Numerical Investigations on Axial Compressive Behavior of Opening Cold-Formed Thin-Wall C-Steel Combined Double-Limb Column
Abstract
:1. Introduction
2. Numerical Simulations on C-Steel Combined I-Section Columns
2.1. Finite Element Models
2.2. Finite Element Model Validations
3. Parametric Analyses on C-Steel Combined I-Section Columns
3.1. Effects of Slenderness Ratio
3.2. Effects of Height to Thickness Ratio of Web
3.3. Effects of Width to Thickness Ratio of Flange
3.4. Effects of Bolt Spacing
3.5. Effects of Opening in the Web
3.5.1. Effects of Opening Ratio of the Web
3.5.2. Effects of Opening Spacing
4. Formulas for Ultimate Compressive Bearing Capacity
4.1. Formulas in Standards
4.1.1. Formulas in Chinese GB 50018 Standard
4.1.2. Formulas in AISI S100-2016 Standard
4.2. Comparisons between the Results of Numerical Analyses and Standards
4.3. Proposed Formulas for Compressive Bearing Capacity of C-Steel Combined I-Section Column
4.3.1. Combined Column without Opening
4.3.2. Combined Column with Openings
5. Conclusions and Future Work
- (1)
- The slenderness ratio has the most significant effect on the ultimate compressive bearing capacity of the combined column. With the increase in the height to thickness ratio and width to thickness ratio, the bearing capacity increases. The bolt spacing has less effect on the bearing capacity.
- (2)
- The openings in the web decrease the ultimate compressive bearing capacity of the combined column. The opening in the web should be considered.
- (3)
- The proposed formulas in this paper can predict the ultimate compressive bearing capacity of the combined columns with or without opening. The accuracy of the proposed formulas is higher than those of the Chinese and AISI S100 standard.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Comparisons of the Bearing Capacities between Numerical Analyses and Standards
λy | NFEM/kN | NCGB/kN | NNAS/kN | NCGB/NFEM | NNAS/NFEM | |
---|---|---|---|---|---|---|
C90-40-15-1.5-300 | 9.9 | 139.8 | 131.5 | 136.3 | 0.941 | 0.975 |
C90-40-15-1.5-600 | 19.8 | 137 | 128.9 | 133.1 | 0.941 | 0.971 |
C90-40-15-1.5-900 | 29.7 | 134 | 126.1 | 129.4 | 0.941 | 0.966 |
C90-40-15-1.5-1200 | 79.1 | 117.1 | 106.5 | 113.4 | 0.909 | 0.968 |
C90-40-15-1.5-1500 | 98.9 | 102.7 | 91.8 | 99.6 | 0.894 | 0.970 |
C90-40-15-1.5-1800 | 118.6 | 87.5 | 74.1 | 84.1 | 0.847 | 0.961 |
C90-40-15-1.5-2400 | 158.2 | 61.4 | 45.2 | 58.8 | 0.736 | 0.957 |
C90-40-15-1.5-3000 | 197.7 | 45.8 | 29.7 | 40.7 | 0.648 | 0.890 |
C120-40-15-1.5-300 | 10.1 | 142.6 | 136.2 | 139.6 | 0.955 | 0.979 |
C120-40-15-1.5-600 | 20.3 | 140.7 | 133.4 | 136.2 | 0.948 | 0.968 |
C120-40-15-1.5-900 | 30.4 | 137.9 | 130.5 | 132.3 | 0.946 | 0.959 |
C120-40-15-1.5-1200 | 81.1 | 120.6 | 109.1 | 114.3 | 0.905 | 0.948 |
C120-40-15-1.5-1500 | 101.4 | 105.8 | 93.2 | 101.7 | 0.881 | 0.961 |
C120-40-15-1.5-1800 | 121.7 | 91.6 | 76.0 | 87.3 | 0.830 | 0.953 |
C120-40-15-1.5-2400 | 162.3 | 65.7 | 50.4 | 60.2 | 0.767 | 0.917 |
C120-40-15-1.5-3000 | 202.8 | 48.9 | 33.2 | 41.4 | 0.679 | 0.847 |
C140-40-15-1.5-300 | 10.4 | 144.8 | 139.0 | 140.2 | 0.960 | 0.968 |
C140-40-15-1.5-600 | 20.7 | 142.6 | 136.2 | 136.8 | 0.955 | 0.959 |
C140-40-15-1.5-900 | 31.0 | 140.1 | 133.1 | 132.7 | 0.950 | 0.948 |
C140-40-15-1.5-1200 | 82.8 | 122.9 | 110.4 | 115.1 | 0.898 | 0.937 |
C140-40-15-1.5-1500 | 103.5 | 107.2 | 93.5 | 103.8 | 0.872 | 0.968 |
C140-40-15-1.5-1800 | 124.2 | 94.1 | 76.0 | 84.7 | 0.808 | 0.900 |
C140-40-15-1.5-2400 | 165.5 | 68.6 | 51.8 | 56.5 | 0.755 | 0.823 |
C140-40-15-1.5-3000 | 206.9 | 50.4 | 35.0 | 43.5 | 0.694 | 0.864 |
C160-40-15-1.5-300 | 10.6 | 146.7 | 137.5 | 142.4 | 0.937 | 0.971 |
C160-40-15-1.5-600 | 21.1 | 144.5 | 135.4 | 141.3 | 0.937 | 0.978 |
C160-40-15-1.5-900 | 31.7 | 142 | 133.0 | 137.0 | 0.937 | 0.965 |
C160-40-15-1.5-1200 | 84.5 | 125.7 | 111.9 | 119.9 | 0.890 | 0.954 |
C160-40-15-1.5-1500 | 105.7 | 109.5 | 93.9 | 96.0 | 0.858 | 0.877 |
C160-40-15-1.5-1800 | 126.8 | 98 | 76.0 | 81.0 | 0.776 | 0.827 |
C160-40-15-1.5-2400 | 169.1 | 69.2 | 51.7 | 67.0 | 0.747 | 0.969 |
C160-40-15-1.5-3000 | 209.3 | 54.7 | 36.6 | 51.6 | 0.669 | 0.944 |
C92.8-41.8-14.8-1.19-270 | 8.5 | 133.6 | 118.0 | 125.6 | 0.883 | 0.940 |
C93.8-41.8-14.7-1.19-270 | 8.5 | 133.5 | 117.9 | 124.9 | 0.883 | 0.936 |
C93.5-41.5-15-1.18-1533 | 96.5 | 102.3 | 84.5 | 97.6 | 0.826 | 0.954 |
C92.5-42-14.5-1.2-1531 | 95.7 | 106.7 | 84.6 | 98.1 | 0.793 | 0.919 |
C91.8-43.2-14.4-1.19-3033 | 184.6 | 44.5 | 32.7 | 40.8 | 0.734 | 0.916 |
C92.8-40.2-15-1.18-3038 | 197.2 | 44.9 | 28.0 | 41.3 | 0.624 | 0.920 |
C142.7-42.9-15.1-1.47-451 | 14.5 | 142.7 | 134.4 | 140.3 | 0.942 | 0.983 |
C144.2-42.8-14.8-1.48-451 | 14.6 | 143.1 | 135.0 | 137.1 | 0.943 | 0.958 |
C142-42.5-15.5-1.48-1532 | 98.8 | 106.2 | 97.8 | 102.7 | 0.921 | 0.967 |
C142-42-15-1.48-1533 | 100.7 | 105.1 | 95.2 | 102.2 | 0.906 | 0.972 |
C140.8-42-15.5-1.49-3034 | 198.0 | 48 | 33.8 | 43.7 | 0.704 | 0.910 |
C141.5-42.3-16-1.47-3033 | 195.4 | 47.7 | 33.6 | 42.9 | 0.705 | 0.899 |
Mean value | -- | -- | -- | -- | 0.847 | 0.939 |
Variance | -- | -- | -- | -- | 0.101 | 0.041 |
Appendix B. Correction Factors of Compression Stability Factor
λy | A/mm2 | Ae/mm2 | φFEM | φ | ξ | |
---|---|---|---|---|---|---|
C90-40-15-1.5-300 | 9.9 | 562.2 | 442.3 | 0.974 | 1.035 | 1.063 |
C90-40-15-1.5-600 | 19.8 | 562.2 | 445.7 | 0.947 | 1.007 | 1.063 |
C90-40-15-1.5-900 | 29.7 | 562.2 | 449.5 | 0.919 | 0.976 | 1.062 |
C90-40-15-1.5-1200 | 79.1 | 562.2 | 479.9 | 0.726 | 0.799 | 1.100 |
C90-40-15-1.5-1500 | 98.9 | 562.2 | 504.7 | 0.595 | 0.666 | 1.119 |
C90-40-15-1.5-1800 | 118.6 | 562.2 | 529.2 | 0.459 | 0.541 | 1.180 |
C90-40-15-1.5-2400 | 158.2 | 562.2 | 529.5 | 0.279 | 0.380 | 1.360 |
C90-40-15-1.5-3000 | 197.7 | 562.2 | 529.5 | 0.184 | 0.283 | 1.540 |
C120-40-15-1.5-300 | 10.1 | 652.2 | 458.2 | 0.973 | 1.019 | 1.047 |
C120-40-15-1.5-600 | 20.3 | 652.2 | 461.9 | 0.946 | 0.997 | 1.054 |
C120-40-15-1.5-900 | 30.4 | 652.2 | 466.0 | 0.917 | 0.969 | 1.057 |
C120-40-15-1.5-1200 | 81.1 | 652.2 | 499.9 | 0.715 | 0.790 | 1.105 |
C120-40-15-1.5-1500 | 101.4 | 652.2 | 529.6 | 0.576 | 0.654 | 1.135 |
C120-40-15-1.5-1800 | 121.7 | 652.2 | 564.7 | 0.440 | 0.531 | 1.206 |
C120-40-15-1.5-2400 | 162.3 | 652.2 | 619.5 | 0.267 | 0.347 | 1.303 |
C120-40-15-1.5-3000 | 202.8 | 652.2 | 619.5 | 0.175 | 0.258 | 1.475 |
C140-40-15-1.5-300 | 10.4 | 712.2 | 468.1 | 0.973 | 1.013 | 1.042 |
C140-40-15-1.5-600 | 20.7 | 712.2 | 472.0 | 0.945 | 0.989 | 1.047 |
C140-40-15-1.5-900 | 31.0 | 712.2 | 476.3 | 0.915 | 0.963 | 1.053 |
C140-40-15-1.5-1200 | 82.8 | 712.2 | 513.0 | 0.705 | 0.784 | 1.113 |
C140-40-15-1.5-1500 | 103.5 | 712.2 | 545.9 | 0.561 | 0.643 | 1.146 |
C140-40-15-1.5-1800 | 124.2 | 712.2 | 583.4 | 0.426 | 0.528 | 1.239 |
C140-40-15-1.5-2400 | 165.5 | 712.2 | 659.8 | 0.257 | 0.340 | 1.325 |
C140-40-15-1.5-3000 | 206.9 | 712.2 | 679.5 | 0.169 | 0.243 | 1.440 |
C160-40-15-1.5-300 | 10.6 | 772.2 | 463.3 | 0.972 | 1.037 | 1.067 |
C160-40-15-1.5-600 | 21.1 | 772.2 | 469.8 | 0.944 | 1.007 | 1.067 |
C160-40-15-1.5-900 | 31.7 | 772.2 | 477.2 | 0.913 | 0.974 | 1.068 |
C160-40-15-1.5-1200 | 84.5 | 772.2 | 527.7 | 0.694 | 0.780 | 1.123 |
C160-40-15-1.5-1500 | 105.7 | 772.2 | 564.1 | 0.545 | 0.636 | 1.166 |
C160-40-15-1.5-1800 | 126.8 | 772.2 | 604.2 | 0.412 | 0.531 | 1.290 |
C160-40-15-1.5-2400 | 169.1 | 772.2 | 684.9 | 0.247 | 0.331 | 1.339 |
C160-40-15-1.5-3000 | 209.3 | 772.2 | 739.5 | 0.162 | 0.242 | 1.496 |
C92.8-41.8-14.8-1.19-270 | 8.5 | 466.5 | 318.7 | 0.978 | 1.107 | 1.132 |
C93.8-41.8-14.7-1.19-270 | 8.5 | 468.4 | 318.5 | 0.978 | 1.107 | 1.132 |
C93.5-41.5-15-1.18-1533 | 96.5 | 464.0 | 359.5 | 0.770 | 0.932 | 1.211 |
C92.5-42-14.5-1.2-1531 | 95.7 | 469.0 | 361.5 | 0.767 | 0.967 | 1.261 |
C91.8-43.2-14.4-1.19-3033 | 184.6 | 468.9 | 436.7 | 0.245 | 0.334 | 1.363 |
C92.8-40.2-15-1.18-3038 | 197.2 | 456.2 | 424.1 | 0.216 | 0.347 | 1.603 |
C142.7-42.9-15.1-1.47-451 | 14.5 | 724.3 | 457.8 | 0.962 | 1.021 | 1.061 |
C144.2-42.8-14.8-1.48-451 | 14.6 | 731.1 | 459.8 | 0.961 | 1.019 | 1.060 |
C142-42.5-15.5-1.48-1532 | 98.8 | 726.9 | 537.7 | 0.596 | 0.647 | 1.086 |
C142-42-15-1.48-1533 | 100.7 | 721.0 | 535.6 | 0.582 | 0.642 | 1.104 |
C140.8-42-15.5-1.49-3034 | 198.0 | 725.0 | 692.3 | 0.160 | 0.227 | 1.420 |
C141.5-42.3-16-1.47-3033 | 195.4 | 722.5 | 689.7 | 0.160 | 0.226 | 1.418 |
λy | Opening Ratio K/% | NFEM | Nu | η | |
---|---|---|---|---|---|
C140-40-15-1.5-300-K0% | 10.4 | 0.0 | 144.8 | 148.2 | 0.977 |
C140-40-15-1.5-300-K7.7% | 10.4 | 7.7 | 127.1 | 148.2 | 0.858 |
C140-40-15-1.5-300-K15.7% | 10.4 | 15.7 | 119.3 | 148.2 | 0.805 |
C140-40-15-1.5-300-K23.7% | 10.4 | 23.7 | 113.2 | 148.2 | 0.764 |
C140-40-15-1.5-300-K32.2% | 10.4 | 32.2 | 108.3 | 148.2 | 0.731 |
C140-40-15-1.5-300-K39.7% | 10.4 | 39.7 | 98.0 | 148.2 | 0.661 |
C140-40-15-1.5-300-K47.4% | 10.4 | 47.4 | 84.7 | 148.2 | 0.572 |
C140-40-15-1.5-300-K54.4% | 10.4 | 54.4 | 63.5 | 148.2 | 0.429 |
C140-40-15-1.5-900-K0% | 31.0 | 0.0 | 140.1 | 142.6 | 0.982 |
C140-40-15-1.5-900-K7.8% | 31.0 | 7.8 | 122.4 | 142.6 | 0.859 |
C140-40-15-1.5-900-K16% | 31.0 | 16.0 | 113.3 | 142.6 | 0.794 |
C140-40-15-1.5-900-K23.7% | 31.0 | 23.7 | 108.0 | 142.6 | 0.757 |
C140-40-15-1.5-900-K32.3% | 31.0 | 32.3 | 104.3 | 142.6 | 0.732 |
C140-40-15-1.5-900-K40.6% | 31.0 | 40.6 | 91.5 | 142.6 | 0.642 |
C140-40-15-1.5-900-K50.2% | 31.0 | 50.2 | 72.1 | 142.6 | 0.506 |
C140-40-15-1.5-900-K58.3% | 31.0 | 58.3 | 44.9 | 142.6 | 0.315 |
C140-40-15-1.5-1500-K0% | 103.5 | 0.0 | 107.2 | 108.8 | 0.985 |
C140-40-15-1.5-1500-K8.1% | 103.5 | 8.1 | 94.4 | 108.8 | 0.868 |
C140-40-15-1.5-1500-K16.2% | 103.5 | 16.2 | 88.2 | 108.8 | 0.810 |
C140-40-15-1.5-1500-K24.3% | 103.5 | 24.3 | 83.0 | 108.8 | 0.763 |
C140-40-15-1.5-1500-K32.6% | 103.5 | 32.6 | 79.6 | 108.8 | 0.732 |
C140-40-15-1.5-1500-K40.4% | 103.5 | 40.4 | 73.1 | 108.8 | 0.672 |
C140-40-15-1.5-1500-K49% | 103.5 | 49.0 | 57.7 | 108.8 | 0.530 |
C140-40-15-1.5-1500-K60.5% | 103.5 | 60.5 | 26.9 | 108.8 | 0.247 |
C140-40-15-1.5-3000-K0% | 206.9 | 0.0 | 50.4 | 52.0 | 0.969 |
C140-40-15-1.5-3000-K7.9% | 206.9 | 7.9 | 44.8 | 52.0 | 0.862 |
C140-40-15-1.5-3000-K16.1% | 206.9 | 16.1 | 41.8 | 52.0 | 0.805 |
C140-40-15-1.5-3000-K24.5% | 206.9 | 24.5 | 39.4 | 52.0 | 0.758 |
C140-40-15-1.5-3000-K32.3% | 206.9 | 32.3 | 37.8 | 52.0 | 0.727 |
C140-40-15-1.5-3000-K39.5% | 206.9 | 39.5 | 34.7 | 52.0 | 0.667 |
C140-40-15-1.5-3000-K51.7% | 206.9 | 51.7 | 24.4 | 52.0 | 0.470 |
C140-40-15-1.5-3000-K62.9% | 206.9 | 62.9 | 9.2 | 52.0 | 0.178 |
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L/mm | h/mm | b/mm | c/mm | t/mm | δ0/mm | λy | A/mm2 | |
---|---|---|---|---|---|---|---|---|
SC-90-A1 | 270 | 92.8 | 41.8 | 14.8 | 1.19 | 0.412 | 8.45 | 466.5 |
SC-90-A2 | 270 | 93.8 | 41.8 | 14.7 | 1.19 | 0.521 | 8.47 | 468.4 |
MC-90-A1 | 1533 | 93.5 | 41.5 | 15.0 | 1.18 | 0.565 | 96.51 | 464.0 |
MC-90-A2 | 1531 | 92.5 | 42.0 | 14.5 | 1.20 | 0.433 | 95.73 | 469.0 |
LC-90-A1 | 3033 | 91.8 | 43.2 | 14.4 | 1.19 | 0.521 | 184.56 | 468.9 |
LC-90-A2 | 3038 | 92.8 | 40.2 | 15.0 | 1.18 | 0.374 | 197.15 | 456.2 |
SC-140-A1 | 451 | 142.7 | 42.9 | 15.1 | 1.47 | 0.646 | 14.47 | 724.3 |
SC-140-A2 | 451 | 144.2 | 42.8 | 14.8 | 1.48 | 0.535 | 14.59 | 731.1 |
MC-140-A1 | 1532 | 142.0 | 42.5 | 15.5 | 1.48 | 0.652 | 98.82 | 726.9 |
MC-140-A2 | 1533 | 142.0 | 42.0 | 15.0 | 1.48 | 0.443 | 100.66 | 721.0 |
LC-140-A1 | 3034 | 140.8 | 42.0 | 15.5 | 1.49 | 0.656 | 197.96 | 725.0 |
LC-140-A2 | 3033 | 141.5 | 42.3 | 16.0 | 1.47 | 0.661 | 195.37 | 722.5 |
Simulation | Experiment | NFE/NTE | Error/% | |||
---|---|---|---|---|---|---|
NFE/kN | Failure Mode | NTE/kN | Failure Mode | |||
SC-90-A1 | 133.6 | Local buckling | 127.7 | Local buckling | 1.046 | 4.62 |
SC-90-A2 | 133.5 | Local buckling | 132.8 | Local buckling | 1.005 | 0.53 |
MC-90-A1 | 102.3 | Local + overall buckling + distortion | 97.7 | Local + overall buckling + distortion | 1.047 | 4.71 |
MC-90-A2 | 106.7 | Local + overall buckling + distortion | 103.0 | Local + overall buckling + distortion | 1.036 | 3.59 |
LC-90-A1 | 44.5 | Overall buckling | 42.6 | Overall buckling | 1.045 | 4.46 |
LC-90-A2 | 44.9 | Overall buckling | 39.9 | Overall buckling | 1.125 | 12.53 |
SC-140-A1 | 142.7 | Local buckling + distortion | 130.7 | Local buckling + distortion | 1.092 | 9.18 |
SC-140-A2 | 143.1 | Local buckling + distortion | 139.6 | Local buckling + distortion | 1.025 | 2.51 |
MC-140-A1 | 106.2 | Local + overall buckling + distortion | 105.8 | Local + overall buckling + distortion | 0.856 | 0.38 |
MC-140-A2 | 105.1 | Local + overall buckling + distortion | 101.0 | Local + overall buckling + distortion | 1.041 | 4.06 |
LC-140-A1 | 48.0 | Overall buckling | 49.2 | Overall buckling | 0.976 | −2.44 |
LC-140-A2 | 47.7 | Overall buckling | 46.9 | Overall buckling | 1.017 | 1.71 |
Mean value | - | - | - | - | 1.026 | 3.82 |
Variance | - | - | - | - | 0.063 | 3.98 |
Bolt Spacing/mm | Increasing Ratio | Increasing Bearing Capacity | |
---|---|---|---|
C140-40-1.5-300 | 40, 60, 80, 100, 120, 150 | 275% | 0.6% |
C140-40-1.5-900 | 50-450, step: 50 | 800% | 0.6% |
C140-40-1.5-1500 | 50-200, step: 5; 200-600, step: 100 | 1100% | 1.1% |
C140-40-1.5-3000 | 50-200, step: 50; 200-600, step: 100 | 1100% | 1.8% |
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He, C.; Cai, Y.; Chen, H. Numerical Investigations on Axial Compressive Behavior of Opening Cold-Formed Thin-Wall C-Steel Combined Double-Limb Column. Buildings 2022, 12, 1378. https://doi.org/10.3390/buildings12091378
He C, Cai Y, Chen H. Numerical Investigations on Axial Compressive Behavior of Opening Cold-Formed Thin-Wall C-Steel Combined Double-Limb Column. Buildings. 2022; 12(9):1378. https://doi.org/10.3390/buildings12091378
Chicago/Turabian StyleHe, Chang, Yong Cai, and Haijun Chen. 2022. "Numerical Investigations on Axial Compressive Behavior of Opening Cold-Formed Thin-Wall C-Steel Combined Double-Limb Column" Buildings 12, no. 9: 1378. https://doi.org/10.3390/buildings12091378