Finite Element for the Analysis of Reinforced Concrete Beams with Non-Uniform Steel Fiber Reinforcement

A method has been developed for calculating and constructing a physically nonlinear finite element of a multilayer reinforcement beam, which allows to calculate the values of displacements, strains and stresses in a characteristic layer. To establish the actual stress-strain state of bent heterogeneous fiber reinforced concrete elements, an experimental study of a steel-fiber-concrete beam with non-uniform fiber reinforcement along the cross-section height (from 0.5 to 2.0%) was carried out. Strains and displacements of the beam at characteristic points are determined, and normal tensile and compressive stresses are obtained. The experimental data obtained were used to verify the finite element of the multilayer reinforcement beam. The developed finite element of the beam was based on the modified theory of calculation of multilayer beams proposed by P.M. Varvak. The multilayer beam model takes into account the curvature of the cross section under the action of shear stresses by including the generalized component of shear strain in the functional of the total potential energy. In addition to the experimental data, nonlinear analysis of a multilayer beam was performed in the Ansys software package. The discrepancy between the calculation results using the developed finite element and the experimental data ranged from 6 to 11%, and from 11 to 15% with the calculation results obtained in Ansys. The developed finite element is integrated into the PRINCE computing complex, and as part of this program it can be used to calculate heterogeneous fiber-reinforced elements.