# Modeling Strategies of Finite Element Simulation of Reinforced Concrete Beams Strengthened with FRP: A Review

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## Abstract

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## 1. Introduction and Background

## 2. Finite Element Model Development Strategies

#### 2.1. Considerations for Element Types

#### 2.2. Considerations for Material Parameters

#### 2.2.1. Concrete

_{c}= concrete compressive stress in MPa corresponding to a specified strain value ε

_{c}, ${f}_{c}^{\prime}$ = concrete compressive strength in MPa.

_{t}. Once the value of the tensile strength of concrete is reached, stress relaxation is simulated with a steep drop of 40% of f

_{t}and then followed by linear descending curve up to a strain value of 6ε

_{t}, where ε

_{t}is the concrete strain value at f

_{t}as shown in Figure 2 [28,48,52]. From this view, the tensile strength of concrete f

_{t}is computed as per Equation (4). Knowing this value, as well as modulus property of concrete, then the strain at this particular tensile strength can be estimated in addition to that at failure. Other properties of concrete include Poisson’s ratio, which can vary between 0.18–0.22 [53].

#### 2.2.2. Steel Reinforcement

_{r}the diameter of the mentioned reinforcements in (mm), N

_{r}the number of reinforcements bars and L

_{1}and L

_{2}is the lengths of two adjacent reinforcement link elements in (mm).

#### 2.2.3. FRP and Adhesive

_{u}is the ultimate slip at ${\tau}_{u}$ in (mm).

_{u}, for the steel reinforcement and the values of ${\tau}_{u}\mathrm{and}$s

_{u}for the GFRP and CFRP materials can be assumed to roughly be 20.25 MPa, 10.1 MPa, 0.42 mm, 0.33 mm, respectively.

_{max}) value. This τ

_{max}corresponds to a slip (s

_{u}) value. Beyond this point, a softening response is registered until the ultimate attained slip (assumed to equal to four times the slip corresponding to the ultimate shear stress) is reached. For transparency, τ

_{max}for round deformed FRP bars can be evaluated using the following expression proposed by Hassan and Rizkalla [60].

_{ct}is the concrete tensile strength in MPa, μ the coefficient of friction. A value of μ = 1 is used as proposed by De Lorenzis and Teng [61] and G

_{1}is a constant taken as 1.0.

#### 2.3. Considerations for Boundary Conditions and Loadings

#### 2.3.1. Monotonic and Cyclic Loading

#### 2.3.2. Fire Loading

^{2}K for standard fire conditions and in the range of 40–50 W/m

^{2}K for hydrocarbon fires [69]. The value of the same coefficient is 4 W/m

^{2}K the unexposed cold surfaces. Heat transfer via radiation requires the input of emissivity (ε) and Stefan-Boltzman radiation (σ) coefficientS with values of 0.7–0.9 and 5.669 × 10

^{−8}W/m

^{2}K

^{4}, respectively [70,71].

#### 2.4. Considerations for Failure Criteria and Convergence Limits

- Yielding of steel reinforcement in tension is followed by concrete crushing when strain in the top compression fibers exceeds 0.003.
- Shear/tension delamination of the concrete cover may occur once the filling layer or substrate cannot sustain the forces induced in the reinforcing steel/cfrp rebars.
- Debonding of the FRP systems from the concrete substrate (delamination of plates/sheets or NSM bar pull-out).

#### 2.5. Considerations for Post-Processing of Results

## 3. Challenges, and Future Research Needs

- Experimental and numerical studies on the thermal and mechanical response of FRP-strengthened beams under cold and hot temperatures.
- Experimental and numerical studies on the creep-rupture behavior and endurance times of FRP-strengthened RC beams.
- Modeling the effects of high concrete strength on the shear and flexural performance of FRP-strengthened beams.
- Experimental and numerical studies on the effects of lightweight concrete on the shear and flexural performance of FRP-strengthened beams.
- Experimental and numerical studies on the long-term deflection behavior of flexural members strengthened with different types of FRP systems.
- Modeling the performance of externally strengthened RC beams anchored with FRP splay anchors under static, cyclic, and fire loadings.

## 4. Summary and Conclusions

- FRP materials offer unique solutions to aging and new structures that exceed those constructed by traditional materials.
- Developing appropriate modeling techniques is warranted given that the performance of FRP-strengthened concrete structures is complicated and complex.
- There is a need for development of appropriate and validated FE models since they provide more economical solutions than testing. It is beneficial in design oriented parametric studies and could be used in lieu of tests in the laboratory.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Typical finite element (FE) models developed in ANSYS for fiber-reinforced polymer (FRP)-strengthened Reinforced Concrete Beams (RC beams) showing different components.

**Figure 4.**Consideration for applied loading in ANSYS and ABAQUS: (

**a**) Monotonic loading; (

**b**) Cyclic loading.

**Figure 5.**Comparison between the failure modes of the experimental and FE models developed in ANSYS: (

**a**) Cover delamination; (

**b**) Debonding.

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**MDPI and ACS Style**

Naser, M.Z.; Hawileh, R.A.; Abdalla, J. Modeling Strategies of Finite Element Simulation of Reinforced Concrete Beams Strengthened with FRP: A Review. *J. Compos. Sci.* **2021**, *5*, 19.
https://doi.org/10.3390/jcs5010019

**AMA Style**

Naser MZ, Hawileh RA, Abdalla J. Modeling Strategies of Finite Element Simulation of Reinforced Concrete Beams Strengthened with FRP: A Review. *Journal of Composites Science*. 2021; 5(1):19.
https://doi.org/10.3390/jcs5010019

**Chicago/Turabian Style**

Naser, M. Z., Rami Antoun Hawileh, and Jamal Abdalla. 2021. "Modeling Strategies of Finite Element Simulation of Reinforced Concrete Beams Strengthened with FRP: A Review" *Journal of Composites Science* 5, no. 1: 19.
https://doi.org/10.3390/jcs5010019