Deflection of FRP Prestressed Concrete Beams

The lower elastic modulus of fiber-reinforced polymer (FRP) bars over steel rebar renders the postcracking deflection of FRP concrete beams critical under serviceability limit states. To predict the deflection of FRP prestressed concrete (PSC) beams, the American Concrete Institute (ACI) utilizes a semiempirical equation of effective moment of inertia (Ie), originally developed and calibrated for steel reinforced concrete beams, and applies a reduction factor to account for the low elastic modulus of FRP bars. In this paper, a mechanics-based relationship for Ie is developed using the moment-curvature behavior of FRP PSC sections. From this a beam deflection equation is derived for general loading conditions. The proposed equation is verified using experimental observations that cover various ratios of the cracked-to-gross moment of inertia (Icr/Ig). The comparative results reveal that the ACI equation unrealistically underestimates the deflection for low Icr/Ig ratios (<0.04), which is the case for lightly reinforced FRP PSC beams and one-way slabs. However, for higher Icr/Ig ratios (>0.08), for which the semiempirical ACI equation was originally calibrated, reasonable predictions are observed. The proposed equation, which offers an implicit flexibility formulation as opposed to the stiffness formulation adopted by ACI, provides more accurate predictions of deflection regardless of the Icr/Ig ratio.