In regions of the North, construction is frequently accomplished on sites with a sandy cushion placed on permafrost. The building is supported on piles formed from metallic tubes, and to preserve the frost, it is raised above the surface of the cushion to a certain height, creating an open interstitial space under the floor. For a cushion up to 7.0 m thick, the pile is very long and flexible, and the vertical force acting on it may approach the critical value and create large additional moments that intensify bending. The familiar geometrically nonlinear problem of longitudinal-transverse bending is developed; here, the stresses, deformations, and displacements will increase progressively with increasing load.Mal'shev and Shishov [1] describe a computational algorithm, which makes it possible to control all these factors. The problem of compression with the bending of a rod free of contact with the ground is solved by the finite-difference method (Fig. 1).The rod is divided into small segments for which equilibrium and strain-compatibility equations are written in the form where EJ is the bending stiffness of the rod.The second derivative of the displacement function υ = υ (x) is written in differential form. The relation between the internal forces Q, M, and N in the cross section (see Fig. 1) is established with allowance for developing strains and displacements [2]
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