Behavior and Reliable Design Methods of Axial Compressed Dune Sand Concrete-Filled Circular Steel Tube Columns
Abstract
:1. Introduction
2. Finite Element Modeling
2.1. Element Type, Interaction, Boundary Conditions, and Mesh
2.2. The Steel Constitutive Model
2.3. The Dune Sand Concrete Constitutive Model
2.4. Model Validation
3. Finite Element Analysis
3.1. Parametric Analysis
3.2. Confinement Analysis and Effectiveness Evaluation
3.2.1. Infilled DS Concrete Strength
3.2.2. Steel Strength
3.2.3. Cross-Sectional Steel Ratio
3.2.4. DS Replacement Ratio
3.3. Axial Compression Comparison of CFCST and DS-CFCST Stub Columns
4. Practical Formula for Bearing Capacity and Reliability Analysis
4.1. Model Simplification
4.2. Formulation
4.3. Formula Validation
4.4. Comparison of Formulas
4.5. Reliability Analysis
4.5.1. Reliability Analysis Method
- Normal variable:
- 2.
- Log-normal variable:
- 3.
- Type I extreme value distribution:
4.5.2. Reliability Analysis Steps
- Variable Identification for Reliability Index: This includes cross-sectional dimensions (D), tube wall thickness (t), load effects (SGk, SQk), model uncertainty (kp), concrete strength (fc), and steel strength (fy). Statistical analysis of kp is performed.
- Resistance Calculation (Nu,r): Varying material strength values are substituted into Equation (10) to determine Nu,r.
- Load Effect Determination: Based on the formula Nu,r ≥ S = γGSGk + γQSQk and the load effect ratio ρL = SQk/SGk, calculate the standard value of the dead load effect SGk = Nu,r/(γG + ρLγQ) and the standard value of the live load effect SQk = ρLSGk.
- MATLAB Random Sampling: Random sampling of D, t, SGk, SQk, kp, fc, fy, and Nu,r is performed N times (N ≥ 100/pf) in MATLAB. These values are then used into limit state Equation (15).
- Reliability Index Calculation (β): The number of instances where Z < 0 is counted, and β is calculated using Equation (17). Error estimation is carried out with Equation (18).
4.5.3. Statistical Parameters of Basic Random Variables
- Statistical parameters of load
- 2.
- Statistical parameters of geometric dimensions
- 3.
- Statistical Parameters of Material Properties
- 4.
- Calculation models’ statistical uncertainty parameters
4.5.4. Reliability Analysis Results
5. Conclusions
- FE model results show good agreement with experimental data, evidenced by a mean value of Nu,Exp/Nu,FE at 1.008 and a CV of 0.040. Load–axial strain curves from the FE analysis align closely with experimental observations, confirming the model’s validity.
- The strength of the infilled DS concrete, steel yield strength, and steel ratio significantly influence the ultimate bearing capacity of DS-CFCST stub columns. Conversely, the DS replacement ratio has a minor impact on load-bearing capacity.
- This study highlights the diminishing effect of DS replacement ratio on steel tube confinement efficacy. However, the relative influence of this factor is minimal compared to other design parameters.
- A simplified, straightforward formula for predicting the axial load-bearing capacity of DS-CFCST columns is proposed. This formula, incorporating a steel tube shape confinement factor, aligns well with experimental and FE-derived results, offering a more accurate and simpler alternative to existing design code formulas.
- Reliability analysis supports balanced design approaches, considering material strengths, reinforcement ratios, loading conditions, and DS replacement ratio. This ensures adherence to the target reliability index, emphasizing the necessity of adequate safety margins against failure in structural systems.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Ecr | Poisson’s Ratio | Dilation Angle | e | fb0/fc0 | K | μ |
---|---|---|---|---|---|---|
(1 − 0.1r) 9500fcu1/3 | 0.2 | 40° | 0.1 | 1.277 | 2/3 | 0.0005 |
Specimen Label | Ref. | D × t × L/mm | r | fcu,r (MPa) | fy (MPa) | Nu,Exp (kN) | Nu,FE (kN) | Nu,Exp/Nu,FE |
---|---|---|---|---|---|---|---|---|
C-3-8-1 | [21] | 160 × 3.46 × 520 | 0.1 | 78 | 363 | 2044 | 2008.36 | 1.018 |
C-3-8-2 | 160 × 3.46 × 520 | 0.1 | 78 | 363 | 2069 | 2008.36 | 1.030 | |
c1-1 | [22] | 200 × 3.82 × 600 | 1 | 65.8 | 432 | 3191 | 3184.42 | 1.002 |
c1-2 | 200 × 3.82 × 600 | 1 | 65.8 | 432 | 3152 | 3184.42 | 0.990 | |
c2-1 | 200 × 2.90 × 600 | 1 | 65.8 | 390 | 2722 | 2705.06 | 1.006 | |
c2-2 | 200 × 2.90 × 600 | 1 | 65.8 | 390 | 2822 | 2705.06 | 1.043 | |
c3-1 | 200 × 1.98 × 600 | 1 | 65.8 | 388 | 2546 | 2355.52 | 1.081 | |
c3-2 | 200 × 1.98 × 600 | 1 | 65.8 | 388 | 2465 | 2355.52 | 1.046 | |
c4-1 | 150 × 3.82 × 450 | 1 | 65.8 | 432 | 1927 | 1887.80 | 1.021 | |
c4-2 | 150 × 3.82 × 450 | 1 | 65.8 | 432 | 1846 | 1887.80 | 0.978 | |
c5-1 | 100 × 3.82 × 300 | 1 | 65.8 | 432 | 1097 | 1059.50 | 1.035 | |
c5-2 | 100 × 3.82 × 300 | 1 | 65.8 | 432 | 1087 | 1059.50 | 1.026 | |
DCFT3020-1 | [39] | 165 × 2.75 × 495 | 0.2 | 36.9 | 344.10 | 1362.08 | 1261.59 | 1.080 |
DCFT3020-2 | 165 × 2.75 × 495 | 0.2 | 36.9 | 344.10 | 1355.95 | 1261.59 | 1.075 | |
DCFT3020-3 | 165 × 2.75 × 495 | 0.2 | 36.9 | 344.10 | 1373.26 | 1261.59 | 1.089 | |
DCFT3040-1 | 165 × 2.75 × 495 | 0.4 | 45.4 | 344.10 | 1397.42 | 1367.02 | 1.022 | |
DCFT3040-2 | 165 × 2.75 × 495 | 0.4 | 45.4 | 344.10 | 1354.69 | 1367.02 | 0.991 | |
DCFT3040-3 | 165 × 2.75 × 495 | 0.4 | 45.4 | 344.10 | 1355.52 | 1367.02 | 0.992 | |
DCFT3060-1 | 165 × 2.75 × 495 | 0.6 | 47.4 | 344.10 | 1326.13 | 1384.66 | 0.958 | |
DCFT3060-2 | 165 × 2.75 × 495 | 0.6 | 47.4 | 344.10 | 1307.63 | 1384.66 | 0.944 | |
DCFT3060-3 | 165 × 2.75 × 495 | 0.6 | 47.4 | 344.10 | 1333.71 | 1384.66 | 0.963 | |
DCFT30100-1 | 165 × 2.75 × 495 | 1 | 46.7 | 344.10 | 1386.47 | 1371.71 | 1.011 | |
DCFT30100-2 | 165 × 2.75 × 495 | 1 | 46.7 | 344.10 | 1339.31 | 1371.71 | 0.977 | |
DCFT30100-3 | 165 × 2.75 × 495 | 1 | 46.7 | 344.10 | 1353.74 | 1371.71 | 0.987 | |
DCFT5020-1 | [39] | 165 × 2.75 × 495 | 0.2 | 60.2 | 344.10 | 1554.74 | 1628.95 | 0.954 |
DCFT5020-2 | 165 × 2.75 × 495 | 0.2 | 60.2 | 344.10 | 1572.32 | 1628.95 | 0.965 | |
DCFT5020-3 | 165 × 2.75 × 495 | 0.2 | 60.2 | 344.10 | 1547.99 | 1628.95 | 0.950 | |
DCFT5040-1 | 165 × 2.75 × 495 | 0.4 | 56.1 | 344.10 | 1501.40 | 1551.12 | 0.968 | |
DCFT5040-2 | 165 × 2.75 × 495 | 0.4 | 56.1 | 344.10 | 1475.20 | 1551.12 | 0.951 | |
DCFT5040-3 | 165 × 2.75 × 495 | 0.4 | 56.1 | 344.10 | 1576.20 | 1551.12 | 1.016 | |
DCFT5060-1 | 165 × 2.75 × 495 | 0.6 | 54.5 | 344.10 | 1573.62 | 1520.29 | 1.035 | |
DCFT5060-2 | 165 × 2.75 × 495 | 0.6 | 54.5 | 344.10 | 1517.90 | 1520.29 | 0.998 | |
DCFT5060-3 | 165 × 2.75 × 495 | 0.6 | 54.5 | 344.10 | 1645.06 | 1520.29 | 1.082 | |
DCFT50100-1 | 165 × 2.75 × 495 | 1 | 50.7 | 344.10 | 1562.55 | 1515.54 | 1.031 | |
DCFT50100-2 | 165 × 2.75 × 495 | 1 | 50.7 | 344.10 | 1529.58 | 1515.54 | 1.009 | |
DCFT50100-3 | 165 × 2.75 × 495 | 1 | 50.7 | 344.10 | 1525.50 | 1515.54 | 1.007 | |
Mean | 1.008 | |||||||
CV | 0.040 |
D (mm) | L (mm) | ρ | R | fcu,0 (MPa) | fy (MPa) |
---|---|---|---|---|---|
500 | 1500 | 0.02, 0.04, 0.06, 0.08 | 0, 0.3, 0.5, 0.7, 1 | 30, 50 | 235 |
50, 70 | 345 | ||||
70 | 420 |
Design Codes | ACI-318 | AISC 360–16 | EC 4 | AIJ |
---|---|---|---|---|
fc, fcu (MPa) | fc ≥ 17.2 | 21 ≤ fc ≤ 69 | 20 ≤ fc ≤ 50 25 ≤ fcu ≤ 60 | fc ≤ 58.8 |
fy (MPa) | - | ≤525 | 235–460 | 235 ≤ fy ≤ 355 |
D/t |
Ref. | Formula | Nu,Eq/Nu,Exp | |
---|---|---|---|
Mean | CV | ||
This paper | 0.972 | 0.054 | |
ACI-318 [45] | 1.262 | 0.055 | |
AISC 360–16 [46] | 1.180 | 0.058 | |
BS EN 1994 [47] | 0.954 | 0.055 | |
AIJ [48] | 1.135 | 0.054 |
Parameter | Dead Load (G) | Office Live Load (QO) | Residential Live Load (QR) |
---|---|---|---|
Mean Value (μ) | 1.060 | 0.698 | 0.859 |
Coefficient of Variation (δ) | 0.070 | 0.288 | 0.233 |
Distribution Type | Normal | Extreme Value Type I | Extreme Value Type I distribution |
Parameter | Q235 (t ≤ 16 mm) | Q235 (t > 16 mm) | Q345 (t ≤ 16 mm) | Q345 (t > 16 mm) |
---|---|---|---|---|
Standard strength (fyk/MPa) | 235 | 225 | 345 | 335 |
Design strength (fyd/MPa) | 215 | 205 | 305 | 295 |
Mean value (μ) | 1.080 | 1.080 | 1.090 | 1.090 |
Coefficient of variation (δ) | 0.080 | 0.080 | 0.070 | 0.070 |
Distribution type | Normal distribution |
Parameter | C30 | C40 | C50 | C60 | C70 |
---|---|---|---|---|---|
Standard strength (fck/MPa) | 20.1 | 26.8 | 32.4 | 38.5 | 44.5 |
Design strength (fcd/MPa) | 14.3 | 19.1 | 23.1 | 27.5 | 31.8 |
Mean value (μ) | 1.374 | 1.342 | 1.337 | 1.332 | 1.292 |
Coefficient of variation (δ) | 0.172 | 0.156 | 0.149 | 0.141 | 0.121 |
Distribution type | Normal distribution |
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Sadat, S.I.; Ding, F.-X.; Wang, M.; Lyu, F.; Akhunzada, K.; Xu, H.; Hui, B. Behavior and Reliable Design Methods of Axial Compressed Dune Sand Concrete-Filled Circular Steel Tube Columns. Appl. Sci. 2024, 14, 6939. https://doi.org/10.3390/app14166939
Sadat SI, Ding F-X, Wang M, Lyu F, Akhunzada K, Xu H, Hui B. Behavior and Reliable Design Methods of Axial Compressed Dune Sand Concrete-Filled Circular Steel Tube Columns. Applied Sciences. 2024; 14(16):6939. https://doi.org/10.3390/app14166939
Chicago/Turabian StyleSadat, Said Ikram, Fa-Xing Ding, Maolong Wang, Fei Lyu, Khalid Akhunzada, Hongchang Xu, and Baoye Hui. 2024. "Behavior and Reliable Design Methods of Axial Compressed Dune Sand Concrete-Filled Circular Steel Tube Columns" Applied Sciences 14, no. 16: 6939. https://doi.org/10.3390/app14166939
APA StyleSadat, S. I., Ding, F.-X., Wang, M., Lyu, F., Akhunzada, K., Xu, H., & Hui, B. (2024). Behavior and Reliable Design Methods of Axial Compressed Dune Sand Concrete-Filled Circular Steel Tube Columns. Applied Sciences, 14(16), 6939. https://doi.org/10.3390/app14166939