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 calculation of a system supported on piles according to the second order theory. The influence of piles as supports on the structure is replaced by elastic supports. In the numerical model, the supports are modeled as elastic springs. To compare the calculation results, a system based on rigid and deformable supports was analyzed. The analysis of the system was performed according to the first order theory and the second order theory, which introduces geometric nonlinearity into the calculation. The process of soil modeling around a pile with replacement springs is presented. The applicability of the described procedure is shown in a numerical example. The comparison of the calculation results was done on numerical models of systems with rigid and elastic supports.

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 discusses the application of approximate methods for determination of the first oscillation period for cantilever and frame structures, frequently used in civil engineering construction works. Based on oscillation analysis of different cantilever and frame structure examples, the paper suggests oscillation forms that can be used for approximate determination of the first oscillation period. The significance of the determination of the basic form and the first oscillation period using approximate methods is in the possibility of estimation of horizontal dynamic loads in preliminary structure system analysis. Computerized processing of dynamic characteristics of complex structural systems requires a number of data registrated, therefore occurrence of errors is highly possible during such a registration. In addition, approximate methods can also be founded useful in confirmation of the first oscillation period calculation results for civil engineering structures.