Cracked Transformed Moment of Inertia of SteelReinforced and FRP-Reinforced Rectangular Beams and Slabs

Cracking in reinforced concrete (RC) slabs and beams subjected to flexural moments reduces their flexural stiffness significantly.At service load conditions, deflections are typically calculated using the effective moment of inertia ( ), which is calculated based on the gross moment of inertia ( ) and the cracked moment of inertia ( ).The latter is based on the transformed properties of the cross-section and requires the calculation of the depth of the compression zone () then the calculation of the moment of inertia.This paper shows that ( ) depends solely on the modular reinforcement ratio ( ) where () is the reinforcement ratio and () is the modular ratio of the reinforcement relative to the concrete.It has been proposed in a previous study that ( ) ranges from 0.005 to 0.16.This range covers the properties of beams and slabs with concrete compressive strength ( ′ ) ranging from 20 to 60 MPa and with reinforcement ratio ranging from minimum to maximum values allowed by the ACI 318 building code.It also covers a wide range of beams and slabs reinforced with FRP bars.Within such a range of ( ), it will be shown that ( ) can be calculated directly using ( = 0.36 ( ) 0.81 3 ), where () and () are the width and effective depth of the cross-section respectively.The error between the exact and the approximate equation is limited.Based on this approximate equation, it is shown that the flexural stiffness of fully cracked elements depends on the ratio and the modulus of elasticity of the reinforcement raised to the power 0.8 and to () raised to the power 2.2.In addition, it is shown that the effect of ( ′ ) on the flexural stiffness is limited.