The brazier effect for buried steel pipelines of finite length

摘要

The bending behavior of long cylindrical shells with flexible-cross-sections is associated with a nonlinear phenomenon,called the Brazier effect,induced by the deformation of the originally circular shape into an oval.This ovalization decreases the moment of inertia of the cross-section and leads to a nonlinear moment-curvature relation characterized by a limit point.In addition,the deformation fo the cross-section increases the axial bending stresses and lowers the structure's local buckling load.In buried pipelines ovalization is partly hampered by the surrounding soil,which provides resistance to parts of the pipe cross-section that tend to deform outwards,making the Brazier effect less pronounced compared to transversely free tubes.In previous work,approximate analytical expressions for the Brazier limit moment and the local buckling moment of infinitely long tubes were derived,accounting for the stiffness of the soil,modeled with linear radial translational springs.In the present paper,this approach is extended for tubes of finite length,where the end fittings of the tube preserve the original circular shape,so that transition zones are formed.To account for that,the deformation of the tube is considered as a two-stage process,namely,first,the tube remains straight and ovalizes in a way which is compatible with the end conditions,while in the second stage it bends as a non-uniform beam subjected to constant bending moment.The nonlinear moment-curvature relation is obtained through energy considerations,wikth a term representing the strain energy of the soil springs.parametric studies are presented to describe the effects of different soil types and length to radius ratios.