis bending moments. For one hyperbolic-paraboloid-like solution, SRJ and RJ safety factors are 3.56192 and 2.03503; for another convex solution they are 2.59539 and 2.04069. Thus actual joint rigidity changes internal-force distribution and optimal shape, so it should be considered during form-finding.
| Link | Paper data | Meaning |
|---|---|---|
| Geometry and variables | 30 m x 30 m span; height 5-20 m; 25 control points, 21 movable, 5 independent; 10 segments per isoparametric direction | keeps free-form continuity and grid regularity with few variables |
| Objectives | minimize I and C, maximize K; qse=0.2 kN/m2, qd=1 kN/m2, qs=1.85 kN/m2, load factors 1.35/1.40 | places assembly, stiffness, and short-term snow safety in one evaluation |
| Pareto performance | SRJ obtains 10 compromise solutions; I/C/-K range ratios are 85.87% / 83.34% / 75.84% | the algorithm provides a broad trade-off set rather than one shape |
| RJ/SRJ crossover | Form 1: SRJ/RJ K=3.56192/2.03503; Form 2: 2.59539/2.04069; weak-axis moment, strong-axis moment, and compression ratios change clearly | actual joint rigidity changes the optimal form-finding result |
Data source: abstract, Sections 2-6, Figs. 1-20, and conclusions.
The paper models a rigid joint zone plus COMBIN39 rotational springs for semi-rigidity, and separates two-longitudinal-edge support A from quadrilateral support B.
This paper investigates elasto-plastic buckling of aluminum alloy single-layer cylindrical reticulated shells with gusset joints and derives practical buckling-capacity formulae. The structures are three-way-grid cylindrical shells with two support conditions: two longitudinal-edge supports A and quadrilateral supports B. The FE model uses BEAM188 for members and rigid joint zones and COMBIN39 rotational springs for gusset-joint semi-rigidity, with a four-linear moment-rotation model calibrated from previous tests. The basic model has 30 m span, f/B=1/6, L/B=2, B/h=100, I300x150x8x10 members, 450 mm diameter and 12 mm thick gusset plates, and 6061-T6 aluminum. Linear buckling comparison shows that rigid-jointed shells have 18.6% and 15.5% higher linear buckling loads than semi-rigid ones under support A and B. Support condition is also crucial: for semi-rigid shells, changing from A to B increases the linear buckling load by 168%. In elasto-plastic nonlinear buckling, considering semi-rigidity reduces the ultimate load factor by 49.7% for support A and 18.7% for support B, and the semi-rigid shells buckle before material capacity is fully used; their maximum Von Mises stresses are only about 51.7%-68.3% of f0.2. The parametric study covers rise-to-span ratio, length-to-span ratio, span-to-thickness ratio, half-span live-load ratio p/g, and initial geometric imperfection. Rise-to-span ratio is relatively less influential, while length, slenderness, asymmetric load, and imperfection matter clearly. Increasing B/h from 100 to 200 reduces capacity by 77.3% for A and 84.1% for B; increasing p/g from 0 to 1 reduces capacity by 51.5% for A and 34.4% for B; increasing imperfection from 0 to B/100 reduces capacity by 42.6% for A and 34.8% for B. Finally, 17,280 numerical results are used to derive formulae with influence factors for load distribution, joint semi-rigidity, material nonlinearity, and initial imperfection. The factors include kJ,l=0.4848, kJ,q=0.7618, kP,l=0.9980, kP,q=0.9586, kIM,l=0.6908, and kIM,q=0.8334, allowing practical design without time-consuming full elasto-plastic analysis.
| Link | Paper data | Meaning |
|---|---|---|
| Basic model | span 30 m; f/B=1/6; L/B=2; B/h=100; I300x150x8x10; gusset plate 450 mm x 12 mm; 6061-T6 | establishes comparable semi-rigid and rigid cylindrical shells |
| Semi-rigidity effect | linear rigid-jointed loads are 18.6% / 15.5% higher; nonlinear semi-rigid load factors drop 49.7% / 18.7%; max semi-rigid stress about 51.7%-68.3% f0.2 | joint semi-rigidity triggers global buckling before material capacity is fully used |
| Parameter sensitivity | B/h 100->200: drop 77.3% / 84.1%; p/g 0->1: drop 51.5% / 34.4%; imperfection 0->B/100: drop 42.6% / 34.8% | span-thickness ratio, load asymmetry, and imperfections are key design risks |
| Formula regression | expanded scheme: spans 15/24/30 m, five rise ratios, six length ratios, four sections, four p/g values, B/300 imperfection; 17,280 results | turns full elasto-plastic analysis into practical design formulae |
Data source: abstract, Sections 2-5, Tables 1-8, Figs. 1-23, and conclusions.
The paper combines SVD denoising, PSO boundary-frequency optimization, and AMD single-mode decomposition to handle low-SNR field vibration signals.
This paper proposes an improved modal-parameter identification method and uses it to analyze damping characteristics of aluminum alloy single-layer reticulated shells. The method chain is SVD denoising, PSO adaptive optimization of AMD boundary segmentation frequencies, and AMD/Hilbert identification of natural frequencies and damping ratios from each single-frequency decay signal. The simulated signal contains three close frequencies of 0.90, 1.10, and 1.30 Hz, all with 1.00% theoretical damping, 50 s duration, 100 Hz sampling, and strong colored noise. The improved method identifies frequencies of 0.91, 1.12, and 1.27 Hz and damping ratios of 1.02%, 1.03%, and 0.97%, with all errors at or below 3%, better than traditional AMD whose damping errors reach 4%-5%. Field tests cover four in-service aluminum reticulated shells: a 45 m x 45 m spherical fixed-boundary shell, a 40 m x 36 m cylindrical fixed-boundary shell, a 192 m x 63 m free-form pinned shell, and a 730 m x 120 m free-form pinned shell. The first three have aluminum plate enclosure, while the fourth is unenclosed. Jumping vertical excitation and rubber-hammer horizontal excitation are used; each acquisition lasts 10 s at 256 Hz. The tests collect 160, 360, 380, and 620 decay records, totaling 1,520. Identified first-six frequencies match corresponding FE frequencies within 5%. The damping ratio follows a three-stage law versus maximum acceleration amplitude: A<0.024 m/s2 is a low-amplitude constant stage, 0.024-0.35 m/s2 is an approximately ln(A) growth stage, and A>=0.35 m/s2 is a high-amplitude constant stage. Mechanistically, low amplitudes are governed mainly by aluminum material damping; medium amplitudes develop frictional sliding among gusset plates, bolts, and H-section members; high amplitudes fully develop joint sliding and reach a high constant damping level. The paper uses frequency ratio 1.5 to separate low- and high-order modes and recommends 2.3% first-order and 1.2% high-order damping in the micro-vibration stage, 4.1% first-order and 1.7% high-order damping in the fully developed stage, and formula-based amplitude-dependent damping in the developing stage.
| Link | Paper data | Meaning |
|---|---|---|
| Simulation validation | theoretical 0.90/1.10/1.30 Hz, damping 1.00%; improved method gives 0.91/1.12/1.27 Hz and 1.02/1.03/0.97%; errors <=3% | outperforms traditional AMD under strong colored noise |
| Field specimens | 45x45 m spherical fixed, 40x36 m cylindrical fixed, 192x63 m free-form pinned, 730x120 m free-form pinned | covers different shapes, scales, boundaries, and enclosure conditions |
| Data scale | decay records 160 / 360 / 380 / 620; 10 s each, 256 Hz; first-six frequency errors vs FE all <5% | field frequency identification is reliable enough for damping-law analysis |
| Damping recommendation | stage thresholds A=0.024 and 0.35 m/s2; micro-vibration first/high-order 2.3%/1.2%; developed first/high-order 4.1%/1.7% | damping is not one constant; it should depend on amplitude and frequency ratio |
Data source: abstract, Sections 2-5, Tables 1-8, Figs. 1-14, and conclusions.
The original consistent imperfection scales the whole mode by L/300, which can over-amplify member curvature; the paper uses L/300 for joints and l/1000 for members.
This paper proposes a modified consistent imperfection method and combines it with machine learning to predict nonlinear buckling capacity of imperfect single-layer reticulated shells. The original consistent imperfection method usually takes the lowest-order linear buckling mode at the origin and scales the entire mode by L/300. When member deformation is non-negligible or joint construction error and member fabrication imperfection have different physical sources, this single amplitude can over-amplify member curvature and can miss the most adverse imperfection direction. The paper splits the linear buckling mode into a joint-displacement component and a member-deformation component: joint displacements are extracted and linearly interpolated along members, and the residual is treated as member deformation. The joint component is then scaled by L/300 and the member component by l/1000. In the Kiewitt-6 example, the first mode has modal strain-energy participation ratios of 86.17% for joint displacement and 13.83% for member deformation. The original method would magnify member imperfection to about 0.017 m, while the qualified steel member limit l/1000 is about 0.004 m, so the capacity judgment can become unrealistic. The paper also shows that both positive and negative imperfection directions should be checked; for a weak-member shell, the negative first mode greatly reduces capacity. The ML part predicts the reduction ratio rim=(Lambda_per-Lambda_im)/Lambda_per using f/L, ring number, section diameter, joint participation ratio, norms of imperfection and incremental displacement, and regional Euclidean distances between imperfection vectors and nonlinear buckling incremental displacement. Samples are generated from L=50 m Kiewitt-6 shells with f/L=1/3, 1/4, 1/5, 1/6, rings 6/8/10/12, ten sections, and pinned or fixed boundaries. Each support condition has 1600 training samples and 270 testing samples. ANN, RBF-SVR, and linear SVR can all identify the adverse imperfection pattern; RBF-SVR is most accurate, while linear SVR yields a practical explicit formula with 90 variables.
| Link | Paper data | Meaning |
|---|---|---|
| Example shell | L=50 m, f/L=1/5, m=6; first-mode energy 25.719 for joints and 4.128 MN m for members | the mode is dominated by joint displacement but member deformation still affects the imperfection amplitude |
| Original-method issue | u_o,m,max=0.104 m; L/300 gives 0.017 m, while l/1000 is about 0.004 m | global scaling can magnify member curvature beyond fabrication limits |
| Sample generation | 4 rise ratios x 4 ring counts x 10 sections x 10 imperfection patterns; 1600 training and 270 test samples per support | covers geometry, boundary, and positive/negative imperfection directions |
| Model performance | pinned RBF-SVR has 98.19% low-error training samples and 98.75% for highest-reduction samples; linear SVR gives a 90-variable formula | balances adverse-pattern identification with engineering interpretability |
Data source: abstract, Sections 2-4, Tables 1-9, Figs. 1-22, and conclusions.
The paper combines diesel pool fire, door-window ventilation, and two fire powers into eight structural fire tests, measuring air, member, joint temperature, and displacement.
This paper conducts eight structural fire tests on an aluminum alloy single-layer reticulated shell with gusset joints, and explains the response using an empirical temperature formula, FDS, and ANSYS thermal-structural analysis. The specimen is an 8 m span, 0.5 m high, five-ring K6 shell with I100x50x4x5 members, 5 mm gusset plates, 6063-T5 aluminum, and six hand-tightened M6 bolts at each member end; fireproof rubber and ceramic fiber cloth cover the shell to retain smoke and heat. Prototype fire powers of 8 MW and 20 MW are scaled by 0.2 to 143.11 kW and 357.77 kW. Center/corner fire and ventilation-controlled/fuel-controlled conditions form tests T1-T8. The fire process has ignition, initial growth, stable combustion, and decay stages, and ventilation-controlled fires are more critical than fuel-controlled fires. The worst case is T7, a high-power corner ventilation-controlled fire, with stable combustion lasting 1396 s and decay 948 s. The maximum measured air temperature is 128 ?, maximum member temperature 85 ?, and maximum gusset-plate temperature 80 ?. Structurally, almost all monitored joints move upward, showing fire-induced arching. T3 and T7 have the most obvious arching, but maximum displacement is below 15 mm and under the serviceability limit L/400=20 mm; no permanent deformation, rupture, or melting is observed after the tests. The empirical formula and FDS both predict horizontal temperature gradients reasonably. ANSYS analysis with FDS temperature fields shows nearly symmetric axial forces under center fire, while corner fire produces larger compression above the fire source. T7 corner fire reaches about 27.356 kN compression, higher than about 23.147 kN in the exterior ring under center fire. During fire exposure, thermal expansion, joint stiffness degradation, and material degradation gradually reduce nonlinear buckling capacity, with corner fire being more disadvantageous.
| Link | Paper data | Meaning |
|---|---|---|
| Specimen | 8 m span, 0.5 m height, five-ring K6; I100x50x4x5 members, 5 mm gusset plates, M6 bolts, 6063-T5 aluminum | the specimen represents real gusset-jointed aluminum shell construction |
| Fire matrix | 143.11/357.77 kW; center/corner fires; door-window states create ventilation- or fuel-controlled fires; eight tests | tests fire location, heat-release rate, and ventilation boundary together |
| Peak response | T7 reaches maximum air/member/gusset temperatures of 128/85/80 ?; maximum displacement is below 15 mm | corner ventilation-controlled fire is worst, yet the shell remains elastic and undamaged |
| Numerical interpretation | FDS and empirical formula fit temperature gradients; ANSYS gives about 23.147 kN exterior-ring compression under center fire and 27.356 kN above corner fire | corner fire creates more localized compression and stronger capacity reduction |
Data source: abstract, Sections 2-5, Tables 1-4, Figs. 1-20, and conclusions.
The paper uses ABAQUS quarter models to reproduce experimental load-displacement curves and failure modes, then performs parametric analysis and derives capacity formulae.
This paper studies the uniaxial tensile bearing capacity of a new bolted ball-cylinder (BBC) joint. The BBC joint is intended for non-purlin spatial truss structures, reducing force-path complexity and material use, but the joint capacity must exceed member capacity. The paper first calibrates ABAQUS FE models against previous tests. It uses C3D8I incompatible eight-node elements, quarter symmetry, bilinear elastoplastic material, contact friction coefficient 0.2, and a loading sequence with 10 N initial bolt force, 5000 N pretension, and monotonic displacement loading. The FE models reproduce excessive cylinder-wall deformation, bolt evulsion, and weld-region stress concentration. JD1/JD2 initial-stiffness errors are 18.06% and 4.21%, and the maximum relative load error at the same displacement is about 11.31%. The parametric study includes 99 models and examines hollow-cylinder diameter, thickness, height, rectangular-tube dimensions, ribbed-stiffener width and thickness, convex washer dimensions, bolt diameter, bolt spacing, and screw-in length. The paper defines the load corresponding to cylinder-opening relative deformation delta=1.5%D as the uniaxial tensile bearing capacity of the BBC joint. JD2/JD3 validation errors under this criterion are 4.75% and 0.51%. Sensitivity results show that increasing cylinder thickness from 8 to 14 mm raises capacity by 56.54%, making thickness more important than outside diameter. Increasing stiffener width from 6 to 14 mm raises capacity by 55.98%, while increasing stiffener thickness from 6 to 12 mm raises it by 18.53%. Rectangular-tube width and length, convex-washer width, and bolt spacing have small effects. Screw-in length is critical for joints without a ribbed stiffener: reducing tb from 20 to 8 mm lowers capacity by 45.47% and also reduces stiffness and ductility; when tb exceeds bolt diameter d, capacity is nearly stable. Finally, the paper derives theoretical-regression formulae using a non-stiffened capacity increase factor gamma, a ribbed-stiffener enhancement factor eta, and a screw-in-length reduction factor xi. The formulae have errors within 5% for 93.94% of FE models, maximum error below 10%, and 6.41% average absolute relative error against three tests, making them practical for engineering design.
| Link | Paper data | Meaning |
|---|---|---|
| Model calibration | C3D8I elements, quarter symmetry, friction 0.2, 5000 N bolt pretension; JD1/JD2 initial stiffness errors 18.06%/4.21% | the FE model is reliable enough for the parametric study |
| Capacity criterion | delta=1.5%D; JD2/JD3 FE capacities 74.74/66.59 kN with 4.75%/0.51% test errors | a deformation criterion avoids relying on a complex final failure point |
| Sensitivity | cylinder thickness 8->14 mm increases 56.54%; stiffener width 6->14 mm increases 55.98%; tb 20->8 mm without stiffener drops 45.47% | effective strengthening comes from local bending resistance and preventing bolt evulsion |
| Formula validation | 93.94% of FE models have error within 5%, maximum error below 10%; three tests have 6.41% average absolute error | theoretical derivation plus regression correction supports engineering estimation |
Data source: abstract, Sections 2-5, Tables 1-7, Figs. 1-20, and conclusions.
The paper reproduces a real tower-retrofit scenario: the member remains loaded, and welding heat input creates a plateau in load-displacement curves.
This paper investigates Q235 in-service angle steel members strengthened by welding under axial compression without unloading. The tests use L80x6 base angles and L62x6 strengthening members, including one unstrengthened specimen JW0, square-tube strengthened JA0-JA3, and L-shaped strengthened JB0-JB3, nine specimens in total. Initial stresses are 0, 0.1fy, 0.2fy, and 0.3fy. Strengthening members are connected by 4 mm fillet welds, using a progressive, discontinuous, and symmetrical welding sequence while the initial axial load is maintained. All strengthened specimens fail by flexural buckling, while the unstrengthened specimen fails by local buckling with flexural-torsional deformation. Test results show that strengthening raises ultimate capacity by about 20%, with a maximum increase of 24.82%. Square-tube JA specimens have better ductility than L-shaped JB specimens, and the L-shaped section is more sensitive to welding heat input and initial load. In load-displacement curves, a higher initial load produces a longer heat-input plateau, while JA/JB ultimate loads remain roughly around 200 kN. Numerically, the paper uses ANSYS indirect thermal-structural coupling: SOLID70 for transient welding temperature fields, SOLID185 for structural analysis, a Gaussian moving heat source, and element birth-death to simulate welding. The first buckling mode with L/1000 amplitude introduces imperfection. FE models reproduce flexural buckling, the plateau, and ultimate loads. For JW0, test/FE/code capacities are 169.06, 168.75, and 176.13 kN; strengthened-specimen ultimate-load deviations are 2.25%-8.80%. Parametric analysis compares square-tube, T-shaped, Z-shaped, and cross-shaped strengthening sections. Square-tube and cross-shaped sections combine high capacity with good ductility, while T/Z sections have high capacity but brittle post-peak drop. When initial stress is no more than 0.4fy, its influence on ultimate capacity can be ignored. Higher slenderness gives stronger benefit: square-tube strengthening at slenderness 94 increases capacity by 38.53%, far above 4.94% at slenderness 63. Increasing strengthening-member thickness raises capacity, but the paper recommends the same thickness as the base member for balancing reinforcement effect and constructability.
| Link | Paper data | Meaning |
|---|---|---|
| Test matrix | L80x6 base, L62x6 strengthening; JW0, JA0-JA3, JB0-JB3; initial stress 0/0.1/0.2/0.3fy | directly represents loaded retrofit of in-service tower angles |
| Capacity | JW0=169.06 kN; JA0=205.46 kN, JB2=211.02 kN; maximum gain 24.82% | welding strengthening improves capacity and ductility |
| FE model | SOLID70/SOLID185, Gaussian moving heat source, element birth-death; strengthened-specimen deviations 2.25%-8.80% | the thermal process and structural response must be coupled |
| Parametric conclusions | square/cross sections combine capacity and ductility; slenderness 94 gives 38.53% gain; t=7 mm gives 31.81% gain | section form, slenderness, and strengthening thickness matter more than simply tolerating high initial load |
Data source: abstract, Sections 2-6, Tables 1-8, Figs. 1-36, and conclusions.
The paper uses a 1/5-scale K6 aluminum spherical shell, 2 MW diesel pool fire, and covered fire field to observe temperature and deformation under destructive fire.
This paper conducts two destructive structural fire tests on an aluminum alloy single-layer spherical reticulated shell with gusset joints, studying fire-induced collapse and the effect of nonuniform temperature fields. The model is a 1/5-scale, 8 m span, 0.5 m high, five-ring K6 aluminum spherical shell on a 3.2 m support structure. Member lengths are 715-1000 mm, gusset joints are connected by M6 stainless bolts, and the shell is covered by 1200 ? ceramic fiber cloth and 300 ? fireproof rubber cloth to retain smoke. The design vertical load is 0.5 kN/m2. The fire uses four 0.7 m x 0.7 m diesel pans, each with 15 L diesel and 7.5 L water. The scaled fire power is 2 MW, corresponding to a 111.8 MW prototype fire. In D-1, the fire is on the ground. After 1212 s of combustion, no collapse or permanent deformation affecting mechanical behavior is observed. Maximum air, member, and gusset temperatures are 509.59 ?, 449.73 ?, and 413.08 ?. The shell arches under heating, reaching 121.51 mm maximum displacement, and then nearly recovers. D-2 is conducted the same day with the fire elevated to 1.35 m. From 378 to 528 s, many members and gusset plates begin melting. At 528 s, the covering cloth burns through and the shell begins to collapse; at 530 s, a fireball exits through the hole, and the test is stopped at 614 s because of obvious failure. D-2 reaches a maximum air temperature of 767.02 ?. Central members melt and rupture, while outside-ring members fail by flexural-torsional buckling caused by thermal-expansion-induced compression. The deformation process has an arching stage and a sinking stage. Both tests show clear horizontal temperature gradients, proving that large-space fire analysis should not assume uniform temperature. Pyrosim/FDS field simulation reproduces the temperature field with acceptable accuracy, and ANSYS structural analysis shows that nonuniform temperature nearly doubles member axial-force magnitudes compared with uniform temperature. Because the outside ring is about 80 ? cooler than the center, the ferrule effect becomes stronger, so ignoring nonuniformity underestimates internal forces.
| Link | Paper data | Meaning |
|---|---|---|
| Specimen and fire | 8 m span, 0.5 m height, five-ring K6; 2 MW diesel pool fire, 111.8 MW prototype; vertical load 0.5 kN/m2 | provides destructive-fire data for aluminum spatial structures |
| D-1 | ground fire; max air/member/gusset 509.59/449.73/413.08 ?; max displacement 121.51 mm; recovers after 1212 s | high temperature does not necessarily cause global collapse; cooler nonuniform regions preserve integrity |
| D-2 | 1.35 m elevated fire; melting at 378 s, collapse at 528 s, fireball at 530 s, stopped at 614 s; max air 767.02 ? | localized extralarge fire drives the deformation from arching into sinking collapse |
| Temperature-field effect | D-2 horizontal temperature difference reaches 378.62 ?; Model-N axial forces are almost 100% higher than Model-U | large-space fire analysis must use field simulation or nonuniform temperature input |
Data source: abstract, Test Program, Results, Simulation, Conclusions, Figs. 1-23, and Tables 1-2.
The system first uses strain energy to choose important monitored members, then converts temperature into failure index Q and six danger levels.
This paper develops a fire safety monitoring system for steel truss structures, aiming to give commanders real-time member status, potential collapse location, and early warning during rescue. The theoretical basis has three layers. First, member importance is defined from the change in total strain energy before and after member failure, helping choose key members for thermocouple placement under cost constraints. Second, member failure index Q is defined from temperature-dependent steel strength reduction and compression-stability reduction, and member state is divided into six danger levels: safe, secondary safe, secondary dangerous, dangerous, critical, and failure. Third, after a member fails, the collapse index Ipc is defined as the ratio of strain energy of affected members to total structural strain energy. The SAP2000 numerical example is an 8 m span, 1 m high Q235 steel truss with 1 m zone width, load combination 1.2g+1.4q, and g=q=0.5 kN/m2. Single-member removal shows chord-member failure produces much larger stress-ratio growth than web-member failure, while double-diagonal webs improve safety. For member 18, Ut=271.34 N m, Ua=210.84 N m, Ipc=0.777, and collapse occurs. Combining the original and modified models, 97% of collapsed cases have Ipc above 0.45, so the collapse-index limit is conservatively set to 0.45. The system uses SQL Server 2017 for the database and Visual Basic / Visual Studio 2017 for the interface. During monitoring, it reads temperature data at a default 60 s interval, updates danger levels, removes the most dangerous member, and calculates internal forces, displacements, and collapse index. Experimental verification uses a previous full-scale steel truss roof fire test: the structure has 8 m diameter, 4.02 m height, six RHS planar steel trusses, purlins, roof panels, 0.439 kN/m2 surface load, and 20 kg/m2 wood-crib fuel density. At 590 s, the system predicts some secondary-safe members will fail within 200 s; at 636 s, it predicts member 20 has 78 s before failure; at 665 s, member 20 approaches critical temperature and becomes dangerous, predicted failure time is 58 s, and Ipc=0.573 exceeds 0.450, triggering collapse warning. At 695 s, multiple members are judged failed. Comparing predicted and measured displacement, the system response at 665 s is closest to measured deformation at 845 s, showing at least 180 s early warning of collapse location.
| Link | Paper data | Meaning |
|---|---|---|
| Theoretical indexes | importance coefficient from total strain energy; failure index Q from temperature reduction; collapse index Ipc=Ua/Ut | turns thermocouple temperature into structural risk states |
| Limit calibration | 8 m span, 1 m high Q235 truss; member 18: Ut=271.34 N m, Ua=210.84 N m, Ipc=0.777; limit 0.45 | chord-member failure is more likely than web-member failure to trigger global risk |
| System implementation | SQL Server 2017 database, Visual Basic / Visual Studio 2017 interface; default 60 s reading interval | supports automatic monitoring and manual checks at the fire-control center |
| Experimental verification | full-scale steel truss roof; 665 s: member 20 dangerous, 58 s to failure, Ipc=0.573; closest to 845 s displacement, 180 s lead | the warning identifies an avoidable collapse area, not just an abstract number |
Data source: abstract, Sections 2-6, Tables 1-2, Figs. 1-15, and conclusions.
The shell height is described by a cubic spline; only Z1, Z2, and Z3 are optimized within +/-0.3 m, and the objective is the nonlinear buckling load Pc itself.
This paper proposes a shape-optimization method for spherical single-layer aluminum reticulated shells with aluminum alloy gusset (AAG) joints. The key idea is to maximize the nonlinear buckling load Pc with imperfections, instead of using the conventional objective of minimizing total strain energy. The shell surface is represented by a cubic spline with seven control points, and structural symmetry reduces the design variables to the vertical coordinates Z1, Z2, and Z3. The node-shifting range is limited to +/-0.3 m so that the optimized surface remains smooth and the architectural form is not significantly changed. The ANSYS finite element model uses BEAM188 for I-section members and joint zones, COMBIN39 for the nonlinear semi-rigid bending stiffness of gusset joints, and a Ramberg-Osgood material model; it is verified against an existing static test. The nonlinear buckling analysis considers both global and member imperfections. A combined symmetric and antisymmetric first buckling mode covers both limit-point and bifurcation-type buckling, while an l/1000 member eccentricity triggers the interaction between flexural-torsional member buckling and global buckling. The basic example has L=40 m, f/L=1/4, 12 rings, I400x200x10x16 members, 16 mm gusset plates, a 300 mm joint zone, eight M14 bolts, hinged supports, and half-span live load with q/g=1/2. After comparing arc-length settings, nsub=500 and amax=2 are adopted. The genetic algorithm in MATLAB uses 50 generations, 50 individuals per generation, an 80% crossover rate, and elitism. With Pc as the objective, Pc increases from 44.972 to 75.064 kN/m2, a 66.91% gain, while the surface stays smooth. With total strain energy as the objective, strain energy decreases only from 102.14 to 100.32 N m and Pc increases only to 48.882 kN/m2, or 8.7%. This shows that nonlinear buckling capacity of AAG-jointed aluminum shells is not strongly correlated with total strain energy or bending strain-energy ratio. To turn the high-cost GA results into practical engineering guidance, the paper conducts parametric analysis for load ratios gamma=q/g of 0, 1/4, 1/2, and 1, and height-to-span ratios f/L=1/4, 1/5, and 1/6. It provides practical design tables containing control-point shifts and explicit cubic-spline coefficients for general-span shells. These tables still improve Pc under different member depths, ring numbers, and support conditions, but are restricted to f/L from 1/6 to 1/4; outside this range, the optimization problem should be solved directly.
| Link | Paper data | Meaning |
|---|---|---|
| Modeling | BEAM188 members and joint zones, COMBIN39 semi-rigid joints, Ramberg-Osgood material, verified by an existing static test | the optimization includes gusset-joint semi-rigidity and material nonlinearity |
| Imperfection | 0.5*(symmetric + antisymmetric) global mode, plus member eccentricity e=l/1000 | captures the adverse coupling between global buckling and member flexural-torsional buckling |
| Objective comparison | Pc objective: 44.972 -> 75.064 kN/m2; strain-energy objective: 44.972 -> 48.882 kN/m2 | directly optimizing nonlinear buckling load is what improves large-deformation stability |
| Design use | f/L=1/4, 1/5, 1/6; gamma=0, 1/4, 1/2, 1; IR about 17%-102% | high-cost GA results become lookup spline coefficients |
Data source: abstract, Sections 2-5, Tables 1-7, Figs. 1-16, and conclusions.
The specimen has six RHS main trusses, purlins, and roof panels; 2206.65 kg of iron sand creates the 0.439 kN/m2 fire-condition surface load.
This paper conducts two nondestructive diesel-pool fire tests and one destructive wood-crib fire test on a full-scale steel roof-truss structure, aiming to obtain whole-structure thermal and structural response under realistic fires and to support a future fire-monitoring system. The specimen is a circular workshop roof with 8 m diameter and 4.02 m total height. It consists of six Q235 RHS planar main trusses, purlins, purlin hangers, and roof panels, with two vertical bracing trusses near the supports to improve ring and lateral stiffness. Designed according to GB50017 and GB50009, it carries a fire-condition surface load of 0.439 kN/m2 using 2206.65 kg of iron-sand buckets, and the maximum member stress-strength ratio is 0.71. The nondestructive scenarios use a 0.7 m x 0.7 m diesel pool fire of about 360 kW, located at the center and corner, with 6 L diesel and the same volume of water each time. Preliminary Pyrosim/FDS simulation gives a maximum joint temperature of about 142.68 ?, indicating no failure. In the two small-fire tests, air and member temperature fields are nonuniform, the structural response is small elastic arching with displacement not exceeding about 1 mm, and no permanent deformation, member buckling, or melting is observed afterward. The destructive scenario uses wood cribs with 20 kg/m2 fire load density, totaling 975 kg of wood in six 1.0 m x 1.0 m x 1.12 m cribs, ignited by a central 2 L diesel pool. The fire process has four stages: 0-210 s ignition, 210-810 s initial growth, 810-900 s stable combustion, and 900-3000 s decay. Fire intensity peaks around 600 s, flames pass through the roof panel at 750 s, more flame appears at 900 s because of roof-panel deformation and water spraying begins, the fire is controlled around 1800 s, and it is extinguished around 3000 s. Thermal response shows that air and component temperatures are close during the initial-growth and stable-combustion stages of the large fire, while the center is hotter; a uniform-temperature assumption is conservative, so field simulation such as FDS is recommended. Structurally, the specimen first arches clearly. Central measurements such as D5 reach maximum upward displacement around 700 s when maximum air temperature is about 890 ? and remain high at 770 s; some LVDTs reach their range around 860 s. After the test, the center vertical displacement is about 480 mm, all web members buckle, and no obvious joint damage is observed. This indicates that when joint capacity is designed higher than member capacity, members fail first in fire. The paper also notes that web buckling causes a sharp drop in vertical stiffness, and roof-panel cracking and uplift can introduce extra oxygen, which should be considered in practical fire design of steel truss roofs.
| Link | Paper data | Meaning |
|---|---|---|
| Specimen | circular roof, 8 m diameter, 4.02 m height; six Q235 RHS main trusses; load q=0.439 kN/m2 | fire response is measured on the whole roof system, not a single member |
| Nondestructive fire | 0.7 m x 0.7 m diesel pool, about 360 kW; center and corner locations; no damage after tests | small localized fires mainly produce recoverable thermal arching |
| Destructive fire | 975 kg wood, 20 kg/m2; fire intensity peaks at 600 s, flame passes roof at 750 s, extinguished at 3000 s | wood-crib fire drives the whole structure into large deformation and instability |
| Failure mechanism | maximum arching around 700 s; some LVDTs reach range around 860 s; after test center displacement about 480 mm, all webs buckle, joints undamaged | web buckling causes a sharp reduction in vertical stiffness |
Data source: abstract, Sections 2-5, Figs. 1-19, and conclusions.
The paper tests H300/H350 simply supported beams and B40/B50 cantilever beams at room temperature and 650 ?, then extends the results through FE analysis into design formulae.
This paper studies the mechanical behavior of Q690 high-strength steel beams at room and elevated temperatures, and develops practical bearing-capacity formulae. The test program includes two member types: series H simply supported beams, H300x150x10x12 and H350x150x10x12, with total length 2840 mm and effective length 2740 mm; and series B cantilever beams, H120x40x4x5 and H120x50x4x5, with total length 1280 mm and effective length 2300 mm. Specimens are tested at room temperature and at 650 ?. Tensile coupon tests show that Q690 has E=206355 MPa, fy=768.64 MPa, and fu=801.17 MPa at room temperature; at 650 ? these decrease to E=60074 MPa, fy=207.03 MPa, and fu=253.67 MPa, showing severe stiffness and strength reduction. The tests show that H300-A and H350-A simply supported beams fail by strength failure at room temperature, with ultimate loads of 973.0 and 1172.0 kN and large deflection plus top-flange local buckling. The other specimens fail by overall flexural-torsional buckling. At elevated temperature, H300-B and H350-B capacities drop to only 91.8 and 102.2 kN, while series B cantilever capacity drops from 17.78/24.89 kN at room temperature to about 4.10-5.19 kN in fire. The FE models use ANSYS SHELL181, include material and geometric nonlinearity, introduce the first overall buckling mode as initial imperfection, and account for self-weight deformation during heating. For series B fire specimens, the nonuniform temperature field is calibrated with SHELL57 steady-state thermal analysis. The FE models reproduce failure modes and load-displacement curves, and ultimate-load errors are at most 8.56%, below 10%. The room-temperature formula is based on the elastic flexural-torsional buckling critical moment Mcr and the Perry formula, with overall stability coefficient phi_b=Mu/(Wp fy). Parametric analysis covers residual stress, stiffener arrangement, loading type, lateral load position, end-moment ratio, five section shapes, and many section dimensions. Residual stress has little influence, stiffeners affect stability within about 5%, fuller bending-moment diagrams reduce the stability coefficient, and loading on the top flange is more unfavorable. Using 29 section dimensions, 13 loading conditions, 377 curves, and 4550 data points, the paper fits a quadratic equivalent-imperfection parameter eta and shifts it by 0.2533 standard deviations to improve reliability, giving a room-temperature Q690 beam formula. The fire formula uses the same framework but covers temperatures from 100 to 800 ?. Results show that capacity drops sharply above 400 ? and that high-temperature stability cannot be described by one unified curve. Temperature-dependent fitting parameters are provided from 20 to 800 ?. Compared with tests and Eurocode 3, the proposed fire formula is closer to the elevated-temperature test data and is suitable for practical design.
| Link | Paper data | Meaning |
|---|---|---|
| Material | 20 ?: E=206355 MPa, fy=768.64 MPa; 650 ?: E=60074 MPa, fy=207.03 MPa | HSS loses strength and stiffness severely at high temperature |
| Test capacity | H300-A/H350-A: 973/1172 kN; H300-B/H350-B: 91.8/102.2 kN; series B fire specimens about 4.10-5.19 kN | fire sharply reduces capacity and shifts behavior to overall flexural-torsional buckling |
| Model validation | ANSYS SHELL181 with first overall buckling-mode imperfection; max ultimate-load error 8.56% | the FE model is reliable enough for large parametric analysis and formula fitting |
| Formula | room temperature: 29 section dimensions x 13 loading conditions, 377 curves, 4550 data points; elevated-temperature parameters from 100-800 ? | complex lateral-torsional buckling behavior is reduced to design-ready stability coefficients |
Data source: abstract, Sections 2-7, Tables 1-8, Figs. 1-40, and conclusions.
The paper uses teeth and grooves 1.5 mm deep and 2.0 mm wide, and observes the full process from friction to sliding, occlusion, and tooth-groove yielding.
This paper studies ductile failure of new occlusive high-strength bolt (OHSB) connections under shear. Eight OCT specimens are tested: OCT1-OCT3 have a single shear plane, and OCT4-OCT8 have double shear planes. Convex teeth and slotted holes are machined on the core plates, concave grooves and circular holes on the cover plates, and the slotted holes remove the contribution of bolt-hole bearing. The teeth and grooves are 1.5 mm deep and 2.0 mm wide. Bolts are grade 10.9 high-strength bolts, and plates are Q235 steel with average E=204.3 GPa, fy=296.3 MPa, and fu=456.8 MPa. The loading process includes installation, 1 kN trial loading to eliminate gaps, and monotonic loading at 200 N/s. All specimens fail ductilely by yielding of the teeth and grooves, with no obvious bolt deformation; ultimate loads range from 42.38 kN for OCT-1 to 537.76 kN for OCT-6. The load-displacement curve has four stages: friction, sliding, tooth-groove occlusion, and failure. ABAQUS models are built as whole, half, or quarter models using C3D8R solid elements, refined mesh near teeth and grooves, finite-sliding penalty-friction and hard-contact interaction, and analysis steps that simulate 10 kN bolt preloading, experimental pretension, bolt-length locking, and displacement loading. FE ultimate-load deviation from tests ranges from 1.30% to 4.50%. Parametric analysis considers friction coefficient, number of grooves, plate width, cover-plate thickness, bolt diameter, and bolt pretension. When friction coefficient rises from 0.10 to 0.45, capacity increases from 353.32 to 477.06 kN, a 35.02% gain. Increasing groove number improves capacity, but beyond 16 grooves deformability drops and brittle plate dislocation may occur, so no more than 16 grooves on one cover plate are recommended. Increasing plate width from 80 to 180 mm raises capacity by 33.2%; thicker cover plates and larger bolt diameters also improve stiffness and capacity. Bolt pretension from 0.2P to 0.8P changes capacity only from 375.17 to 382.87 kN, so its effect is slight. Based on effective width we, effective groove number ne, and moment equilibrium at the tooth-groove contact, the paper derives a design formula for double-shear OHSB ductile failure and fits the pressure-arm correction coefficient gamma. The formula has a maximum error of 7.42% and average error of 1.77% against FE models; against corrected double-shear tests, maximum and average errors are 12.93% and 6.15%. It applies to double-shear OHSB connections governed by ductile yielding of teeth and grooves.
| Link | Paper data | Meaning |
|---|---|---|
| Tests | eight OCT specimens; teeth/grooves 2.0 mm wide and 1.5 mm deep; Q235 plates and grade 10.9 bolts | directly observes OHSB force transfer and failure under shear |
| Curve stages | friction, sliding, occlusion, and failure; tooth-groove yielding controls final capacity | capacity comes from occlusion, not only bolt friction |
| Parameters | mu=0.10->0.45: 353.32->477.06 kN; plate width 80->180 mm: +33.2%; pretension 0.2P->0.8P: 375.17->382.87 kN | surface treatment and geometry matter more; pretension only needs to compact the plates |
| Formula | effective width we, effective groove number ne, correction gamma; FE average error 1.77%, test average error 6.15% | reduces complex contact plasticity into a double-shear ductile-failure design formula |
Data source: abstract, Sections 2-7, Tables 1-6, Figs. 1-28, and conclusions.
The paper tests 6082-T6, 6N01-T6, 6061-T6, 6061-T4, and 7020-T6 at -100, -50, 0, 20, 100, 200, and 300 ?.
This technical note studies mechanical properties of structural aluminum alloys at high and low temperatures through 169 tensile specimens. The materials are 6082-T6, 6N01-T6, 6061-T6, 6061-T4, and 7020-T6. The 6xxx alloys use plate specimens, while 7020-T6 uses bar specimens. Test temperatures are 300, 200, 100, 20, 0, -50, and -100 ?. A video extensometer with a 20 mm optical gauge length is used; specimens are heated or cooled with nitrogen, held for at least 15 min, and loaded at 0.5 mm/min until fracture. Results show that low temperature increases elastic modulus, ultimate strength, and nominal yield strength, while high temperature reduces them significantly. Elastic modulus is approximately normally distributed. The average E rises from 68090.52 MPa at 20 ? to 73750.27 MPa at -100 ?, but falls to 49815.48 MPa at 300 ?. The paper proposes a piecewise constitutive model: the first range uses Ramberg-Osgood, the second range uses a parabola with continuous and smooth transition, and epsilon0=1% is recommended as the piecewise strain. This model fits stress-strain curves at different temperatures well. SEM fracture analysis shows that 6xxx alloys at 20 ? have mixed laminated cleavage and dimples; at high temperature the dimples become larger and clearer, while at low temperature more and deeper circular dimples appear. 7020-T6 shows well-distributed deep dimples from -100 to 300 ?. Low-temperature improvement is explained by grain refinement, higher critical resolved shear stress, and stronger work hardening; high temperature causes strength decline through more intense particle motion and thermal activation, while plasticity improves. Quadratic temperature influence factors are fitted for elastic modulus kE(T), ultimate strength k1(T), and nominal yield strength k2(T), with 95% upper and lower bounds. The equations are effective from -100 to 200 ?; above 200 ?, the 95% lower bound or EC9 reduction factors are recommended for safety. For ductility, elongation is lowest around 20 ? and increases at low temperature. 6N01-T6, 6061-T6, and 6061-T4 show obvious ductility drop above 200 ?, while 6082-T6 and 7020-T6 do not. The paper notes that high-temperature tests are steady-state, and future transient tests are needed to better represent real fire exposure.
| Link | Paper data | Meaning |
|---|---|---|
| Test matrix | 6082-T6, 6N01-T6, 6061-T6, 6061-T4, 7020-T6; 169 specimens; -100, -50, 0, 20, 100, 200, 300 ? | covers key cold-region and fire temperature ranges for aluminum spatial structures |
| Elastic modulus | mean E: 73750.27 MPa at -100 ?, 68090.52 MPa at 20 ?, 49815.48 MPa at 300 ? | low-temperature improvement and high-temperature degradation are clear in stiffness |
| Constitutive model | first range R-O, second range parabolic; recommended epsilon0=1%; continuous and smooth at transition | fits temperature-dependent turning behavior better than a single R-O curve |
| Design recommendation | kE, k1, k2 fitted as quadratics; effective from -100 to 200 ?; above 200 ? use 95% lower bound or EC9 | turns material tests into design factors for extreme temperatures |
Data source: abstract, Test Program, Test Results, Constitutive Relationship, Microanalysis, Temperature Influence Factors, Conclusions, Tables 1-7, and Figs. 1-12.
The paper tests eight joints, each connecting six I100x50x4x5 members through two circular gusset plates and eight M6 stainless-steel bolts.
This paper investigates hysteretic behavior of aluminum alloy gusset (AAG) joints through cyclic loading tests on eight specimens. Each joint connects six 905 mm long 6063-T5 I-section members (I100x50x4x5) using two 240 mm diameter aluminum gusset plates and eight M6 stainless-steel bolts, with 60-degree angles between adjacent members. Variables include gusset-plate thicknesses of 2, 3, 4, and 5 mm, plate material 6061-T6 or 6061-T4, existence of shear connectors, and six-point or two-point loading. Material tests give 6061-T6 plates E=72246 MPa, f0.2=364.16 MPa, fu=406.05 MPa; 6061-T4 plates E=69169 MPa, f0.2=147.76 MPa, fu=245.99 MPa; and 6063-T5 members E=65364 MPa, f0.2=177.40 MPa, fu=206.80 MPa. The cyclic loading program follows AISC, with relative rotation from 0.375% to 10%, two or three cycles per level, at 10 min/round, after a 20% estimated ultimate preload to eliminate gaps. Test phenomena have four deformation stages: initially no obvious deformation with a crisp sound from the joint zone; then member bending and joint-zone deformation that recover on unloading; then either global torsion and member flexural-torsional deformation for thick plates, buckling of free and central gusset regions for some thin plates, or central plate buckling; finally member rupture or excessive torsion, sudden rupture of bottom-plate connection regions, or block tearing of the bottom plate. Failure mode depends on the ratio of gusset-plate thickness to member-flange thickness. Thick-plate specimens A1, A2, and D1 mainly fail by member rupture, local buckling, and flexural-torsional buckling. Thin-plate specimens B1, B2, C1, and C2 mainly fail by gusset-plate block tearing and free-region buckling. D2 shows both failure types. The P-delta hysteresis curves describe the whole specimen, while M-theta curves describe the joint zone. The mechanical response is summarized into five phases: elastic, bolt slipping, hole-wall bearing, peak, and failure. Bolt-hole clearance causes clear pinching, so P-delta loops are not plump; M-theta loops are plumper, showing the joint zone dissipates more energy than the whole specimen. Specimens with 6061-T4 plates have larger ultimate displacement and plumper loops than 6061-T6 specimens, but more post-peak degradation. Thick-plate series A loops are plumper than thin-plate series B; shear connectors improve some specimens; and in two-point loading the non-loaded members show plumper loops, indicating good load-transfer capacity. Skeleton curves show series A has the highest ultimate load and initial stiffness, while series D is lowest; two-point loading weakens strength and deformation capacity. Relative rotation at key phases is above 1/15 for all specimens, indicating favorable deformation capacity. Strength degradation is not obvious before peak load, but stiffness degrades rapidly at first, stays nearly stable in middle loading grades, and drops again after peak.
| Link | Paper data | Meaning |
|---|---|---|
| Specimen | I100x50x4x5 members, 905 mm long; 240 mm gusset plates; eight M6 bolts; 60-degree member angle | specimens represent common gusset joints in aluminum single-layer shells |
| Failure | A1/A2/D1 thick plates: member rupture, local and flexural-torsional buckling; B/C thin plates: gusset block tearing and free-region buckling; D2 has both | when the plate is too strong members fail first; when too thin the gusset tears first |
| Hysteresis | P-delta loops show pinching; M-theta loops are plumper; 6061-T4 has larger ultimate displacement but stronger post-peak degradation | energy dissipation mainly comes from the joint zone, while bolt slip limits whole-specimen loop fullness |
| Degradation | relative rotation exceeds 1/15; pre-peak strength reduction factor is near 1; loop stiffness drops early, stabilizes, then drops after peak | deformation ability is good, but seismic energy dissipation is limited by slip and stiffness degradation |
Data source: abstract, Sections 2-4, Tables 1-5, Figs. 1-25, and conclusions.
The tests establish the elevated-temperature beam-column response, then ANSYS extends it to wider materials, sections, slenderness, and temperatures.
This paper studies flexural-torsional bearing capacity of aluminum alloy members under eccentric compression at elevated temperatures. Fourteen 6063-T5 I100x50x4x5 members with 900 mm effective length are tested at 20, 200, and 300 ?, with eccentricities of 10 and 30 mm and repeated specimens. The mean material properties are E=65364 MPa, f0.2=177.40 MPa, and fu=206.80 MPa. All specimens fail by flexural-torsional buckling dominated by flexural deformation, without local buckling. Capacity decreases as temperature and eccentricity increase. Typical ultimate loads are about 60-62 kN at 20 ? and e=10 mm, about 47 kN at 20 ? and e=30 mm, about 43-46 kN and 34-36 kN at 200 ?, and about 18-23 kN for valid 300 ? specimens. At 300 ?, the upper part of the specimen is hotter, so maximum lateral deflection appears about 100-150 mm above the mid-height. ANSYS SHELL181 models include material/geometric nonlinearity, Ramberg-Osgood material behavior, L/1000 initial imperfection, and a 250-300 ? linear thermal field for 300 ? tests; ultimate-load error is at most 8.38% and averages 1.63%. Parametric analysis covers 6061-T6 and 6063-T5, I/T sections, nine section specifications, 100/200/300 ?, and normalized slenderness from 0.25 to 2.75, giving 432 correlation curves. All curves lie above the linear interaction curve, so the paper proposes a GB50429-based linear correlation formula for temperatures below 300 ?; EC9 is more conservative and can be used for re-checking important structures.
| Link | Paper data | Meaning |
|---|---|---|
| Test | Fourteen 6063-T5 I-members; 20/200/300 ?; e=10/30 mm; at least 15 min soak | directly observes elevated-temperature eccentric beam-column buckling |
| Capacity | 20 ?,e=10 mm: 60.17/61.82 kN; 200 ?,e=30 mm: 35.71/34.09 kN; valid 300 ? specimens about 17.86-23.54 kN | both temperature and eccentricity reduce stability capacity |
| Model | SHELL181, Ramberg-Osgood, L/1000 imperfection; 250-300 ? thermal gradient at 300 ? | captures the nonuniform heating effect on buckling location |
| Formula | two alloys, two section types, nine specifications, three temperatures, slenderness 0.25-2.75, 432 curves | turns complex flexural-torsional buckling into a usable linear design interaction |
Data source: abstract, Sections 2-6, Tables 1-6, Figs. 1-21, and conclusions.
The tests separate thick/thin plates and six-/three-point loading to see whether the gusset tears or buckles first.
This paper studies out-of-plane flexural behavior of AAG joints below 300 ?. Nine joints connect six 905 mm long 6063-T5 H100x50x4x5 members with 240 mm diameter gusset plates, using eight M6 stainless-steel bolts on one flange. Variables include 4 mm or 2 mm plate thickness, 20/200/300 ?, and six-point or three-point loading. The 6061-T6 plates have E=72246 MPa, f0.2=364.16 MPa, and fu=406.05 MPa. Failure modes below 300 ? remain the same as at room temperature: thick-plate specimens fail mainly by member rupture or buckling, while thin-plate specimens suffer block tearing in tensile gusset regions and local buckling in compression regions; bolts show no obvious deformation. Thin-plate B2-20/200/300 ultimate loads are 35.58/29.76/12.84 kN, and three-point loaded C2-20/200/300 ultimate loads are 34.04/31.22/28.44 kN, showing the effects of temperature and load transfer. Thick-plate A4 specimens fail outside the heated joint zone, so joint safety is maintained. Moment-rotation curves follow a four-linear model: bolt-fixed, bolt-slipping, hole-wall bearing, and failure. Initial stiffness below 300 ? barely decreases and may increase because thermal expansion narrows bolt gaps, while ultimate moment decreases with temperature. ABAQUS C3D8R contact models with DC3D8 heat transfer are validated, then parametric studies cover alloy state, plate thickness, center-region radius, and temperature. Formulae are derived for local buckling, block tearing, and four-linear stiffness; maximum errors are 7.16% for local buckling and 17.43% for block tearing.
| Link | Paper data | Meaning |
|---|---|---|
| Configuration | six H100x50x4x5 members, 240 mm gusset, eight M6 bolts, 2 or 4 mm plate | represents common aluminum reticulated-shell joints |
| Test loads | B2-20/200/300: 35.58/29.76/12.84 kN; C2-20/200/300: 34.04/31.22/28.44 kN | temperature and loading path govern thin-plate joint performance |
| Stiffness | B2 Kf: 186.46/187.46/181.15 kN m/rad; C2 Kf: 144.93/236.29/170.18 | initial stiffness does not simply decrease; bolt gap and thermal expansion matter |
| Formulae | local buckling max error 7.16%; block tearing max error 17.43%; four-linear model fits M-theta curves | usable for AAG joint fire-design estimates below 300 ? |
Data source: abstract, Sections 2-6, Tables 1-9, Figs. 1-26, and conclusions.
The measured effective length correlates more stably with net length, so joint semi-rigidity can be folded into a net-length framework.
This paper studies in-plane effective length of members in single-layer reticulated shells with AAG joints. It separates two boundary effects: the semi-rigidity of the AAG joint itself, k1, and the rotational restraint from adjacent members, k2, while accounting for stiffness reduction of adjacent members under compression. The experimental program tests five axially compressed members with AAG joints, all I100x50x4x5, with 240 mm diameter, 5 mm thick gusset plates and eight M6 bolts. Three specimens are 1.0 m long and two are 1.2 m long; net lengths are 760 and 960 mm. The material is 6061-T4, with plate E=69088 MPa and f0.2=184.40 MPa, and member E=65364 MPa and f0.2=177.40 MPa. All specimens fail by global buckling about the minor axis, with ultimate loads of 118.28-145.71 kN. ABAQUS C3D8R contact models have a maximum ultimate-load error of 3.47%. Inflection points from FE contours give effective lengths of 393-396 mm for 1.0 m specimens and 505 mm for 1.2 m specimens, or 0.393-0.421l and 0.517-0.526ln; the net-length ratio fluctuates less. Thus k1 can be represented by an effective length close to a fixed-ended member using net length. For k2, the paper derives adjacent-member rotational stiffness and a compression reduction factor eta=1-N/NE, recommending an Euler load for a fixed-near/hinged-far member in real structures. Solving the bending equilibrium gives K factors from 0.500 to 0.981, with l0=mu ln; taking l0=ln is conservative. A K6 shell example shows that ignoring adjacent-member compression overestimates critical load by at least 50%. The proposed K factors have an average error of 4.61% and are on the safe side.
| Link | Paper data | Meaning |
|---|---|---|
| Specimens | I100x50x4x5; 240 mm x 5 mm gusset; total length 1000/1200 mm; net length 760/960 mm | measures the k1 effect using real joint boundaries |
| Ultimate loads | 1mA/B/C: 129.29/132.53/145.71 kN; 1.2mA/B: 118.28/118.91 kN; max FE error 3.47% | FE is reliable for inflection-point identification and theory |
| Effective length | l0=393-396 mm or 505 mm; l0/l=0.393-0.421; l0/ln=0.517-0.526 | net length is the better reference for AAG member effective length |
| Example | 8.3-22 m K6 shells; Pcr(1) is at least 50% larger than Pcr(2); K table average error 4.61% | compression weakening of adjacent members must enter local stability design |
Data source: abstract, Sections 2-6, Tables 1-6, Figs. 1-20, and conclusions.
The method suits existing trusses or shell tubular joints without removing the original joint.
This paper proposes a grouted sleeve retrofit for existing tubular T-joints and validates it with seven specimens. The joints consist of a 168x8 mm chord and a 114xtb mm brace. A constant 180 kN chord compression, about 15% of pure chord axial capacity, is applied first, then brace compression is increased to failure. ZHU1 with 6 mm brace thickness and ZHI1 with 4 mm brace thickness are unreinforced references. Five reinforced specimens use D14 expansive grout and 6 mm sleeves, varying grout thickness of 7 or 19.5 mm, sleeve length coefficient of 1 or 1.5, and weld or CFRP sleeve assembly. Material tests give mean steel E=205109 MPa, fy=322.56 MPa, fu=481.04 MPa, and mean grout compressive strength 52.18 MPa. Unreinforced joints mainly fail by large plastic deformation of the chord, while reinforced joints show weld cracking, FRP cracking, chord plastic deformation near sleeve ends, and combined sleeve-chord plastic deformation, proving that the sleeve changes the failure path. Ultimate loads are 272.5 kN for ZHU1 and 289.3 kN for ZHI1; reinforced ZHU2/ZHU3/ZHU4 reach 456.8/467.6/450.4 kN, and ZHI2/ZHI3 reach 446.3/499.6 kN. Compared with unreinforced joints, capacity increases by 54.3%-72.7%, initial stiffness by 6.6%-38.4%, and ultimate displacement by 180.6%-244.6%. Welded and CFRP sleeves perform similarly; increasing sleeve length coefficient from 1 to 1.5 raises ZHI3 capacity by 11.9% and stiffness by 18.9% over ZHI2.
| Link | Paper data | Meaning |
|---|---|---|
| Matrix | 168x8 mm chord, 114x6 or 114x4 mm brace; D14 grout; 6 mm sleeve; td=7/19.5 mm; alpha=1/1.5 | covers grout thickness, sleeve length, and assembly method |
| Loads | ZHU1/ZHI1: 272.5/289.3 kN; ZHU2/ZHU3/ZHU4: 456.8/467.6/450.4 kN; ZHI2/ZHI3: 446.3/499.6 kN | external sleeves greatly improve static joint capacity |
| Stiffness/deformability | initial stiffness increases 6.6%-38.4%; ultimate displacement increases 180.6%-244.6% | improves deformation capacity as well as strength |
| Key parameter | ZHI2 -> ZHI3: alpha 1 -> 1.5, capacity +11.9%, initial stiffness +18.9% | sleeve extension length governs retrofit efficiency |
Data source: abstract, Sections 2-6, Tables 1-5, Figs. 1-16, and conclusions.
A central joint is loaded while joint displacement, member force, plate stress, and support displacement are measured.
This paper studies global buckling through a full AAG-jointed single-layer shell test and FE analysis. The Kiewitt-6 shell has an 8 m span, 0.5 m height, 5 rings, 210 I100x50x4x5 members, and 91 AAG joints. The gusset plates are 5 mm thick, with six hand-tightened M6 stainless-steel bolts connecting each flange. The material is 6063-T5: plate E=71879 MPa and f0.2=144.3 MPa; member E=65364 MPa and f0.2=177.4 MPa. Initial geometric imperfection is measured before loading, with maximum 54.95 mm, minimum 9.93 mm, and average 33.88 mm. The central joint is loaded by two hydraulic jacks through a rod-spreader beam, in four loading stages for initial stiffness, buckling load, post-buckling, and final collapse. Around 20 kN in the first stage, AAG joints enter bolt slipping; after unloading at 64.3 kN, central joint residual displacement is 37.82 mm, 65% of the maximum. In the second stage, buckling occurs at 74.55 kN and J1 displacement reaches 162 mm before unloading. The third stage reaches 94.7 kN, confirming snap-through buckling, and the final stage collapses at 99.7 kN by fracture of the bottom flange near the loading joint. Support displacement is negligible; member L1 enters plasticity in the third and final stages; AAG plate Mises stress remains below 144.3 MPa and mostly elastic. The ANSYS model uses BEAM188 members/rigid joint zones and COMBIN39 semi-rigid joint springs; buckling load is 75.29 kN versus 74.55 kN in test, with average maximum-load error 2.1% and displacement error 3.8%. Parametric analysis shows FE-shell1 with AAG bending behavior has ultimate load 9.13 kN/m2, FE-shell2 with only rigid joint zones has 11.54 kN/m2, FE-shell3 with only semi-rigid springs has 8.06 kN/m2, and fully rigid FE-shell4 has 10.37 kN/m2. Thus rigid joint zones increase initial stiffness, but semi-rigid bending weakens buckling capacity. Before shell instability, joints mainly stay in the bolt-fixed phase; later slip, bearing, and ultimate moment have negligible influence.
| Link | Paper data | Meaning |
|---|---|---|
| Shell | 8 m span, 0.5 m height, 5 rings; 210 I100x50x4x5 members; 91 AAG joints | a full spatial system, not an isolated member |
| Loading path | first stage 64.3 kN; second-stage buckling 74.55 kN; third stage 94.7 kN; final fracture 99.7 kN | post-buckling capacity remains; final failure is controlled by members near the loaded joint |
| Local response | support displacement about 0.82 mm max; L1 enters plasticity in stages 3/final; plate stress below 144.3 MPa | the test mainly reflects global buckling and member plasticity, not gusset yielding first |
| Model | FE buckling 75.29 kN vs test 74.55 kN; average max-load error 2.1%, displacement 3.8% | the semi-rigid spring model is reliable for parametric analysis |
Data source: abstract, Sections 2-6, Tables 1-4, Figs. 1-33, and conclusions.
In the basic 70 m K6 model, the rigid shell reaches 10.37 kN/m2, while the AAG semi-rigid shell reaches 9.13 kN/m2.
This paper systematically studies elasto-plastic stability of K6 single-layer reticulated shells with AAG joints and proposes practical buckling-load formulae from more than 8000 FE models. ANSYS BEAM188 models members and rigid joint zones, while COMBIN39 nonlinear springs model the four-linear out-of-plane bending stiffness of AAG joints. Parameters include spans of 40/50/60/70 m, height-to-span ratios 1/4, 1/5, 1/6, 1/7, rings 16/18/20/22, four I-section families M1-M4 with corresponding J1-J4 joints, linear/nonlinear joint stiffness, elastic/elasto-plastic material, load ratios p/g=0, 1/4, 1/2, 1, pinned/fixed supports, and imperfections of 0, S/1000, S/500, S/300, S/200, and S/100. The FE model is first verified by the 8 m test shell, with 75.29 kN buckling versus 74.55 kN in test. For the basic 70 m, f/L=1/7, 16-ring, M4, fixed-support, p/g=0 model, elastic buckling of the rigid shell is 15.05 kN/m2, 16.94% above the semi-rigid shell at 12.5 kN/m2; elasto-plastic ultimate load is 10.37 kN/m2 for the rigid shell, 11.92% above the AAG semi-rigid shell at 9.13 kN/m2. Parametric studies show that higher span-to-thickness ratio reduces capacity and can lower the AAG/rigid ratio to about 84.5%; larger height-to-span ratio raises capacity and the ratio, with some AAG shells exceeding rigid shells at 1/4; more rings increase capacity; better joint bending behavior improves capacity; material nonlinearity has weaker influence on AAG shells than rigid shells; higher p/g reduces capacity; support condition has relatively small influence; and initial imperfections sharply reduce capacity, with effects stabilizing beyond S/300. Formulae first fit CL from 2048 rigid-shell models, then CJ from 768 semi-rigid models with 92.8% within +/-10% error, CP from 768 elasto-plastic models with 90.4% within +/-10%, and finally CIM from 4096 imperfect-shell results. CIM has mean 0.367 and standard deviation 0.043; the 95% value is 0.296, below the 0.4-0.7 used for steel rigid-joint shells, showing AAG shells are more imperfection-sensitive.
| Link | Paper data | Meaning |
|---|---|---|
| Basic comparison | elastic buckling: 15.05 vs 12.5 kN/m2; elasto-plastic ultimate: 10.37 vs 9.13 kN/m2 | ignoring AAG semi-rigidity overestimates stability capacity |
| Parameter range | S=40-70 m; f/L=1/4-1/7; 16-22 rings; p/g=0-1; imperfections 0 to S/100 | formulae are fitted over an engineering parameter space, not one example |
| Formula fit | CL: 2048 models; CJ: 768 models, 92.8% within +/-10%; CP: 768 models, 90.4% within +/-10% | compresses FE data into fast design factors |
| Imperfection | CIM max 0.574, min 0.244, mean 0.367, SD 0.043; 95% value 0.296 | AAG shells are more sensitive to initial imperfections than steel rigid-joint shells |
Data source: abstract, Sections 2-7, Tables 1-14, Figs. 1-24, and conclusions.
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