Shear Strengthening of Reinforced Concrete (RC) with FRP Sheets Using Different Guidelines ()

Bashir H. Osman^{}

Civil Engineering Department, College of Engineering, University of Sinnar, Sinnar, Sudan.

**DOI: **10.4236/wjet.2023.112020
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Civil Engineering Department, College of Engineering, University of Sinnar, Sinnar, Sudan.

The aim of this study is to investigate the influence of fiber reinforcement polymer (FRP) on shear behavior of reinforcement concrete (RC) beams with various guidelines. The FRP thickness, beam depth and concrete strength at ultimate load are considered as main strength parameters. A finite element (FE) by using ANSYS computer program was used to analyze the reinforced concrete beams. The numerical models were used to investigate the effect of beam depth, concrete strength, CFRP sheet configuration, and CFRP sheet thickness on the behavior of reinforced concrete beams strengthened with CFRP sheets compared with different guidelines. The results from ACI guideline show little difference compared with FE, which make it suitable for RC beams strengthened with FRP sheets.

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Osman, B. (2023) Shear Strengthening of Reinforced Concrete (RC) with FRP Sheets Using Different Guidelines. *World Journal of Engineering and Technology*, **11**, 281-292. doi: 10.4236/wjet.2023.112020.

1. Introduction

In the last decade, the use of Fiber-Reinforced Polymer (FRP) composites in strengthening and repairing of structures has continuously increased because it has several advantages over other materials. Beside low weight and an economical way, epoxy resin and FRP composites provide high resistance to corrosion and mechanical strengths of structures repair or rehabilitation ( [1] [2] [3] ).

Over the last two decades, many researches were carried out on the strengthening of RC beams using FRP composites using different methods such as externally strengthening, near-surface mounted (NSM) strengthening, and embedded section (internal strengthening) ( [4] [5] [6] [7] [8] ). Furthermore, some studies [9] [10] [11] [12] investigate the flexural behavior of pre-damaged reinforced concrete (RC) beams repaired by using grids and engineered cementitious composite (ECC) and carbon fiber reinforced polymer (CFRP) under sustained load. Their results showed that most of the beams failed by debonding. Furthermore, the proposed repairing technique was effective in enhancing the flexural stiffness and bearing capacity of pre-damaged RC beams. Moreover, they proposed a mathematical model to calculate the flexural capacities of the repaired beams and the results were in accordance with excremental results. Six RC beams strengthened with CFRP sheets under static and fatigue loading were studied by Min, *et al.* [13] to show the failure mechanism. The results showed that acceleration the fatigue failure of the specimens is due to coupling of stresses between accumulated fatigue damage in the steel reinforcement and fatigue debonding of the CFRP plate. Jia, J., *et al.* [14] used the novel models of Extreme Learning Machine (ELM) in co-operation with Particle Swarm Optimization (PSO), Teaching-Learning based Optimization (TLBO), and gray wolf optimizer (GWO) to investigate the debonding strength of FRP. The results predicted from ELM-GWO showed the best performance compared with ELM-PSO and ELM-TLBO.

2. Material Properties and Codes of Practice Used in This Study

Based on this study, a prediction model was proposed by considering all common parameters that influence the ultimate shear capacity of a strengthened beam including concrete strength (
${{f}^{\prime}}_{c}$ ), effective height of the beam (*d*), FRP thickness (*t _{f}*), and strengthening configuration (completely wrapped, U-jacketing, and side bonding). The obtained results were compared with that recommended design guide given by different guidelines ( [13] [14] [15] [16] [17] ). Beam geometry and materials properties were illustrated in Figure 1 and Table 1, respectively.

Figure 1. Geometrical details of proposed RC beams.

Table 1. The properties of materials used in this study.

3. FE Model Description

Numerical Modeling

A finite element analysis (FEA) by using ANSYS [18] computer program was used to analysis the reinforced concrete beams. SOLID65 element, was used to model the concrete as this element is capable of modeling cracking in tension and crushing in compression. An eight nodes three degrees of freedom at each node: translations of the nodes in x, y, and z-directions used to define the element.

Steel reinforcement was modeled using link 8 element and which consists of two nodes with three degrees of freedom in each node. The FE model for the rebar was assumed to be a bilinear isotropic, elastic-perfectly plastic material, and identical in tension and compression. Solid element with an eight-node, solid 45, was used to simulate the plates in the supports and the loading points. This element has defined with eight nodes of three degrees of freedom at each node translation in the nodal *y*-, *x*-, and *z*-directions.

FRP sheet was modeled using Shell41 element. This element allows for different material layers with different orientations and orthotropic material properties in each layer. Since the FRP materials considered as orthotropic materials, they showed different properties in each direction. The relationship between ${v}_{xy}$ and ${v}_{yx}$ is illustrated in Equations (1) and (2) ( [15] [18] [19] ):

$1-{v}_{xy}^{2}\left(\frac{{E}_{y}}{{E}_{x}}\right)-{v}_{yz}^{2}\left(\frac{{E}_{z}}{{E}_{y}}\right)-{v}_{xz}^{2}\left(\frac{{E}_{z}}{{E}_{x}}\right)-2{v}_{xy}{v}_{yz}{v}_{xz}\left(\frac{{E}_{z}}{{E}_{x}}\right)=\text{Positive}$ (1)

${G}_{xy}={G}_{xz}=\frac{{E}_{x}{E}_{y}}{{E}_{x}+{E}_{y}+2{v}_{xy}{E}_{x}},{G}_{yz}=\frac{{E}_{z}\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}{E}_{y}}{2\left(1+{v}_{yz}\right)}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}{v}_{yx}=\frac{{E}_{y}}{{E}_{x}}{v}_{xy}$ (2)

In this study, Poisson’s ratios of: 0.22, 0.22 and 0.30 are used for
${v}_{xy}$ ,
${v}_{xz}$ , and
${v}_{yz}$ *, *respectively, which are widely used in the related published literature based on this subject. Contact elements TARGE170 and CONTA174 are used to model the contact between concrete and FRP. To study the contact between two elements, the surface of one element is considered as a contact surface (e.g. FRP) and the other body surface considered as a target surface (e.g. concrete). The contact and target pair concepts has been widely used in finite element models. As used in this study, the FRP was considered as the contact surface which is associated with the deformable body; the concrete was considered as the target surface which must be the rigid surface [20] .

4. Comparison of Different Method with Design Guidelines

Following the previous discussion on the behavior of FRP shear-strengthened beams, it is of interest to see how the measured shear capacity compares with the predictions from available design guidelines. Three design guidelines are considered in this study which compared with American Concrete Institute (ACI) (2008) such as Traintafillou and Anton 2000, carolin and taljsten 2005 and Zhichao and cheng 2005. The equations used in this part of this study related with below guides:

4.1. ACI Equation

Simplified method: the above equation is not so simple to use as a design equation, the ACI code permits use of below equation:

${V}_{c}=\frac{1}{6}\sqrt{{{f}^{\prime}}_{c}}{b}_{w}d$ (3)

For beams with shear reinforcement, the ACI consider nominal shear strength, ${V}_{n}$ as flow:

${V}_{n}={V}_{c}+{V}_{s}$ (4)

Which
${V}_{c}$ = shear strength of concrete;
${V}_{s}$ = shear strength of shear reinforcement. Shear strength for inclined stirrup at an angle *α* with horizontal suggested as:

${V}_{s}=\frac{{A}_{v}{f}_{yv}\left(\mathrm{sin}\alpha +\mathrm{cos}\alpha \right)d}{s}$ (5)

Which
${A}_{v}$ ,
${f}_{yv}$ are area of shear reinforcement in distance *s* and is the yield strength of shear reinforcement respectively.

When *α* = 90˚ (vertical stirups are used) the above equation reduces to

${V}_{s}=\frac{{A}_{v}{f}_{yv}d}{s}$ , but $\varnothing {V}_{s}\ge {V}_{s}$ (6)

The nominal shear strength of an FRP-strengthened concrete member can be determined by adding the contribution of the FRP external shear reinforcement to the contributions from the reinforcing steel (stirrups, ties, or spirals) and the concrete. An additional reduction factor
${\psi}_{f}$ * *is applied to the contribution of the FRP system.

$\phi {V}_{n}=\phi \left({V}_{c}+{V}_{s}+{\psi}_{f}{V}_{f}\right)$ (7)

The reduction factor ${\psi}_{f}$ of 0.85 is recommended for the three-sided FRP U-wrap or two-opposite-sides strengthening schemes. Insufficient experimental data exist to perform a reliability analysis for fully-wrapped sections; however, there should be less variability with this strengthening scheme as it is less bond independent, and therefore, the reduction factor ${\psi}_{f}$ of 0.95 is recommended. Figure 2 illustrates the dimensional variables used in shear-strengthening calculations for FRP laminates. The contribution of the FRP system to shear strength of a member is based on the fiber orientation and an assumed crack pattern. The shear strength provided by the FRP reinforcement can be determined by calculating the force resulting from the tensile stress in the FRP across the assumed crack. The shear contribution of the FRP shear reinforcement is then given by:

${V}_{f}={A}_{fv}{f}_{fe}\left(\mathrm{sin}\alpha +\mathrm{cos}\alpha \right){d}_{fv}/{s}_{f}$ (8)

where: ${A}_{fv}=2n{t}_{f}{w}_{f}$

Figure 2. Illustration of the dimensional variables used in shear-strengthening calculations for repair, retrofit, or strengthening using FRP laminates.

For reinforced concrete column and beam members completely wrapped by FRP

${\epsilon}_{fe}=0.004\le 0.75{\epsilon}_{fu}$

FRP systems that do not enclose the entire section (two- and three-sided wraps) have been observed to delaminate from the concrete before the loss of aggregate interlock of the section. For this reason, bond stresses have been analyzed to determine the usefulness of these systems and the effective strain level that can be achieved. The effective strain is calculated using a bond-reduction coefficient
${\kappa}_{v}$ * *applicable to shear:

${\epsilon}_{fe}={\kappa}_{v}{\epsilon}_{fu}\le 0.004$ , The bond-reduction coefficient can be computed from:

${K}_{v}={k}_{1}{k}_{2}{L}_{e}/11900{\epsilon}_{fu}\le 0.75$

The active bond length Le is the length over which the majority of the bond stress is maintained. This length is given by:

${L}_{e}=\frac{23300}{{\left({n}_{f}{t}_{f}{E}_{f}\right)}^{0.58}}$

The bond-reduction coefficient also relies on two modification factors, *k*_{1} and *k*_{2}, that account for the concrete strength and the type of wrapping scheme used, respectively. Expressions for these modification factors are given in:

${k}_{1}={\left(\frac{{{f}^{\prime}}_{c}}{27}\right)}^{2/3}$ , ${k}_{1}=\{\begin{array}{l}\frac{{d}_{fv}-{L}_{e}}{{d}_{fv}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}\text{\hspace{0.17em}}\text{forUwarps}\\ \frac{{d}_{yv}-2{L}_{e}}{{d}_{yv}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{fortwosidesbonded}\end{array}$

4.2. Traintafillou and Anton 2000 Equation for FRP Contribution

$\begin{array}{l}{\rho}_{f}=\frac{2{w}_{f}\ast {t}_{f}}{b\ast {s}_{f}}\\ {\epsilon}_{fe}=0.17{\left({f}_{c}^{2/3}/{E}_{f}{\rho}_{f}\right)}^{0.3}{\epsilon}_{fu}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{for}\text{\hspace{0.17em}}\text{full}\text{\hspace{0.17em}}\text{warp}\\ {V}_{f}=\left(2{w}_{f}{t}_{f}{E}_{f}{\epsilon}_{fe}{d}_{f}\right)/{s}_{f}\end{array}$

$\begin{array}{l}{\Gamma}_{f}=\left({E}_{f}{\rho}_{f}\right)/{f}_{c}^{2/3}\left(\frac{a}{d}\right)\\ {\epsilon}_{fe}=0.72{\epsilon}_{fu}{\text{e}}^{-0.0431{\Gamma}_{f}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{forthreeortwosides}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{or}\\ {\epsilon}_{fe}=0.00065{\left(\frac{{f}_{c}^{2/3}}{{E}_{f}{\rho}_{f}}\right)}^{0.56}\end{array}$ (9)

4.3. Carolin and Taljsten 2005 Equation

${V}_{f}=\left(\eta {\epsilon}_{cr}{E}_{f}{t}_{f}{r}_{f}z\mathrm{cos}\theta \right)/\mathrm{sin}\alpha ,\text{\hspace{0.17em}}{\epsilon}_{fe}=\eta {\epsilon}_{cr},\text{\hspace{0.17em}}\eta =0.6,\text{\hspace{0.17em}}{r}_{f}={b}_{f}/{s}_{f},\text{\hspace{0.17em}}{\epsilon}_{fe}={\epsilon}_{cr}$ (10)

4.4. Zhichao and Cheng 2005 Equation

$\begin{array}{l}{V}_{f}=\left(2{w}_{f}{t}_{f}{E}_{f}{\epsilon}_{fe}{d}_{f}\right)/{s}_{f},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\epsilon}_{fe}=R{\epsilon}_{fu}\\ {\rho}_{f}=(2{w}_{f}{t}_{f})/b{s}_{f}\\ R=1.4871{\left({\rho}_{f}{E}_{f}/{f}_{c}\right)}^{-0.7488}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{or}\\ R=0.5622{\left({\rho}_{f}{E}_{f}\right)}^{2}-1.2188\left({\rho}_{f}{E}_{f}\right)+0.778\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{whichissmall}\\ R=\left(0.0042{\left({f}_{c}\right)}^{2/3}{w}_{f}\right)/{\left({E}_{f}{t}_{f}\right)}^{0.58}{\epsilon}_{fu}{d}_{f}\end{array}$ (11)

4.5. Zhichao and Cheng 2005

$\begin{array}{l}{V}_{f}=\left(2{w}_{f}\ast {t}_{f}\ast {E}_{f}\ast {\epsilon}_{fe}\ast {d}_{f}\right)/{s}_{f},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{V}_{c}={\left({f}_{c}\right)}^{0.5}\ast b\ast d/6\\ R=\left(0.0042{\left({f}_{c}\right)}^{2/3}\ast {w}_{f}\right)/{\left({E}_{f}\ast {t}_{f}\right)}^{0.58}\ast {\epsilon}_{fu}\ast {d}_{f}\\ {\epsilon}_{fe}=R\ast {\epsilon}_{fu},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{p}_{f}=\left(2{w}_{f}\ast {t}_{f}\right)/b\ast {s}_{f}\end{array}$ (12)

5. Results and Discussion

The main goal for this work is to study the influence of fiber reinforcement polymer (FRP) on shear behavior of RC beams with various guidelines. The purpose was also to study the strength parameters such as, FRP thickness, beam depth and concrete strength at ultimate load.

5.1. FRP Thickness

Table 2 shows the effect of FRP thickness on the shear strength, which plotted in Figure 3.

Table 2 and Figure 3 show that the FRP thickness has a grater effects on concrete strength, the results predicted from Carolin equation showed under estimation compared with those from FE program. Furthermore, the ACI guideline showed acceptable differences compared with the other guidelines when compared with FE.

5.2. Effect of Concrete Strength

Table 3 shows the effect of FRP thickness on the shear strength, which plotted in Figure 4.

5.3. Effect of Beam Depth

Table 4 shows the effect of FRP thickness on the shear strength, which plotted in Figure 5.

(a) Full warp(b) U warp(c) 2s warp

Figure 3. Effect of FRP thickness on beams strength using different configurations (a) Full warp (b) U-warp (c) 2 sides warp.

Table 2. Effect of FRP thickness on the strength.

Table 3. Effect of concrete strength on shear strength.

Table 4. Effect of beam depth on shear strength.

(a)(b)(c)

Figure 4. Effect of concrete strength on beams strength using different configurations (a) Full warp (b) U-warp (c) 2 sides warp.

(a)(b)(c)

Figure 5. Effect of beam depth on beams strength using different configurations (a) Full warp (b) U-warp (c) 2 sides warp.

6. Conclusions

Based on the results of analysis using ANSYS software and different design guidelines on reinforced concrete RC beams strengthened with fiber reinforcement polymer (FRP) and reported in literature the following conclusions are:

1) The use of FRP strengthening has greater effect in the stiffness of the concrete.

2) The finite element models were able to accurately predict the load capacities for the simulated RC beams. This confirms the validity of the developed FE models and reliability of the FE simulation.

3) For the FRP shear contribution, the ACI equation is believed to be the most appropriate for practical design. However, for the fully wrapped scheme, the ACI method appears to predict the FRP shear contribution with a relatively high discrepancy.

4) The ACI model predicted the ultimate capacity of RC beams based on the beam geometry and concrete compressive strength without considering the effect of the longitudinal reinforcement.

5) The theoretical prediction of ultimate shear strength on the basis of methods used in this study gives results over estimate compared with the other design guidelines values in most of the beams.

6) Use ACI assumptions because it gives results with more reliable safety factors than other theorems according to results on the previous literature of RC beams in case of using analytical theorems in RC beams analysis.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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