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2024-09-20 18:40本頁(yè)面
【正文】 duction coefficient has changed the key variable in the equation from the modulus of elasticity to the relative reinforcement ratio as shown in the following equation: （10）Moment–Curvature Approach The moment–curvature approach for deflection calculation is based on the first principles of structural analysis. When a moment–curvature diagram is known, the virtual work method can be used to calculate the deflection of structural members under any load as （11）where L=simply supported length of the section。 and m=bending moment due to a unit load applied at the point where the deflection is to be calculated. A moment–curvature approach was taken by Faza and GangaRao (1992), who defined the midspan deflection for fourpoint bending through the integration of an assumed moment curvature diagram. Faza and GangaRao (1992) made the assumption that for fourpoint bending, the member would be fully cracked between the load points and partially cracked everywhere else. A deflection equation could thus be derived by assuming that the moment of inertia between the load points was the cracked moment of inertia, and the moment of inertia elsewhere was the effective moment of inertia defined by Eq.(1). Through the integration of the moment curvature diagram proposed by Faza and GangaRao (1992), the deflection for fourpoint loading is defined according to the following equation: （12）where ɑ =shear span. Eq.(12) has limited use because it is not clear what assumptions for the application of the effective moment of inertia should be used for other load cases. However, it worked quite accurately for predicting the deflection of the beams tested by Faza and GangaRao (1992). The CSA S80602 (CSA 2002) suggests that the moment–curvature method of calculating deflection is well suited for FRP reinforced members because the moment–curvature diagram can be approximated by two linear regions: one before the concrete cracks, and the second one after the concrete cracks (Razaqpur et al. 2000). Therefore, there is no need for calculating curvature at different sections along the length of the beam as for steel reinforced concrete. There are only three pairs of moments with corresponding curvature that define the entire moment–curvature diagram: at cracking, immediately after cracking, and at ultimate. With this in mind, simple formulas were derived for deflection calculation of simply supported FRP reinforced beams and are used in CSA S80602 (CSA 2002). The deflection due to fourpoint bending can be found using the following equation: （13）Verification of Proposed Methods The nine methods of deflection calculation presented in this paper were used to analyze 197 simply supported beams and slabs tested by other investigators. Material and geometric properties of the beams used in this investigation could not be published due to the extent of the statistical sample but can be found in Mota(2005). Table 1 shows the range of some of the important properties of the members in the database. All information used in the analysis, such as cracking moment and modulus of elasticity of concr
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