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Keywords: stability

FLAT BENDING SHAPE STABILITY OF RECTANGULAR CROSS-SECTION WOODEN BEAMS WHEN FASTENING THE EDGE STRETCHED FROM THE BENDING MOMENT

https://doi.org/10.58224/2618-7183-2022-5-4-5-18
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 5-18 p.
Abstract
The article presents the solution to the problem of calculating the lateral buckling of wooden beams with a narrow rectangular section, taking into account intermediate point fixing in the edge stretched from the bending moment. The structure is considered as an orthotropic plate, the calculation is performed by the finite element method (FEM). To obtain a result that is valid for any beam geometry, the system of FEM equations is reduced to a dimensionless form. The dimensionless parameter that determines the value of the critical load is calculated based on the solution of the generalized eigenvalue problem. The numerical calculation algorithm is implemented in the MATLAB environment. The developed technique is verified by comparison with calculations in the LIRA and ANSYS software systems using flat and volumetric finite elements. A comparison is also made with the calculation formula presented in the Russian design standards for wooden structures SP 64.13330.2017 for the coefficient, taking into account intermediate fixing, with pure bending. It has been established that this dependence rather roughly takes into account the fastening from the bending plane of the edge stretched from the bending moment. Using the package Curve Fitting Toolbox of the MATLAB environment, we have selected refined formula for the coefficient, which can be used in engineering calculations.
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IMPROVING THE CALCULATION OF FLEXIBLE CFST-COLUMNS, TAKING INTO ACCOUNT STRESSES IN THE SECTION PLANES

https://doi.org/10.34031/2618-7183-2021-4-3-41-53
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 41-53 p.
Abstract
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 geometric 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 formulation 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.
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ENERGY METHOD BASED ON THE STABILITY OF THE FLAT SHAPE OF THE CANTILEVER STRIP BEND TAKING INTO ACCOUNT ITS OWN WEIGHT

https://doi.org/10.34031/2618-7183-2020-3-1-76-82
 76-82 p.
Abstract
The problem of bending a strip by a force applied at the end is not of practical interest. Such method of loading and securing the ends is interesting only because it is most convenient to implement it on experience, which makes it possible to verify the Prandtl theory. When conducting experiments, there is a need for two corrections: it is necessary to evaluate the influence of the self-weight of the strip and the effect of increasing or decreasing the point of force application. As we are talking about small corrections, it is quite enough to use only the first approximation for calculations. An effective version of the energy method is recommended. It is used to calculate rectangular cantilever strips for stability of a flat bending shape, taking into account its own weight. The essence of this variant of the method is to use the Lagrange variational principle instead of the condition for equality of the potential strain energy and the work of external forces. The proposed approach allows us to perform machine implementation of calculations and take into account an arbitrary number of members of the series. The presented solution of the problem for the cantilever beam takes into account its own weight and the action of concentrated force.
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