Design Approach for Calculating Deflection of FRP-Reinforced Concrete

Deflection of reinforced concrete is typically computed with an effective moment of inertia $I_e$ that accounts for nonlinear behavior after the concrete cracks. Existing expressions for $I_e$ tend to overpredict the member stiffness of concrete reinforced with fiber-reinforced polymer (FRP) bars, and an alternative expression is used as the basis for developing a practical design approach to compute deflection. The proposed expression has a rational basis that incorporates basic concepts of tension stiffening to provide a reasonable estimate of deflection for both steel and FRP-reinforced concrete without the need for empirically derived correction factors. Calculation of deflection with the proposed expression for $I_e$ is recommended using the code value for the elastic modulus $E_c$ of concrete because computed values of deflection are relatively insensitive to variations in $E_c$, and shrinkage restraint is taken into account by using a reduced cracking moment less than the code-based value of the cracking moment $M_{cr}$. $I_e$ is conservatively based on the moment at the critical section (where the member stiffness is lowest), unless more accuracy is required with an integration-based expression that gives an equivalent moment of inertia $I_e^{\prime }$ to account for the variation in stiffness along the member length. Recommendations are validated by comparison with a database of deflection test results for FRP-reinforced concrete.