# Flexural Behavior of GFRP Tubes Filled with Magnetically Driven Concrete

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Investigation

#### 2.1. Magnetically Driven Concrete

#### 2.2. GFRP Tubes

#### 2.3. Reinforcing Bars and GFRP Bars

#### 2.4. Magnetic Vibration Device and Test Specimens

- The first letters indicate that the type of the bars, where the prefix letter “G” refers to GFRP bars while the letter “R” refers to steel reinforcing bars.
- The following four digits “2000” indicate the length of the specimen in mm.
- The following three digits “300” indicate the outer diameter of the specimen in mm.
- The following two digit “12” is the nominal thickness of the GFRP tube in mm.
- The last character “A” refers to the specimen was vibrated using vibrating tube while the character “B” refers to the specimen was vibrated using magnetic method.

#### 2.5. Bending Test

## 3. Test Results

#### 3.1. Material Test Results

_{cu}) obtained on 150 mm cubic specimens at 28 days for concrete vibrated by magnetic method and vibrating tube were 44 MP and 46 MPa, respectively. Concrete cubic specimens used the same materials as the beam specimens. The compressive test of concrete cubic followed the Chinese Standard [15]. Compressive tests were carried out on 28-day concrete cubic specimens cured in standard environment specified in Chinese Standard [15]. The compressive strengths were the average value of three concrete cubic specimens.

#### 3.2. Beam Test Results

#### 3.2.1. Load-Displacement Curves

#### 3.2.2. Load-Strain Curves

#### 3.2.3. Failure Mode and Ultimate Strength

_{u}= 0.6 N

_{u}/2 and M

_{u}= 0.5 N

_{u}/2 for 2000 mm and 1500 mm specimens, respectively. Specimen G2000-300-12A has the maximum ultimate strength of moment (M

_{u}), while specimen G2000-180-8 has the minimum maximum ultimate strength of moment (M

_{u}). It is shown the 1500 mm specimens have relative large N

_{u}value when compared with 2000 mm specimens having the same cross section, which may due to the failure mode. The comparison between specimen series A and B indicates that the vibration method has a negligible effect on the ultimate strength of test specimens.

## 4. Design of Elastic Stiffness

#### 4.1. Method 1

_{scm}of concrete-filled steel tubes specified in GB 50936 [16] could be calculated using Equations (1)–(6), the material properties of GFRP tubes were used in the equations:

_{sc}could be calculated as Equations (4) and (5)

_{s}is the cross section area of GFRP tube (mm

^{2}); A

_{c}is the cross section area of concrete (mm

^{2}).

#### 4.2. Method 2

_{eff}of concrete-filled steel tubes specified in Eurocode [17] could be calculated using Equation (7). The measured material properties of GFRP bars were used in the calculation of G series test specimens.

_{eff}are smaller than the flexural stiffness B

_{scm}, since the confined effect on concrete is not considered in Eurocode [17]. The load versus mid-span deflection curves calculated using the results in Table 6 are compared with the test results in Figure 5. It is shown that the predictions from GB [16] agree with test results well for specimen series 2000-180-8 and specimens having length of 1500 mm. For other test specimens, the predictions from Eurocode agree with the test results well.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

E_{scm} | the elastic bending modulus of concrete-filled tubes |

I_{s} | the moment of inertia of GFRP tube |

I_{c} | the moment of inertia of concrete |

E_{s} | the elastic modulus of GFRP |

E_{c} | the elastic modulus of concrete |

E_{cm} | secant modulus of elastic of concrete, E_{cm} = 9500 (f_{ck} + 8)^{1/3} |

I_{sc} | the moment of inertia of concrete-filled tubes |

A_{s} | the cross section area of GFRP tube |

A_{c} | the cross section area of concrete |

K_{e} | 0.6 is a correction factor |

E_{a} | the elastic modulus of GFRP tube |

I_{a} | the moment of inertia of GFRP tube |

f_{ck} | the characteristic cylinder compressive strength of the concrete at the age considered |

## References

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**Figure 5.**Load-displacement curves of test specimens and predictions (

**a**) Series G2000-300-8 (

**b**) Series G2000-300-12 (

**c**) Series R2000-300-8 (

**d**) Series R2000-300-12 (

**e**) Series 2000-180-8 (

**f**) Specimen R1500-300-8A (

**g**) Series R1500-300-12 (Note: GB is prediction from GB Standard [16] and EC is prediction from Eurocode [17]).

**Figure 7.**Load-strain curves of specimen series G2000-300-8. (

**a**) Specimen G2000-300-8A (

**b**) Specimen G2000-300-8B.

**Figure 8.**Load-strain curves of specimen series R2000-300-12. (

**a**) Specimen R2000-300-12A (

**b**) Specimen R2000-300-12B.

Water | Cement | Sand | Coarse Steel Slag |
---|---|---|---|

210 | 525 | 524 | 1115 |

Test Specimen | L (mm) | D (mm) | t (mm) | d (mm) | n (mm) |
---|---|---|---|---|---|

G2000-300-8A | 2000 | 300.2 | 7.98 | 6 | 6 |

G2000-300-8B | 1999 | 300.1 | 7.98 | 6 | 6 |

G2000-300-12A | 2001 | 299.7 | 11.98 | 6 | 6 |

G2000-300-12B | 2002 | 300.3 | 12.01 | 6 | 6 |

R2000-300-8A | 2001 | 300.2 | 8.01 | 6 | 6 |

R2000-300-8B | 1998 | 300.1 | 8.01 | 6 | 6 |

R2000-300-12A | 2000 | 300.0 | 12.01 | 6 | 6 |

R2000-300-12B | 2000 | 299.8 | 12.02 | 6 | 6 |

G2000-180-8A | 2001 | 180.1 | 8.00 | 6 | 6 |

R2000-180-8B | 2002 | 180.2 | 7.98 | 6 | 6 |

R1500-300-8A | 1501 | 300.3 | 7.99 | 6 | 6 |

R1500-300-12A | 1499 | 300.1 | 12.02 | 6 | 6 |

R1500-300-12B | 1502 | 300.2 | 12.03 | 6 | 6 |

GFRP Tube | Water-Absorption Rate (%) | Degree of Cure (%) | Density (kg/m ^{3}) | f_{u}(MPa) | E (GPa) |
---|---|---|---|---|---|

Series A | 0.14 | 92.7 | 1987.1 | 371.9 | 39.2 |

Series B | 0.14 | 92.5 | 1985.2 | 373.1 | 38.9 |

Series C | 0.15 | 95.9 | 2066.5 | 342.6 | 36.8 |

Specimens | E (GPa) | f_{y} (MPa) | f_{u} (MPa) | ε_{u} (%) |
---|---|---|---|---|

GFRP bar | 31.8 | --- | 519 | 1.4 |

Reinforcing bar | 205 | 375 | 465 | --- |

Stirrups | 201 | 330 | 415 | --- |

Specimens | N_{u} (kN) | M_{u} (kN·m) |
---|---|---|

G2000-300-8A | 708.5 | 212.6 |

G2000-300-8B | 696.5 | 209.0 |

G2000-300-12A | 1126.0 | 337.8 |

G2000-300-12B | 1083.0 | 324.9 |

R2000-300-8A | 686.9 | 206.1 |

R2000-300-8B | 723.0 | 216.9 |

R2000-300-12A | 1001.2 | 300.4 |

R2000-300-12B | 1043.0 | 312.9 |

G2000-180-8A | 357.1 | 107.1 |

R2000-180-8B | 366.0 | 109.8 |

R1500-300-8A | 1058.0 | 264.5 |

R1500-300-12A | 1276.1 | 319.0 |

R1500-300-12B | 1121.1 | 280.3 |

Specimens | B_{scm} (N·mm^{2}) | (EI)_{eff} (N·mm^{2}) |
---|---|---|

G2000-300-8A | 2.03262 × 10^{13} | 9.16117 × 10^{1}^{2} |

G2000-300-8B | 2.03262 × 10^{13} | 9.16117 × 10^{1}^{2} |

G2000-300-12A | 2.70496 × 10^{13} | 9.85801 × 10^{1}^{2} |

G2000-300-12B | 2.70496 × 10^{13} | 9.85801 × 10^{1}^{2} |

R2000-300-8A | 2.03262 × 10^{13} | 9.15116 × 10^{1}^{2} |

R2000-300-8B | 2.03262 × 10^{13} | 9.15116 × 10^{1}^{2} |

R2000-300-12A | 2.70496 × 10^{13} | 9.84799 × 10^{1}^{2} |

R2000-300-12B | 2.70496 × 10^{13} | 9.84799 × 10^{1}^{2} |

G2000-180-8A | 3.54573 × 10^{1}^{2} | 1.26122 × 10^{1}^{2} |

R2000-180-8B | 2.03262 × 10^{13} | 1.27145 × 10^{1}^{2} |

R1500-300-8A | 2.03262 × 10^{13} | 9.15116 × 10^{1}^{2} |

R1500-300-12A | 2.70496 × 10^{1}^{3} | 9.84799 × 10^{1}^{2} |

R1500-300-12B | 2.70496 × 10^{1}^{3} | 9.84799 × 10^{1}^{2} |

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**MDPI and ACS Style**

Xie, F.; Chen, J.; Dong, X.; Feng, B.
Flexural Behavior of GFRP Tubes Filled with Magnetically Driven Concrete. *Materials* **2018**, *11*, 92.
https://doi.org/10.3390/ma11010092

**AMA Style**

Xie F, Chen J, Dong X, Feng B.
Flexural Behavior of GFRP Tubes Filled with Magnetically Driven Concrete. *Materials*. 2018; 11(1):92.
https://doi.org/10.3390/ma11010092

**Chicago/Turabian Style**

Xie, Fang, Ju Chen, Xinlong Dong, and Bing Feng.
2018. "Flexural Behavior of GFRP Tubes Filled with Magnetically Driven Concrete" *Materials* 11, no. 1: 92.
https://doi.org/10.3390/ma11010092