A Mixed-Approach Analysis of Deformations in Pipe Bends. Part 3. Calculation of Bend Axis Displacements by the Method of Initial Parameters

A problem of deformation of a curved shell loaded by internal pressure, axial force, and temperature difference is discussed. Physical equations are derived whereby the displacements and angles of rotation of the line of centers of mass of cross sections of a shell are related to loading parameters. A general constitutive set of equations for a curved element during its deformation is given. Using a method of initial parameters, an analytical solution is obtained for the differential equations for displacements and angles of rotation of the center line allowing for the action of distributed forces and moments.     

Stress State of Bent Buried Pipelines

The authors consider edge effects in buried pipelines that occur in the region of joining of a straight buried pipe and a bent insert (factory bend, elbow, or an elastically bent segment). The action of those effects results in the appearance of additional bending moments, which are proportional to the difference between the axial force in an infinite straight pipeline and that in a closed-end pipe, and depend on the geometrical parameters of the pipeline and physical-mechanical characteristics of the soil. Specific examples of analysis of elastic interaction of a pipeline with the soil for pipe bends with various radii of the bend arc are offered. It is shown that additional bending stresses may exceed appreciably the stresses from the axial force, and therefore, they should be taken into account when designing and building pipelines. The solution for an elastically bent segment has been obtained and analyzed.     

The ultimate ductile state model for a pipe with an axial through crack

A statistically admissible solution has been constructed for a pipe with an axial through crack. The boundaries of the limit region have been obtained and the strength conditions on its boundary have been formulated. The extension of the distribution of forces and moments beyond the limit region boundary has been substantiated. The results obtained for a pipe with closed ends are in fair agreement with the experimental data. The influence of the axial force and the property anisotropy upon the fracture stress has been studied. The possibility of considering several cracks is analysed.     

Use of a ductile fracture model for pipes with axial defects for analysis of results of full-scale experiments

We consider the use of a ductile fracture model for pipes with axial defects, loaded by internal pressure, for calculation of the limiting burst pressure P_LL. We describe procedures for hydraulic and pneumatic testing of full-size pipes performed at VNIIST (All-Union Scientific Research Institute for the Construction of Trunk Pipelines, Moscow), and also the scheme for application of a surface notch. We have done a comparative analysis of the value of P_LL calculated from the relationships determined on the basis of a ductile fracture model for cylindrical bodies with cracks and the value obtained using familiar empirical formulas. Based on the calculations, we plot graphs for the distribution of the deviation of the calculated burst pressure from the true burst pressure as a function of the relative crack length ². We demonstrate the considerable effectiveness of the ductile fracture model for pipes with defects, which allows us to take into account the real shape of the defect and additional mechanical actions (longitudinal forces, bending moments).Translated from Problemy Prochnosti, No. 6, pp. 5–15, November–December, 1996.     

Weighting-function construction for an elliptical normal-detachment crack in an unbounded body

Weighing-function expressions are given for an elliptic normal-detachment crack in an infinite body, which have been used to calculate K₁ for uniform and linear load distributions in the range in (ratio of the minor and major axes of the ellipse) from 0.2 to 1. These K₁ are compared with theoretical values to judge the accuracy of the weighing functions. Good accuracy (about 6%) is provided by the weighing functions constructed with elliptic coordinates and on the bases of the Oore- Burns general treatment in combination with Rice's formula, apart from points on the major axis. An integral condition is derived for the weighing function, and this is used in refinement of the unknown weighing function.Translated from Problemy Prochnosti, No. 5, pp. 60–69, May, 1993.     

Classical Approach to Analyzing the Influence of Edge Boundary Conditions on Stresses and Flexibility of Pipe Elastic Bend

A new analytical method is proposed for the analysis of boundary effect in a pipe bend portion loaded by bending moment combined with internal pressure. The proposed method is based on the simplifying hypotheses, which make possible to represent all deformation- and force-related parameters in terms of the tangential displacement assumed in the form of the Fourier series expansion by the circumferential coordinate. A set of quadric differential equations by axial coordinate containing unknown displacement expansion coefficients is derived. We obtained an analytical approximate solution for a pipe bend portion and precise solution for a straight pipe, which are expressed via Krylov functions. We formulate the application procedure for the method of initial parameter, where the values of tangential and longitudinal displacements, axial and tangential forces are used as boundary conditions. We present the equations relating the above-mentioned parameters in the initial and end sections of the pipe bend portion. The results obtained are compared with the available published data. __________ Translated from Problemy Prochnosti, No. 4, pp. 64 – 94, July – August, 2005.