# Calculation of Reasonable Tension Value for Longitudinal Connecting Reinforcement of CRTSII Slab Ballastless Track

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## Abstract

**:**

## 1. Introduction

## 2. Longitudinal Joint Construction of CRTSII Slab Ballastless Track

#### 2.1. Construction Sequence of Ballastless Track

#### 2.2. Tensioning Sequence of Longitudinal Reinforcement

- Step1: Tension the inside locks of the two joints.
- Step2: Symmetrically tension the two inside locks near the two joints that have been stretched. This tensioning step is carried out with two joints step by step.
- Step3: Tension the middle locks of the two middle joints after the six inside locks have been stretched.
- Step4: Continue symmetrically tensioning the two inside locks near the joints that have been stretched and, at the same time, tension the two middle locks near the joints that have been stretched.
- Step5: Tension the outside locks of the two middle joints after the six middle locks have been stretched.

## 3. Calculation Model and Experimental Verification

#### 3.1. Cohesive Zone Model

_{f}, and the corresponding displacement is δ

_{1}. The interface stress increases linearly before it reaches the ultimate bonding strength τ

_{f}. Stage 2: Softening stage—the interface stress decreases linearly when the relative displacement is greater than δ

_{1}. The relative displacement reaches δ

_{f}when the bonding strength drops to zero. Stage 3: Failure stage—the model starts to fail when the relative displacement is greater than δ

_{f}. G

_{f}is defined as the fracture energy and its value is the area enclosed by the triangle.

#### 3.2. Finite Element Model and Model Parameters

#### 3.3. Experimental Verification

## 4. Mechanical Analysis in Tensioning Process

## 5. Check and Calculation in Operating Period

#### 5.1. Original Design Check and Calculation

_{Δt}= αΔt.

_{s}= −0.23.

_{s}= E

_{s}·(ε

_{Δt}+ ε

_{s}),

_{s}is the elastic modulus of reinforcement.

_{s}·A

_{s},

_{s}is the cross-sectional area of a single connecting reinforcement.

_{s,c}= (N + N

_{ten})/A

_{s,all},

_{s,all}is the total cross-sectional area of six reinforcements and N

_{ten}is the tension force.

_{s,a}= N/E

_{s}/A

_{s,all}.

_{cr}= l

_{cr,max}·(ε

_{s,a}− ε

_{c,a}),

_{cr}is the calculated value of the crack width in mm, l

_{cr,}

_{max}is the maximum crack spacing in mm, ε

_{s,a}is the average strain of reinforcement, and ε

_{c,a}is the average strain of concrete.

_{cr,}

_{max}. As the strain of concrete is much smaller than that of reinforcement, the average strain of concrete is considered to be 0.

#### 5.2. Application of Prestress on Postcast Concrete

#### 5.3. Calculation of Reasonable Tension Value

_{los}= ΔtαE

_{s}A

_{s,all}.

_{pre}= N

_{los}.

_{s,c}= (N + N

_{ten}− N

_{los})/A

_{s,all}.

_{s,a}= (N − N

_{pre})/E

_{s}/A

_{s,all}.

_{ten}= 2N

_{los}= 2ΔtαE

_{s}A

_{s,all}.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**Push test on single rail pad and its result. (

**a**) Push test on single rail pad. (

**b**) Testing and simulated result of push test.

**Figure 8.**Tension points and test results of longitudinal reinforcement. (

**a**) Measuring point of tensioning of longitudinal connecting reinforcement. (

**b**) Testing result of tensioning of longitudinal connecting reinforcement.

**Figure 9.**Vertical displacement of the track slab after the longitudinal connecting reinforcement is tensioned. (

**a**) Track slab longitudinal path. (

**b**) Testing result.

**Figure 10.**Damage evolution under positive temperature gradient load with different tension force (

**a**–

**d**), 100–400 kN.

**Figure 17.**The relationship between crack width and temperature difference between concrete and reinforcement.

**Figure 18.**The relationship among reinforcement stress, tension force, and temperature difference value.

**Figure 19.**Temperature and tension force range to guarantee appropriate reinforced stress and crack width.

Components | Young’s Modulus (Pa) | Poisson Ratio | Thermal Expansion Coefficient (°C^{−1}) |
---|---|---|---|

Track slab | 3.25 × 10^{10} | 0.2 | 1 × 10^{−5} |

CA mortar | 8 × 10^{9} | 0.2 | - |

Concrete base | 2.55 × 10^{10} | 0.2 | - |

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**MDPI and ACS Style**

Chen, L.; Chen, J.; Wang, J.
Calculation of Reasonable Tension Value for Longitudinal Connecting Reinforcement of CRTSII Slab Ballastless Track. *Appl. Sci.* **2018**, *8*, 2139.
https://doi.org/10.3390/app8112139

**AMA Style**

Chen L, Chen J, Wang J.
Calculation of Reasonable Tension Value for Longitudinal Connecting Reinforcement of CRTSII Slab Ballastless Track. *Applied Sciences*. 2018; 8(11):2139.
https://doi.org/10.3390/app8112139

**Chicago/Turabian Style**

Chen, Long, Jinjie Chen, and Jianxi Wang.
2018. "Calculation of Reasonable Tension Value for Longitudinal Connecting Reinforcement of CRTSII Slab Ballastless Track" *Applied Sciences* 8, no. 11: 2139.
https://doi.org/10.3390/app8112139