The paper presents a simultaneous numerical analysis of the geometric and material nonlinearity of the beams. It describes a process of determining the bearing capacity of a stratified cross-section of a beam made of homogeneous and isotropic material in linear and nonlinear domains of material behaviour. Material nonlinearity is analysed by the variation of the cross-sectional stiffness of the beam on bending EI in the stiffness matrix of the system obtained according to the first-order theory. Geometric nonlinearity is introduced into the calculation using the geometric stiffness matrix of the system. Numerical examples present an application of the procedure for solving problems of nonlinear structure analysis. The calculation results obtained in accordance with the procedure described in the paper are compared with the results of the SCIA software package.

The paper presents a procedure for numerical modelling of the rod cross-section bearing capacity. Equilibrium between cross sectional forces and cross-sectional stresses is determined by iterative procedures. According to the described procedure, the load-bearing capacity of the cross-section is determined according to the isotropic linear and nonlinear behavior of the material, for homogeneous and inhomogeneous cross-sections. The nonlinear behavior of the material reduces the stiffness of the cross section of the rod EA and EI, with a significant increase in the deformation values ε and κ. The applicability of the calculation and analysis of obtained results is presented using numerical examples.

This paper presents a numerical analysis of a reinforced concrete beam in which the concrete and reinforcement are above the yield strength of the material. Further, the procedure for determining the relationship between the cross-sectional forces and the deformations of the layered cross-section of a rod is described. For a short rod with reduced stiffness of the EI and EA cross-sections, a stiffness matrix with variable members is formed. The applicability of the proposed analysis method for the material nonlinearity in a beam calculation is demonstrated through a numerical example. The aim of the present paper is to show the flow of plastification and the load deformation of the system nodes. Finally, the results of the manual deformation calculation system are compared with the results from SCIA software.