# Mechanical Behavior of Circular Steel Tubular Beam-Columns Corroded Uniformly in Atmospheric Environment

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Program

#### 2.1. Test Specimens

_{0}and W

_{1}are the mass of the same specimen before and after corrosion; D

_{w}is the corrosion ratio, according to Equation (1); N′

_{t}is the load carrying capacity of corroded specimen; Ψ

_{N}is the degradation ratio of load carrying capacity of specimen, Ψ

_{N}= (N

_{t}− N′

_{t})/N

_{t}× 100%; N

_{t}is the load carrying capacity of non-corroded specimen; k′

_{y}is the stiffness of corroded specimen; Ψ

_{k}is the degradation ratio of stiffness of specimen, Ψ

_{k}= (k

_{y}− k′

_{y})/k

_{y}× 100%; k

_{y}is the stiffness of non-corroded specimen; and μ is the ductility factor.

#### 2.2. Accelerated Corrosion Test

_{w}was calculated according to Equation (1).

#### 2.3. Material Properties

_{w}, and the test results were calculated based on the size of non-corroded specimens. The material tensile test was performed by using a universal testing machine (MTS), and the loading rate did not exceed 1.05 mm/min. The tensile fracture mode of non-corroded steel specimen was typical ductile fracture. With the increase of corrosion ratio, the necking phenomenon of corroded specimens obviously weakened, and the steel fracture gradually changed from ductile fracture to brittle fracture. The tensile fracture morphology of specimens is shown in Figure 2.

_{w}and f

_{y}, f

_{u}, E, and ψ were established by linear regression with the least square method, as shown in Equation (2). It can be found that, with the increase of corrosion degree, the mechanical properties of the corroded steel decrease significantly, and the degradation law of each parameter has a linear relationship with the corrosion ratio.

_{y}, f

_{u}, E, and ψ as well as f′

_{y}, f′

_{u}, E′, and ψ′ are the yield strength, tensile strength, elasticity modulus, and percentage elongation of no-corroded and corroded steel, respectively.

#### 2.4. Test Setup

#### 2.5. Instrumentation

## 3. Experimental Procedure and Observations

#### 3.1. Concentrically Loaded Specimen

#### 3.2. Eccentrically Loaded Specimen

## 4. Experimental Results and Analysis

#### 4.1. Load–Strain Curves

#### 4.1.1. Concentrically Loaded Specimen

_{1}and ε

_{2}are the longitudinal strain and transverse strain of concave side of mid-section, ε

_{3}and ε

_{4}are the longitudinal strain and transverse strain of convex side of mid-section, and the measured yield strain ε

_{y}is 1650 με. It can be seen that the strain change laws of specimens are basically the same. During the elastic phase, the strain of mid-section is synchronously increased, longitudinally compressed, and circumferentially tensioned. After entering the elastic–plastic stage, the stress state begins to change, the longitudinal compressive strain and the transverse tensile strain of convex side gradually decrease, while the longitudinal compressive strain and transverse tensile strain of concave side continue to increase, which is due to the additional bending moment caused by the second-order effect of member flexure. After the peak load, the longitudinal strain of the convex side gradually changes from compressive strain to tensile strain, and the transverse strain gradually changes from tensile strain to compressive strain. The longitudinal compressive strain and transverse tensile strain of concave side continue to increase. At peak load, the strain of each specimen is in the elastic–plastic stage.

#### 4.1.2. Eccentrically Loaded Specimen

#### 4.2. Load–Axial Displacement Curves

#### 4.3. Degradation Analysis of Load Carrying Capacity

#### 4.4. Degradation Analysis of Stiffness

## 5. Calculation of Load Carrying Capacity

#### 5.1. Comparison Calculations of Load Carrying Capacity

_{cs}and N

_{cm}are the load carrying capacities of specimens calculated considering the section reduction and the material degradation, respectively. It can be seen that the calculation results of three specifications have a certain safety margin, and N

_{cs}is slightly larger than N

_{cm}in the results, which are basically the same.

- (1)
- GB50017-2017$$\frac{N}{\phi A{f}_{y}}+\frac{\beta M}{{\gamma}_{m}W\left(1-0.8N/{N}_{Ex}^{\prime}\right){f}_{y}}\le 1.0$$$${N}_{Ex}^{\prime}={\pi}^{2}EA/\left(1.1{\lambda}_{x}^{2}\right)$$
^{2}; β is the equivalent moment factor; M is the required moment strength, N⋅mm; γ_{m}is the plastic adaption coefficient; and W is the gross section modulus, mm^{3}. - (2)
- EN 1993-1-1$$\frac{{N}_{Ed}}{\frac{{\chi}_{y}{N}_{Rk}}{{\gamma}_{M1}}}+{k}_{yy}\frac{{M}_{y,Ed}+\Delta {M}_{y,Ed}}{{\chi}_{LT}\frac{{M}_{y,Rk}}{{\gamma}_{M1}}}+{k}_{yz}\frac{{M}_{z,Ed}+\Delta {M}_{z,Ed}}{\frac{{M}_{z,Rk}}{{\gamma}_{M1}}}\le 1.0$$$$\frac{{N}_{Ed}}{\frac{{\chi}_{z}{N}_{Rk}}{{\gamma}_{M1}}}+{k}_{zy}\frac{{M}_{y,Ed}+\Delta {M}_{y,Ed}}{{\chi}_{LT}\frac{{M}_{y,Rk}}{{\gamma}_{M1}}}+{k}_{zz}\frac{{M}_{z,Ed}+\Delta {M}_{z,Ed}}{\frac{{M}_{z,Rk}}{{\gamma}_{M1}}}\le 1.0$$
_{Ed}, M_{y}_{,Ed}, and M_{z}_{,Ed}are the design values of the compression force and the maximum moments about the y-y and z-z axis along the member, respectively; N_{Rk}, M_{y}_{,Rk}, and M_{z}_{,Rk}are the characteristic value of resistance to compression and the characteristic value of resistance to bending moments about the y-y and z-z axis along the member, respectively; ΔM_{y}_{,Ed}and ΔM_{z}_{,Ed}are the moments due to the shift of the centroidal axis; χ_{y}and χ_{z}are the reduction factors due to flexural buckling; χ_{LT}is the reduction factor due to lateral torsional buckling; γ_{M}_{1}is the partial factor, 1.0; and k_{yy}, k_{yz}, k_{zy}, and k_{zz}are the interaction factors. - (3)
- ANSI/AISC 360-16When $\frac{{P}_{r}}{{P}_{c}}\ge 0.2$$$\frac{{P}_{r}}{{P}_{c}}+\frac{8}{9}\left(\frac{{M}_{rx}}{{M}_{cx}}+\frac{{M}_{ry}}{{M}_{cy}}\right)\le 1.0$$When $\frac{{P}_{r}}{{P}_{c}}<0.2$$$\frac{{P}_{r}}{2{P}_{c}}+\left(\frac{{M}_{rx}}{{M}_{cx}}+\frac{{M}_{ry}}{{M}_{cy}}\right)\le 1.0$$
_{r}is the required axial strength, kips (N); P_{c}is the design axial strength, P_{c}= ϕ_{c}P_{n}, kips (N); M_{r}is the required flexural strength, kip⋅in (N⋅mm); M_{c}is the design flexural strength, M_{c}= ϕ_{b}M_{n}, kip⋅in (N⋅mm); ϕ_{c}is the resistance factor for compression, 0.9; ϕ_{b}is the resistance factor for flexural, 0.9; x is the subscript relating symbol to major axis bending; and y is the subscript relating symbol to minor axis bending.

_{w}= 20%) of specimens is large, the load carrying capacities of specimens with different slenderness ratios and diameter-to-thickness ratios are compared, as shown in Figure 12 and Figure 13, where δ is the relative error, δ = (N

_{cs}− N

_{cm})/N

_{cs}× 100%; λ is the slenderness ratio, λ = l/i; l is the length of circular steel tube; i is the radius of gyration of circular steel tube; and D/t is the diameter-to-thickness ratio. As shown in Figure 12, with the increase of slenderness ratio, the difference between the two methods becomes smaller and smaller. With the slenderness ratio 66 as the limit, the difference between N

_{cs}and N

_{cm}decreases first and then increases with the ascent of eccentricity (e = 0~100 mm). Figure 13 shows that, when the diameter-to-thickness ratio is relatively small, the load carrying capacity calculated by three specification formulas considering the material degradation method is higher than that calculated by the section reduction method, but such a small diameter-to-thickness ratio is not usually used in practical engineering. In the common range of engineering, the calculation results of the three specifications are not the same, among which the difference of calculation results of GB 50017-2017 increases slightly with the increase of the diameter-to-thickness ratio, and the overall difference is not more than 3%. However, the calculation results of EN 1993-1-1 and ANSI/AISC 360-16 all show mutation points. This is mainly resulted from the finer classification of steel tubes in these two specification calculation formulas, and the calculation formulas or parameters of different categories of steel tubes are slightly different. When considering material degradation or section reduction to simulate uniform corrosion, two methods can be used to calculate different categories of steel tubes, and then different parameters or calculation formulas will be taken.

#### 5.2. Accuracy Analysis of Load Carrying Capacity Calculation Method

_{cs}by the above three specifications and the test results N

_{t}of specimens are shown in Figure 14. It can be found that the ultimate load carrying capacities of specimens calculated based on section reduction are close to the test results, and have a certain safety margin, indicating the feasibility of this method. Considering that N

_{cm}and N

_{cs}are basically the same, the method of material degradation for load carrying capacities can also be proved feasible. After comparison, the conservative degree of calculation results of three specifications indicates a descending order of ANSI/AISC 360-16, GB50017-2017, and EN 1993-1-1.

#### 5.3. Comparison of One-Sided Corrosion and Two-Sided Corrosion

_{co}and N

_{ct}are the load carrying capacities of the specimens calculated by considering one-sided corrosion and two-sided corrosion, respectively. It can be seen that N

_{ct}is slightly larger than N

_{co}, but the results are basically the same.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The tensile fracture morphology of specimens: (

**a**) D

_{w}= 0.00%; (

**b**) D

_{w}= 4.54%; and (

**c**) D

_{w}= 9.41%.

**Figure 4.**Experimental phenomena of the specimen C0-90: (

**a**) elastic stage; (

**b**) failure stage; and (

**c**) rust peeling.

**Figure 5.**Experimental phenomena of the specimen C15-90: (

**a**) elastic stage; (

**b**) failure stage; and (

**c**) rust peeling.

**Figure 6.**Load–strain curves of specimens: (

**a**) C0-0; (

**b**) C0-30; (

**c**) C0-90; (

**d**) C0-180; (

**e**) C0-270; and (

**f**) C0-360.

**Figure 7.**Load–strain curves of specimens: (

**a**) C15-0; (

**b**) C15-30; (

**c**) C15-90; (

**d**) C15-180; (

**e**) C15-270; and (

**f**) C15-360.

**Figure 8.**Load–strain curves of specimens: (

**a**) C35-0; (

**b**) C35-30; (

**c**) C35-90; (

**d**) C35-180; (

**e**) C35-270; and (

**f**) C35-360.

**Figure 9.**Load–axial displacement curves of specimens: (

**a**) concentrically loaded; (

**b**) eccentricity of 15 mm; and (

**c**) eccentricity of 35 mm.

**Figure 12.**Relationship between δ and λ: (

**a**) GB50017-2017; (

**b**) EN 1993-1-1; and (

**c**) ANSI/AISC 360-16.

**Figure 13.**Relationship between δ and D/t: (

**a**) GB50017-2017; (

**b**) EN 1993-1-1; and (

**c**) ANSI/AISC 360-16.

**Figure 14.**Comparison of the tested results and load carrying capacity predicted by using the section reduction method: (

**a**) GB50017 – 2017; (

**b**) EN 1993-1-1; and (

**c**) ANSI/AISC 360-16.

**Figure 15.**Comparison of the load carrying capacity of the specimens with one-sided corrosion and with two-sided corrosion: (

**a**) GB50017 – 2017; (

**b**) EN 1993-1-1; and (

**c**) ANSI/AISC 360-16.

**Figure 16.**Relationship between δ and λ: (

**a**) GB50017-2017; (

**b**) EN 1993-1-1; and (

**c**) ANSI/AISC 360-16.

**Figure 17.**Relationship between δ and D/t: (

**a**) GB50017-2017; (

**b**) EN 1993-1-1; and (

**c**) ANSI/AISC 360-16.

Specimen ID | D/mm | t/mm | e/mm | T/d | W_{0}/kg | W_{1}/kg | D_{w}/(%) | N′_{t}/kN | Ψ_{N}/(%) | k′_{y}/(×10^{7} N/m) | Ψ_{k}/(%) | μ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

C0-0 | 89.82 | 4.07 | 0 | 0 | 9.02 | 9.02 | 0 | 391.5 | — | 13.73 | — | 1.59 |

C0-30 | 89.74 | 4.28 | 0 | 30 | 9.41 | 8.96 | 4.78 | 377.9 | 3.47 | 13.09 | 4.63 | 1.35 |

C0-90 | 89.10 | 4.44 | 0 | 90 | 9.44 | 8.87 | 6.04 | 363.8 | 7.08 | 12.12 | 11.71 | 1.47 |

C0-180 | 89.00 | 4.24 | 0 | 180 | 8.83 | 7.59 | 13.99 | 313.3 | 19.97 | 11.27 | 17.92 | 1.62 |

C0-270 | 89.06 | 4.01 | 0 | 270 | 8.65 | 7.15 | 16.81 | 295.6 | 24.50 | 10.28 | 25.13 | 1.47 |

C0-360 | 89.30 | 4.15 | 0 | 360 | 8.48 | 6.77 | 20.22 | 316.8 | 19.08 | 11.12 | 19.02 | 1.75 |

C15-0 | 89.80 | 4.01 | 15 | 0 | 8.90 | 8.90 | 0 | 239.8 | — | 9.72 | — | 4.45 |

C15-30 | 89.36 | 3.98 | 15 | 30 | 8.77 | 8.45 | 3.65 | 238.1 | 0.71 | 9.36 | 3.66 | 3.83 |

C15-90 | 89.04 | 4.1 | 15 | 90 | 8.54 | 7.97 | 6.67 | 217.8 | 9.17 | 9.39 | 3.40 | 4.39 |

C15-180 | 89.02 | 4.2 | 15 | 180 | 8.50 | 7.38 | 13.23 | 191.6 | 20.10 | 7.25 | 25.42 | 3.24 |

C15-270 | 89.20 | 4.18 | 15 | 270 | 8.49 | 6.89 | 18.85 | 191.7 | 20.06 | 7.28 | 25.10 | 2.80 |

C15-360 | 89.22 | 4.12 | 15 | 360 | 8.42 | 6.76 | 19.66 | 181.3 | 24.40 | 8.18 | 15.82 | 5.01 |

C35-0 | 89.60 | 3.86 | 35 | 0 | 8.73 | 8.73 | 0 | 152.4 | — | 6.39 | — | 7.17 |

C35-30 | 89.78 | 4.03 | 35 | 30 | 8.97 | 8.65 | 3.56 | 166.7 | −9.38 | 6.20 | 2.98 | 6.62 |

C35-90 | 89.84 | 4.43 | 35 | 90 | 9.01 | 8.52 | 5.49 | 170.5 | −11.88 | 6.02 | 5.81 | 6.11 |

C35-180 | 89.08 | 4.41 | 35 | 180 | 8.65 | 7.16 | 17.17 | 143.1 | 6.10 | 4.96 | 22.49 | 5.71 |

C35-270 | 89.60 | 3.93 | 35 | 270 | 8.58 | 7.12 | 17.12 | 140.5 | 7.81 | 5.00 | 21.80 | 7.58 |

C35-360 | 89.16 | 4.07 | 35 | 360 | 8.52 | 6.72 | 21.12 | 133.8 | 12.20 | 4.28 | 33.03 | 5.77 |

Group ID | D_{w}/(%) | E/(×10^{5} MPa) | f_{y}/MPa | f_{u}/MPa | ψ/(%) |
---|---|---|---|---|---|

A1 | 0.00 | 2.02 | 330.43 | 467.00 | 31.47 |

A2 | 2.42 | 1.95 | 332.29 | 479.03 | 35.64 |

A3 | 3.11 | 1.96 | 303.51 | 481.71 | 32.47 |

A4 | 4.54 | 1.98 | 329.17 | 449.65 | 31.03 |

A5 | 9.41 | 1.81 | 299.16 | 418.33 | 22.94 |

A6 | 9.74 | 1.80 | 286.97 | 431.09 | 27.62 |

A7 | 11.35 | 1.71 | 288.40 | 395.46 | 25.39 |

**Table 3.**Analysis results of specimens by using section reduction method and material degradation method.

Specimen ID | N_{t}/kN | GB 50017-2017 | EN 1993-1-1 | ANSI/AISC 360-16 | |||
---|---|---|---|---|---|---|---|

N_{cs}/kN | N_{cm}/kN | N_{cs}/kN | N_{cm}/kN | N_{cs}/kN | N_{cm}/kN | ||

C0-0 | 391.5 | 341.5 | 341.5 | 342.8 | 342.8 | 302.4 | 302.4 |

C0-30 | 377.9 | 339.8 | 338.8 | 341.1 | 340.0 | 300.8 | 299.9 |

C0-90 | 363.8 | 344.0 | 342.7 | 345.2 | 343.9 | 304.3 | 303.2 |

C0-180 | 313.3 | 299.8 | 296.6 | 300.8 | 297.6 | 265.2 | 262.4 |

C0-270 | 295.6 | 275.0 | 271.0 | 275.9 | 272.0 | 243.3 | 239.8 |

C0-360 | 316.8 | 272.7 | 267.7 | 273.6 | 268.7 | 241.2 | 236.9 |

C15-0 | 239.8 | 203.1 | 203.1 | 222.3 | 222.3 | 193.5 | 193.5 |

C15-30 | 238.1 | 192.4 | 191.9 | 210.5 | 210.0 | 183.3 | 182.9 |

C15-90 | 217.8 | 190.0 | 189.2 | 207.8 | 207.0 | 181.1 | 180.3 |

C15-180 | 191.6 | 179.8 | 178.0 | 196.6 | 194.7 | 171.3 | 169.7 |

C15-270 | 191.7 | 167.4 | 164.8 | 183.0 | 180.2 | 159.5 | 157.0 |

C15-360 | 181.3 | 163.6 | 160.8 | 178.8 | 175.9 | 155.8 | 153.2 |

C35-0 | 152.4 | 130.3 | 130.3 | 146.2 | 146.2 | 129.9 | 129.9 |

C35-30 | 166.7 | 130.8 | 130.6 | 146.8 | 146.5 | 130.4 | 130.1 |

C35-90 | 170.5 | 139.5 | 139.0 | 156.4 | 156.0 | 139.0 | 138.6 |

C35-180 | 143.1 | 119.0 | 117.5 | 133.3 | 131.6 | 118.6 | 117.1 |

C35-270 | 140.5 | 108.7 | 107.2 | 121.9 | 120.2 | 108.3 | 106.8 |

C35-360 | 133.8 | 105.6 | 103.6 | 118.2 | 116.1 | 105.2 | 103.2 |

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## Share and Cite

**MDPI and ACS Style**

Wu, Z.; Wei, Y.; Wang, X.; Huang, C.; Jiang, S.-F.
Mechanical Behavior of Circular Steel Tubular Beam-Columns Corroded Uniformly in Atmospheric Environment. *Appl. Sci.* **2020**, *10*, 1998.
https://doi.org/10.3390/app10061998

**AMA Style**

Wu Z, Wei Y, Wang X, Huang C, Jiang S-F.
Mechanical Behavior of Circular Steel Tubular Beam-Columns Corroded Uniformly in Atmospheric Environment. *Applied Sciences*. 2020; 10(6):1998.
https://doi.org/10.3390/app10061998

**Chicago/Turabian Style**

Wu, Zhaoqi, Yuan Wei, Xintao Wang, Chao Huang, and Shao-Fei Jiang.
2020. "Mechanical Behavior of Circular Steel Tubular Beam-Columns Corroded Uniformly in Atmospheric Environment" *Applied Sciences* 10, no. 6: 1998.
https://doi.org/10.3390/app10061998