# Study of Periodical Temperature Change Induced Deformation of an Inclined Steel Arch Bridge Exposed to Actual Environment Based on Synchronous Multi-Member Thermal Simulation

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## Abstract

**:**

## 1. Introduction

## 2. Theory of Thermal Boundary Condition

#### 2.1. Environmental Parameter

#### 2.2. Setting of Thermal Boundary

## 3. Finite Element Simulation of Bridge

#### 3.1. Engineering Project Background

#### 3.2. FE Modeling of Bridge

^{3}, modulus of elasticity of 21.1 GPa and Poisson ratio 0.25. In general, for the FE modeling of the bridge by using ANSYS program, quadrilateral 4 nodes SHELL181 element is used for representation of steel components, and LINK180 element for modeling of the hanger.

#### 3.3. Structural Temperature Distribution

#### 3.4. Structural Response with Thermal Load

## 4. Combination of Structural Thermal Effect

#### 4.1. Turkstra’s Rule Combination Theory

#### 4.2. Turkstra’s Rule Combination of Thermal Effects

## 5. Conclusions

- The effect values derived from current specifications are conservative, and the effects under the action of the real temperature field will exceed it. The effect under changing temperature is in linearly positive correlation with temperature, but different components show different variation trends. The temperature difference between different components and the environment is significantly affected by season.
- The combination result, using Turkstra’s rule, can reflect the combined effect of the temperature effect of different components, to a certain extent. But the method is not conservative enough since there is a lack of consideration for the adverse case. The JCSS method can consider all the adverse case and has the ability to locate the occurrence time of the maximum, but it is too conservative, due to the stationary binomial process assumption.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Structural response with actual environmental thermal load. (

**a**) Transverse displacement. (

**b**) Longitudinal displacement. (

**c**) Vertical displacement. (

**d**) Girder-arch relative displacement. (

**e**) Cable force.

Thermal Parameters | Value | Thermal Parameters | Value |
---|---|---|---|

Thermal conductivity (W/m·K) | 58.2 | Poisson’s ratio | 0.25 |

Specific heat (J/kg·K) | 480 | Elastic modulus (N/m^{2}) | 2.11 × 10^{11} |

Density (kg/m^{3}) | 7850 | Thermal expansion coefficient (1/K) | 12 × 10^{−6} |

Radiation absorption ratio | 0.7 |

Seasons | $\mathbf{\Delta}\mathit{T}$between component and environment (°C) | $\mathbf{\Delta}\mathit{T}$of components between day and night (°C) | ||||

Girder | Arch | Hanger | Girder | Arch | Hanger | |

Spring | 6.34 | 8.72 | 11.71 | 8.71 | 11.10 | 15.23 |

Summer | 4.91 | 7.11 | 10.84 | 10.40 | 12.79 | 19.10 |

Autumn | 5.08 | 10.69 | 10.78 | 9.70 | 15.65 | 17.80 |

Winter | 5.58 | 12.36 | 11.07 | 9.04 | 16.07 | 16.34 |

Seasons | $\Delta T$between components in day (°C) | $\Delta T$between components in night (°C) | ||||

Girder-Arch | Girder-Hanger | Arch-Hanger | Girder-Arch | Girder-Hanger | Arch-Hanger | |

Spring | −2.26 | −5.4 | −3.14 | 0.02 | 0.86 | 0.83 |

Summer | −2.06 | −6.15 | −4.09 | 0.19 | 1.95 | 1.75 |

Autumn | −5.66 | −5.89 | −0.23 | 0.36 | 1.22 | 0.85 |

Winter | −6.82 | −5.62 | 1.21 | 0.24 | 0.95 | 0.71 |

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**MDPI and ACS Style**

Yang, H.; Zhao, X.; Fu, L.; Ruan, X.; Li, Y.; Chen, D.
Study of Periodical Temperature Change Induced Deformation of an Inclined Steel Arch Bridge Exposed to Actual Environment Based on Synchronous Multi-Member Thermal Simulation. *Sustainability* **2022**, *14*, 10042.
https://doi.org/10.3390/su141610042

**AMA Style**

Yang H, Zhao X, Fu L, Ruan X, Li Y, Chen D.
Study of Periodical Temperature Change Induced Deformation of an Inclined Steel Arch Bridge Exposed to Actual Environment Based on Synchronous Multi-Member Thermal Simulation. *Sustainability*. 2022; 14(16):10042.
https://doi.org/10.3390/su141610042

**Chicago/Turabian Style**

Yang, Huizhu, Xinying Zhao, Lilei Fu, Xin Ruan, Yue Li, and Dixin Chen.
2022. "Study of Periodical Temperature Change Induced Deformation of an Inclined Steel Arch Bridge Exposed to Actual Environment Based on Synchronous Multi-Member Thermal Simulation" *Sustainability* 14, no. 16: 10042.
https://doi.org/10.3390/su141610042