Strengthening of reinforced concrete beams with FRP reinforced systems (FRP plate or strips) have been utilize from around 1980s. FRP systems can be used for increasing shear strength of reinforced concrete beams by completely or partially wrapping FRP systems around reinforced concrete member.

Since, most of reinforced concrete beams are constructed monolithically with other continuous members such as slabs or walls, therefore complete wrapping of FRP plates is not possible in most cases.

Directing FRP fibers perpendicular to potential shear cracks is effective in providing extra shear strength. Moreover, enhancing shear strength might lead to flexural failure which is more ductile failure hence more desired compare with brittle shear failure.

The additional shear strength achieved by applying FRP plates or strips depends on number of factors such as beam geometry, existing concrete strength, and applied wrapping scheme.

There are three main types of FRP systems which includes Aramid, Glass, and Carbon FRPs. The Carbon Fiber Reinforced Polymer plate which is a high quality but expensive type of FRP plate, is shown in Figure-1.

Externally bonding of FRP systems have been applied successfully for strengthening reinforced concrete beams in shear and for improving bridges especially in the United States of America.

Shear design procedures provided by Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI 440.2R-08) is used in this article.

**Figure-1: Carbon Fiber Reinforced Polymer Plate**

Table of Contents

**Wrapping of ****FRP Plates or Strips to RCC Beams**

There are three major wrapping schemes that applied in the shear strengthening of reinforced concrete beams:

- Completer wrapping
- U- Shaped wrapping scheme
- Two side wrapping scheme

**Complete Wrapping of FRP Plates**

This type is most efficient wrapping method. FRP system is wrapped around the concrete element completely as shown in Figure-2. As beams are monolithically poured it is hard to have all four sides available for wrapping. This method is suitable for strengthening of column.

**Figure-2: Common Wrapping Scheme for Shear Strengthening by utilizing FRP Plates or Strips**

**U- Shaped Wrapping Scheme**

This is used for cases where the beam is integrated with slabs and only three sides are available to use as shown in both Figure-2 and Figure-3.

**Figure-3: U-Shaped FRP Wrapping for Shear Strengthening of RCC Beams**

**Two side wrapping scheme of FRP Plates**

In this case two sides of the member are bonded to the FRP system as shown in Figure-2 and Figure-4.

**Figure-4: Two Sided FRP Systems for Strengthening of RCC Beams**

Moreover, all three scheme types used for reinforced concrete elements to increase shear strength but the most efficient is full wrapped followed by three-sided bonding then two-sided bonding FRP systems.

Furthermore, it is possible to either wrap all schemes continuously or discretely. In the latter case, center to center spacing between strips must be equal or smaller than (*d/4+strip width*).

Finally, U-shaped and two-sided wrapping are subjected to de-bonding failure and therefore their strains are limited by shear bond reduction coefficient (*k _{v}*).

The shear bond reduction coefficient is the function of applied wrapped scheme type, concrete strength, and the stiffness of FRP strengthening system. ACI 440.2 R-08 provides an equation to compute (*k _{v}*):

**Where:**

: design rupture strain of FRP system

*l _{e}*: Active bonded length over which most of shear stress is transferred between concrete and FRP system. The active bond length is calculated as follow:

*k _{1}*,

*k*: Two modification factors which take concrete strength and wrapping scheme respectively into consideration. These modification factors are computed by the following equations:

_{2}The formula used to compute (*k _{2}*) for U-shaped scheme is:

For two-sided scheme (*k _{2}*) is expressed as follow:

**Where:**

*d _{f}*: Effective depth of the FRP shear strengthening systems. It is equal to the full height of the section in the case of U-shaped scheme whereas, in two-sided bond is the distance from main steel reinforcement to the top of FRP system.

**Shear Design of Externally Bonded FRP Systems**

The design shear strength of strengthened concrete beams should be greater than the applied shear force (*V _{u}*).

The nominal shear strength of strengthened concrete members is estimated by combining shear strength of concrete (*V _{c}*), shear reinforcement which is either tie, or spiral (

*V*

_{s}) and shear strength provided by FRP system (

*V*).

_{f}Moreover, an extra reduction factor is applied to the FRP system shear strength.

**Where: **

*V _{c}*: shear strength of concrete which can be calculated as per the equation provided by ACI 318-11.

*V _{s}*: shear strength of steel reinforcement that can be calculated as per the formula provided by ACI 318-11.

: Strength reduction factor applied for shear strength of FRP systems which is 0.95 for fully wrapped member and 0.85 for U-shaped and two-sided wrapped element.

*V _{f}*: is shear strength provided by FRP systems and can be computed as per the following formula:

**Where:**

*A _{fv}*: shear strengthening FRP system area calculated by equation-8

*f _{fe}*: Effective tensile strength of FRP system obtained at failure of the section

: Angle between FRP plates or strips and horizontal axis of reinforced concrete beam

*d _{f}*: Effective depth of the FRP shear strengthening systems. It is equal to the full height of the section in the case of U-shaped scheme whereas, in two-sided bond is the distance from main steel reinforcement to the top of FRP system.

*s _{f}*: Spacing of FRP strips from center to center

*n*: Number of plies of FRP strengthening system

*t _{f}*: Nominal thickness of one ply of FRP strengthening system

*w _{f}*: Width of FRP strengthening strips and equal to

*s*in the case of continuous FRP strengthening system

_{f}*E _{f}*: Longitudinal modulus of FRP strengthening system

: Effective longitudinal strain of FRP plates or strips

The effective strain of FRP strengthening system is the peak strain that can be achieved at nominal strength and is controlled by failure modes of FRP strengthening system. It can be calculated for each wrapping scheme as follow:

**For fully wrapped scheme:**

**For U-shaped scheme and two-sided wrapping:**

When FRP strengthening, system is employed to increases shear strength of concrete element, shear reinforcement limit used for ordinary steel shear reinforcement must be utilized for both stirrups and FRP strengthening system:

*Concrete and steel reinforcement shear strength in equation-6 can be calculated by the following equations which are taken from ACI 318-11:*

**Concrete shear strength formula:**

**Where:**

: is one for normal concrete

*F _{c}‘*: Compressive strength of concrete

*b _{w}*: Width of the web for T-section or just (

*b*) for rectangular section

*d*: Depth of concrete section

**Shear strength of steel reinforcement formula:**

**For vertical stirrups:**

**For inclined stirrups:**

**Where:**

*A _{v}*: are of stirrups and shall be taken twice the area of the bar in circular tie, hoop, or spiral.

*f _{yt}*: Specified yield strength of stirrups

*d*: Effective depth of the section

*s*: is the spacing between stirrups

: Angle between inclined stirrups and longitudinal axis of the element

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