**Bond between Concrete and FRP Bars in NSM Technique**

The most important factor that controls the performance of concrete elements improved by the NSM FRP bar is the bond between concrete and FRP bars so proper understanding of bond behavior is substantially significant for enhancing the reinforced concrete beams successfully.
Bar-resin and resin-concrete are the two interfaces included in the NSM FRP. Tensile stress is generated in the FRP reinforcement after loading of the structure. The resultant stress imposed by the lug of FRP bar on the adhesive material is acts at an angle **Fig.1: Forces Between NSM FRP Bar and Epoxy**

**Fig.2: Typical Distribution of Stress Around FRP Bars**

*d*: bar diameter

*f*: Stress in the NSM FRP bar

_{FRP}*L*: Embedment length required to develop stress in the NSM FRP bar And the radial stress can be calculated as follow:

_{d}_{2}or Gā

_{2}whichever provide larger value:

_{1}, G

_{2}, and Gā

_{2}: Coefficients determined from finite element analysis All stresses which are mentioned above are shown in Figure-2. Finally, the embedment length required to avoid concrete split failure can be expressed as:

_{ct}and f

_{epoxy}: are the concrete and epoxy tensile strength, respectively

**Bond between NSM FRP Strip and Concrete**

Since NSM FRP strips have two sides, so there is two bonded side area between FRP strip and concrete. An analytical model has been developed to estimate the interfacial shear stress of the FRP strip.
Not only does the model taken the two-side bonded area into consideration but also the continuous declining of flexural stiffness because of concrete cracking.
It is considered that large concentration of shear stresses at the end of the strips cause the strip debonding. When simply supported beam subjected to point load (P) at the midspan, the shear stress at the point where FRP strip is terminated can be evaluated as follow:
*t*: is the thickness of the NSM FRP strips.

_{f}*n*: is the modular ratio between concrete FRP and concrete.

*P*: is the concentrated failure load.

*l*: is the unbonded length of the strip

_{o}*y*: is the distance from the neutral axis of the beam to the NSM FRP strips.

_{eff}*I*: is the effective moment of inertia of enhanced element.

_{eff}*x*: is the distance between the end of the NSM FRP strip to the beam support.

*G*: is the shear modulus of the binder agent.

_{a}*t*: is the thickness of the adhesive materials

_{a}*E*: is the elastic modulus of the FRP strips. When the shear stress, which depends on the concrete properties, reaches the maximum value, debonding will take place. It is demonstrated that, the failure of strengthened beams is started and controlled by concrete shear strength. Moreover, strength and adhesion properties of other kinds of materials such as epoxy, and NSM FRP strip are much stronger than concrete. Furthermore, the ultimate shear stress in the strengthened beam can be computed if both compressive and tensile strength of concrete are known by applying the following equation.

_{f}*f*: Compressive strength of concrete after 28 days

_{c}'*f*: Tensile strength of concrete The magnitude of the load that causes the failure of strengthened beam can be found by substituting equation 9 into equation 7. Regarding development length, it relies on FRP strip dimensions, concrete properties, adhesive properties, internal steel reinforcement ratio, reinforcement arrangement, type of loading, and groove width. The development length of FRP strip can be calculated by considering these steps. Firstly, calculate loading failure for various embedment lengths, consequently a curve which represent failure envelope because of strip debonding at cut off point is produced as shown in Figure-3. Secondly, apply a cracked section analysis at sections of ultimate induced normal stresses and calculate maximum load need to rupture the strip as shown in Figure-3. Thirdly, find the development length at the intersection of the line corresponds to the strip flexural failure with curve representing debonding failure at the end of the strip. Finally, it should be said that, development length will prevent brittle failure due to strip debonding and guarantee complete composite action between concrete and FRP strip.

_{ct}**Fig.3: Procedure to Estimate Development Length of NSM Strips**

**Bond between Concrete and Externally Bonded FRP Sheet**

In this technique, one side of the FRP sheet is bonded with concrete by applying adhesive materials and a model has been developed which takes continuous reduction of flexural stiffness due to concrete cracking into consideration.
The shear stress (*t*: is the thickness of the NSM FRP sheet.

_{f}*n*: is the modular ratio between concrete FRP and concrete.

*P*: is the concentrated failure load.

*l*: is the unbonded length of the sheet yeff: is the distance from the neutral axis of the beam to the NSM FRP sheet.

_{o}*l*: is the effective moment of inertia of enhanced element.

_{eff}*G*: is the shear modulus of the binder agent.

_{a}*t*: is the thickness of the adhesive materials

_{a}*E*: is the elastic modulus of the FRP sheet.

_{f}*E*: is the concrete modulus of elasticity

_{c}*E*: is the modulus of elasticity of adhesive material

_{a}*I*: is the moment of inertia of FRP sheet

_{f}*b*: is the width of FRP sheet

_{f}*M*: is the applied moment on the strengthened concrete cross section at cut off points

_{a}*V*: shear force in the strengthened concrete beam at the FRP sheet cut off point The combination of both shear and normal stresses at cut off point of FRP sheet may be employed for the determination of externally bonded FRP sheet delamination. The relationship between shear and normal stresses in terms of concrete compressive and tensile strength may be expressed as:

_{o}**Read More:**

**Strengthening of RCC Beams in Shear using Externally Bonded FRP Plates or Strips**