Numerical Study of Circular Concrete Filled Steel Tubes Subjected to Pure Torsion
Abstract
:1. Introduction
2. Research Significance
3. Material Models
3.1. Stress-Strain Model of Steel
3.2. Compressive and Tensile Stress-Strain Model of Concrete
4. Modelling
5. Verifications
5.1. Moment-Rotation Curve
5.1.1. Comparing with the Test Results Obtained by Beck and Kiyomiya
5.1.2. Comparing with the Experimental Results Obtained by Han and Zhong
5.1.3. Comparing with the Experimental Data Obtained by Le et al.
6. Load Transferring Mechanism
7. Parametric Study
7.1. Effect of Yield Strength of Steel on the Torsional Behaviour of CFSTs
7.2. Effect of Concrete Strength on the Torsional Behavior of CFSTs
7.3. Analyses of the Numerical Results
8. Correlation Analyses
9. Conclusions
- The distribution of stress exhibited a mechanism of torsional moment transferring. Moving from one end section to the middle section of the CFST, the moment sustained by steel tube decreased while that of concrete increased. The stress of steel at the end regions was greater than that at the middle region. On the contrary, the stress on concrete at the end regions was smaller than that at the middle region.
- Concrete strength marginally affected the moment-rotation behavior of the CFSTs. Improving the behavior and capacity of the CFST was not the main function of concrete, while its main function was to prevent buckling of steel tubes and thus to make steel tubes work more effectively.
- The steel strength did not affect the elastic stiffness; however, it decisively affected the nominal yield strength and the plastic behavior of the CFSTs. When the yield steel strength increased from 235 to 420 MPa, the nominal yield torsional moment of the CFSTs increased by approximately 50%.
- Correlation analyses were performed to see the correlation degree between the mechanical properties and parameters of the CFSTs. The results showed that the parameters related to the steel tube had higher correlation coefficients than those related to concrete. Interestingly, the yield torsional moment of steel tube had the strongest correlation with the nominal yield moments of the CFSTs followed by D/t ratio, while the compressive strength of concrete came in the last position.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
D | diameter of steel tube |
t | thickness of steel tube |
L | length of CFST |
L′ | length of rigid blocks |
Es | elastic modulus of steel |
fy | yield strength of steel |
fu | ultimate strength of steel |
εy | yield strain of steel |
εu | ultimate strain of steel |
εc | strain of concrete |
εo | strain corresponding to maximum stress of concrete |
f′c | maximum stress of concrete |
Ec | elastic modulus of concrete |
μ | coefficient of friction |
p | normal pressure |
ξ | confinement factor |
τy | yield shear strength of steel |
ke | elastic stiffness |
kp | plastic stiffness |
Mo | moment at the intersection of the plastic branch and the vertical axis |
θ | rotation |
Ws | torsional inertia modulus of cross section of steel tube |
As | cross sectional area of steel tube |
Ac | cross sectional area of concrete |
Me | elastic moment |
My | yield moment |
X, Y | variables |
, | means of the variables X and Y |
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No. | Subgroup | Dimension D × t × L (mm) | Yield Strength of Steel (MPa) | Ultimate Strength of Steel (MPa) | Compressive Strength of Concrete (MPa) |
---|---|---|---|---|---|
1 | CFST-AN | 140 × 2.3 × 1000 | 302.5 | 406.6 | 24.2 |
2 | CFST-BN | 140 × 3.0 × 1000 | 302.5 | 406.6 | 24.2 |
3 | CFST-CN | 140 × 3.5 × 1000 | 302.5 | 406.6 | 24.2 |
4 | CFST-AH | 140 × 2.3 × 1000 | 302.5 | 406.6 | 33.3 |
5 | CFST-BH | 140 × 3.0 × 1000 | 302.5 | 406.6 | 33.3 |
6 | CFST-CH | 140 × 3.5 × 1000 | 302.5 | 406.6 | 33.3 |
No. | Sub Group | t | fy | fu | f′c | D/t | As | Ac | ξ | Ws | Wsfy | Me | ke | kp | Mo | My | Increaseof My |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
mm | MPa | MPa | MPa | mm2 | mm2 | mm3 | N.mm | kNm | kNm/rad/m | kNm | % | ||||||
1 | CFST-A | 2.3 | 235 | 359.6 | 24.2 | 60.9 | 995.0 | 14,398.8 | 0.671 | 67,397.3 | 15,838,371 | 9.51 | 441.7 | 23.4 | 13.3 | 14.0 | |
2 | CFST-A | 2.3 | 345 | 452.0 | 24.2 | 60.9 | 995.0 | 14,398.8 | 0.985 | 67,397.3 | 23,252,076 | 13.10 | 438.0 | 18.5 | 18.6 | 19.5 | 38.8 |
3 | CFST-A | 2.3 | 390 | 475.8 | 24.2 | 60.9 | 995.0 | 14,398.8 | 1.114 | 67,397.3 | 26,284,956 | 15.90 | 449.0 | 17.3 | 20.4 | 21.2 | 51.2 |
4 | CFST-A | 2.3 | 420 | 500.9 | 24.2 | 60.9 | 995.0 | 14,398.8 | 1.199 | 67,397.3 | 28,306,876 | 16.72 | 424.7 | 17.3 | 20.4 | 21.2 | 51.6 |
5 | CFST-A | 2.3 | 302.5 | 406.6 | 20 | 60.9 | 995.0 | 14,398.8 | 1.045 | 67,397.3 | 20,387,690 | 11.58 | 452.6 | 14.7 | 16.1 | 16.7 | |
6 | CFST-A | 2.3 | 302.5 | 406.6 | 30 | 60.9 | 995.0 | 14,398.8 | 0.697 | 67,397.3 | 20,387,690 | 11.68 | 469.9 | 22.8 | 16.1 | 16.9 | 1.3 |
7 | CFST-A | 2.3 | 302.5 | 406.6 | 40 | 60.9 | 995.0 | 14,398.8 | 0.523 | 67,397.3 | 20,387,690 | 11.78 | 501.2 | 23.1 | 16.0 | 16.7 | 0.4 |
8 | CFST-A | 2.3 | 302.5 | 406.6 | 50 | 60.9 | 995.0 | 143,98.8 | 0.418 | 67,397.3 | 20,387,690 | 11.64 | 492.2 | 22.6 | 16.1 | 16.9 | 1.2 |
9 | CFST-A | 2.3 | 302.5 | 406.6 | 60 | 60.9 | 995.0 | 14,398.8 | 0.348 | 67,397.3 | 20,387,690 | 11.69 | 504.7 | 21.4 | 16.5 | 17.3 | 3.6 |
1 | CFST-B | 3.0 | 235 | 359.6 | 24.2 | 46.7 | 1291.2 | 14,102.6 | 0.889 | 86,593.0 | 20,349,365 | 13.49 | 542.3 | 17.8 | 17.5 | 18.1 | |
2 | CFST-B | 3.0 | 345 | 452.0 | 24.2 | 46.7 | 1291.2 | 14,102.6 | 1.305 | 86,593.0 | 29,874,600 | 18.94 | 537.3 | 17.0 | 22.8 | 23.6 | 30.1 |
3 | CFST-B | 3.0 | 390 | 475.8 | 24.2 | 46.7 | 1291.2 | 14,102.6 | 1.476 | 86,593.0 | 33,771,286 | 20.41 | 537.3 | 15.2 | 25.1 | 25.8 | 42.5 |
4 | CFST-B | 3.0 | 420 | 500.9 | 24.2 | 46.7 | 1291.2 | 14,102.6 | 1.589 | 86,593.0 | 36,369,078 | 20.92 | 537.3 | 13.9 | 26.6 | 27.3 | 50.6 |
5 | CFST-B | 3.0 | 302.5 | 406.6 | 20 | 46.7 | 1291.2 | 14,102.6 | 1.385 | 86,593.0 | 26,194,395 | 15.57 | 525.1 | 15.7 | 19.8 | 20.4 | |
6 | CFST-B | 3.0 | 302.5 | 406.6 | 30 | 46.7 | 1291.2 | 14,102.6 | 0.923 | 86,593.0 | 26,194,395 | 15.99 | 542.3 | 17.1 | 22.0 | 22.7 | 11.1 |
7 | CFST-B | 3.0 | 302.5 | 406.6 | 40 | 46.7 | 1291.2 | 14,102.6 | 0.692 | 86,593.0 | 26,194,395 | 16.20 | 551.5 | 16.9 | 22.1 | 22.8 | 11.7 |
8 | CFST-B | 3.0 | 302.5 | 406.6 | 50 | 46.7 | 1291.2 | 14,102.6 | 0.554 | 86,593.0 | 26,194,395 | 16.39 | 561.8 | 16.5 | 22.3 | 22.9 | 12.3 |
9 | CFST-B | 3.0 | 302.5 | 406.6 | 60 | 46.7 | 1291.2 | 14,102.6 | 0.462 | 86,593.0 | 26,194,395 | 16.52 | 568.4 | 16.6 | 22.3 | 23.0 | 11.4 |
1 | CFST-C | 3.5 | 235 | 359.6 | 24.2 | 40.0 | 1500.9 | 13,892.9 | 1.049 | 99,940.9 | 23,486,113 | 15.04 | 605.3 | 20.7 | 18.3 | 18.9 | |
2 | CFST-C | 3.5 | 345 | 452.0 | 24.2 | 40.0 | 1500.9 | 13,892.9 | 1.540 | 99,940.9 | 34,479,612 | 21.32 | 598.5 | 19.1 | 24.6 | 25.4 | 34.2 |
3 | CFST-C | 3.5 | 390 | 475.8 | 24.2 | 40.0 | 1500.9 | 13,892.9 | 1.741 | 99,940.9 | 38,976,953 | 22.92 | 585.2 | 17.4 | 27.1 | 28.0 | 47.9 |
4 | CFST-C | 3.5 | 420 | 500.9 | 24.2 | 40.0 | 1500.9 | 13,892.9 | 1.875 | 99,940.9 | 41,975,180 | 23.29 | 590.2 | 16.2 | 28.8 | 29.6 | 56.6 |
5 | CFST-C | 3.5 | 302.5 | 406.6 | 20 | 40.0 | 1500.9 | 13,892.9 | 1.634 | 99,940.9 | 30,232,124 | 17.36 | 584.5 | 15.6 | 21.9 | 22.5 | |
6 | CFST-C | 3.5 | 302.5 | 406.6 | 30 | 40.0 | 1500.9 | 13,892.9 | 1.089 | 99,940.9 | 30,232,124 | 17.85 | 602.8 | 20.1 | 23.0 | 23.8 | 5.6 |
7 | CFST-C | 3.5 | 302.5 | 406.6 | 40 | 40.0 | 1500.9 | 13,892.9 | 0.817 | 99,940.9 | 30,232,124 | 17.97 | 611.1 | 18.3 | 23.6 | 24.3 | 7.8 |
8 | CFST-C | 3.5 | 302.5 | 406.6 | 50 | 40.0 | 1500.9 | 13,892.9 | 0.654 | 99,940.9 | 30,232,124 | 18.05 | 618.0 | 19.9 | 23.2 | 23.9 | 6.3 |
9 | CFST-C | 3.5 | 302.5 | 406.6 | 60 | 40.0 | 1500.9 | 13,892.9 | 0.545 | 99,940.9 | 30,232,124 | 18.15 | 623.4 | 19.3 | 23.3 | 24.1 | 6.5 |
Parameter | Absolute Correlation Coefficient | Order |
---|---|---|
Wsfy | 0.9709 | 1 |
D/t | 0.7412 | 2 |
Ws | 0.7299 | 3 |
As | 0.7291 | 4 |
Ac | 0.7291 | 5 |
t | 0.7288 | 6 |
fy | 0.6425 | 7 |
fu | 0.6364 | 8 |
ξ | 0.6152 | 9 |
f′c | 0.0608 | 10 |
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Le, K.B.; Cao, V.V. Numerical Study of Circular Concrete Filled Steel Tubes Subjected to Pure Torsion. Buildings 2021, 11, 397. https://doi.org/10.3390/buildings11090397
Le KB, Cao VV. Numerical Study of Circular Concrete Filled Steel Tubes Subjected to Pure Torsion. Buildings. 2021; 11(9):397. https://doi.org/10.3390/buildings11090397
Chicago/Turabian StyleLe, Khanh Ba, and Vui Van Cao. 2021. "Numerical Study of Circular Concrete Filled Steel Tubes Subjected to Pure Torsion" Buildings 11, no. 9: 397. https://doi.org/10.3390/buildings11090397