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10 1.1.2 Basis of the LRFD Sectional Design Model section analysis is performed that uses the MCFT to solve for the angle of diagonal compression, longitudinal stress, The LRFD Sectional Design Model is derived from the and shear stress in each layer (19). In a typical analysis, the MCFT, a behavioral model that can be used to predict the cross section will be divided into more than 100 layers. The shear-stress versus shear-strain response of an element sub- LRFD Section Design Model is also derived from the jected to in-plane shear and membrane forces. The theory MCFT, but developing this hand-based general shear design consists of constitutive, compatibility, and equilibrium rela- method (20) required several additional simplifications and tionships that enable determination of the state of stress assumptions to be made. The most significant of these was (fx, fy, vxy) in structural concrete corresponding to a specific that the distribution of shear stress over the depth of the sec- state of strain (x, y, xy) as shown in Figure 6. tion was taken as the value at mid-depth as calculated by the The full implementation of the MCFT is possible in a MCFT using the designer-calculated longitudinal strain, x, two-dimensional continuum analysis tool, such as that done at mid-depth. in program VecTor2 (18). The MCFT is also implemented Additional assumptions that were made in the development in Response 2000, a multilayer sectional analysis tool that of the LRFD Sectional Design Model were that the shape of can predict the response of a section to the simultaneously the compressive stress-strain response of the concrete was occurring actions of axial load, prestressing, moment, and parabolic with a strain at peak stress of -0.002, and, for mem- shear. In Response 2000, the plane section assumption is bers with Av Av,min, that the spacing of the cracks was used which constrains the distribution of shear stress over 12 inches and the size of the maximum aggregate was 0.75 the depth of the section. For each layer, an equivalent dual inches. Figure 6. MCFT for predicting shear response of an element.