# Numerical Study of FRP Reinforced Concrete Slabs at Elevated Temperature

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material Behaviour at High Temperatures

**Figure 1.**Comparing Bisby’s and Saafi’s models; (

**a**) Strength reduction; (

**b**) Elastic modulus degradation for GFRP at elevated temperatures.

## 3. Heat Conduction Simulation in Reinforced Concrete Members

## 4. Load Capacity Model

- (1)
- Slabs are exposed to fire from the bottom of the slab only
- (2)
- Slabs carry loads in bending in one direction only (one-way slab)
- (3)
- Slabs are simply-supported and no axial restraint or axial forces are present
- (4)
- The bond of FRP bars to concrete is unaffected by heat, and
- (5)
- Plane sections remain plane throughout the analysis.

_{FRP,b}) increases continuously. Thus, at each time step, ρ

_{FRP,b}is recalculated using temperature adjusted characteristics of FRP.

_{FRP,b}is calculated, the existing FRP ratio (ρ

_{FRP}) is compared to ρ

_{FRP,b}to identify whether failure will be by crushing of concrete or by FRP rupture. In the case of slabs, with two or more layers of FRP the possibility of rupture in each FRP layer is considered at every time step, especially when the ultimate strain of FRP decreases as the temperature increases. For example in a slab with two layers of reinforcement, in some occasions the section reaches a higher flexural capacity because the bottom layer ruptures before the concrete crushes. The ultimate strain of concrete is set to be constant and equal to 0.0035. However the mechanical rupture strain of the FRP bars varies throughout the fire exposure as shown in Figure 4. The curves in this figure were obtained by a combination of the strength and modulus curves presented in Figure 1.

**Figure 4.**Comparison of the models proposed by Bisby and Saafi for ultimate strain of GFRP bars at elevated temperatures.

_{FRP}is greater than ρ

_{FRP,b}, the governing failure mechanism is concrete crushing and the strain at top compression layer is 0.0035. The strain in FRP bars is determined using strain compatibility. As the strength of the FRP decreases due to temperature effects, the neutral axis depth decreases resulting in a smaller concrete stress block.

_{FRP}is less than ρ

_{FRP,b}, the FRP will rupture before the concrete crushes. The strain in FRP bars is set to their ultimate strain at that temperature. Hence, the stress in the bar is known and the resultant tensile force can be calculated. A subroutine checks many different neutral axis depths to satisfy equilibrium of tensile and compressive forces in the slab cross-section. Once the equilibrium criterion is fulfilled and the neutral axis is determined, strains and stresses are calculated for any point in the section. The resultant forces and moment resistance are calculated once all the stresses are determined and this gives the moment resistance of concrete slab at any instant of fire exposure. The known parameters of the analysis are FRP reinforcement ratio, which is calculated beforehand by conforming to ACI 440.1R [7] serviceability limitations, as well as dimensions of the slabs, and material properties of reinforced concrete at room temperature.

## 5. Slabs with One Layer of FRP

Slab number | Thickness (mm) | Rebar type | f'_{c} (MPa) | cover (mm) | L (mm) | Spacing (mm) | A_{f,req} ^{*} | M_{n} ^{**} (kN·m) | M_{cr} | Deflection (mm) Ma/Mcr = 1.5 |
---|---|---|---|---|---|---|---|---|---|---|

1 | 180 | GFRP | 30 | 30 | 3600 | 150 | 1006 | 77.6 | 17.8 | 4.1 |

2 | 180 | GFRP | 30 | 40 | 3600 | 150 | 1243 | 74.1 | 17.8 | 4.1 |

3 | 180 | GFRP | 30 | 50 | 3600 | 150 | 1576 | 70.2 | 17.8 | 4.1 |

4 | 180 | GFRP | 30 | 60 | 3600 | 150 | 2051 | 65.6 | 17.8 | 4.0 |

5 | 180 | GFRP | 30 | 70 | 3600 | 150 | 2754 | 59.9 | 17.8 | 4.0 |

6 | 180 | GFRP | 30 | 80 | 3600 | 150 | 3845 | 53.1 | 17.8 | 3.9 |

7 | 250 | GFRP | 30 | 30 | 5000 | 150 | 1235 | 156.4 | 34.2 | 5.7 |

8 | 250 | GFRP | 30 | 40 | 5000 | 150 | 1446 | 153.5 | 34.2 | 5.7 |

9 | 250 | GFRP | 30 | 50 | 5000 | 150 | 1719 | 149.7 | 34.2 | 5.6 |

10 | 250 | GFRP | 30 | 60 | 5000 | 150 | 2072 | 145.4 | 34.2 | 5.6 |

11 | 250 | GFRP | 30 | 70 | 5000 | 150 | 2530 | 140.2 | 34.2 | 5.5 |

12 | 250 | GFRP | 30 | 80 | 5000 | 150 | 3136 | 134.0 | 34.2 | 5.4 |

13 | 300 | GFRP | 30 | 30 | 6000 | 150 | 1409 | 222.6 | 49.3 | 6.9 |

14 | 300 | GFRP | 30 | 40 | 6000 | 150 | 1617 | 227.2 | 49.3 | 6.8 |

15 | 300 | GFRP | 30 | 50 | 6000 | 150 | 1879 | 223.9 | 49.3 | 6.7 |

16 | 300 | GFRP | 30 | 60 | 6000 | 150 | 2206 | 220.2 | 49.3 | 6.7 |

17 | 300 | GFRP | 30 | 70 | 6000 | 150 | 2614 | 215.7 | 49.3 | 6.6 |

18 | 300 | GFRP | 30 | 80 | 6000 | 150 | 3122 | 210.0 | 49.3 | 6.5 |

_{a}/M

_{cr}= 1.50 is 1719 mm

^{2}. Placing the required amount of reinforcement to satisfy serviceability criteria gives a nominal moment resistance 150 kN·m. The cracking moment (M

_{cr}) of the slab is 34 kN·m. Exposed to fire from below, the slab loses its moment capacity as a consequence of thermal degradation of the mechanical properties of the FRP. The initial flexural capacity of the slab drops to the applied moment (M

_{a}= 51 kN·m) at 140 min. It should be mentioned that the resistance model given by the model does not include member reduction factors as recommended by ACI 216 [22]. The maximum likely crack width is calculated using the following equation:

_{f}= reinforcement stress; β = ratio of distance between neutral axis and tension face to distance between neutral axis and centroid of reinforcement; dc = thickness of cover from tension face to center of closest bar; and s = bar spacing. Since crack width is a function of stress in the FRP bars, the design is affected by the service load level as expressed by the M

_{a}/M

_{cr}ratio. Three common ratios of 1, 1.25, and 1.5 are selected for the M

_{a}/M

_{cr}ratio.

**Figure 7.**Moment capacities of 180 mm thick slabs with various cover depths in fire, M

_{a}/M

_{cr}= 1.5, (

**a**) 180 mm thick slab; (

**b**) 250 mm; (

**c**) 300 mm.

_{a}/M

_{cr}ratio during the design process does not significantly affect the failure time of the slab within the range of M

_{a}/M

_{cr}between 1.0 and 1.5. This effect is illustrated in Figure 8 where moment resistance (M

_{r}) curves are normalized versus applied load or service load (M

_{a}). While slabs with different M

_{a}/M

_{cr}ratios behave differently in the beginning, they approach each other when the moment capacity reaches the service load level. For example, a slab with an initial M

_{a}/M

_{cr}= 1, has approximately the same fire endurance as a slab with M

_{a}/M

_{cr}=1.5. Obviously in a slab with M

_{a}/M

_{cr}= 1.5 the amount of reinforcement is higher due to crack width requirements but this extra reinforcement does not increase the fire endurance.

## 6. Strength-Domain and Temperature-Domain Failure

_{a}). Figure 9 illustrates a considerable conservative prediction of temperature domain model. For instance, for a 180 mm slab, the fire endurance prediction of temperature domain failure for cover of 30 mm is 41% of the strength-domain failure. This is even lower for a slab with higher concrete cover. For the same slab with cover of 60 mm, the ratio is 24%. Bisby’s model for GFRP behaviour at fire is used here to predict the fire performance of the slabs. The results of strength-domain result would be closer to temperature-domain results if a more conservative FRP material model (e.g., Saafi’s model) is used in the calculation. For example, for a 180 mm thick slab with 50 mm of cover, Figure 5 shows that Saafi’s model would estimate the fire endurance as 85 min compared to 75 min for the temperature-domain approach as shown in Figure 9.

**Figure 9.**Strength-domain fire rate versus temperature-domain of CSA-S806 for (

**a**) slab 180; and (

**b**) 250 mm.

## 7. Slabs with Two Layers of FRP

_{a}/M

_{cr}in all simulations is equal to 1.5 since fire endurance was found to be independent of the service load level. Sample moment capacity curves during fire are shown in Figure 10. As expected, a slab with two layers of GFRP reinforcement outperforms a slab with same amount of reinforcement placed in one layer in terms of fire endurance. For example, a slab with GFRP placed at two layers with covers of 30 and 60 mm achieves approximately 2 h of fire endurance while the same slab with one layer of GFRP has a fire endurance of only 100 min. While the initial strength of the slab is higher for the one-layer slab, the decline in strength is faster during the fire exposure. Thus, the slab with two layers of reinforcement has more gradual fire degradation than the slab reinforced with one layer.

**Figure 10.**Prediction of the flexural capacity in fire of a slab with two layers; (

**a**) Slab thickness of 180 mm; (

**b**) Slab thickness of 250 mm.

**Figure 11.**Fire endurance of one-layer compared to two-layer FRP reinforced concrete slab (

**a**) 180 mm, (

**b**) 250 mm, and (

**c**) 300 mm.

**Figure 12.**Comparison of flexural capacities of one-layer slab (180 mm) with two-layer with the same area of reinforcement for three cover thicknesses.

## 8. Conclusions

- Concrete cover thickness drastically influences the fire endurance of the slabs.
- The validity of the temperature-domain method for fire endurance (i.e., specifying a critical temperature for the reinforcement to represent failure) is investigated against the strength-domain method. Since the temperature-domain method is developed from the behaviour of steel reinforced concrete members in fire, it is not entirely applicable to FRP reinforced concrete members and represents a lower bound of the expected fire endurance.
- The results for two-layer FRP reinforced slabs show that by changing the distribution of the required reinforcement from one layer to two layers (using the same amount of FRP reinforcement), fire endurance of the slabs increases. The increase is more notable for thicker slabs.
- The results are greatly influenced by the implemented thermal strength degradation of FRP materials. Comprehensive tensile tests at various temperatures are needed to improve the FRP material degradation models especially with different FRP materials available in the market.
- The model should be extended to simulate the effects of temperature on the bond of FRP to concrete.

## Acknowledgements

## Conflicts of Interest

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**MDPI and ACS Style**

Adelzadeh, M.; Hajiloo, H.; Green, M.F.
Numerical Study of FRP Reinforced Concrete Slabs at Elevated Temperature. *Polymers* **2014**, *6*, 408-422.
https://doi.org/10.3390/polym6020408

**AMA Style**

Adelzadeh M, Hajiloo H, Green MF.
Numerical Study of FRP Reinforced Concrete Slabs at Elevated Temperature. *Polymers*. 2014; 6(2):408-422.
https://doi.org/10.3390/polym6020408

**Chicago/Turabian Style**

Adelzadeh, Masoud, Hamzeh Hajiloo, and Mark F. Green.
2014. "Numerical Study of FRP Reinforced Concrete Slabs at Elevated Temperature" *Polymers* 6, no. 2: 408-422.
https://doi.org/10.3390/polym6020408