Glass Fiber Reinforced Concrete Behavioral Studies in Flexure

Sumit Guha^*
*Correspondence: Sumit Guha, National Institute of Technology (NIT) Durgapur, West Bengal and Sr. Technical Officer, CSIR-Central Glass & Ceramic Research Institute (CSIR-CGCRI), Kolkata, India, Email:

Keywords

Composite materials • GFRP reinforcement • GFRP RC beams, • Flexural behaviour • FEM analysis

Introduction

Fiber-reinforced polymer (FRP) bars have emerged as an alternative reinforcement for concrete structures. On the one hand, this kind of reinforcement exhibits such properties like corrosion resistance, electromagnetic neutrality and high cut-ability. As a result it can have many applications, especially in structures used in marine environments, in chemical plants, when electromagnetic neutrality is needed, or in temporary structures. On the other hand, FRP bars have low modulus of elasticity and high tensile strength. Due to their mechanical properties, deflections and cracking of FRP RC flexural members are larger than of traditional RC members. As a result, the design of FRPRC beams is often governed by the serviceability limit states.

This paper presents the results of a numerical study in which three GFRP RC beams were tested in four- point bending. The aim of this simulation was to examine the failure mechanism and deflection of simply supported GFRP RC beams depending on the reinforcement ratio. The dimensions of the specimen and properties of concrete and GFRP bars were assumed on the basis of an experimental study. The results of the numerical simulations were compared with code formulations with the results of experiments.

Research Methodology

Numerical simulations test specimen

The numerical model of beams was created on the basis of the beam which is shown in Figure 1. The numerical study consisted in investigating the flexural behaviour of three beams with varying GFRP reinforcement (Table 1). All beams had a cross-section of 0.14 × 0.19 m², a total length of 2.05 m and a span of 1.80 m. The shear reinforcement consisted of 8 mm round steel stirrups placed at intervals of 70 mm. In the pure bending zone no stirrups were provided. Two 6 mm steel bars were used as top reinforcement to hold the stirrups.

Material properties concrete

All beams had a target concrete compressive strength of 30 MPa. The properties of concrete were evaluated from cylindrical specimens. They are presented in Table 2.

GFRP

GFRP ribbed bars were used as a flexural reinforcement. The experimentally determined mechanical properties of reinforcement are shown in Table 3.

Model of the beam

The finite element (FE) model of considered beams was implemented in ABAQUS environment. The analysis was performed on 2D model and the following assumptions were adopted:

• Concrete damage plasticity (CDP) model of concrete was assumed

•Tension stiffening effect was taken into account

• GFRP reinforcement was assumed as a linear elastic isotropic material

• Steel reinforcement was assumed as a linear elastic- plastic material with isotropic hardening

• The reinforcement was modelled as 2-node truss elements embedded in 4-node elements of plane stress (Figure 2).

The model of beams consisted of two different types of finite elements:

• T2D2 – 2-node 2D truss elements

• CPS4R – 4-node plane stress elements with reduced integration.

The concrete was modelled as concrete damage plasticity material, which is based on the brittle- plastic degradation model. For concrete under uniaxial compression, the stress-strain curve shown in Figure 3 was adopted. It is composed of the parabolic ascending branch and a descending branch extended up to the ultimate strain εcu [1].

The tension stiffening effect was taken into account by applying a modified formula (Eq.1) to describe the behaviour of concrete under tension (Figure 4):

σt = Ec.Єt, where Єt ≤ Єcr and σt = fctm (Єcr/ Єt)ⁿ where Єt ≥ Єcr ----(1)

Where E_c is the modulus of elasticity of concrete, ε_t is the tensile strain of concrete, εcr is the tensile strain at concrete cracking, fctm is the average tensile strength of concrete and n is the rate of weakening

Result and Discussion

Failure mode & ultimate mode

The results of the numerical simulation and the experimental studies [2,3] shown that all the beams failed in a brittle mode due to concrete crushing. The results of FE analysis are presented in Figure 5. It was assumed that the value of the maximum compressive concrete strains is about 0.0042.

According to ACI 440.1R-06, the failure mode is governed by concrete crushing when the reinforcement ratio ρf is greater than the balanced reinforcement ratio ρfb:

Pf = Af/bd (2)

Pfb = 0.85ß1 (fc/ffu)[(Ep.Єcu)/(ffuEf Єcu=ffu] (3)

Where Af is the area of GFRP reinforcement, b is the width of the section and d is the effective depth. In Eq. (3), b1 is the ratio of depth of equivalent rectangular stress block to depth of the neutral axis, fc is the concrete compressive strength, ffu is the design tensile strength of GFRP reinforcement, Ef is the modulus of elasticity of FRP, and εcu is the maximum concrete strain [2]. The actual and balanced reinforcement ratios are compared in Table 4. All the beams had higher reinforcement ratios than ρfb, hence according to code [2], failure by concrete crushing was expected in all of them. This mode of failure was confirmed by the numerical analysis and the results of experiments.

Experimental (EXP), numerical (FEM) and theoretical [1,2] ultimate loads are compared in Table 5. There is good agreement between the experimental and numerical results, whereas ultimate loads calculated according to the codes [2,4] are underestimated. Their values are lower than the values of loads obtained in the experimental tests [3] by about 26-31% and 10-15% for ACI and EC2, respectively. These differences can be caused by the value of the maximum concrete compressive strain εcu which is assumed in these codes – 0.0030 for ACI and 0.0035 for EC2. The results of experiments [5] show that the actual ultimate concrete strain εcu is about 0.0042- 0.0047. On the basis of the results shown in Table 5, it can be said that the reinforcement ratio has an influence on the flexural strength of the beams. The increase in the reinforcement ratio results in the increase in the ultimate loads of the beams.

Deflections

Figures 6-8 show the numerical, theoretical and experimental load-deflection curves for all beams. The results of the numerical analysis correspond well with the results obtained in the experiments.

Comparing theoretical predictions obtained based on ACI (Eq. 4) and EC2 (Eq. 5) with the results of experimental tests, it can be observed that up to the service load (deflection d<L/250) there is good agreement between theoretical and actual values of deflections. For higher loads these codes underestimate deflections. These differences can be connected with the fact that these theoretical approaches use a simplified linear stress-strain constitutive relationship for concrete.

Ie = [Mcr/Ma]³ßdIg + [1-(Mcr/Ma)³]Icr ≤ Ig (4)

δ = ζ δII+ (1-ζ) δ1 (5)

Eq. 4 shows the expression for an effective moment of inertia Ie of the concrete section according to ACI, where Ig is the gross moment of inertia of concrete section, Icr is the moment of inertia of the cracked section, Mcr is the cracking moment, Ma is the maximum moment in the member and bd is the reduction coefficient related to the reduced tension stiffening effect. Eq. 5 shows the formulation for deflections d according to Eurocode 2 [1], where dI is un-cracked state deflection, dII is fully cracked-state deflection and z is the coefficient related to the tension stiffening effect.

As can be observed in Figures 6-8, the reinforcement ratio has a significant effect on the stiffness of the RC beams. As expected, higher deflections are obtained for lower reinforcement ratios and vice versa.

Data availability statement

Data available on request due to privacy/ethical restrictions Data subject to third party restrictions. The data that support the findings of this study are available from the author upon reasonable request over mail as mentioned in the manuscript.

Conclusion

This paper presents the results of numerical, theoretical and experimental study of the flexural behavior of GFRP RC beams. Based on these results, the following conclusions may be drawn:

• The reinforcement ratio has a significant effect on the flexural behavior of the GFRP RC beams. The increase in the reinforcement ratio results in the increase in the ultimate loads and in the stiffness of the beams.

• The failure mode is governed by concrete crushing when the reinforcement ratio ρf is greater than the balanced reinforcement ratio ρfb (according to ACI 440.1R-06). All beams behave almost linearly up to the moment of failure, which takes place at relatively large deflections.

• At the service load level, the deflections calculated according to ACI 440. 1R-06 and Eurocode 2 are in close agreement with the results of the experiments. For higher loads these codes underestimate deflections.

• The ultimate loads calculated according to ACI 440.1R-06 and Eurocode 2 are underestimated. This underestimation can be caused by the value of the ultimate concrete strain εcu which is assumed in these codes. It is lower than the value of εcu obtains in experiments.

• The nonlinear model of concrete, which was adopted in the study, reflects relatively well the behavior of the actual concrete.

References

1. En, B.S. "1-1. Eurocode 2: Design of concrete structures–Part 1-1: General rules and rules for buildings." European Committee for Standardization (CEN) (2004).
2. American Concrete Institute Committee 440. "Guide for the Design and Construction of Structural Concrete Reinforced with FRP Bars." American Concrete Institute, (2006).
3. Systèmes, Dassault. "Abaqus analysis user’s manual, Simula Corp." Providence, RI, USA 3 (2007).
4. Benmokrane, Brahim, Omar Chaallal, and Radhouane Masmoudi. "Glass fibre reinforced plastic (GFRP) rebars for concrete structures." Constr Build Mater 9 (1995): 353-364.
5. Kiran, S.T., and R.K. Srinivasa. "Comparison of Compressive and Flexural Strength of Glass Fiber Reinforced Concrete with Conventional Concrete."Int. J. Appl. Eng. Res 11 (2016): 4304-4308.