Effective Moment of Inertia for Calculating Deflections of Concrete Members Containing Steel Reinforcement and Fiber-Reinforced Polymer Reinforcement

This study reevaluates the effective moment of inertia expression that was first proposed by Branson in 1963 and currently is incorporated in the ACI Code. Effective moment curvature relationships are compared. The flexural behavior at service load levels and application to beams with fiber-reinforced polymer (FRP) reinforcement are examined. It is found that Branson’s expression is valid for members with steel reinforcement ratios greater than 1%. However, this expression overestimates member stiffness at lower reinforcement ratios and gives a member deflection less than expected, as demonstrated by comparison with test results. Branson’s approach also underestimates deflection of slender walls with a central layer of reinforcement, as well as deflection of FRP-reinforced concrete beams. The author presents an alternative formulation of the effective moment of inertia that is applicable to all ranges of reinforcement ratio for both steel and FRP reinforcement without the need to apply correction factors.