## 1635 Design of FRP Shear Strengthening Systems

FRP strengthening systems can be used to increase the shear capacity of concrete beams and columns. FRP strengthening systems are applied to the webs of beams (or columns) and function in an analogous fashion to internal steel shear reinforcement. Because FRP shear strengthening systems are applied to concrete members that are often monolithic with other continuous members (such as floors and walls), it is not always possible "wrap" the FRP strengthening system completely around the member (which is the desirable condition). The FRP strengthening system must therefore be terminated at the top of the web (a three-sided "U-wrap") or both at the top and at the bottom of the web (a two-sided system).

The non-fully wrapped systems are susceptible to detachment failures (similar to flexural strengthening) and their strains are limited by a shear bond-reduction coefficient, kv.

The nominal shear capacity of an FRP strengthened concrete member with existing steel shear reinforcing is determined by adding the contribution of the FRP strengthening system to the existing shear capacity, given as

where

sf and

where Vc is the existing shear capacity of the concrete, Vs is the shear capacity of the existing steel shear reinforcement, Vf is the shear capacity of the FRP strengthening system, /fe = Ef efu is the effective tensile stress in the FRP at ultimate, a is the inclination of the fiber in the FRP strengthening system to transverse axis (the horizontal axis in a beam or the vertical axis in a column), df is the effective depth of the FRP strengthening system, sf is the center-to-center spacing of the FRP shear strengthening strips, and wf is the width of the FRP shear strengthening strip. (For a continuous FRP shear strengthening sheet or fabric sf = wf.) The FRP capacity reduction factor, Cf, is taken as 0.95 for completely wrapped sections (contact-critical) and as 0.85 for two- or three-sided wrapped sections (bond-critical).

The effective strain in the FRP shear strengthening system is limited to prevent detachment failures and also to maintain the integrity of the concrete aggregate interlock in the concrete member. For completely wrapped FRP shear strengthening systems the maximum effective strain in the FRP strengthening system at failure is limited to efe = 0.004 < 0.75efu (16.86)

For three-sided or two-sided shear strengthening the effective shear strain in the FRP strengthening system at failure is limited to efe = kvefu < 0.004 (16.87)

where the shear bond-reduction coefficient is a function of the concrete strength, the wrapping type used, and the stiffness of the FRP strengthening system. Empirical equations for determining this coefficient are given in the ACI 440.2R-02 guide.

Mechanical anchorages can be used to anchor two- or three-sided wraps in the compression zone of the web; however, design guidance is not provided by the ACI 440.2R-02 for this at the present time.

Limits on spacing of discreet FRP shear strengthening strips and the maximum shear strength enhancement that can be obtained using FRP strengthening are provided in the ACI 440.2R-02 guide.

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