Numerical analysis of the bending performance influencing factors of FRP reinforced concrete beams

Wang Wenyuan1, Fan Cheng2

1.Research Center for Numerical Tests on Material Failure, Dalian University, Dalian, 116622,China

2. Research Center for Numerical Tests on Material Failure, Dalian University, Dalian, 116622,China ,*249592174@qq.com(The corresponding author) Abstract: The low elastic modulus of FRP bars and their non-yielding characteristics result in large deflections and wide cracks in concrete beams reinforced with FRP bars. In order to study the bending performance of FRP reinforced concrete beam ,the finite element software ABAQUS was used to simulate the bending properties of the FRP reinforced concrete beam. The results of numerical simulation are in good agreement with other experimental results , which verified the correctness of the finite element model and analyzed the bending performance influencing factors of FRP reinforced concrete beam. Keywords: FRP bars ; load-displacement curve ; concrete beam ; Bending Performance ; ABAQUS ; finite element analysis

1. Introduction

FRP bars is a new type of composite material, with anti-magnetic, electrical insulation, resistance to fatigue, corrosion, small of creep, light weight and high strength..Therefore, replace reinforced with FRP bars for reinforcing concrete structures can effectively solve the problem of steel corrosion, it can also solve the problem of concrete damage caused by the steel corrosion and damage. In addition, FRP bars to meet the special requirements of certain structures, such as anti-electromagnetic interference and so on. In 1996, Dolan according to the experimental study of priestesses FRP reinforcement member of analyzed and summarized by the factors of the influence of priestesses FRP bars. In 2005 , Wegian and Abdalla And others stress the performance of FRP bars concrete beams were studied. And the results show that: FRP bars crack width of concrete beams than ordinary concrete beam is wider when shear, and analyzed the influencing factors of the tensile reinforcement ratio and concrete strength affecting the performance of FRP bars concrete beam flexural properties. Although our study time for FRP bars is not long, the research progress rapidly. In 2009, Xu Xinsheng, the Professor of Jinan University, factors FRP bars concrete beam deflection studied experimentally and with ANASYS finished finite element analysis.

Damage model of concrete shaping in ABAQUS have the advantage of the convergence of computing accurate and easy. In this paper, We use ABAQUS to analyze numerical of flexural properties of FRP bars to concrete beams., and the experimental results were compared to others for verify the correctness of the established finite element model. AT the same time, we provide the basis for the study of bending performance of FRP bars concrete beam.

2. Finite Element Analysis

2.1 Constitutive relation

2.1.1 Concrete constitutive relationship The uniaxial compressive stress - strain of concrete using expression by concrete structural design codes

provided, as follows:

(1 )c cd E , (1)

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2

1 , 11

1 , 11

cn

cc

c

nx

n xd

xx x

, (2)

,

,

c rc

c c r

f

E

, (3)

,

, ,

c c r

c c r c r

En

E f

, (4)

,rc

x

(5)

Among them, αc is concrete uniaxial compressive stress - strain curve segment decreased parameter values. Take αc = 0.74; fc,r is the representative value uniaxial compressive strength of concrete, its value can be based on actual needs were taken fc , fck or fcm. This article take fck . εc,r is compressive strain of concrete peak. Take εc,r =1470*10. dc is parameters for concrete damage evolution and according to equation (2).

Concrete uniaxial tensile stress - strain relationship using the stress - strain relations of Shen Jumin and as

shown in equation (6). In the formulas, x=ε/εp，y=σ/σp，σp =0.26(1.25fc’)2/3 and σp is the peak tensile stress. εp is peak tensile strain and εp=43.1σp .

6

1.7

(1.2 0.2 ) ( )

( )0.31 ( 1)

p p

pp

x x

x

x x

(6)

2.1.2 FRP bars constitutive relation The stress – strain of FRP bars is a linear relationship can be expressed as σf=Efεf .And Ef is the elastic modulus of FRP bars.

Fig. 1 FRP bars concrete beam finite element model Fig. 2 FRP bars stress strain relation curve

2.2 Finite Element Modeling

2.2.1 Plastic damage model set and plastic damage factors to determine the parameters of Plastic damage model parameters in the plastic module references expansion angle φ = 300. Flow potential

eccentricity take program defaults 0.1. Initial equivalent biaxial compressive yield stress and the initial biaxial compressive yield stress equivalent to the initial uniaxial compressive yield stress ratio fb0 / fc0 take 1.16. Tensile and compressive radial partial amount of the second stress invariants ratio Kc taken by 0.6667. ABAQUS selected text shaping damage model based on the need to calculate the tensile cracking strain εck relationship with that pull factor bt damage and compression inelastic strain relationship εin and compression damage factor of dc . See the following equation (7):

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1 ,( , )(1/ 1) /

ck pl

k c

Ed k t c

b E

(7)

Wherein, εin =ε-σ/Ec is inelastic strain in case of concrete compression. εpl=bkεin,ck are forming concrete tensile and compressive strain in case. bk(bc,bt) are forming strain and inelastic strain or cracking strain scaling factor. ABAQUS material properties need to enter the parameters in Table I and Table II. Model specific size is Table III.

Tab. II Material properties of steel Tab. I Material properties of concrete

fcu(Mpa) Ec(Mpa) µ fc(Mpa) ft(Mpa)

31.5 30000 0.2 20.1 2.01

Tab. III The size of the specimen and reinforcement

2.2.2 Cell division, boundary conditions and the applied load mode Concrete reduced integration unit with eight-node solid element C3D8R, reinforced nodes using two

dimensional linear rod elements T3D2. When you need to set a rigid model Pad loading point and at the support and connection with the concrete connections with the tie, which is to prevent stress concentration. Since the beam is modeled as a whole, the degree of freedom of the beam end bearing 1,2,3 three directions all the constraints, the other end of the second direction bearing only constraint freedom. Boundary conditions: only the bottom surface of the center line constraint node, allowing the beam under load angular displacement can occur.

Compression bar

stirrup Load point block

0.25 0.25 0.3

E(Mpa) 200000 200000 200000

fy(Mpa) 380 308 400

speci

men B( m

m)

H(m

m)

L(m

m)

tensile

bars

reinfo

rcemen

t

Compres

sion

steel

ffu(Mp

a)

E(Gp

a)

①

BL1-1

180 250 190

0

2GFRPΦ

9.5

0.315

%

2Φ16 993 72

②BL1-2

180 250 190

0 3GFRPΦ9.5

0.473

% 2Φ16 993 72

③BL1-3

180 250 190

0 4GFRPΦ9.5

0.63% 2Φ16 993 72

④TL1-1

180 250 190

0 2CFRPΦ9.5

0.315

% 2Φ16 1779 136

⑤TL1-2

180 250 190

0 3CFRPΦ9.5

0.473

% 2Φ16 1779 136

⑥TL1-3

180 250 190

0 4CFRPΦ9.5

0.63% 2Φ16 1779 136

⑦TL2-1

180 250 190

0 2CFRPΦ9.5

0.315

% 2CFRPΦ9.5

1779 136

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Loading: symmetrical load during analysis in one-third of the loading imposed displacement control model beams, load transfer to the node is in accordance with the principle of displacement equivalent.

2.3 Verification Model

In order to verify the correct calculation of the finite element method, the use of the finite element model to ABAQUS finite element FRP reinforced concrete beam flexural performance analysis, and theoretical calculations are compared with the measured experimental values. From Figures 3, 4 and 5 of this article can be seen in the calculation results and the literature of the experimental results and the calculation results are in good agreement. And verify the correctness and validity of selected concrete constitutive finite element model.

3. Analysis of Model

In order to further investigate the flexural properties of FRP bars concrete beams, the paper main factors affecting FRP reinforced concrete beam flexural properties were analyzed.

3.1 Effect of FRP bars for reinforcement ratio

Fig. 3 Different reinforcement ratio of BL beam

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Fig. 4 Different reinforcement ratio of TL beam

From Figures 6 and 7 can be seen FRP reinforcement ratio greater impact on the performance of the beam by force. With the increase of reinforcement ratio, the bearing capacity has greatly improved. But almost no change in the cracking load. Because when the concrete cracking, stress FRP bars is small, cracking performance depends on the tensile strength of concrete. With the increase of reinforcement ratio, horizontal section after cracking shorten. At the same time stiffness has also been reduced stiffness. And Reinforcement ratio of large specimens slight reduction in reinforcement ratio smaller than the lower specimen.

①The GFRP bars of reinforcement ratio of specimen BL1- ②1 was 0.315%, the specimen BL1-2 ③reinforcement ratio is 0.473%, the specimen BL1-3 reinforcement rate is 0.63%. As can be seen from Figure 6,

GFRP reinforced concrete beams bearing capacity of an average of 36.59%.The reinforcement rate of specimen ④ TL1- ⑤1 is 0.315%,of specimen TL1- ⑥2 is 0.473%, of specimen TL1-3 is 0.63%. As can be seen from Figure 7, the bearing capacity of CFRP bars concrete beams by an average of 26.21%.

3.2 FRP bars type of influence

① BL1- ④1 specimen and specimen TL1- ②1 as a group, specimen and specimen BL1- ⑤2 TL1-2 as a group. These two sets of specimens of this type only consider the reinforcement affected by factors, in addition to the different types that stretch, the other parameters are the same. From Figures 8 and 9 can be seen a greater impact on the type of FRP bars flexural properties of FRP reinforced concrete beams. Carrying Capacity of CFRP tendons (carbon fiber reinforced ribs) concrete beams than GFRP bars (glass fiber reinforcing ribs) concrete beams. Because the concrete cracking entirely by stretch under tension, while the tensile strength of CFRP tendons was higher than in the GFRP bars. From Figures 8 and 9 can also be seen concrete beams have had a large displacement, but this does not affect its function. And in normal use can be improved by prestressing and other methods applied so as to achieve full use of high bearing capacity of FRP reinforced concrete beams characteristics.

3.3 the influence of the thickness of concrete cover

② ⑤Figures 10 and 11 belong to the specimens and only consider concrete protective layer thickness of the load - displacement curve of influence. As can be seen from the figure that at the lower load level, the protective layer thickness of FRP reinforced concrete beams with little bending performance. And as the load increases, the large protective layer thickness of the beam deformation is larger. This shows that the bearing capacity of the thickness of the protective layer to improve not conducive to improving the beam. Because the increase in thickness of protective layer section reduced by lowering the effective height of the bearing capacity of the beam. Due to the characteristics of FRP reinforcement has good corrosion resistance, suggest that in the engineering construction in situations.

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Fig. 5 Contrast figure of TL1-1and BL1-1

Fig. 6 Contrast figure of TL1-2and BL1-2

Fig. 7 Different layer of BL1-2 load-displacement curve

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Fig. 8 Different layer of TL1-2 load-displacement curve

that could satisfy the requirement of protective layer to reduce the thickness of protection layer, this is conducive to give full play to the characteristics of FRP reinforced high tensile strength.

4. conclusion

(1) ABAQUS can correct for FRP reinforced concrete beams for finite element analysis. The results are in good agreement with the experimental results. Load - displacement curve shape with the experimental results are close. Verify that the finite element model of correctness and concrete constitutive selected correctness. Types of FRP bars and effects on the bending properties of the type of beam is larger, the influence of the protective layer thickness is smaller. (2)The main problem is the presence of paper using ABAQUS finite element analysis ignores the bond-slip between FRP tendons and concrete. Although this will make the carrying capacity of a certain high, easier in terms of modeling and computational convergence performance. In this study, a convenient and versatile method can provide a basis for the subsequent analysis of FRP reinforced concrete.

5. References

[1] Zhang Jianwei, Deng Zongcai, Du Xiuli. The application of prestressed FRP in concrete structure and development. [J]. Earthquake engineering, 2006, 22 (1) : 133-139. [2] Wang Maolong, Zhu Fusheng, Jin Yan. Prestressed FRP reinforced concrete beam bending performance test research. [J]. Concrete, 2006 (12) : 35-38. [3] Benmokrane B，Tighiouart B，and Chaallal O. Bond Strengthand Load Distribution of GFRP Reinforeing bars in concrete ACI Materials Joumal[J]. 1996，Vol. 93(3):246-253 [4] F.M.Wegian,H.A.Abdalla. Shear capacity of concretebeams reinforced with fiber reinforced polymers[J]. CompositeStructures, 2005, 71: 130-138 [5] Xu Xinsheng, Cao Kai, Yan Yuben. The deflection of FRP reinforced concrete beam characteristics and influence factors analysis. The 19th annual national conference on structure engineering. 2010, 11. The classification number TU375.1 [6] Shen Jumin, Wang Chuanzhi, Jiang Jianjing. With plate and shell finite element limit analysis of reinforced concrete [M]. Beijing: tsinghua university press, 1993 [7] Lee, Fenves. Plastic-damage model for cyclic loading of concrete structures. Journal of Engineering Mechanics,1998,124（8）：892-900. [8] ABAQUS Inc. Abaqus theory manual [M]. 2007. [9] ABAQUS Inc. Abaqus users manual [M]. 2007.. [10] Concrete structure design code,GB 50010-2010. [11]Xu Xinsheng, Ji Tao, Zheng Yongfeng, FRP reinforced concrete beam deflection and calculation methods, the characteristics of engineering mechanics, 2009, 26 (1-6) : 171-175

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