Stiffness of reinforced concrete structures under bending with transverse and longitudinal forces

The authors developed a model for single reinforced concrete strips in block wedge and arches between inclined cracks and approximated rectangular cross-sections using small squares in matrix elements. From the analysis of the works of N.I. Karpenko and S.N. Karpenko the "nagel" Qs forces in the longitudinal tensile reinforcement and crack slip D _s , as a function of the opening width and concrete deformations in relation to the cosine of the angle q . The experimental " nagel " forces Q_s,exp and crack slip D_crc,exp dependences for the connection between D_crc,exp and 0 а h/₀ in the form of an exponent for the reinforcement deformations e _s × m_s,3 and spacing 1_x are determined. The forces have been calculated for two to three cross-sections (single composite strips) of reinforced concrete structures.

On the bases of accepted hypothesis, a new effect of reinforced concrete and a joint modulus x_m in a strip of composite single local shear zone for the difference of mean relative linear and angular deformations g_{zx,stitch,sum,i} of mutual displacements of concrete (or reinforcement) are developed. The hypothesis allows one to reduce the order of the system of differential equations of Rzhanitsyn and to obtain in each joint the total angular deformations of concrete and the "nagel" effect of reinforcement. The curvature of the composite bars has a relationship from the total bending moment of the bars to the sum of the rigidities. The stiffness physical characteristics of the matrix from the compressed concrete area and the working reinforcement are obtained in a system of equations of equilibrium and deformation, as well as physical equations.

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