# Axial Compression Performance of Square Thin Walled Concrete-Filled Steel Tube Stub Columns with Reinforcement Stiffener under Constant High-Temperature

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Study

#### 2.1. Design and Fabrication of Specimens

#### 2.2. Testing Setup

#### 2.3. Test Process

#### 2.4. Experimental Results and Failure Modes

#### 2.5. Analysis of Test Results

_{y}), yield displacement (△

_{y}), peak load (i.e. residual bearing capacity N

_{u}after fire exposure), peak displacement (△u), and 0.85 Nu after peak load (△0.85) and ductility coefficient (μ

_{△}with the expression in Equation (1)). The geometric drawing method was employed to find the yield load and the yield displacement of the load–displacement curve by making a characteristic line, as shown in Figure 7. First, the peak tangent U was used as the horizontal tangent of the curve, intersecting the origin tangent (EA) at point A, passing the point A as the vertical axis of the displacement axis, intersecting the curve at point B, connecting the line OB to the line AU at point C, and passing the point C. The vertical line of the displacement axis intersects the point Y, which is the yield point. Hence, the horizontal and vertical coordinates Δy and N

_{y}corresponding to the Y point are the yield displacement and the yield load, respectively.

## 3. Numerical Analysis of Finite Field Model

#### 3.1. Model Establishment

#### 3.1.1. Temperature Field Model

^{2}·°C) [25]. The interaction between the concrete and the inner surface of the steel tube is determined by the interaction. The means of heat transmission is heat conduction. Surface-to-surface contact is adopted. The outside surface of the concrete is the main surface, and the inner surface of the steel tube is the secondary surface. Due to the shrinkage deformation of the concrete during the curing process of the specimen, the interface between the steel tube and the concrete has a gap, and a series of physical and chemical reactions occur inside the specimen at high temperature, which changes the compositions, contents, and states of the media at the interface, and is sometimes accompanied by water migration. In this study, the contact thermal resistance of the steel tube and concrete in the CFST columns is set as 0.01 (m

^{2}·°C)/W.

#### 3.1.2. Mechanical Field Model

_{s}denotes the steel stress, ε

_{sσ}denotes the steel strain, ε

_{p}denotes the steel strain corresponding to maximum stress, and T denotes the temperature. In this study, ${\epsilon}_{\mathrm{p}}=4\times {10}^{-6}{f}_{y}$, $f\left(T,0.001\right)=\left(50-0.04T\right)\times \left[1-\mathrm{exp}\left(-30+0.03T\right)\sqrt{0.001}\right]\times 6.9$, and $f\left[T,\left({\epsilon}_{\mathrm{s}\mathsf{\sigma}}-{\epsilon}_{\mathrm{p}}+0.001\right)\left]=\left(50-0.04T\right)\times \right[1-\mathrm{exp}\left(-30+0.03T\right)\sqrt{{\epsilon}_{\mathrm{s}\mathsf{\sigma}}-{\epsilon}_{\mathrm{p}}+0.001}\right]\times 6.9$.

_{sth}denotes free expansion strain of the steel.

_{c}denotes the concrete stress, ε

_{cσ}denotes the concrete strain, and ε

_{max}denotes the concrete strain corresponding to maximum stress. In this study, ${\epsilon}_{\mathrm{max}}=0.0025+\left(6T+0.04{T}^{2}\right)\times {10}^{-6}$. ${f}_{c}^{\prime}\left(T\right)$ denotes the compressive strength of concrete at temperature T, and its mathematical expression is given as follows.

_{th}denotes free expansion strain of the concrete.

_{ctr}denotes transient strain of the concrete.

_{ct}denotes the concrete stress in tension, ε denotes the tensile strain of the concrete, ε

_{cr}denotes the concrete tensile strain corresponding to maximum stress, E

_{c}denotes the elastic modulus of the concrete, and ${f}_{t}^{\prime}$ denotes axial tensile strength. Here, ${f}_{t}^{\prime}=0.09{f}_{c}^{\prime}$ and ${\epsilon}_{cr}={f}_{t}^{\prime}\left(T\right)/{E}_{c}\left(T\right)$.

- (1)
- The contacts between inner surfaces of the steel hollow section and the concrete are set as surface-to-surface contact. The normal contact property is general hard contact while the tangential contact property is defined by friction. The interfacial friction coefficient is set as 0.35 [29].
- (2)
- The concrete and the rebar are set as embedding constraints.
- (3)
- The binding constraint tie is set between the steel tube and the steel bar.

#### 3.2. Validation of Finite Element Models

#### 3.3. Mechanism Analysis

#### 3.3.1. Stress Analysis of Concrete

#### 3.3.2. Influence of Reinforcing Ribs

#### 3.3.3. Interaction between Concrete and Steel Tubular

## 4. Conclusions

- (1)
- The buckling curvatures of the steel tube are in the middle of the column and the adjacent areas, the locations of which are not the same on different sides. The buckling curvature of the non-stiffened specimen is higher than that of the stiffened specimen. There is no obvious damage of the concrete, except the damage on the opposite sides of the steel tube buckling curvature position of the oblique line, which forms the shear surface. Consequently, the failure of each specimen is shear damage.
- (2)
- Residual bearing capacity and compressive stiffness of the test specimen decreases significantly with the increase of the temperature. Compared with the specimen under normal temperature, the ultimate bearing capacities of the specimens at 100 °C, 200 °C, 400 °C, 600 °C, and 800 °C decrease by 7.72%, 12.3%, 17.64%, 35.55%, and 75.83%, and the compressive stiffness values decrease by 11.79%, 14.83%, 63.12%, 72.24%, and 90.49%, respectively. Among them, when the temperature exceeds 200 °C, the mechanical properties of the specimen begin to be greatly reduced, the ultimate bearing capacity decreases rapidly, and the ductility coefficient decreases with the increase of the temperature. The addition of stiffened steel bars has a positive impact on improving the mechanical properties of concrete filled steel tubes. The critical temperature of the test specimen is between 200 °C and 400 °C. It shows that the decrease rates of residual bearing capacity and compressive stiffness of the specimen increase after the temperature exceeds 200 °C. This is mainly because the concrete strength decreases rapidly after the furnace temperature exceeds the critical temperature.
- (3)
- Using the finite element software ABAQUS, the model of thin-walled square steel tubular short column with stiffening bars under constant temperature is established. The stress distribution of the concrete, steel tube, and reinforcing rib of the specimen were analyzed. With the increase of temperature, the longitudinal stress gradient of the concrete increases while the stress value decreases. Compared with non-stiffened specimens, the longitudinal stress in the center of the section increases, the stress gradient increases, and the overall distribution tends to be homogeneous. The transverse restraint of the stiffener can restrict the outer buckling of the steel tube and change the buckling mode. The stress distribution of the steel plate becomes relatively uniform and the restraint effect of the concrete is enhanced due to setting of the reinforcing rib.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**View of specimens after test (

**a**) DS-20; (

**b**) DS-100; (

**c**) DS-200; (

**d**) DS-200-0; (

**e**) DS-400; (

**f**) DS-600; (

**g**) DS-600-0; (

**h**) DS-800.

**Figure 5.**View of specimens after opening steel tubes (

**a**) DS-20; (

**b**) DS-100; (

**c**) DS-200; (

**d**) DS-200-0; (

**e**) DS-400; (

**f**) DS-600; (

**g**) DS-600-0; (

**h**) DS-800.

**Figure 6.**Load–displacement diagram (

**a**) effects of different temperatures (

**b**) effects of stiffening rib of steel bar.

**Figure 9.**Load–displacement of experiment and numerical simulation (

**a**) DS-20; (

**b**) DS-100; (

**c**) DS-200; (

**d**) DS-200-0; (

**e**) DS-400; (

**f**) DS-600; (

**g**) DS-600-0; (

**h**) DS-800.

**Figure 10.**Load-strain curve comparisons between experimental and numerical results (

**a**); SC-1 (

**b**) SC-2; (

**c**) SC-3; (

**d**) SC-4; (

**e**) SC-5; (

**f**) SC-6.

**Figure 11.**Stress distribution of concrete in the middle cross section of columns (

**a**) DS-20-0.75; (

**b**) DS-20-1; (

**c**) DS-100-0.75; (

**d**) DS-100-1; (

**e**) DS-200-0.75; (

**f**) DS-200-1; (

**g**) DS-400-0.75; (

**h**) DS-400-1; (

**i**) DS-600-0.75; (

**j**) DS-600-1; (

**k**) DS-800-0.75; (

**l**) DS-800-1.

**Figure 12.**The lateral stress distribution of concrete (

**a**) DS-20-0.75; (

**b**) DS-20-1; (

**c**) DS-100-0.75; (

**d**) DS-100-1; (

**e**) DS-200-0.75; (

**f**) DS-200-1; (

**g**) DS-400-0.75; (

**h**) DS-400-1; (

**i**) DS-600-0.75; (

**j**) DS-600-1; (

**k**) DS-800-0.75; (

**l**) DS-800-1.

**Figure 13.**The vertical stress distribution of concrete (

**a**) DS-200-0-0.75; (

**b**) DS-200-0-1; (

**c**) DS-200-0.75; (

**d**) DS-200-1; (

**e**) DS-600-0-0.75; (

**f**) DS-600-0-1; (

**g**) DS-600-0.75; (

**h**) DS-600-1.

**Figure 14.**The lateral stress distribution of concrete (

**a**) DS-200-0-0.75; (

**b**) DS-200-0-1; (

**c**) DS-200-0.75; (

**d**) DS-200-1.

**Figure 15.**The lateral stress distribution of concrete (

**a**) DS-600-0-0.75 (

**b**) DS-600-0-1 (

**c**) DS-600-0.75 (

**d**) DS-600-1.

**Figure 16.**The vertical stress distribution of concrete (

**a**) DS-200-0-0.75; (

**b**) DS-200-0-1; (

**c**) DS-200-0.75; (

**d**) DS-200-1; (

**e**) DS-600-0-0.75; (

**f**) DS-600-0-1; (

**g**) DS-600-0.75; (

**h**) DS-600-1.

**Figure 17.**The lateral stress distribution of concrete (

**a**) DS-200-0-0.75; (

**b**) DS-200-0-1; (

**c**) DS-200-0.75; (

**d**) DS-200-1; (

**e**) DS-600-0-0.75; (

**f**) DS-600-0-1; (

**g**) DS-600-0.75; (

**h**) DS-600-1.

**Figure 18.**The Mises stress distribution of the steel tube (

**a**) DS-200-0-0.75; (

**b**) DS-200-0-1; (

**c**) DS-200-0.75; (

**d**) DS-200-1.

**Figure 19.**The Mises stress distribution of the steel tube (

**a**) DS-600-0-0.75 (

**b**) DS-600-0-1 (

**c**) DS-600-0.75 (

**d**) DS-600-1.

**Figure 20.**The Mises stress distribution of bar stiffeners (

**a**) DS-200-0.75; (

**b**) DS-200-1; (

**c**) DS-600-0.75; (

**d**) DS-600-1.

**Figure 21.**Distributions of the restraining force of steel tube to concrete (

**a**) DS-200-REF; (

**b**) DS-200; (

**c**) DS-600-REF; (

**d**) DS-600.

**Figure 22.**Relationship between restraining force and axial displacement (

**a**) middle of column; (

**b**) top of column.

Specimen | B × t_{s} × H(mm × mm × mm) | Diameter of Stiffening Bar d × Spacing (mm × mm) | Temperature (°C) |
---|---|---|---|

DS-20 | 160 × 2 × 480 | 6 × 80 | 20 (Ambient Temperature) |

DS-100 | 160 × 2 × 480 | 6 × 80 | 100 |

DS-200-0 | 160 × 2 × 480 | none | 200 |

DS-200 | 160 × 2 × 480 | 6 × 80 | 200 |

DS-400 | 160 × 2 × 480 | 6 × 80 | 400 |

DS-600-0 | 160 × 2 × 480 | none | 600 |

DS-600 | 160 × 2 × 480 | 6 × 80 | 600 |

DS-800 | 160 × 2 × 480 | 6 × 80 | 800 |

^{a}Named specimen as follows: DS denotes square column, the first number represents heated temperature (°C), and the second number represents whether or not stiffening column.

Steel Types | f_{y} (Mpa) | f_{u} (Mpa) | E_{s} (Mpa) | Elongation δ_{10} (%) |
---|---|---|---|---|

Steel plate (t_{s} = 2 mm) | 338.5 | 451.3 | 197600 | 38.79 |

Steel bar (d_{s} = 6 mm) | 376.7 | 467.8 | 184300 | 26.7 |

F_{cu}_{,28}/(Mpa) | f_{cu,test} (Mpa) | E_{c}_{,28} (× 10^{4} Mpa) | E_{c},_{test} (× 10^{4} Mpa) | Concrete Age (Day) |
---|---|---|---|---|

32.3 | 41.9 | 2.241 | 3.527 | 97 |

Specimen | DS-20 | DS-100 | DS-200-0 | DS-200 | DS-400 | DS-600-0 | DS-600 | DS-800 |
---|---|---|---|---|---|---|---|---|

Temperature (°C) | 20 | 100 | 200 | 200 | 400 | 600 | 600 | 800 |

Time (min) | 0 | 1 | 2.5 | 2.5 | 5 | 7.5 | 7.5 | 10 |

Specimen | EA (10^{6} kN) | N_{y} (kN) | △_{y} (mm) | N_{u} (kN) | △_{u} (mm) | △_{0.85} (mm) | μ_{△} |
---|---|---|---|---|---|---|---|

DS-20 | 0.789 | 1079.487 | 1.763 | 1177.53 | 2.92 | 3.62 | 1.24 |

DS-100 | 0.696 | 951.060 | 2.208 | 1086.63 | 3.15 | 4.91 | 1.56 |

DS-200 | 0.672 | 858.748 | 2.725 | 1032.73 | 5.46 | 7.63 | 1.40 |

DS-400 | 0.291 | 763.468 | 6.822 | 969.78 | 12.61 | 15.93 | 1.26 |

DS-600 | 0.219 | 568.282 | 8.901 | 758.89 | 14.59 | 19.79 | 1.36 |

DS-800 | 0.075 | 215.331 | 9.303 | 284.62 | 15.85 | 21.25 | 1.34 |

DS-200-0 | 0.675 | 847.427 | 2.749 | 1050.72 | 4.15 | 6.06 | 1.46 |

DS-600-0 | 0.221 | 523.305 | 7.494 | 695.92 | 12.87 | 17.22 | 1.34 |

**Table 6.**The parameters of the specimens in ref. [30].

Specimen | D (mm) | t (mm) | f_{cu} (MPa) | f_{y} (MPa) | Temperature (°C) |
---|---|---|---|---|---|

SC-1 | 133 | 4.5 | 40.8 | 324 | 20 |

SC-2 | 133 | 4.5 | 40.8 | 324 | 200 |

SC-3 | 133 | 4.5 | 40.8 | 324 | 300 |

SC-4 | 133 | 4.5 | 40.8 | 324 | 500 |

SC-5 | 133 | 4.5 | 40.8 | 324 | 600 |

SC-6 | 133 | 4.5 | 40.8 | 324 | 900 |

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**MDPI and ACS Style**

Lyu, X.; Xu, Y.; Xu, Q.; Yu, Y.
Axial Compression Performance of Square Thin Walled Concrete-Filled Steel Tube Stub Columns with Reinforcement Stiffener under Constant High-Temperature. *Materials* **2019**, *12*, 1098.
https://doi.org/10.3390/ma12071098

**AMA Style**

Lyu X, Xu Y, Xu Q, Yu Y.
Axial Compression Performance of Square Thin Walled Concrete-Filled Steel Tube Stub Columns with Reinforcement Stiffener under Constant High-Temperature. *Materials*. 2019; 12(7):1098.
https://doi.org/10.3390/ma12071098

**Chicago/Turabian Style**

Lyu, Xuetao, Yang Xu, Qian Xu, and Yang Yu.
2019. "Axial Compression Performance of Square Thin Walled Concrete-Filled Steel Tube Stub Columns with Reinforcement Stiffener under Constant High-Temperature" *Materials* 12, no. 7: 1098.
https://doi.org/10.3390/ma12071098