On the Mises girder
The Mises girder gives the simplest example of the elastic system, which demonstrates the nonlinear behavior, the bifurcation, and the non-unique equilibrium state. The classical Mises girder consists of two elastic compressible rods attached at a slight angle to each other. The typical mode of its loss in stability under the vertical forces is the buckling into the mirror-reflected form. The critical force is equal to the limiting point on the curve «force-deflection». In this paper by using the Bernoulli-Euler model the bending of linearly elastic rods is taken into consideration in addition. As a result the bifurcation of equilibrium of the straight form of the compressed rods is possible. The interaction of two possible buckling modes is investigated, namely the mode with limiting point on the curve «force-deflection» and the mode of bifurcation of the rectilinear rod form. The critical force is found for the various values of the girder parameters, forces distribution, and boundary conditions. The approximate analytical solution is compared with the exact numerical solution which describes the non-linear bending of rods.