# Long-Term Loading Experimental Research of Prestressed Glulam Beams Based on Creep Influence

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Design

#### 2.1. Specimen Design and Grouping

#### 2.2. Loading Device and Arrangement of Measuring Points

## 3. Test Results and Analysis

#### 3.1. Experimental Phenomena

#### 3.2. Stress Variation of Prestressed Steels

#### 3.3. Deflection Variation of Mid-Span

#### 3.4. Creep Coefficient θ

#### 3.5. Calculation Formula of Long-Term Stiffness B

_{2}.

_{s}—Short-term stiffness of prestressed flexural members calculated in accordance with standard combinations.

_{k}, M

_{q}—Moment calculated according to the loading standard combination and quasi-permanent combination, take the maximum moment in calculation section.

_{1/2}—Mid-span deflection

_{2}—Mid-span arching value after applying prestress.

_{P}—Elastic modulus of prestressed steel wire.

_{P}—Reinforcement area of prestressed steel wire.

_{m}—Elastic modulus of wood.

_{m}—Section moment of inertia of test beam.

## 4. Conclusions

- (1)
- When the prestress value was unchanged and the number of prestressed steel wire was 2, 4, and 6, the steel wire stress decreased by 33.07%, 37.26%, and 50.04% from the beginning of loading to the end of the test. When the number of steel wires remained unchanged and the preload values were 0 kN, 3.079 kN, and 6.158 kN, the total stress of steel wires decreased by 28.90%, 36.59%, and 36.63%. With the increase of the number of steel wires, the preload value increased, and the stress loss of steel wires increased.
- (2)
- When the prestress value was constant and the number of prestressed steel wires were 2, 4, and 6, the ratios of mid-span long-term deflection of the beam to the total deflection were respectively 61.5%, 54.8%, and 40.9%. When the number of steel wires remained unchanged and the preload values were 0 kN, 3.079 kN, and 6.158 kN, the long-term deflection in the middle of the span accounted for 60.7%, 54.8%, and 39.3% of the total deflection, respectively. With the increase of the number of steel wires, the preload value increased and the proportion of long-term deflection decreased.
- (3)
- Through the analysis of the experimental data, fitting, and derivation, we obtained the value of the creep coefficient θ under normal conditions. The greater the number of wires, the greater the prestress value, and the smaller the value of θ. The other hand, when the number of steel wires was the same, the larger the total pre-force value, the smaller the creep coefficient θ. The formula for calculating the long-term stiffness B of wooden beams based on the creep effect was proposed.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Long-term loading scheme and layout of measuring points. (

**a**) Layout of measuring points for long-term loading test. (

**b**) Long term loading test device diagram.

**Figure 3.**State diagrams of prestressed glulam beams. (

**a**) Test for 10 days. (

**b**) Test for 20 days. (

**c**) Test for 30 days. (

**d**) Test for 40 days.

Group A | Group B | ||||
---|---|---|---|---|---|

Beam Number | Number of Steel Wires | Total Prestress (kN) | Beam Number | Number of Steel Wires | Total Prestress (kN) |

LA1-1 | 2 | 3.079 | LB1-1 | 4 | 0 |

LA1-2 | 2 | 3.079 | LB1-2 | 4 | 0 |

LA2-1 | 4 | 3.079 | LB2-1 | 4 | 3.079 |

LA2-2 | 4 | 3.079 | LB2-2 | 4 | 3.079 |

LA3-1 | 6 | 3.079 | LB3-1 | 4 | 6.158 |

LA3-2 | 6 | 3.079 | LB3-2 | 4 | 6.158 |

Number | LA1-1 | LA1-2 | LA2-1 | LA2-2 | LA3-1 | LA3-2 |

Loading Value (kN) | 3.35 | 3.35 | 4.35 | 4.35 | 6.35 | 6.35 |

Number | LB1-1 | LB1-2 | LB2-1 | LB2-2 | LB3-1 | LB3-2 |

Loading Value (kN) | 2.20 | 2.20 | 4.35 | 4.35 | 6.35 | 6.35 |

Test Time | Interval of Machine Acquisition | Interval of Manual Acquisition |
---|---|---|

Day 1 | 0.25 h/time | 0.25 h/time |

Day 2, 3 | 0.25 h/time | 0.5 h/time |

Day 4, 5 | 0.5 h/time | 1 h/time |

Day 6, 7 | 0.5 h/time | 2 h/time |

Day 8~14 | 1 h/time | 4 h/time |

Day 15~45 | 2 h/time | 12 h/time |

Serial Number | Short-Term Deflection (mm) | Long-Term Deflection (mm) | Total Deflection (mm) |
---|---|---|---|

LA1 | 4.76 | 7.60 | 12.36 |

LA2 | 6.39 | 7.75 | 14.14 |

LA3 | 7.81 | 5.40 | 13.21 |

LB1 | 3.20 | 4.94 | 8.14 |

LB2 | 6.39 | 7.75 | 14.14 |

LB3 | 8.00 | 5.18 | 13.18 |

Serial Number | Coefficient | ||
---|---|---|---|

A | B | C (×10^{−6}) | |

LA1 | 1.766 | 0.011 | 4.622 |

LA2 | 3.889 | 0.016 | 8.510 |

LA3 | 5.289 | 0.010 | 4.347 |

LB1 | 4.085 | 0.010 | 5.171 |

LB2 | 3.889 | 0.016 | 8.510 |

LB3 | −17.61 | 0.012 | 5.514 |

Serial Number | Final Value of Total Deflection (mm) | Short-Term Deflection (mm) | Long-Term Deflection (mm) | Creep Coefficient θ |
---|---|---|---|---|

LA1 | 13.14 | 4.76 | 8.38 | 2.51 |

LA2 | 14.51 | 6.39 | 8.11 | 2.27 |

LA3 | 13.89 | 7.81 | 6.08 | 1.78 |

LB1 | 8.92 | 3.20 | 5.72 | 2.79 |

LB2 | 14.51 | 6.39 | 8.11 | 2.27 |

LB3 | 13.29 | 8.00 | 5.29 | 1.74 |

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**MDPI and ACS Style**

Wang, T.; Di, J.; Zuo, H.
Long-Term Loading Experimental Research of Prestressed Glulam Beams Based on Creep Influence. *Sustainability* **2022**, *14*, 9937.
https://doi.org/10.3390/su14169937

**AMA Style**

Wang T, Di J, Zuo H.
Long-Term Loading Experimental Research of Prestressed Glulam Beams Based on Creep Influence. *Sustainability*. 2022; 14(16):9937.
https://doi.org/10.3390/su14169937

**Chicago/Turabian Style**

Wang, Tong, Jing Di, and Hongliang Zuo.
2022. "Long-Term Loading Experimental Research of Prestressed Glulam Beams Based on Creep Influence" *Sustainability* 14, no. 16: 9937.
https://doi.org/10.3390/su14169937