Motivated by the response of industrial piping under seismic loading conditions, the present study examines the behavior of steel process piping elbows, subjected to strong cyclic loading conditions. A set of experiments is conducted on elbow specimens subjected to constant-amplitude in-plane cyclic bending, resulting into failure in the low-cycle-fatigue range. The experimental results are used to develop a low-cycle-fatigue curve within the strain-based fatigue design framework. The experimental work is supported by finite element analyses, which account for geometrical and material nonlinearities. Using advanced plasticity models to describe the behavior of elbow material, the analysis focuses on localized deformations at the critical positions where cracking occurs. Finally, the relevant provisions of design codes (ASME B31.3 and EN 13480) for elbow design are discussed and assessed, with respect to the experimental and numerical findings.Copyright © 2012 by ASME

Pipe Elbows Under Strong Cyclic Loading

An overview of the mechanical behavior of steel pipe (elbows) is offered, based on previously reported analytical solutions, numerical results and experimental data. The behavior of pipe bends is characterized by significant deformations and stresses, quite higher than the ones developed in straight pipes with the same cross-section. Under bending loading (in-plane and out-of-plane) the main feature of the response is cross-sectional ovalization, which influences bending capacity and is affected by the level of internal pressure. Bends subjected to cyclic in-plane bending exhibit fatigue damage, leading to base metal cracking at the elbow flank. Using advanced finite element tools, the response of pipe elbows in buried pipelines subjected to ground-induced actions is also addressed, with emphasis on soil-pipeline interaction. Finally, the efficiency of special-purpose finite elements for modelling pipes and elbows is briefly discussed.

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Mechanical Behavior of Steel Pipe Bends: An Overview

The paper examines the nonlinear elastic-plastic response of internally pressurized 90 deg pipe elbows under in-plane and out-of-plane bending. Nonlinear shell elements from a general-purpose finite element program are employed to model the inelastic response of steel elbows and the adjacent straight parts. The numerical results are successfully compared with real-scale experimental measurements. The paper also presents a parametric study, aimed at investigating the effects of diameter-to-thickness ratio and moderate pressure levels on the ultimate bending capacity of 90 deg elbows, focusing on the failure mode (local buckling or cross-sectional flattening) and the maximum bending moment. Special attention is given to the response of 90 deg elbows under out-of-plane bending moments.

Ultimate Bending Capacity and Buckling of Pressurized 90 deg Steel Elbows

The paper investigates the response of elbows under in-plane bending and pressure, through nonlinear finite element tools, supported by experimental results from real-scale tests. The finite element analysis is mainly based on a nonlinear three-node tube element, capable of describing elbow deformation in a rigorous manner, considering geometric and material nonlinearities. Furthermore, a nonlinear shell element from a general-purpose finite element program is employed in some special cases. Numerical results are compared with experimental data from steel elbow specimens. The comparison allows the investigation of important issues regarding deformation and ultimate capacity of elbows, with emphasis on relatively thin-walled elbows. The results demonstrate the effects of pressure and the influence of straight pipe segments. Finally, using the numerical tools, failure of elbows under bending moments is examined (cross-sectional flattening or local buckling), and reference to experimental observations is made.

Nonlinear Response and Failure of Steel Elbows Under In-Plane Bending and Pressure

Low-Cycle Fatigue of Pressurized Steel Elbows Under In-Plane Bending

Bending moments on bends in pipelines may cause severe ovalization and stresses, both in longitudinal and circumferential directions. The bending stiffness depends not only on the radius of the bend, the diameter-to-wall-thickness ratio and the internal or external pressure, but also on the length of the bend, the loads due to the surrounding soil and the bending direction. After start of yielding, the bending moment may still increase considerably. For example, it can be shown that for bends with a radius-to-diameter ratio equal to 3, the maximum moment may be 2 or 3 times greater than the moment where first yielding started. Also the rotation capacity (the ability to follow imposed deformation) is many times greater than elastic theory can predict. In this paper, the strnctural behaviour of bends is analyzed. Improved analytical models for elastic design and new analytical models for plastic design are presented. The results of the analytical models are compared with test results and the results of finite element calculations. NOMENCLATURE : Difference in pressure between inside and outside of pipeline P = Pi P u : Earth pressure : Directly transmitted earth pressure : Indirectly transmitted earth pressure (support reaction) : Equivalent earth pressure to transform Q; to a quantity Qd which gives same average plate moments in circumferential direction as Q; does : Radius of nonloaded bend : Radius of bend including additional curvature due to bending : Radius of bend including additional curvature and increased by r for negative bending or decreased by r for positive bending : Average (or mean) radius ~ r = D/2 : Pipe wall thickness : Pipe wall thickness in straight pipe and bend, respectively : Displacement of an element of pipe circumference along circumference and perpendicular to circumference, respectively; also w = L1D/2 : Total increase in curvature in deformation step concerned : Increase in curvature, due to ovalization : Increase in curvature, due to longitudinal yielding : Increase in ovalization, due to longitudinal yielding : Loading angle, bearing angle for Qd and for Q; and Qeq' respectively : Angle of unloaded bend : Change of a : Relative change of a ~ 1] = Llala : 1] associated with Me] and Me2' respectively : Bend characteristic ~ A = tR/r2 : Poisson's ratio : Bend characteristic ~ If/= PR2/Ert : Slope of yield surface

R.J. van Foeken

Papers

Strength And Deformation Capacity Of Bends In Pipelines