## 1634 Design of FRP Flexural Strengthening Systems

Flexural strengthening is achieved by attaching an FRP strengthening system (bonded strip or saturated dry fabric) to the underside (or soffit) of a flexural member to increase the effective tensile force resultant in the member and thereby increase the moment capacity of the member. This is analogous to adding steel strengthening strips (or plates) to the soffit of a member. However, two fundamental differences exist. First, the FRP strengthening system behaves in a linear elastic fashion and does not yield, and second, the FRP strengthening system is more susceptible to detachment (debonding or delamination) failures than steel plate systems. Epoxy bonded steel plates are typically anchored with steel bolts at their ends in addition to the epoxy bonding. Since the steel plates themselves will yield at a similar strain to the internal steel reinforcing, the stress level in the steel strengthening system is limited. In the case of FRP strengthening with FRP systems having ultimate tensile strengths exceeding 300 ksi (see Table 16.5 and Table 16.6) the stress level in the FRP can be significantly higher than that in steel strengthening systems. In the event that the internal steel reinforcing yields before the FRP strengthening system fails (the desired failure mode) the concrete member will undergo large deflections and cracking. All these factors lead to the greater likelihood that the FRP strengthening system will detach from the concrete long before it achieves its ultimate tensile capacity.

Strengthening of members in flexure can only be achieved if there is sufficient additional compressive capacity in the concrete to allow for the increase in internal moment. Therefore, flexural strengthening is most suitable for concrete members that are lightly to moderately reinforced, having steel reinforcement in the range of 20 to 40% of the balanced ratio. This is not uncommon in reinforced concrete members, especially in older structures.

The existing tensile strain in the concrete at the location of the applied FRP strengthening system due to sustained loads when the FRP strengthening system is applied should be accounted for in design calculations if a shoring system is not used.

The key to flexural strengthening with FRP strengthening systems is to understand the failure modes of the system. These include rupture of the FRP strengthening system, detachment of the FRP strengthening system (due to a variety of delamination or debonding modes), or compressive failure of the concrete. All of these modes can occur either before or after the internal steel has yielded. The desired mode of failure is concrete compressive failure after the internal steel has yielded with the FRP strengthening system still attached. This is often difficult to achieve and the mode of FRP detachment (or less frequently rupture) at large deflections after the internal steel has yielded is often achieved.

The FRP strengthening system can detach in a number of modes. The FRP system can delaminate from the concrete substrate (due to failure in the concrete, the adhesive layer, or the FRP laminate itself) either at the ends (due to high peeling and shear stresses) or in the interior of the beam due to flexural and shear cracks in the beam at large deflections. For a detailed discussion on detachment failure modes see Teng et al. (2001). Analytical methods to predict the various detachment failure modes are still not fully developed and the ACI 440.2R-02 guide limits the tensile strain level in the FRP strengthening system to prevent delamination failure by the use of an empirically obtained bond-dependent coefficient, km, which is a function of the unit stiffness of the FRP system and is defined as where efu is the ultimate strain in the FRP, n is the number of layers (or plies) of FRP strips or sheets or fabrics, Ef is the longitudinal tensile modulus of the FRP composite in the case of strips or the longitudinal modulus of the fibers in the strengthening direction in the case of sheets or fabrics, and tf is the thickness of an individual strip in the case of FRP strips or the net thickness of the fibers in a single sheet or fabric in the case of sheets or fabrics.

The strain level in the FRP strengthening system is limited by the strain in the concrete or the ultimate strain in the FRP system and is given as

where efe is the effective ultimate strain in the FRP at failure, ecu is the ultimate compressive strain in the concrete (0.003), c is the depth of the neutral axis, h is the depth of the section, and fib; is the existing tensile strain in the concrete substrate at the location of the FRP strengthening system. The effective stress, ffe, in the FRP is the ultimate strength of the FRP that can be achieved at failure and is linearly related to the ultimate strain as ffe = Ef fife

The nominal moment capacity, Mn, of the strengthened section (with an existing layer of tensile steel reinforcement only) is given as with and

Asfs + Afffe fs = Es fis = Es (fife + fibi) ( h-) < fy

where As is the area of the tensile steel, fs is the stress in the steel at failure, d is the depth of the steel reinforcing, b1 is the depth ratio of the equivalent Whitney stress block, Af is the area of the FRP strip or the fibers in a dry fiber system, g is the concrete stress resultant factor (0.85 when concrete compressive failure governs), b is the width of the section, and fy is the yield stress in the reinforcing steel. The solution to the above equations is typically found by a trail and error method by assuming a number of plies (or layers) of strengthening and calculating the resulting nominal moment. The desirable failure mode is achieved when the internal steel has yielded. Therefore, the current stress state in the steel can be assumed to be at yield and then checked. If the steel has not yielded before FRP rupture or detachment occurs, a new design should be attempted with a different strengthening system or a different number of plies.

The stresses in the steel and the FRP strengthening system at service loads should be determined using an elastic cracked section and checked against appropriate stress limits for sustained loads on FRP strengthened structures (ACI 440.2R-02 2002).

Mechanical anchorages or FRP wraps can be used to enhance the attachment of the FRP strengthening system to the concrete beam, especially at the ends of the FRP strengthening system. Design guidance is not provided by the ACI 440.2R-02 for this at the present time.

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