Abstract. In the article the technique of calculation of a three-layer beam with a lightweight filler taking into account the creep of the middle layer is given. The problem reduces to a second-order differential equation, which is solved numerically by the method of finite differences. An example of a calculation is presented for a hinged at the ends beam under the action of a uniformly distributed load. The linear Maxwell-Thompson equation is used as the creep law. Solution was performed in software package Matlab.

Concrete-filled steel tubular (CFST) columns are widely used in construction due to effective resistance to compression and bending joint action. However, currently, there is no generally accepted effective calculation method considering both nonlinearities of the materials and lateral compression. The article proposes the finite element analysis method of concrete-filled steel tubular columns in a physically nonlinear formulation by reducing a three-dimensional problem to a two-dimensional one based on the hypothesis of plane sections. The equations of Geniev’s concrete theory of plasticity are used as relations establishing the relationship between stresses and strains. The technique was tested by comparing the solution with the calculation in a three-dimensional formulation in the LIRA-SAPR software package and with the experimental data of A.L. Krishan and A.I. Sagadatov. It has been established that the effective area of operation of circular-section columns are small eccentricities of the longitudinal force. The proposed approach can be applied to analyzing the stress–strain state and bearing capacity of pipe-concrete columns of arbitrary cross-sections. There are no restrictions on the composition of concrete, and the shell material can be steel and fiberglass.

The article presents the derivation of equations describing the pre-buckling behavior of three-layer rods in the presence of shear deformation and creep of the middle layer. The test problem for a rod with a filler made of polyurethane foam is solved. A technique has been developed for calculating the critical time under loads which values exceed the long critical ones.

The article presents the derivation of the FEM equations, which make possible to calculate short concrete-filled steel tubular columns in a plane elastic formulation. Steel tube is modeled by 1D bar finite elements. The obtained results are compared with the results of calculations using 3D solid and shell finite elements.

the article is devoted to a newly developed complex finite element that allows modeling concrete-filled steel tubular columns taking into account the compression of the concrete core from the steel tube, as well as ge-ometric nonlinearity. The derivation of the resolving equations, as well as expressions for the elements of the stiffness matrix, is based on the hypothesis of plane sections. The complex testing of the finite element was performed using the program code written by the authors in the MATLAB language and the ANSYS software, as well as the analysis of the effectiveness of the new FE in comparison with the classical methods of modeling CFST-columns in modern software systems. A significant decrease in the order of the system of FEM equations is demonstrated in comparison with the modeling of CFST-structures in a volumetric formu-lation in existing design complexes using SOLID elements for a concrete core with 3 degrees of freedom in each of the nodes, and SHELL elements for a steel tube with 6 degrees of freedom in each of the nodes, with a comparable accuracy in determining the stress-strain state. The behavior of steel and concrete in the presented work is assumed to be linearly elastic, however, the described calculation method can be generalized to the case of using nonlinear deformation models of materials.