The inverse strength problem for evaluation of bending stresses in pipelines during ground movements

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Three variants of the engineering solution of inverse problems regarding the strength of pipeline sections bent as a result of ground movements or during an earthquake are proposed. The feature of this approach consists in calculation of stresses not by the forces acting on the pipe, but by the displacements or deflections. Therefore, full-scale measurements of the detected deviation of the pipe position from the planned pipeline route should be taken as initial data for estimating the values of additional bending stresses. The first problem considered is the assessment of the risk of pipeline malfunction upon sagging or bulging of the supports of aboveground pipelines. The problem is solved in the beam approximation. The pipeline is considered a statically indeterminate beam, one of the supports of which is forcibly moved to a given distance. For a once statically indeterminate beam, a system of four equations — two equilibrium equations and two integral equations for deflections — was solved numerically. The calculated values of three reactions of the supports and the angle of rotation of the pipe section on the first support are used to calculate bending moments, stresses and deflection lines. The problem for a thrice statically indeterminate beam under strain loading was also solved. The second goal is to model the stress-strain state of the pipeline proceeding from the tables of experimental data on the values of pipe deflections and their coordinates. The problem was also solved numerically, using the procedures of smoothing, linear interpolation and sequential differentiation. It is shown that taking into account the possible ambiguous solution of the inverse problem, we should not rely on the calculated values of transverse forces and distributed loads. It is enough to limit ourselves to the second coordinate derivative of the deflection. The third goal is to prevent accidents at the design stage. It is proposed to create a list of normalized deflection functions for modeling possible emergency situations for pipeline sections placed in difficult ground-geological conditions and seismically dangerous zones. The examples of such functions are given.