In-plane Opening Bending Moment Research Articles

Development of new improved plastic collapse moment equations of pressurized different angled pipe bends under bending moments

In a piping system, pipe bends are more flexible than straight pipes because of their curved geometry, supplemented by higher stress and strain concentration, leading to one of the crucial components in piping industries. Therefore, safe design of pipe bends is essential for smooth running of the piping system, and plastic collapse moment is one of its criteria. This paper utilizes three-dimensional finite element analyses to model empirical solutions for the plastic collapse moment for different angled pipe bends subjected to combined pressure and in-plane closing, in-plane opening, and out-of-plane bending moments. Plastic collapse moments for 30∘ to 180∘ pipe bends are determined for elastic perfectly plastic and strain hardening materials, employing large geometry change option and internal pressure effect. It is observed from results that pressure effect is more prominent in thinner pipe bends of larger bend angle under all bending cases. For in-plane opening and out-of-plane bending moments, collapse moment increases and then decreases with increase in pressure intensity for all sizes of pipe bend. However, for in-plane opening bending moment, collapse moments keep on decreasing for thicker ([Formula: see text] = 11.33) pipe bends. Finally, the study presents new improved plastic collapse moment solutions for different angled pipe bends under bending moment and internal pressure, derived from the finite element results of elastic perfectly plastic and strain hardening material models.

Development of an improved structural integrity assessment correlation for circumferential through-wall cracked 90° shape-distorted pipe bends subjected to in-plane opening bending moment

A detailed and systematic assessment of the plastic collapse load of 90° shape imperfect pipe bends subjected to in-plane opening bending was conducted by implementing three-dimensional non-linear finite element analyses. The material considered in the analysis is the elastic-perfectly plastic type with a large change geometry option. Shape distortions in the pipe's cross-section and through-wall circumferential crack at the intrados region were the defects analyzed in this study. Ovality [Formula: see text] and thinning [Formula: see text] were varied from 0% to 20% with a 5% incrementation, and crack angles of 45°, 60°, and 90° were considered at the intrados. The twice-elastic slope method effectively evaluates the plastic collapse moment as mandated by the ASME B&PV code NB-3213.25, section III. The reaction moment and angular rotation curves were generated for all pipe bend models. The outcomes of the analysis revealed that the plastic collapse moment load of pipe bends was affected by through-wall circumferential crack and [Formula: see text], while thinning produced negligible effect, which was subsequently excluded from the analysis. The combined effect of through-wall circumferential crack and [Formula: see text] produces a consequential influence on the pipe bend at 45° angle, which is severe at 60°, and even more critical at 90°. In the analysis, the plastic collapse moment for short bend radius was reduced, while that of thin-walled pipe bends increased with an increase in thickness and bend radius. The plastic collapse moment of the present analysis was validated using experimental data acquired from open literature. An enhanced structural correlation assessment was proposed for through-wall circumferential crack shape-distorted 90° pipe bends.

Determination of bend angle and shape imperfection effect on collapse load of pipe bends under in-plane opening moment

This study uses a three-dimensional nonlinear finite-element method to investigate the effects of bend angle ([Formula: see text]) and shape imperfection on the collapse load of pipe bends subjected to in-plane opening bending moment using large displacement analysis. ABAQUS was used to create a pipe bend model, whereas by virtue of symmetry about the longitudinal axis, half of the pipe bend model was built. The bend angle was varied from 30° to 180° with an interval of 30°, and shape imperfections, namely ovality ( Co) and thinning ( Ct), were varied from 0% to 20% each at 5% intervals. Elastic-perfectly plastic is thought to be the material of choice for the pipe bend. The results show that the bend angle has a significant impact on the collapse load of pipe bends between 30° and 120°, after which a significant decline was observed. The ovality impact increases with an increase in bend angle for pipe bends with a large thickness, whereas the opposite effect was found for smaller thicknesses with a small bend radius. The effect of bend radius and thickness was significant for large bend angles. Thinning ( Ct) and thickening ( Cth) have no effect on collapse load. A new mathematical equation has been proposed to predict the integrated effect of bend angle and shape imperfection.

Development of a new improved structural integrity assessment correlation for throughwall axially cracked 90° shape imperfect pipe bends under in-plane opening bending moment

In the present work, a systematic and detailed investigation on the plastic collapse load of 90° structurally defected pipe bends under in-plane opening bending was performed using three-dimensional finite element (FE) analyses. The analysis considers the material behavior as elastic-perfectly plastic (EPP) with a large strain formulation option. The structural defects in the pipe bend models included were ovality at mid-portion and throughwall axial crack (TAC) at the crown portion. Ovality varied from 0 to 20 % with 5 % increment at each step while the normalized throughwall axial crack (TAC) parameter length a/D from 0 to 1 with an increment of 0.2 in each step. As per the recommendation of clause NB-3213.25 in Section III of ASME B&PV code, Twice-elastic slope (TES) technique was extensively used to determine the plastic collapse moment (PCM) for all simulated pipe bend models from their corresponding reaction moment versus angular rotation curve. The analysis illustrated that both ovality and throughwall axial crack (TAC) significantly affected PCM load of pipe bends and when combined, the effect was almost double. In pipe bend models with thin walls and short bend radius, both ovality and TAC were found to be more vulnerable and the effect decreased with an increase in bend radius and thickness. The experimental results for pipe bend's plastic collapse moment available in open literature were used to validate the present finite element (FE) procedure and a new improved structural assessment correlation proposed for pipe bends with ovality and TAC defects.

B2 stress index for structurally distorted pipe bends under in-plane opening bending moment

The present study determines the effect of shape imperfections on the B2 index of pipe bends subjected to in-plane opening moment using 3D nonlinear finite element (FE) methodology. The analysis considers the large strain formulation option and the material behavior is elastic-perfectly plastic. The reaction moment versus angular rotation curves are plotted for all the simulated pipe bends and the plastic collapsing moments are determined using Twice-elastic slope technique as recommended in ASME B&PV, section III (clause NB-3213.25). The B2 stress index was computed for each model from their respective collapse moment. The variable wall thickening in the pipe bend's cross section yields negligible effect and the presence of ovality has a momentous effect on B2 stress indices. A mathematical equation is suggested to compute B2 stress index for pipe bends with ovality subjected to in-plane opening bending moment.

Determination of collapse loads in pipe bends with ovality and variable wall thickness under internal pressure and in-plane opening moment

The combined effect of ovality and variable wall thickness on collapse load of pipe bends under in-plane opening bending moment with internal pressure was investigated using finite element limit analysis considering large geometric change effect. The material was assumed to be elastic–perfectly plastic. The collapse moments were obtained from moment-rotation curves drawn for each bend using twice-elastic-slope method. Thickening/thinning effect on collapse load is very minimal and can be neglected. The effect of ovality is significant with the reduction of collapse load by a maximum of 39.1% for the maximum internal pressure and ovality considered. Based on the finite element results, a mathematical expression is proposed to determine collapse load of the pipe bends with ovality and this equation has been verified with experimental collapse loads.

Plastic collapse loads in shape-imperfect pipe bends under in-plane opening bending moment

The combined effect of ovality and thinning/thickening on collapse load of pipe bends under in-plane opening bending moment was investigated using finite element limit analysis considering large geometric change effect. The material is assumed to be elastic-perfectly plastic. Twice-elastic-slope method is used to obtain collapse moment from moment–rotation curves drawn for each bend. Variation of thickness due to thinning in the cross section of pipe bend produces negligible effect on collapse load. The effect of ovality is significant except for pipe ratio 20 with λ = 0.5. A new closed-form solution is proposed to determine collapse moment of pipe bends with ovality and it is validated with existing experimental data.

Experimental Study on the Plastic Collapse Load of Elbows Subjected to In-Plane Opening Bending Moment

Pipe elbows are the most critical components in any piping system. However, the earlier experiments on cracked elbows were focused mainly on the determination of limit load of through wall cracked elbow. The experimental results of plastic collapse load of seven carbon steel 900 elbows, subjected to in-plane opening bending moment, are reported in this work. Among the selected specimens, three were defect-free elbows and six had axial surface cracks at the intrados, crown or at extrados. Test arrangement and the collapse behavior with and without cracks were presented. The plastic collapse loads were then obtained on the basis of experimental results. Reasonably good matching between test results and existing estimation formulae has been observed.

Numerical Study of Defect Free Elbows Subjected to In-Plane Bending Moment

Elbow is a type of components widely used in a piping system, and so it is very important to know the plastic carrying capacity of elbow. In this study, the elastic-plastic behavior of elbows with various ratios of t/rm and relative bending radius R/rm were investigated in detail by using of three-dimensional (3D) non-linear finite element (FE) analyses, assuming elastic-perfectly-plastic material behaviour and taking geometric nonlinearity into account. The analyses indicated that elbow exhibited different behavior obviously at the elastic-plastic states subjected to In-Plane opening bending moment and closing bending moment. The closed form equations of elbow involving effect of tangent pipes were established.

Elastic–plastic analysis of an elbow with a through-wall axial crack at crown under in-plane bending

Piping elbows under bending moment are vulnerable to cracking at crown. The structural integrity assessment requires knowledge of the J-integral. The J-integral values for axially through-wall cracked thick elbows under in-plane bending moment are not available in open literature. This paper presents the J-integral results for 90°, long radius elbows subjected to in-plane opening bending moment based on a large number of finite element analyses covering a wide range of standard geometries. The non-linear elastic–plastic finite element analyses were performed using WARP3D software. Both geometric and material non-linearity were considered in the study. The geometry considered were for R m/ t = 5, 6, 7.5, 9, 12, 15, 20 and 25 with crack angles of 9°, 18°, 27° and 36° and strain hardening exponent, ‘ n’ varied for 2, 3, 5, 7 and 10.