Evolution of Confinement Stress in Axially Loaded Concrete-Filled Steel Tube Stub Columns: Study on Enhancing Urban Building Efficiency
Abstract
:1. Introduction
2. Confining Stress
2.1. Cross-Sectional Shape
2.2. The Ratio of
2.3. CS of Concrete Core
2.4. Depth-to-Thickness Ratio of ST (D/t)
3. Proposed Confining Stress–Axial Strain Model for Circular CFST Stub Columns
The Yield Strain of the ST ()
4. Finite Element Modeling
4.1. Element Type and Mesh
4.2. Interaction between the Concrete Core and the Steel Tube
4.3. Material Modeling
4.3.1. Steel Property
4.3.2. Concrete Property
5. Results and Discussion
6. Comparison of the Results from Tests, Finite Element Model and Design Codes
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Cross-sectional area of the concrete core | |
Cross-sectional area of the steel tube | |
Depth of the steel tube | |
Depth of the concrete core | |
Elastic modulus of concrete | |
Elastic modulus of steel | |
Compressive strength of unconfined concrete | |
Compressive strength of confined concrete | |
Confining stress | |
Effective confining stress | |
Residual stress of the concrete core | |
The yield stress of steel | |
Axial stress in the steel tube | |
Hoop stress in the steel tube | |
Confinement effectiveness coefficient | |
Axial strain | |
First axial strain at which the interaction between the concrete core and the steel tube occurs | |
Strain at peak stress () of unconfined concrete | |
Strain at peak stress () of confined concrete | |
Axial strain at which the lateral strain of the concrete core is equal to | |
Yield strain of steel | |
Yield strain of the steel tube | |
Lateral strain of the concrete core | |
Lateral strain of the steel tube | |
The cross-sectional deformation of the steel tube | |
The cross-sectional deformation of the concrete core | |
Poisson’s ratio of the concrete core | |
Poisson’s ratio of the steel tube | |
Coefficient of confinement |
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R | R2 | RMSE | RRMSE | MAE | MAPE | |
---|---|---|---|---|---|---|
0.98 | 0.97 | 0.069 | 0.19 | 0.045 | 17.29 | 0.09 |
Specimen | D (mm) | t (mm) | (mm) | (MPa) | (MPa) | (kN) | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
CFST-LA-1 | 153 | 1.54 | 99.3 | 306 | 345 | 73.2 | 0.72 | 1823 | 0.69 | 0.93 | 0.99 | 0.78 | 0.88 |
CFST-LA-2 | 1842 | 0.68 | 0.92 | 0.98 | 0.77 | 0.87 | |||||||
CFST-LA-3 | 1872 | 0.67 | 0.91 | 0.96 | 0.76 | 0.86 | |||||||
CFST-LB-1 | 250 | 2.48 | 100.8 | 500 | 326 | 73.2 | 0.67 | 4871 | 0.75 | 0.92 | 0.98 | 0.77 | 0.86 |
CFST-LB-2 | 4528 | 0.81 | 0.99 | 1.05 | 0.82 | 0.92 | |||||||
CFST-LB-3 | 4733 | 0.77 | 0.95 | 1.01 | 0.79 | 0.88 | |||||||
CFST-LC-1 | 372 | 3.64 | 102.2 | 744 | 320 | 73.2 | 0.68 | 9163 | 0.85 | 1.07 | 1.15 | 0.9 | 1.01 |
CFST-LC-2 | 9996 | 0.78 | 0.98 | 1.05 | 0.82 | 0.93 | |||||||
CFST-LC-3 | 9604 | 0.81 | 1.02 | 1.09 | 0.86 | 0.96 | |||||||
CFST-LD-1 | 469 | 4.66 | 100.6 | 938 | 291 | 73.2 | 0.61 | 15,827 | 0.85 | 0.97 | 1.04 | 0.81 | 0.91 |
CFST-LD-2 | 16,670 | 0.8 | 0.92 | 0.99 | 0.77 | 0.86 | |||||||
CFST-LD-3 | 15,239 | 0.88 | 1.01 | 1.08 | 0.84 | 0.94 | |||||||
CFST-MA-1 | 157 | 2.48 | 63.3 | 314 | 326 | 73.2 | 0.67 | 2117 | 0.78 | 0.93 | 0.96 | 0.77 | 0.85 |
CFST-MA-2 | 2058 | 0.8 | 0.96 | 0.99 | 0.79 | 0.87 | |||||||
CFST-MA-3 | 2068 | 0.8 | 0.95 | 0.99 | 0.79 | 0.87 | |||||||
CFST-MB-1 | 282 | 4.36 | 64.8 | 564 | 322 | 73.2 | 0.65 | 6811 | 0.78 | 0.92 | 0.96 | 0.76 | 0.84 |
CFST-MB-2 | 6380 | 0.83 | 0.99 | 1.03 | 0.82 | 0.9 | |||||||
CFST-MB-3 | 6860 | 0.77 | 0.92 | 0.95 | 0.76 | 0.84 | |||||||
CFST-MC-1 | 358 | 5.66 | 63.2 | 716 | 290 | 73.2 | 0.62 | 9947 | 0.84 | 0.99 | 1.04 | 0.82 | 0.91 |
CFST-MC-2 | 10,045 | 0.83 | 0.98 | 1.03 | 0.81 | 0.9 | |||||||
CFST-MC-3 | 9609 | 0.87 | 1.03 | 1.08 | 0.85 | 0.94 | |||||||
CFST-MD-1 | 474 | 7.42 | 63.9 | 948 | 317 | 73.2 | 0.64 | 17,787 | 0.84 | 1 | 1.04 | 0.83 | 0.96 |
CFST-MD-2 | 18,306 | 0.82 | 0.97 | 1.01 | 0.8 | 0.94 | |||||||
CFST-MD-3 | 17,885 | 0.84 | 0.99 | 1.03 | 0.82 | 0.96 | |||||||
CFST-HA-1 | 153 | 3.64 | 42 | 306 | 320 | 73.2 | 0.68 | 2264 | 0.75 | 0.93 | 0.95 | 0.76 | 0.82 |
CFST-HA-2 | 2274 | 0.75 | 0.93 | 0.94 | 0.76 | 0.82 | |||||||
CFST-HA-3 | 2205 | 0.77 | 0.96 | 0.97 | 0.79 | 0.84 | |||||||
CFST-HB-1 | 235 | 5.66 | 41.5 | 470 | 290 | 73.2 | 0.62 | 5390 | 0.73 | 0.89 | 0.92 | 0.73 | 0.79 |
CFST-HB-2 | 5047 | 0.78 | 0.95 | 0.98 | 0.78 | 0.84 | |||||||
CFST-HB-3 | 5096 | 0.77 | 0.94 | 0.97 | 0.77 | 0.83 | |||||||
CFST-HC-1 | 393 | 9.38 | 41.9 | 786 | 312 | 73.2 | 0.63 | 13,936 | 0.8 | 0.99 | 1.01 | 0.81 | 0.87 |
CFST-HC-2 | 14,406 | 0.78 | 0.96 | 0.98 | 0.79 | 0.84 | |||||||
CFST-HC-3 | 14,161 | 0.79 | 0.97 | 0.99 | 0.8 | 0.86 | |||||||
CFST-HD-1 | 477 | 11.36 | 42 | 954 | 310 | 73.2 | 0.63 | 20,237 | 0.81 | 1 | 1.02 | 0.82 | 0.88 |
CFST-HD-2 | 20,462 | 0.8 | 0.99 | 1.01 | 0.81 | 0.87 | |||||||
CFST-HD-3 | 19,854 | 0.83 | 1.02 | 1.04 | 0.84 | 0.9 |
Specimen | D (mm) | t (mm) | (mm) | (MPa) | (MPa) | (kN) | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
CC4-A-2 | 149 | 2.96 | 50.4 | 3 | 308 | 25.4 | 0.83 | 941 | 0.86 | 1.14 | 1.03 | 0.93 | 0.98 |
CC4-A-4-1 | 149 | 2.96 | 50.3 | 3 | 308 | 40.5 | 0.74 | 1064 | 0.97 | 1.23 | 1.19 | 1.02 | 1.07 |
CC4-A-4-2 | 50.4 | 1080 | 0.96 | 1.21 | 1.17 | 1 | 1.06 | ||||||
CC4-A-8 | 149 | 2.96 | 50.5 | 3 | 308 | 77 | 0.59 | 1781 | 0.9 | 1.05 | 1.12 | 0.89 | 0.97 |
CC4-C-2 | 301 | 2.96 | 101.5 | 3 | 279 | 25.4 | 0.75 | 2382 | 1.02 | 1.25 | 1.21 | 1.03 | 1.2 |
CC4-C-4-1 | 300 | 2.96 | 101.4 | 3 | 279 | 41.1 | 0.67 | 3277 | 1.04 | 1.22 | 1.26 | 1.02 | 1.17 |
CC4-C-4-2 | 3152 | 1.09 | 1.27 | 1.31 | 1.06 | 1.22 | |||||||
CC4-C-8 | 301 | 2.96 | 101.5 | 3 | 279 | 80.3 | 0.53 | 5540 | 1.08 | 1.2 | 1.32 | 1.02 | 1.15 |
CC4-D-2 | 450 | 2.96 | 152 | 3 | 279 | 25.4 | 0.75 | 4415 | 0.88 | 1.31 | 1.32 | 1.09 | 1.31 |
CC4-D-4-1 | 450 | 2.96 | 152 | 3 | 279 | 41.1 | 0.67 | 6870 | 0.81 | 1.19 | 1.26 | 1 | 1.15 |
CC4-D-4-2 | 6985 | 0.8 | 1.17 | 1.24 | 0.99 | 1.13 | |||||||
CC4-D-8 | 450 | 2.96 | 152 | 3 | 279 | 85.1 | 0.51 | 11,665 | 0.89 | 1.28 | 1.43 | 1.09 | 1.25 |
CC6-A-2 | 122 | 4.54 | 26.9 | 3 | 576 | 25.4 | 1.55 | 1509 | 0.8 | 1.12 | 0.99 | 0.96 | 0.95 |
CC6-A-4-1 | 122 | 4.54 | 26.8 | 3 | 576 | 40.5 | 1.39 | 1657 | 0.81 | 1.11 | 1.02 | 0.95 | 0.95 |
CC6-A-4-2 | 1663 | 0.81 | 1.1 | 1.02 | 0.94 | 0.95 | |||||||
CC6-A-8 | 122 | 4.54 | 26.8 | 3 | 576 | 77 | 1.11 | 2100 | 0.81 | 1.04 | 1.04 | 0.9 | 0.91 |
CC6-C-2 | 239 | 4.54 | 52.5 | 3 | 507 | 25.4 | 1.36 | 3035 | 0.89 | 1.21 | 1.04 | 1 | 1.11 |
CC6-C-4-1 | 238 | 4.54 | 52.5 | 3 | 507 | 40.5 | 1.22 | 3583 | 0.91 | 1.19 | 1.09 | 0.99 | 1.1 |
CC6-C-4-2 | 52.4 | 3647 | 0.9 | 1.17 | 1.07 | 0.98 | 1.08 | ||||||
CC6-C-8 | 238 | 4.54 | 52.4 | 3 | 507 | 77 | 0.98 | 5578 | 0.84 | 1.02 | 1.03 | 0.87 | 0.93 |
CC6-D-2 | 361 | 4.54 | 79.4 | 3 | 525 | 25.4 | 1.41 | 5633 | 0.77 | 1.18 | 1.03 | 0.97 | 1.14 |
CC6-D-4-1 | 361 | 4.54 | 79.4 | 3 | 525 | 41.1 | 1.26 | 7260 | 0.75 | 1.12 | 1.06 | 0.93 | 1.07 |
CC6-D-4-2 | 360 | 79.3 | 7045 | 0.77 | 1.14 | 1.08 | 0.96 | 1.1 | |||||
CC6-D-8 | 360 | 4.54 | 79.4 | 3 | 525 | 85.1 | 0.97 | 11,505 | 0.73 | 1.06 | 1.11 | 0.9 | 1.04 |
CC8-A-2 | 108 | 6.47 | 16.7 | 3 | 853 | 25.4 | 2.29 | 2275 | 0.85 | 1.15 | 1.14 | 1.05 | 0.96 |
CC8-A-4-1 | 109 | 6.47 | 16.8 | 3 | 853 | 40.5 | 2.05 | 2446 | 0.84 | 1.13 | 1.13 | 1.02 | 0.98 |
CC8-A-4-2 | 108 | 16.7 | 2402 | 0.85 | 1.13 | 1.14 | 1.03 | 0.98 | |||||
CC8-A-8 | 108 | 6.47 | 16.7 | 3 | 853 | 77 | 1.64 | 2713 | 0.84 | 1.09 | 1.15 | 1 | 0.97 |
CC8-C-2 | 222 | 6.47 | 34.3 | 3 | 843 | 25.4 | 2.26 | 4964 | 0.91 | 1.27 | 1.08 | 1.09 | 1.18 |
CC8-C-4-1 | 222 | 6.47 | 34.3 | 3 | 843 | 40.5 | 2.03 | 5638 | 0.89 | 1.2 | 1.07 | 1.04 | 1.14 |
CC8-C-4-2 | 5714 | 0.88 | 1.19 | 1.06 | 1.03 | 1.13 | |||||||
CC8-C-8 | 222 | 6.47 | 34.4 | 3 | 843 | 77 | 1.62 | 7304 | 0.85 | 1.09 | 1.05 | 0.95 | 1.04 |
CC8-D-2 | 337 | 6.47 | 52.1 | 3 | 823 | 25.4 | 2.21 | 8475 | 0.81 | 1.22 | 1.02 | 1.04 | 1.2 |
CC8-D-4-1 | 337 | 6.47 | 52 | 3 | 823 | 41.1 | 1.97 | 9668 | 0.81 | 1.2 | 1.06 | 1.02 | 1.21 |
CC8-D-4-2 | 9835 | 0.79 | 1.18 | 1.05 | 1.01 | 1.19 | |||||||
CC8-D-8 | 337 | 6.47 | 52 | 3 | 823 | 85.1 | 1.52 | 13,776 | 0.75 | 1.09 | 1.07 | 0.94 | 1.09 |
Specimen | D (mm) | t (mm) | (mm) | (MPa) | (MPa) | (kN) | Ref. | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
CU-040 | 200 | 5 | 40 | 3 | 265.8 | 27.15 | 0.7 | 2013 | 0.77 | 1.1 | 1.06 | 0.84 | 0.86 | Hu, Huang [18] |
CU-070 | 280 | 4 | 70 | 3 | 272.6 | 31.15 | 0.7 | 3025 | 0.88 | 1.11 | 1.1 | 0.91 | 0.97 | |
CU-150 | 300 | 2 | 150 | 3 | 341.7 | 27.23 | 0.9 | 2608 | 0.73 | 1.12 | 1.04 | 0.92 | 1.12 | |
C1 | 140.8 | 3 | 47 | 4.3 | 285 | 28.18 | 0.79 | 881 | 1.07 | 1.41 | 1.3 | 1.15 | 1.21 | Schneider [38] |
C2 | 141.4 | 6.5 | 21.7 | 4.3 | 313 | 28.805 | 0.83 | 1825 | 0.89 | 1.27 | 1.16 | 1.05 | 0.96 | |
C3 | 140 | 6.68 | 21 | 4.4 | 537 | 28.18 | 1.37 | 2715 | 0.92 | 1.28 | 1.18 | 1.1 | 1.03 | |
3HN | 150 | 3.2 | 46.9 | 450 | 287.4 | 28.7 | 0.75 | 1000 | 0.87 | 1.14 | 1.05 | 0.93 | 0.97 | Tomii [37] |
CS-1 | 219 | 6.3 | 34.8 | 600 | 300 | 163 | 0.39 | 6880 | 0.94 | 1.06 | 1.23 | 0.91 | 1 | Liew, Xiong [40] |
SFE | 159 | 4.8 | 33.1 | 650 | 433 | 64.5 | 4.09 | 2150 | 0.97 | 1.18 | 1.22 | 1.04 | 1.05 | Johansson and Gylltoft [35] |
Specimen | D (mm) | t (mm) | (mm) | (MPa) | (MPa) | (kN) | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
S30CS50B | 165 | 2.82 | 58.5 | 580.5 | 363.3 | 48.3 | 0.83 | 1662 | 0.86 | 1.04 | 1.05 | 0.89 | 0.93 |
S20CS50A | 190 | 1.94 | 97.9 | 663.5 | 256.4 | 41 | 0.6 | 1678 | 0.81 | 0.92 | 0.98 | 0.79 | 0.87 |
S16CS50B | 190 | 1.52 | 125 | 664.5 | 306.1 | 48.3 | 0.67 | 1695 | 0.76 | 1.02 | 1.09 | 0.87 | 0.96 |
S12CS50A | 190 | 1.13 | 168.1 | 664.5 | 185.7 | 41 | 0.5 | 1377 | 0.79 | 0.95 | 1.06 | 0.82 | 0.92 |
S10CS50A | 190 | 0.86 | 220.9 | 659 | 210.7 | 41 | 0.57 | 1350 | 0.67 | 0.96 | 1.06 | 0.82 | 0.92 |
S30CS80A | 165 | 2.82 | 58.5 | 580.5 | 363.3 | 80.2 | 0.68 | 2295 | 0.89 | 1.02 | 1.1 | 0.88 | 0.93 |
S20CS80B | 190 | 1.94 | 97.9 | 663.5 | 256.4 | 74.7 | 0.49 | 2592 | 0.86 | 0.94 | 1.05 | 0.81 | 0.9 |
S16CS80A | 190 | 1.52 | 125 | 663.5 | 306.1 | 80.2 | 0.56 | 2602 | 0.75 | 0.99 | 1.11 | 0.85 | 0.95 |
S12CS80A | 190 | 1.13 | 168.1 | 662.5 | 185.7 | 80.2 | 0.39 | 2295 | 0.88 | 1.04 | 1.19 | 0.89 | 1.02 |
S10CS80B | 190 | 0.86 | 220.9 | 663.5 | 210.7 | 74.7 | 0.46 | 2451 | 0.64 | 0.91 | 1.03 | 0.78 | 0.88 |
S30CS10A | 165 | 2.82 | 58.5 | 577.5 | 363.3 | 108 | 0.6 | 2673 | 0.96 | 1.07 | 1.2 | 0.93 | 1 |
S20CS10A | 190 | 1.94 | 97.9 | 660 | 256.4 | 108 | 0.41 | 3360 | 0.92 | 0.99 | 1.13 | 0.85 | 0.96 |
S16CS10A | 190 | 1.52 | 125 | 661.5 | 306.1 | 108 | 0.49 | 3260 | 0.78 | 1.02 | 1.16 | 0.88 | 0.98 |
S12CS10A | 190 | 1.13 | 168.1 | 660 | 185.7 | 108 | 0.34 | 3058 | 0.87 | 1.03 | 1.18 | 0.88 | 1.01 |
S10CS10A | 190 | 0.86 | 220.9 | 662 | 210.7 | 108 | 0.39 | 3070 | 0.72 | 1.02 | 1.17 | 0.88 | 0.99 |
Mean | 0.83 | 1.06 | 1.08 | 0.9 | 0.98 |
Min | 1.09 | 1.41 | 1.43 | 1.15 | 1.31 |
Max | 0.64 | 0.89 | 0.92 | 0.73 | 0.79 |
STD | 0.085 | 0.116 | 0.098 | 0.103 | 0.117 |
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Shariati, M.; Pourteymuri, M.; Naghipour, M.; Toghroli, A.; Afrazi, M.; Shariati, M.; Aminian, A.; Nematzadeh, M. Evolution of Confinement Stress in Axially Loaded Concrete-Filled Steel Tube Stub Columns: Study on Enhancing Urban Building Efficiency. Sustainability 2024, 16, 7544. https://doi.org/10.3390/su16177544
Shariati M, Pourteymuri M, Naghipour M, Toghroli A, Afrazi M, Shariati M, Aminian A, Nematzadeh M. Evolution of Confinement Stress in Axially Loaded Concrete-Filled Steel Tube Stub Columns: Study on Enhancing Urban Building Efficiency. Sustainability. 2024; 16(17):7544. https://doi.org/10.3390/su16177544
Chicago/Turabian StyleShariati, Mahdi, Mahsa Pourteymuri, Morteza Naghipour, Ali Toghroli, Mohammad Afrazi, Morteza Shariati, Arman Aminian, and Mahdi Nematzadeh. 2024. "Evolution of Confinement Stress in Axially Loaded Concrete-Filled Steel Tube Stub Columns: Study on Enhancing Urban Building Efficiency" Sustainability 16, no. 17: 7544. https://doi.org/10.3390/su16177544