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【正文】 iform moment of inertia throughout the beam length, and use of deflection equations derived from linear elastic analysis. The effective moment of inertia, Ie, is based on semiempirical considerations, and despite some doubt about its applicability to conventional reinforced concrete members subjected to plex loading and boundary conditions, it has yielded satisfactory results in most practical applications over the years. In North American codes, deflection calculation of flexural members are mainly based on equations derived from linear elastic analysis, using the effective moment of inertia, Ie, given by Branson’s formula (1965) （1）=cracking moment。=moment of inertia of the gross section。 =moment of inertia of the cracked section transformed to concrete。 and =effective moment of inertia. Research by Benmokrane et al. (1996)suggested that in order to improve the performance of the original equation, Eq.(1) will need to be further modified. Constants to modify the equation were developed through a prehensive experimental program. The effective moment of inertia was defined according to Eq.(2) if the reinforcement was FRP （2） Further research has been done in order to define an effective moment of inertia equation which is similar to that of Eq.(1), and converges to the cracked moment of inertia quicker than the cubic equation. Many researchers (Benmokrane et al. 1996。 Brown and Bartholomew 1996。 Toutanji and Saafi 2000) argue that the basic form of the effective moment of inertia equation should remain as close to the original Branson’s equation as possible, because it is easy to use and designers are familiar with modified equation is presented in the following equation: （3） A further investigation of the effective moment of inertia was performed by Toutanji and Saafi (2000). It was found that the order of the equation depends on both the modulus of elasticity of the FRP, as well as the reinforcement ratio. Based on their research, Toutanji and Saafi (2000) have remended that the following equations be used to calculate the deflection of FRPreinforced concrete members: （4）WhereIf Otherwise （5） m =3where =reinforcement ratio。 =modulus of elasticity of FRP reinforcement。 and =modulus of elasticity of steel reinforcement. The ISIS Design Manual M0301 （Rizkalla and Mufti 2001） has suggested the use of an effective moment of inertia which is quite different in form pared to the previous equations. It suggests using the modified effective moment of inertia equation defined by the following equation to be adopted for future use: （6）where=uncracked moment of inertia of the section transformed to concrete. Eq. （6） is derived from equations given by the CEBFIP MC90 (CEBFIP 1990). Ghali et al. (2001) have verified that Ie calculated by Eq.（6） gives good agreement with experimental deflection of numerous beams reinforced with different types of FRP materials. According to ACI (ACI 2003), the moment of inertia equation for FRPRC is dependent on the modulus of elasticity of the FRP and the following express
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