Stiffness of reinforced concrete structures under bending considering shear and axial forces (part 1)

The paper provides a physical and computational model for determining the parameters of limit states of reinforced concrete structures under complex stress state such as bending with effect of axial and shear forces. The forward and backward transitions for determining the stiffness matrix coefficients of reinforced concrete bar structures with inclined and normal cracks have been constructed on the basis of the adopted cross-section discretization scheme and the duality theorem between force and deformation parameters by A.R. Rzhanitsyn. Determination of the stiffness of structures in the zone of inclined cracks was performed on the basis of the model of composite strips into which the zone with inclined cracks is divided. It is assumed a hypothesis about the character of deformation distribution in a complexly stressed reinforced concrete element with inclined cracks. For this model the effective shear modulus has been obtained. It allows to determine the average relative linear and angular strains of concrete and reinforcement at the point adjacent to the shear joint between inclined cracks. Using this model and the experimentally obtained value of the relative shear in the inclined crack, the dowel forces in the reinforcing bar crossed by the inclined crack were determined. The use of the obtained analytical dependences in the practice of designing reinforced concrete structures allows to clarify significantly the definition of displacements and width of opening of inclined and normal cracks, as well as to bring the calculation and physical model based on experimental data as close as possible.

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