# The Push-Over Test and Numerical Analysis Study on the Mechanical Behavior of the GFRP Frame for Sustainable Prefabricated Houses

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## Abstract

**:**

## 1. Introduction

## 2. GFRP Frame and Experimental Setup

#### 2.1. GFRP Frame

#### 2.2. Experimental Setup

## 3. Experimental Observations and Discussions of the Pushover Test

#### 3.1. Single-Span Frames

#### 3.1.1. Frame FP1

#### 3.1.2. Frame FP1T

#### 3.1.3. Frame FP1C

#### 3.1.4. Comparison of the Three Single-Span Frames

#### 3.2. Double-Span Frames

#### 3.2.1. Frame FP2

#### 3.2.2. Frame FP2TC

#### 3.2.3. Frame FP2CT

#### 3.2.4. Comparison of the Three Double-Span Frames

## 4. Nonlinear Pushover Numerical Analysis

## 5. The Comparison of the Experimental and Numerical Analysis Results

## 6. Conclusions

- Single-span Frame FP1T with tension bracing had a 165% increase in initial stiffness and 69% increase in ultimate strength, and Frame FP1C with compression braced had a 65% increase in initial stiffness and 11% increase in maximum load.
- Double-span Frame FP2TC had a 23% increase in initial stiffness and a 189% increase in ultimate strength, and Frame FP2CT had a 19% increase in initial stiffness and a 111% increase in ultimate strength. The failure mode of GFRP frames begins from the buckling of the compression brace. At this stage, there is no damage to the overall beams and columns, which means that the second component can be replaced as there is an early warning of failure.
- Since the FRP composite material structural member is brittle, so the SAP2000 analysis was set up to analyze brittle material failure by using the hinge-overwrite command to simulate the GFRP frame’s reaction to the pushover force.
- The numerical structural results have an absolute error rate of less than 4% when they are compared with the experimental results. This proves the use of SAP2000 has an acceptable accuracy while saving time and cost in engineering practice.
- The numerical structural analysis of the GFRP frame depends on the data of the moment versus rotation relationship derived from the experiment and the hinge-overwrite coefficients. The performed structural analysis in this manuscript may not be feasible for different GFRP structural members and systems.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 16.**The illustration figure of the structural analysis model and the locations of the plastic hinges of Frame FP2CT.

**Figure 17.**The force-displacement relationships of Frame FP1 using different hinge-overwrite parameters.

**Figure 18.**The experimental and numerical-analysis force-displacement relationships of all the GFRP frames.

Member | Section | Specification |
---|---|---|

GFRP double web I type component | As beams and columns of the GFRP frame | |

GFRP rectangular tube type component | As bracings of the GFRP frame | |

Metal joint | As the beam-column joint | |

Bracing joint | For locking the bracings to the frame joint | |

Filling steel block | Inserted inside the GFRP bracing to avoid damage of the bracing from shearing due to bolt pressure |

Section | |||
---|---|---|---|

Material Property | |||

Area (cm^{2}) | 23.47 | 5.23 | |

Moment of inertia (cm^{4}) | 848.56 | 35 | |

Elastic modulus (kN/cm^{2}) | E_{x} = 1722 | E_{x} = 1722 | |

E_{y} = 551 | E_{y} = 551 | ||

E_{z} = 551 | E_{z} = 551 |

Frame | FP1 | FP1T | FP1C |
---|---|---|---|

Linear Stiffness (kN/cm) | 15.9 | 42.2 | 26.2 |

Ultimate Strength (kN) | 33.3 | 56.4 | 36.9 |

Relative Displacement at Ultimate Strength (cm) | 4.8 | 2.0 | 1.4 |

Drift Ratio (%) | 3.9% | 1.6 | 1.1 |

Dissipated Energy * (kN-m) | 154.5 | 216.9 | 192.3 |

Failure Locations |

Frame | FP2 | FP2TC | FP2CT |
---|---|---|---|

Linear stiffness (kN/cm) | 20.8 | 60.1 | 43.8 |

Maximum load (kN) | 41.6 | 51.3 | 49.4 |

Relative displacement at maximum load (cm) | 5.4 | 2.2 | 2.7 |

Drift ratio (%) | 4.5 | 1.8 | 2.2 |

Dissipated energy * (kN-m) | 212.4 | 300.9 | 282.6 |

Failure locations |

Frame | Column | Tension Bracing | Compression Bracing |
---|---|---|---|

FP1 | 0.2 | - | - |

FP1T | 0.2 | 0.09 | - |

FP1C | 0.2 | - | 0.09 |

FP2 | 0.6 | - | - |

FP2TC | 0.6 | 0.2 | 0.1 |

FP2CT | 0.6 | 0.4 | 0.1 |

Frame | Ultimate Strength (kN) | ||
---|---|---|---|

Experiment | Numerical Analysis | Absolute Error (%) | |

FP1 | 33.3 | 32.3 | 3 |

FP1T | 56.4 | 57.4 | 1.8 |

FP1C | 36.9 | 36.4 | 1.4 |

FP2 | 41.6 | 40.4 | 2.9 |

FP2TC | 51.3 | 53.2 | 3.7 |

FP2CT | 49.4 | 48.9 | 1 |

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**MDPI and ACS Style**

Li, Y.-F.; Lai, J.-Y.; Yu, C.-C. The Push-Over Test and Numerical Analysis Study on the Mechanical Behavior of the GFRP Frame for Sustainable Prefabricated Houses. *Sustainability* **2019**, *11*, 6753.
https://doi.org/10.3390/su11236753

**AMA Style**

Li Y-F, Lai J-Y, Yu C-C. The Push-Over Test and Numerical Analysis Study on the Mechanical Behavior of the GFRP Frame for Sustainable Prefabricated Houses. *Sustainability*. 2019; 11(23):6753.
https://doi.org/10.3390/su11236753

**Chicago/Turabian Style**

Li, Yeou-Fong, Jian-Yu Lai, and Chung-Cheng Yu. 2019. "The Push-Over Test and Numerical Analysis Study on the Mechanical Behavior of the GFRP Frame for Sustainable Prefabricated Houses" *Sustainability* 11, no. 23: 6753.
https://doi.org/10.3390/su11236753