Inelastic Buckl ing of PipelInes under Combined Loads (1975)

ABSTRACT Investigation of the buckling characteristics of offshore pipelines produced solutions to nonlinear equilibrium and compatibility equations that demonstrate the pre- and postbuckling configurations of pipelines under combined loads. In general, this study enhances our understanding and insight into the nature of pre- and postbuckling behavior of pipelines having low diameter-to-thickness (D/t) ratios - i.e., in the range from 20 to 100. INTRODUCTION When laying a pipeline with a typical lay barge operation (Figure 1), most buckling occurs in regions of combined loadings of longitudinal bending moment and external pressure. These areas are the sag region and in the overbend region, often toward the lower tip of the stinger. The stresses that develop during the pipeline laying operation may be significantly above the elastic limit of the material. Buckling formulations based on elastic deformations are therefore incapable of properly describing prebuckling and postbuckling behavior. During the past 6 years analytical and experimental research has been conducted at Battelle's Columbus Laboratories to investigate the elastoplastic pre- and postbuckling characteristics of offshore pipelines. The goal of this research was to develop an experimentally verified analytical method that would predict the buckling strength of undersea pipelines and to provide a comprehensive understanding and insight into the nature of pre- and postbuckling behavior of cylinders having low diameter to thickness (D/t) ratios, i.e., D/t's in the range from 20 to 100. Although this work was directed toward pipelines, the general concepts are applicable to any cylindrical shells under such loads. ANALYTICAL FORMULATION The stresses developed during the laying of pipelines are for the most part the result of bending and hydrostatic pressure. Generally speaking, stability solutions to problems involving combined loading - one of which is bending - are quite difficult. However, it has been shown by Vol'mir(l) and again by Kemper, et ale (2), that in the case of elastic buckling the problem may be simplified since the critical longitudinal buckling stress caused by bending is equal to the critical longitudinal buckling stress caused by pure axial load.. Based on these works, a simplifying assumption that appears justifiable, at least from the standpoint of providing a lower bound to the buckling load, is that the longitudinal buckling strain calculated according to hydrostatic pressure and axial load is equal to or less than the longitudinal buckling strain that results from the combined loads of hydrostatic pressure and pure bending. When stresses are in excess of the elastic limit, the material behavior is termed nonlinear, plastic, 'or inelastic. The concern for this behavior dates back nearly a century. Historically, while studying the inelastic behavi0J:" of column buckling, two theories evolved: the tangent modulus theory and the double modulus theory. If a structure is loaded to a stress below the elastic limit, the material essentially follows the same stress-strain path when unloaded. The tangent modulus theory assumes that this stress-strain behavior is also true above the elastic limit.