CALCULATION OF THE FLAT BENDING SHAPE STABILITY OF RECTANGULAR CROSS SECTION BEAMS WITH REGARD TO CREEP

Abstract

Objectives. The article presents the conclusion of the resolving equation for calculating the stability of the flat form of deformation of prismatic beams, taking into account the rheological properties of the material.Method. The problem is reduced to a second-order differential equation for the twist angle, which is solved numerically by the finite difference method in combination with the Euler method.Result. The obtained differential equation allows one to take into account the presence of initial imperfections in the form of the initial deflection of the beam, the initial angle of twist, and also the eccentricity of the applied load. The solution of the test problem for a cantilever polymer beam under the action of a concentrated force is presented. The non-linear Maxwell-Gurevich equation is used as the creep law. The value of the long-term critical load is introduced and it is shown that with a load less than the long-term critical creep is limited. It has been established that, as with the squeezed rods, with a load less than the long-term critical, the growth rate of the displacements with time decays. When F = F_dl, the displacements grow at a constant speed, and when F> F_dl, the growth rate of displacements increases with time. The results obtained confirm the validity of the chosen method.Conclusion. A universal resolving equation is obtained for calculating the stability of a flat shape of bending of rectangular beams, suitable for arbitrary creep laws.

Keywords

• stability
• flat bending shape
• creep
• numerical methods
• initial imperfections