PSI - Issue 40

A.G. Khakimov et al. / Procedia Structural Integrity 40 (2022) 214–222 A.G. Khakimov / Structural Integrity Procedia 00 (2022) 000 – 000

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Nomenclature 

angle between axis and tangent to pipeline axis coefficient of linear thermal expansion

α 1

β С

wave number

longitudinal stiffness of support with a single arch

* * ,    deformation E , J, R i modulus of elasticity, moment of inertia and inner radius of pipeline cross section F i pipeline clear cross-sectional area G acceleration k curvature of pipeline axial line L distance between supports

λ , χ , β 1 , γ

constants

bending moment

M

bending moment in section B

M B

M B 1 , M B 2 bending moments in section B from lateral distribution forces and effective cross-sectional compressive load in pipeline M A bending moment in section A * * , N N  circumferential and longitudinal forces per unit length n quantity of semi-waves  Poisson ’ s ratio Р longitudinal compression force р 0 pressure on the fluid surface at a height Н from pipeline p i 0 , p e 0 fluid pressure inside and outside the pipeline at a design depth p i , p e pressure inside and outside pipeline p * pressure gradient P 0 cr critical value of compression force P cr 1 effective axial compressive load in pipeline P cr 2 change in critical axial compressive load due to the effect of lateral distribution forces P E critical value of static longitudinal compression force affecting pipeline Q cutting force q intensity of distributed buoyancy force q ( x ) lateral distribution forces  i ,  e fluid densities inside and outside pipeline  , h , F density, wall thickness and pipeline cross-sectional area σ max maximum compressive stresses in dangerous section B σ t yield point T change in the pipeline temperature U i fluid velocity in pipeline w 0 small initial x -axis misalignment W 0 n amplitude of small initial misalignment w small x -axis misalignment W n amplitude of small misalignment W moment of resistance in pipeline cross section x, z rectangular coordinates