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

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**

*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*). 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 (

_{v}*k*):

_{v}**Where:**

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

_{e}*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}*k*) for U-shaped scheme is:

_{2}*k*) is expressed as follow:

_{2}**Where:**

*d*: 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.

_{f}**Shear Design of Externally Bonded FRP Systems**

The design shear strength of strengthened concrete beams *V*). The nominal shear strength of strengthened concrete members is estimated by combining shear strength of concrete (

_{u}*V*), shear reinforcement which is either tie, or spiral (

_{c}*V*

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

*V*). Moreover, an extra reduction factor is applied to the FRP system shear strength.

_{f}**Where:**

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

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

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

_{f}**Where:**

*A*: shear strengthening FRP system area calculated by equation-8

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

_{fe}*d*: 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.

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

_{f}*n*: Number of plies of FRP strengthening system

*t*: Nominal thickness of one ply of FRP strengthening system

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

_{f}*s*in the case of continuous FRP strengthening system

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

_{f}**For fully wrapped scheme:**

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

*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:**

*F*: Compressive strength of concrete

_{c}'*b*: Width of the web for T-section or just (

_{w}*b*) for rectangular section

*d*: Depth of concrete section

**Shear strength of steel reinforcement formula:**

**For vertical stirrups:**

**For inclined stirrups:**

**Where:**

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

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

_{yt}*d*: Effective depth of the section

*s*: is the spacing between stirrups

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