PSI - Issue 20

A.A. Antonov et al. / Procedia Structural Integrity 20 (2019) 270–277 A.A. Antonov et al. / Structural Integrity Procedia 00 (2019) 000–000

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3. Discussion and results Based on the results of monitoring the changes in the planned-high-altitude positions of the underwater crossing of TGPL obtained by the above-described instrumental methods, the basics of assessing the dynamics of the stress strain state (SSS) of pipe welded joints were summarized. As a result of the search and determination of the depth by the line locator and parallel conduction of geodetic surveys, the points of the gas pipeline axis were established in terms of terrain and depth (3-dimensional space). The data obtained show the deviations of the pipeline from a straight line both vertically (depth) and horizontally (plan). To determine the stress caused by these deviations, it is necessary to find the curvature radii of the pipeline route axis. From pointwise data, it is impossible to calculate the radii of curvature with acceptable accuracy. Continuous data are required. In experimental science, if it is necessary to plot a continuous curve point by point, the form of which is unknown, an interpolation method using cubic splines is often applied. Cubic spline proposed by Bakhvalov et al. (2004) gives a small interpolation error (proportional to the fourth-order derivative, which is an order lower than the value of almost straight curves) and differs in that the first and second derivatives of the plotted curve are continuous. This is enough to calculate the physical characteristics related to the curve. In the intervals between adjacent measured points n and n + 1, the curve is modeled by a cubic polynomial: �(�) � � �� (� � � � ) � � � �� (� � � � ) � � � �� (� � � � ) � � �� �(�) � � �� (� � � � ) � � � �� (� � � � ) � � � �� (� � � � ) � � �� (1) �(�) � � �� (� � � � ) � � � �� (� � � � ) � � � �� (� � � � ) � � �� In each interval, the coefficients of the polynomials are their own. They are calculated using the "matching" condition, i.e., the measured point n is analyzed (the interval n is on the left, the interval n-1 is on the right): 1) the values of the curves on the left and the right are equal to each other and to the measured value; 2) the first and second derivatives on the left and the right coincide. By restoring the curve, it is possible to calculate the radii of curvature at any point using the formula [4]: � � � (�� � ��� � ��� � ) � (�� � ��� � ��� � )(�� � ��� � ��� � )�(�� �� ��� �������� �� ) (2) where x� � � � � � ; x� � � � �� � � ; y� � � � � � ; y� � � � �� � � ; z� � � � � � ; z� � � � �� � � (3) With a known radius of curvature R of a bent gas pipeline, the moment of forces M by Landau (1989), the moment of inertia of the cross-section of the pipeline by Ikrin (2004) are calculated, and taking into account technological and operational factors, the stress-strain state of the pipe welded joints operated in difficult climatic and freezing-soil conditions is determined. Herewith, the main factors determining the stress-strain state include the changes in the curvature radii of the axis of the trunk gas pipeline during its annual deformation in the watercourse and heaving or thermal subsidence on the floodplain areas of the underwater gas pipeline. The values of the curvature radii of the pipeline axis depending on the level of deflection, heaving or thermal subsidence are determined as well and compared with the maximum allowable value of the radius of its elastic curvature. In the case of gradual bending of the trunk gas pipeline below the maximum allowable value of the radius of its elastic bending, elastoplastic deformation of the gas pipeline develops in a single section. Further reduction of the pipeline bending radius leads to the intensive development of elastoplastic deformation and its localization in the section of operational or structural-technological stress concentrators.