# A Study on the Strength and Fatigue Properties of Seven-Wire Strands in Hangers under Lateral Bending

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## Abstract

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## 1. Introduction

## 2. Discussion on the Types and Boundary Conditions of Hangers, as Well as Arch Bridge Structures

#### 2.1. Type of Hangers

#### 2.2. Boundary Conditions of the Hanger and Bridge Deck Structure

## 3. Study on the Main Bending Form of Hangers

#### 3.1. Theoretical Formulation for the Bending Angle and Maximum Bending Stress of Hangers

_{1}of the hangers caused by the longitudinal deformation of the bridge decks (as shown in Figure 6) of the i-th hanger on the right side of the center of the bridge is

#### 3.2. Validation of the Theoretical Formulations by FEM and Defining the Main Form of the Bending of Hangers

## 4. Finite Element Analysis and Experimental Study on the Ultimate Tensile Strength of Seven-Wire Strands under Lateral Bending

#### 4.1. Stress Characteristics of Parallel Seven-Wire Strands in Hangers under Lateral Bending

#### 4.2. Ultimate Tensile Strength of the Seven-Wire Strands under Lateral Bending

#### 4.3. Experimental Study on the Ultimate Tensile Strength of the Seven-Wire Strands under Lateral Bending

## 5. Strength Check and Fatigue Properties of Seven-Wire Strands in Hangers under Lateral Bending

#### 5.1. Strength Check of Seven-Wire Strands in Hangers under Lateral Bending

#### 5.2. The Fatigue Properties of Seven-Wire Strands under Lateral Bending

#### 5.3. Advice to Mitigate the Adverse Influence of Lateral Bending on the Seven-Wire Strands in Hangers

- (1)
- The tied arch structure can be used for TABs to mitigate the adverse influence of lateral bending of hangers effectively when the tied arch structure meets the requirements of the topography. The bridge deck of the tie arch structure is straightly connected to the arch rib at both ends of the arch rib; therefore, the arch rib can restrict the longitudinal deformation of the bridge deck. The extent of lateral bending could be significantly decreased in this way.
- (2)
- Hinged connections could be used for short hangers that are closed to the abutment instead of fixed connections. The shorter length and larger longitudinal deformation of the lower end of the short hangers when compared with those of the long hangers makes lateral bending more apparent with short hanger. Therefore, when fixed connections are used in the hangers for HTABs and TABs with floating deck structures, fixed connections could be replaced by hinged connections for short hangers. This method might make the hangers require more devices for their connections and slightly increase the cost of constructing bridges.
- (3)
- A jointless bridge structure should be used [46]. A jointless bridge does not have expansion joints, and the abutment is directly connected to the superstructure of the bridge, which could decrease the deformation of the bridge decks [47,48]. When compared with a tied arch structure, the abutments of jointless bridges would suffer lateral forces from the decks, which require a stronger design for lateral abutment loads. Therefore, this method is suitable when the bridges have good rigid foundations.

## 6. Conclusions

- (1)
- We conclude that end-fixed hangers consisting of parallel seven-wire strands of HTABs and TABs with a floating deck structure can produce significant bending deformation based on the investigations of types of hangers, boundary conditions, and arch bridge structures. The bending deformation of hangers can exert an adverse influence on the strength of the hangers.
- (2)
- We propose that lateral bending causes the uneven loading of the parallel seven-wire strands in hangers based on the study of the mechanical model of hangers under lateral bending deformation. The seven-wire strand that is located at the outer edge of the hangers will bear the maximum bending stress and it can be regarded as under the most unfavorable loading conditions in all the parallel seven-wire strands. The properties of the seven-wire strands under the most unfavorable loading conditions and the maximum bending stress that they bear decide the safety of the hangers.
- (3)
- FEM developed and verified the theoretical formulation for the lateral bending angle and maximum bending stress in hangers. According to the results of the calculations using the formulas and FEM, the bending of hangers is mainly caused by the different displacements along the longitudinal direction of the bridge at both ends of the hangers and the bending that is caused by the rotation of the bridge deck can be ignored. Moreover, FEM and tests obtained the ultimate tensile strength of the seven-wire strands under lateral bending. The S–N curve that could reflect the fatigue properties of seven-wire stands under lateral bending is also obtained based on the ultimate tensile strength of the seven-wire strands under lateral bending. It was found that the ultimate tensile strength and fatigue properties of the seven-wire strands significantly decrease when lateral bending is considered. Therefore, the adverse influence of lateral bending on hangers cannot be ignored, and a method for checking the strength of seven-wire strands in hangers considering lateral bending is proposed.
- (4)
- Several measures are proposed for mitigating the adverse influence of lateral bending on hangers, such as using tied arch structures as much as possible, replacing fixed connections with hinged connections for short hangers, and using a jointless bridge structure. Synthetically speaking, using tied arch structures might produce fewer side effects is more strongly recommended than using other methods.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Liu, J.F.; Li, Y.B.; Zhang, Q.W. Mechanical behavior of damaged strand suspender with asymmetric broken wires in arch bridges. J. Tongji Univ.
**2019**, 47, 451–457. [Google Scholar] - Zhong, S.T. The Concrete-Filled Steel Tubular Structures; Tsinghua University Press Publishers: Beijing, China, 2003. [Google Scholar]
- He, W.; Chen, H. Characteristics and Related Research of through and Half through Arch Bridges in China. Appl. Mech. Mater.
**2014**, 488–489, 509–512. [Google Scholar] [CrossRef] - Li, Y.; Lv, D.G.; Sheng, H.F. Fatigue Reliability Analysis of the Stay Cables of Cable-Stayed Bridge under Combined Loads of Stochastic Traffic and Wind. Key Eng. Mater.
**2011**, 456, 23–35. [Google Scholar] [CrossRef] - Qu, Y.; Zhang, H.; Zhao, R.; Liao, L.; Zhou, Y. Research on the Method of Predicting Corrosion width of Cables Based on the Spontaneous Magnetic Flux Leakage. Materials
**2019**, 12, 2154. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Winkler, J.; Georgakis, C.; Fischer, G.; Wood, S.; Ghannoum, W. Structural Response of a Multi-Strand Stay Cable to Cyclic Bending Load. Struct. Eng. Int.
**2015**, 25, 141–150. [Google Scholar] [CrossRef] - Sophianopoulos, D.S.; Michaltsos, G.T.; Cholevas, H.I. Static and dynamic responses of suspended arch bridges due to failure of cables. Arch. Appl. Mech.
**2019**, 89, 2281–2312. [Google Scholar] [CrossRef] - Wang, D.; Yang, Q.; Liu, Y. Analysis of cable bending stiffness effect on test accuracy of anchor span tension for long-span suspension bridge. J. Comput. Mech.
**2015**, 32, 174–179. [Google Scholar] - Zheng, W. Bending Stress of Stay Cables of Cable-stayed Bridges and Probe into Control Countermeasures. Technol. Highw. Transp.
**2013**, 5, 90–93. [Google Scholar] - Huang, B.; Li, Y.; Zhu, L.; Zhang, W. Effects of Towers’ Random Sectional Bending Stiffness on Dynamic Characteristics of Large-Span Cable-Stayed Bridge. J. Southwest Jiaotong Univ.
**2014**, 49, 202–207. [Google Scholar] - Xu, J.; Zhou, J.; Lei, S. Wire Stress Distribution among Damaged Cable Based on FEM Analysis. In Proceedings of the 2014 7th International Conference on Intelligent Computation Technology and Automation, Changsha, China, 25–26 October 2014; pp. 995–997. [Google Scholar]
- Guo, Y.L. Cable Corrosion Analysis and Damage Monitoring. Appl. Mech. Mater.
**2014**, 578–579, 1302–1305. [Google Scholar] [CrossRef] - Zhu, J.S.; Yi, Q. Non-uniformity of stress impact factor of suspenders on half-through or through arch bridges. J. Vib. Shock
**2012**, 31, 5–10. [Google Scholar] - Chen, W.F.; Lian, D. Bridge Engineering Handbook: Superstructure Design; Taylor & Francis: Boca Raton, FL, USA, 2014. [Google Scholar]
- Gimsing, N.J.; Georgakis, C.T. Cable Supported Bridges, Concept & Design, 3rd ed.; John Wiley & Sons: New York, NY, USA, 2012. [Google Scholar]
- Habib, T. Inspection and Maintenance of Bridge Stay Cable Systems; Transportation Research Board: Washington, DC, USA, 2005. [Google Scholar]
- Cu, V.H.; Han, B.; Nguyen, T.N. Optimal parameters of viscous damper for hanged cables in arch bridges. KSCE J. Civ. Eng.
**2016**, 20, 847–854. [Google Scholar] [CrossRef] - Chen, B.; Su, J.; Lin, S.; Chen, G.; Zhuang, Y.; Tabatabai, H. Development and Application of Concrete Arch Bridges in China. J. Asian Concr. Fed.
**2017**, 3, 12–19. [Google Scholar] [CrossRef] - Shiu, K.N.; Tabatabai, H. Measured thermal response of concrete box-girder bridge. Transp. Res. Record
**1994**, 1460, 94–105. [Google Scholar] - Zhang, C. Study on thermal expansion coefficient of bridge decks. Shanxi Sci. Technol. Transp.
**2008**, 2, 52–55. [Google Scholar] - Li, P.J.; Wang, R.H.; Zhang, Y.; Qiu, B.; Zhou, X.R.; Ma, Y.; Tian, H. Precisely Identifying Method for Geometric Stiffness of Section of Cable Strut; Guangxi Transportation Research Institute: Nanning, China, 2012. [Google Scholar]
- Timoshenko, S.P.; Gere, J.M. Theory of Elastic Stability; McGraw Hill: New York, NY, USA, 1961. [Google Scholar]
- Cheng, Y.L.; Xu, H.C.; Yu, Y.G. Accident analysis of lowered/half supported tied arch bridges and enlightments for bridge detection. J. FuJian Univ. Technol.
**2013**, 11, 213–217. [Google Scholar] [CrossRef] - Hawileh, R.; Rahman, A.; Tabatabai, H. 3-D FE modeling and low-cycle fatigue fracture criteria of mild steel bars subjected to axial and bending loading. In Proceedings of the McMat, Joint ASME/ASCE/SES Conference on Me-chanics and Materials, Baton Rouge, LA, USA, 1–3 June 2005. [Google Scholar]
- Ministry of Transport of the People’s Republic of China. General Code for Design Highway Bridges and Culverts JTG D60-2004; China Communications Press: Beijing, China, 2004.
- Yu, Y.; Chen, Z.; Liu, H.; Wang, X. Finite element study of behavior and interface force conditions of seven-wire strand under axial and lateral loading. Constr. Build. Mater.
**2014**, 66, 10–18. [Google Scholar] [CrossRef] - Li, H. The Determination of Friction Coefficient between Parallel Wires in Stay Cables. Appl. Mech. Mater.
**2013**, 351–352, 250–253. [Google Scholar] [CrossRef] - ANSYS Help Documents; SAS IP, Inc.: Cary, NC, USA, 2015.
- Chen, Y.; Meng, F.; Gong, X. Parametric modeling and comparative finite element analysis of spiral triangular strand and simple straight strand. Adv. Eng. Softw.
**2015**, 90, 63–75. [Google Scholar] [CrossRef] - Hayashi, Y.; Nakano, M.; Shirahama, S.; Yoshihara, N. Characteristics of Developed High-Strength Prestressing Strand. In Proceedings of the Third International Conference on Sustainable Construction Materials and Technology, Kyoto, Japan, 18–21 August 2013. [Google Scholar]
- Wu, Z.J.; Ding, Z.; Sun, C.P.; Zhang, L.M. Finite element analysis of section stress and failure mode of steel strand. China Sci.
**2018**, 13, 2623–2628. [Google Scholar] - Bao, Y.; Wierzbicki, T. On fracture locus in the equivalent strain and stress triaxiality space. Int. J. Mech. Sci.
**2004**, 46, 81–98. [Google Scholar] [CrossRef] - Xie, K.Z.; Wang, H.; Guo, X.; Zhou, J.X. Study on the safety of the concrete pouring process for the main truss arch structure in a long-span concrete-filled steel tube arch bridge. Mech. Adv. Mater. Struct.
**2019**, 1–10. [Google Scholar] [CrossRef] - Tabatabai, H.; Ciolko, A.T.; Dickson, T.J. Implications of Test Results from Full-Scale Fatigue Tests of Stay Cables Composed of Seven-Wire Prestressing Strands. In Proceedings of the Fourth International Bridge Engineering Conference, San Francisco, CA, USA, 28–30 August 1995; Volume 1, pp. 266–277. [Google Scholar]
- Qin, S.Q. Control Method of Stress-Free Status for Erection of Cable-Stayed Bridges. Bridge Constr.
**2003**, 2, 31–34. [Google Scholar] - Liao, Y.; Zhan, J.H.; Li, C. Application of Stress-Free Status Control Method in Bridge Construction Control. Appl. Mech. Mater.
**2014**, 587–589, 1412–1415. [Google Scholar] [CrossRef] - Technical Code for Concrete-Filled Steel Tube Arch Bridges; Ministry of Housing and Urban-Rural Development of the People’s Republic of China; Chinese Planning Press: Beijing, China, 2013. (In Chinese)
- Pang, J.C.; Li, S.X.; Zhang, Z.F. General relations between S–N curve parameters and tensile strength of steels with a wide strength range. In Proceedings of the 12th Cross Strait Conference on Destructive Science and Material Testing, Beihai, China, 17 November 2018. [Google Scholar]
- Hawileh, R.A.; Rahman, A.; Tabatabai, H. Evaluation of the Low-Cycle Fatigue Life in ASTM A706 and A615 Grade 60 Steel Reinforcing Bars. J. Mater. Civ. Eng. ASCE
**2010**, 22, 65–76. [Google Scholar] [CrossRef] - Vukelic, G.; Vizentin, G. Damage-induced stresses and remaining service life predictions of wire ropes. Appl. Sci.
**2017**, 7, 107. [Google Scholar] [CrossRef] [Green Version] - Hawileh, R.A.; Tabatabai, H.; Abu-Obeidah, A.; Balloni, J.; Rahman, A. Evaluation of the Low-Cycle Fatigue Life in Seven Steel Bar Types. J. Mater. Civ. Eng. ASCE
**2015**. [Google Scholar] [CrossRef] - Ma, L. Study on fatigue performance of domestic 1860 MPa low relaxation prestressed steel strand. Rail Stand. Desk
**2000**, 20, 21–23. [Google Scholar] - Lee, Y.; Pan, J.; Hathaway, R.; Barkey, M. Fatigue Testing, Analysis, and Design: Theory and Applications; Elsevier’s Science & Technology: Burlington, VT, USA, 2004. [Google Scholar]
- Gu, A.B.; Xu, J.L. Structural Analysis of Short Suspenders of Half Through or Through Arch Bridge. Highway
**2002**, 5, 8–10. [Google Scholar] - Sun, H.; Ma, J.; Yu, B. Study on Suspender’s Fatigue Performance of Half-through CFST Arch Bridge due to Vehicular Loads. Adv. Eng. Forum
**2012**, 5, 189–194. [Google Scholar] [CrossRef] [Green Version] - Lin, J.; Briseghella, B.; Xue, J.; Tabatabai, H.; Huang, F.; Chen, B. Temperature Monitoring and Response of Deck-Extension Side-by-Side Box Girder Bridges. J. Perform. Constr. Facil. ASCE
**2020**, 34, 04019122. [Google Scholar] [CrossRef] - Huang, F.; Shan, Y.; Chen, G.; Lin, Y.; Tabatabai, H.; Briseghella, B. Experiment on Interaction of Abutment, Steel H-Pile and Soil in Integral Abutment Jonitless Bridges (IAJBs) under Low-Cycle Pseudo-Static Displacement Loads. Appl. Sci.
**2020**, 10, 1358. [Google Scholar] [CrossRef] [Green Version] - Briseghella, B.; Zordan, T. An innovative steel-concrete joint for integral abutment bridges. J. Traffic Transp. Eng.
**2015**, 2, 209–222. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**(

**a**) Fracture of hangers of half-through and through arch bridges (HTABs and TABs); (

**b**) Hangers under lateral bending.

**Figure 6.**Lateral bending deformation of the hangers under the longitudinal deformation of bridge decks.

**Figure 13.**Mechanical model of the parallel seven-wire strands in the hangers considering lateral bending deformation.

**Figure 19.**(

**a**) The ultimate tensile strength of seven-wire strands versus lateral bending angle; and, (

**b**) the curve fitting of ultimate tensile strength—lateral bending angle.

**Table 1.**The ultimate tensile strengths of the seven-wire strands at different lateral bending angles by finite element analysis.

$\mathbf{Lateral}\text{}\mathbf{Bending}\text{}\mathbf{Angles}\text{}\mathit{\theta}$ (mard) | $\mathbf{Ultimate}\text{}\mathbf{Tensile}\text{}\mathbf{Strength}\text{}{\mathit{\sigma}}_{\mathit{u}}\text{}\left(\mathbf{MPa}\right)$ |
---|---|

0 | 1805.6 |

5 | 1732.1 |

10 | 1665.7 |

15 | 1584.2 |

20 | 1499.3 |

25 | 1442.8 |

30 | 1399.2 |

**Table 2.**Ultimate tensile strengths of the seven-wire strands at different lateral bending angles in the tests.

$\mathbf{Lateral}\text{}\mathbf{Bending}\text{}\mathbf{Angle}\text{}\mathit{\theta}$ (mard) | $\mathbf{Ultimate}\text{}\mathbf{Tensile}\text{}\mathbf{Strength}\text{}\mathbf{of}\text{}\mathbf{the}\text{}\mathbf{Seven}-\mathbf{Wire}\text{}\mathbf{Strands}\text{}{\mathit{\sigma}}_{\mathit{u}}\text{}\left(\mathbf{MPa}\right)$ | |
---|---|---|

Results of Tests | Average Value | |

0 | 1978.5 | 1954.7 |

1957.1 | ||

1928.5 | ||

10 | 1821.4 | 1809.5 |

1814.2 | ||

1792.8 | ||

20 | 1621.1 | 1616.4 |

1621.1 | ||

1607.1 | ||

30 | 1471.4 | 1445.2 |

1435.7 | ||

1428.5 |

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**MDPI and ACS Style**

Zhou, Y.; Deng, N.; Yang, T.
A Study on the Strength and Fatigue Properties of Seven-Wire Strands in Hangers under Lateral Bending. *Appl. Sci.* **2020**, *10*, 2160.
https://doi.org/10.3390/app10062160

**AMA Style**

Zhou Y, Deng N, Yang T.
A Study on the Strength and Fatigue Properties of Seven-Wire Strands in Hangers under Lateral Bending. *Applied Sciences*. 2020; 10(6):2160.
https://doi.org/10.3390/app10062160

**Chicago/Turabian Style**

Zhou, Yiming, Nianchun Deng, and Tao Yang.
2020. "A Study on the Strength and Fatigue Properties of Seven-Wire Strands in Hangers under Lateral Bending" *Applied Sciences* 10, no. 6: 2160.
https://doi.org/10.3390/app10062160