# Eccentric Compressive Behavior of Round-Ended Rectangular Concrete-Filled Steel Tubes with Different Central Angles

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Research Methods

#### 2.1. Experimental Program

#### 2.1.1. Specimens Preparation

^{3}); sand (677 kg/m

^{3}); aggregate (1152 kg/m

^{3}); water (180 kg/m

^{3}) in a 1:1.73:2.95:0.46 ratio. The mean cubic compressive strength, f

_{cu}, was 30 MPa. Three cylinders with a diameter of 150 mm and a height of 300 mm were used to conduct the axial compressive experiment and provided the mean cylindrical strength ${f}_{\mathrm{c}}^{\prime}=$ 25.7 MPa.

#### 2.1.2. Test Method

#### 2.2. Finite Element Method (FEM)

_{c}is not suitable for a CDP model [24]; however, an equation between d and d

_{c}was proposed by the Sidoroff energy equivalent theory [25,26], which is expressed as:

## 3. Results and Discussion

_{u}, which possibly corresponded with the development of local buckling at the mid-length.

_{m}is the lateral displacement and N

_{u}is the peak axial load. The curves were in good agreement with the half-sinusoid curves. It is feasible to predict the peak load and lateral deflection of the RRCFST columns under eccentric compression.

#### 3.1. Failure Model

_{y}) is required for proper material use.

#### 3.2. Axial Load and Mid-Length Lateral Deformation Relationship

_{m}) curves are exhibited in Figure 8. The initials EX and FEM stand for experimental and finite element model findings, respectively. FEM ignores the specimen’s original defects; thus, the FEM curves in the elastic–plastic range are somewhat higher than the experimental curves in Figure 8a–c.

_{m}curves for specimens with an eccentric ratio of 0.3 and central angles of 60° or 120° exhibited the same characteristics as in Figure 8a, implying that the eccentric ratio did not influence the RRCFST column deformation law.

_{u}/kN) for the FEM (N

_{uf}/kN) and experiment (N

_{ue}/kN) specimens are compared in Table 3. The average ratio of N

_{uf}/N

_{ue}is 1.014, with a dispersion coefficient of 0.042. A good agreement is presented between the finite element model and experiment results of eccentric bearing capacity.

#### 3.3. Parameter Analysis on Material Utilization

_{p}is the plastic compressive resistance of the column cross-section, and can be defined as follows [30]:

#### 3.4. Confinement Effect

#### 3.5. Calculation and Verified of Eccentric Compression Bearing Capacity

_{1}is the reduction factor of the slenderness ratio, equal 1.0 for stub columns, φ

_{e}is reduction factor of eccentric ratio which is fitting by the experimental results and can be expressed as Equation (14):

_{ua}is the axial bearing capacity of RRCFST columns with different central angle, which had been deduced in reference [31], and determined by:

## 4. Conclusions

- (1)
- The typical failure mode of RRCFST stub columns is buckling of the steel tube in the compression zone; this local buckling is accompanied by concrete shear damage when the θ is minor. Increased θ, reduced κ and enhanced f
_{y}contribute to improving the local buckling resistance of RRCFSTs, while optimizing the design parameter combinations between them needs further study; - (2)
- Specimens in FEM and experiment reveal similar deformation and bearing capacity, which represents another possible method to study the eccentric performance of RRCFSTs in addition to experiments: numerical simulations;
- (3)
- Typical ductility quantification methods are ineffective for RRCFSTs under static load due to the favorable post-yield deformation ability, and additional tests are necessary to evaluate their performance and response during dynamic activity;
- (4)
- Material efficiency can be improved with an increased θ and a reduced κ. SI, i.e., material utilization, rises by 0.2% to 3% for every 60° increase in θ, which is particularly noticeable with a large eccentricity. And it reduces by 2.7% to 8.3% for a 0.5 increase in aspect ratio, but there is an unknown tendency as the steel strength changes. SI is always less than 1.0 when axial force and bending moment work together;
- (5)
- Study of the confined effect verified the assumptions discussed in the failure modes. A smaller κ and larger θ contribute to enhancing the confinement effect at the round-ended part, resulting in less local buckling occurring at columns. However, local buckling still occurred in the rectangular part due to the weaker interaction relationship between the steel tube and concrete;
- (6)
- Current codes cannot be used to calculate the eccentric ultimate bearing capacity of RRCFST stub columns with different center angles. A simplified calculating approach has been demonstrated and validated in this study.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**The strain curves of the normal section of the RRCFST columns: (

**a**) PY0.5−180−e2; (

**b**) PY1−180−e1−Q235.

**Figure 7.**Failure modes: (

**a**) κ = 1 and 1.5, with different θ and f

_{y}; (

**b**) κ = 0.5, with different θ and eccentric ratio; (

**c**) Different f

_{y}.

**Figure 8.**Axial load vs. mid-length lateral displacement curves: (

**a**) κ = 1, with different θ; (

**b**) κ = 0.5, with different θ; (

**c**) θ = 180°, with different θ; (

**d**) Different f

_{y}.

**Figure 9.**SI for columns with different paraments: (

**a**) central angle, θ; (

**b**) aspect ratio of cross-section, κ; (

**c**) strength of steel tube, f

_{y}.

**Figure 11.**Contact stress between steel tube and concrete at mid-length for RRCFST columns with different parameters: (

**a**) central angle; (

**b**) aspect ratio.

Identifier | H × B × L/mm^{3} | (κ, θ) | i/mm | e/2i | e/mm |
---|---|---|---|---|---|

PY1-0-e1 | 153 × 148 × 450 | (1, 0) | 43.35 | 0.15 | 13.01 |

PY1-60-e1 | 189 × 153 × 550 | (1, 60) | 51.48 | 0.15 | 15.44 |

PYRE1-60-e1 | 187 × 151 × 550 | (1, 60) | 51.48 | 0.15 | 15.44 |

PY1-120-e1 | 232 × 152 × 650 | (1, 120) | 62.19 | 0.15 | 18.66 |

PYRE1-120-e1 | 235 × 150 × 650 | (1, 120) | 62.19 | 0.15 | 18.66 |

PY0.5-180-e1-Q235 | 225 × 150 × 675 | (1, 180) | 57.96 | 0.15 | 17.39 |

PY1-180-e1-Q235 | 300 × 150 × 920 | (1, 180) | 79.02 | 0.15 | 25 |

PY1.5-180-e1-Q235 | 375 × 150 × 1160 | (1.5, 180) | 100.31 | 0.15 | 30.09 |

PY1-60-e2 | 188 × 152 × 550 | (1, 60) | 51.48 | 0.3 | 30.89 |

PY1-60-e2-Q235 | 188 × 152 × 550 | (1, 60) | 51.48 | 0.3 | 30.89 |

PY1-120-e2 | 237 × 150 × 650 | (1, 120) | 62.19 | 0.3 | 37.31 |

PY1-120-e2-Q235 | 235 × 150 × 650 | (1, 120) | 62.19 | 0.3 | 37.31 |

PY0.5-60-e2 | 110 × 153 × 445 | (0.5, 60) | 30.1 | 0.3 | 18.06 |

PY0.5-120-e2 | 156 × 155 × 500 | (0.5, 120) | 41 | 0.3 | 24.60 |

PY0.5-180-e2 | 224 × 152 × 650 | (0.5, 180) | 58 | 0.3 | 34.80 |

Identifier | f_{y}/MPa | f_{u}/MPa | E_{s}/GPa | γ |
---|---|---|---|---|

Q235 | 279 | 418.5 | 225 | 0.27 |

Q345 | 361 | 541.5 | 240 | 0.27 |

Identifier | N_{uf} | N_{ue} | Ratio (N_{uf}/N_{ue}) |
---|---|---|---|

PY1-0-e1 | 1140 | 1187 | 0.960 |

PY1-60-e1 | 1301 | 1287 | 1.011 |

PYRE1-60-e1 | 1301 | 1306 | 0.996 |

PY1-120-e1 | 1510 | 1450 | 1.041 |

PYRE1-120-e1 | 1510 | 1489 | 1.014 |

PY0.5-180-e1-Q235 | 1406 | 1478 | 0.951 |

PY1-180-e1-Q235 | 1758 | 1638 | 1.073 |

PY1.5-180-e1-Q235 | 1825 | 1732 | 1.054 |

PY1-60-e2 | 1086 | 1136 | 0.956 |

PY1-60-e2-Q235 | 957 | 981 | 0.976 |

PY1-120-e2 | 1275 | 1248 | 1.022 |

PY1-120-e2-Q235 | 1116 | 1020 | 1.094 |

PY0.5-60-e2 | 715 | 717 | 0.997 |

PY0.5-120-e2 | 952 | 954 | 0.998 |

PY0.5-180-e2 | 1278 | 1205 | 1.061 |

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**MDPI and ACS Style**

Ren, Z.; Li, Q.; Wang, G.; Wei, W.; Abbas, M.A.A.M.
Eccentric Compressive Behavior of Round-Ended Rectangular Concrete-Filled Steel Tubes with Different Central Angles. *Materials* **2022**, *15*, 456.
https://doi.org/10.3390/ma15020456

**AMA Style**

Ren Z, Li Q, Wang G, Wei W, Abbas MAAM.
Eccentric Compressive Behavior of Round-Ended Rectangular Concrete-Filled Steel Tubes with Different Central Angles. *Materials*. 2022; 15(2):456.
https://doi.org/10.3390/ma15020456

**Chicago/Turabian Style**

Ren, Zhigang, Qi Li, Gaoyu Wang, Wei Wei, and Mohammed A. A. M. Abbas.
2022. "Eccentric Compressive Behavior of Round-Ended Rectangular Concrete-Filled Steel Tubes with Different Central Angles" *Materials* 15, no. 2: 456.
https://doi.org/10.3390/ma15020456