In two parts of the work, numerical and physical modeling of the deformation of the bar in the channel under axial compression is carried out. The regularities of nonlinear bending of the bar in the plane are revealed. Bar shapes are determined by the load history and can differ at the same force value. The solution is to find the shape with the lowest potential energy. The first part of the work describes the numerical model of the bar and the results of its application. The shapes of the bar bending under gradual loading are obtained, the studies coinciding with V.I. Feodosev’s analytical solution. Further research shows that the solution to the problem has a more complex ramified structure with various additional shapes. Deformation of the bar under gradual loading occurs in the form of a sequential variant appearance of bending waves in the bar under forces determined by the degree of non-uniformity of the lengths of potentially unstable sections and forming a range of shape instability. In variant transitions from one initial shape with a loss of stability, it is possible to obtain various subsequent shapes that differ in the sequence of deformation of the sections with one number of half-waves, or the number of generated half-waves. When a straight bar is loaded in one step, an increase in the force leads to a sequential increase in the number of bending half-waves in the corresponding ranges of the existence of shapes. The results obtained can be applied to the analysis of the operation of such bar objects as drill, casing, tubing strings in the well and cased pipelines, pipelines in the well and tunnel.

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In some practical applications, bars are loaded with the pressure of liquids and gases. Although the work of such objects is well studied and described in a large number of papers, some of the latter have wrongful provisions. For example, the equilibrium equations of a pipeline often include axial force instead of equivalent force, which reduces the accuracy of estimating the bending shape and acting stresses. The problem of accounting for pressure is due to the objectively more complex type of this loading in comparison with the forces of weight and insufficient distribution of the known provisions in engineering. This review and methodological paper focuses on a set of issues related to the loading of a bar by pressure. In the research, first, we obtained vector and linearized equations of equilibrium of the bar taking into account the load from the surface pressure. Then, we substantiated the equivalence of loading the bar with pressure and weight load determined by Archimedes’ law. Finally, we gave provisions for taking into account the pressure in the study of the equilibrium, stability, deformation, and strength of the bar. As an example, the effect of pressure in the problems of laying a pipeline on the seabed and evaluating the longitudinal stability of the bar is shown.

The paper considers the problem of supports optimal arrangement in pulling a pipeline through the well during construction of the submerged crossing by the directional drilling method. Part 1 of the paper presents results of using the pipeline rod model with the transition section located on fixed supports with the variable lift height. Conditions for optimizing the supports positioning provide for the absence of contact loads at the pipeline inlet into the well and the minimum stresses within the crossing limits, or the minimum supports’ reactions on the section. The number of supports used and the required pipeline height were determined. The influence of the span length between the supports with uniform and non-uniform supports positioning in the drilling fluid presence in the well was evaluated. Effect of tensile or compressive axial force in the pipeline on the supports arrangement was studied. Consequences of one of the supports failure during the pipeline pulling were analyzed. The operating range of the pipeline lifting height on the supports was found according to criterion of the supports coming out from under the load that determines the required pipeline positioning accuracy. According to the calculation results, the pipeline bend shape, the acting stresses diagram and the supports reaction were displayed. With the optimal arrangement of supports, impact on the pipeline during the pulling process is limited to the technologically necessary minimum not affecting the subsequent crossing operation.

The paper considers the problem of supports optimal arrangement in pulling a pipeline through the well during construction of the submerged crossing by the directional drilling method. Part 1 of this work presented results of using the pipeline rod model with positioning the transition section on the fixed supports with the variable lift height. Part 2 simulates the use of a group of the movable supports. Initially, the group working stroke is carried out accompanied by the supports positioning towards the well with a decrease in the pipeline height. After a stop in the final position, the group is being restructured taking the initial position for the next motion cycle. When the supports are moved, optimality conditions are met in the form of the missing contact load behind the well inlet and minimum stresses in the transition section, or the minimum supports reaction. The supports are brought to their initial state by taking the first support behind the last support, or by moving each of the supports in turn to the required position. The presented solution allows pulling through at the technologically determined minimum impact of the mounting loads on the pipeline.