In-plane Closing Bending Moment Research Articles

Risk assessment of strain hardened pipe bends with shape imperfections under in-plane closing bending moment

Risk assessment of strain hardened pipe bends with shape imperfections under in-plane closing bending moment

Development of a new improved closed-form plastic collapse moment solution for structurally distorted and through-wall axially cracked 90° pipe bends subjected to in-plane closing bending moment

Plastic collapse loads of 90° pipe bends with structural defects subjected to in-plane closing bending are systematically examined in this study using three dimensional nonlinear finite element (FE) analyses. The analyses consider the large strain formulation option with the pipe bend material assumed to be of the elastic perfectly plastic (EPP) type. Pipe bends are analyzed by changing the ovality at the mid-section which is varied from 0% to 20% by 5% per step. The through-wall axial crack (TAC) parameter at the pipe bend's crown is varied from 0 to 1 by 0.2 per step. Moment rotation curves are drawn for all simulated pipe bend models and plastic collapse moment (PCM) loads are determined from the corresponding moment rotation curves using the Twice-Elastic-Slope (TES) methodology as recommended by clause NB-3213.25 in section III of ASME B&PV code. Both ovality and TAC of pipe bends significantly affects their plastic collapse moments (PCM) and this almost doubles when ovality and TAC act together. The observed effect of ovality and TAC on pipe bends having thin walled and short bend radius does not significantly change with increasing wall thickness and bend radius. The present FE analysis is validated using experimental PCM loads of pipe bends available in open literature. The crack closing effect of pipe bends during closing bending is examined. Based on the analysis, an improved structural integrity assessment equation for shape imperfect pipe bends with TAC is developed for in-plane closing bending moment loads.

Investigation on structural integrity of shape distorted 90° back-to-back pipe bends under in-plane closing bending moment

PurposeThe aim of this study is to ensure the structural integrity of 90° back-to-back (B2B) pipe bends by developing a closed-form numerical solution for estimating the collapse load of shape distorted 90° B2B pipe bends using non-linear finite element (FE) analysis.Design/methodology/approachThe collapse behaviour of 90° B2B pipe bends with ovality (Co) and thinning (Ct) has been evaluated by non-linear FE approach. Moment load is applied in the form of in-plane closing moment (IPCM). The current FE approach was evaluated by the numerical solution for the plastic collapse moment of pipe bends, which has been published in the literature. The collapse moments were obtained from the twice elastic slope (TES) method using the moment-rotation curve of every individual model.FindingsThe implication of Ct/Cth on collapse load is found to be highly insignificant in terms of increasing bend radius and Co. Co weakens the geometry, and its effect on the collapse load is substantial. A closed-form numerical solution has been proposed to calculate the collapse load of 90° B2B pipe bend with shape imperfections.Originality/valueThe implications of shape distortion (Co and Ct) in the failure analysis (collapse load) of 90° B2B pipe bends has not been investigated and reported.

New empirical equations for determining plastic collapse moment of initially imperfect pipe bends under internal pressure and in-plane closing bending moment

New empirical equations for determining plastic collapse moment of initially imperfect pipe bends under internal pressure and in-plane closing bending moment

Combined effect of shape distortion and bend angle on collapse load of pipe bends under in-plane closing bending moment and internal pressure

PurposeThe purpose of this paper is to quantify the combined effect of shape distortion and bend angle on the collapse loads of pipe bends exposed to internal pressure and in-plane closing bending moment. Non-linear finite element analysis with large displacement theory was performed considering the pipe bend material to be elastic perfectly plastic.Design/methodology/approachOne half of the pipe bend model was built in ABAQUS. Shape distortion, namely, ovality (Co) and thinning (Ct), were each varied from 0% to 20% in steps of 5% and bend angle was varied from 30° to 180° in steps of 30°.FindingsThe findings show that ovality has a significant impact on collapse load. The effect of ovality decreases with an increase in bend angle for small thickness. The opposite effect was observed for large thickness pipe bends. The influence of ovality was more for higher bend angles. Ovality impact was almost negligible at certain internal pressure denoted as nullifying point (NP). The latter increased with an increase in pipe bend thickness and decreased with increase in pipe bend radius. For small bend angles one NP was observed where ovality impact is negligible and beyond this point the ovality effect increased. Two NPs were observed for large bend angles and ovality effect was maximum between the two NPs. Thinning yielded a minimal effect on collapse load except for small bend angles and bend radii. The influence of internal pressure on thinning was also negligible.Originality/valueInfluence of shape distortions and bend angle on collapse load of pipe bend exposed to internal pressure and in-plane closing bending has been not revealed in existing literature.

Effect of structural deformations and bend angle on the collapse load of pipe bends subjected to in-plane closing bending moment

PurposeThe purpose of this study is to investigate the effect of structural deformations and bend angle on plastic collapse load of pipe bends under an in-plane closing bending moment (IPCM). A large strain formulation of three-dimensional non-linear finite element analysis was performed using an elastic perfectly plastic material. A unified mathematical solution was proposed to estimate the collapse load of pipe bends subjected to IPCM for the considered range of bend characteristics.Design/methodology/approachABAQUS was used to create one half of the pipe bend model due to its symmetry on the longitudinal axis. Structural deformations, i.e. ovality (Co) and thinning (Ct) varied from 0% to 20% in 5% steps while the bend angle (ø) varied from 30° to 180° in steps of 30°.FindingsThe plastic collapse load decreases as the bend angle increase for all pipe bend models. A remarkable effect on the collapse load was observed for bend angles between 30° and 120° beyond which a decline was noticed. Ovality had a significant effect on the collapse load with this effect decreasing as the bend angle increased. The combined effect of thinning and bend angle was minimal for the considered models and the maximum per cent variation in collapse load was 5.76% for small bend angles and bend radius pipe bends and less than 2% for other cases.Originality/valueThe effect of structural deformations and bend angle on collapse load of pipe bends exposed to IPCM has been not studied in the existing literature.

Determination of plastic, shakedown and elastic limit loads of 90°pressurized pipe bends with shape imperfections

This study determines the plastic, shakedown and elastic limit loads and the corresponding regimes of 90° pressurized pipe bends with shape imperfections subjected to cyclic in-plane closing bending moment. Three dimensional FE analyses with small strain formulation was performed. The induced shape imperfections are ovality and thinning, which were varied from 0% to 20% with a 5% increment at every step. Plastic limit load was determined from the moment rotation curve while shakedown and elastic limit loads were determined by using Abdalla's simplified technique (ST). The analysis indicates that the presence of ovality produces considerable effect on plastic limit loads. Thinning alters plastic limit loads only for long bend radius models with no ovality when normalised internal pressure ratio is unity and in other cases its effect is minimal. Presence of ovality and thinning has a remarkable effect on shakedown and elastic limit loads and their regimes though the thinning effect is insignificant at higher ovality (10%–20%). Bree diagram was constructed for the reference pipe bend models. It was observed that the failure of pipe bends is due to either reversed plasticity or ratcheting. Mathematical equations are proposed to express the generated plastic, shakedown and elastic limit moment boundaries for the analyzed pipe bend models.

Limit load analysis of thick-walled as-fabricated pipe bends under in-plane moment loading and internal pressure

The fabrication of pipe bends by rotary bending results in geometrical imperfections as manifested by cross-sectional ovality and wall thickness variations which affect their load carrying capacity and hence their performance during service. Previous studies ignored the exact distribution of these imperfections and adopted either ideal pipe bend shape (IB) or assumed the distribution these imperfections in their analysis by a simplified assumed shape model (AS). The objective of the present work is to investigate the effect of the presence of the inherited geometrical imperfections as obtained from the rotary pipe bending process of 90° pipe bends including the presence of residual stresses on their load carrying capacities as compared with the IB and AS models. The present work is conducted by means of non-linear finite element modeling considering both material and geometrical non-linearities. Rotary pipe bending process is simulated with basic tooling configuration to obtain the as-fabricated 90° pipe bend after accounting for springback. Results of this step were verified against published experimental results and analytical solutions. The pipe bend was then subjected to different combinations of in-plane moment and internal pressure in order to construct a comparative limit load diagram. The IB model for the pipe bend results in non-conservative results, while AS model results in acceptable results compared to results of the as-fabricated shape. Results have also shown that presence of residual stresses improves the pipe performance under in-plane closing bending moment.

Determination of ovality and wall thinning effects on B2 stress indices for pipe bends under in-plane closing bending moment

The present work evaluates the combined effect of variable wall thickness and ovality on the B2 stress index of bends under in-plane closing moment using finite element analysis. The material chose...

Determination of critical angle of circumferential throughwall crack for structurally distorted 90° pipe bends under bending moment with and without internal pressure

Throughwall circumferential cracks (TWC) in elbows can considerably minimize its collapse load when subjected to in-plane bending moment. The existing closed-form collapse moment equations do not adequately quantify critical crack angles for structurally distorted cracked pipe bends subjected to external loading. Therefore, the present study has been conducted to examine utilizing elastic-plastic finite element analysis, the influence of structural distortions on the variation of critical TWC of 90° pipe bends under in-plane closing bending moment without and with internal pressure. With a mean radius ( r) of 50 mm, cracked pipe bends were modeled for three different wall thickness, t (for pipe ratios of r/ t = 5,10,20), each with two different bend radius, R (for bend ratios of R/r = 2,3) and with varying degrees of ovality and thinning (0 to 20% with increments of 5%). Finite element analyses were performed for two loading cases namely pure in-plane closing moment and in-plane closing bending with internal pressure. Normalized internal pressures of 0.2, 0.4, and 0.6 were applied. Results indicate the modification in the critical crack angle due to the pronounced effect of ovality compared to thinning on the plastic loads of pipe bends. From the finite element results, improved closed-form equations are proposed to evaluate plastic collapse moment of throughwall circumferential cracked pipe bends under the two loading conditions.

Evaluation of postulated cross sections with ovality and thinning for 90° pipe bends with circumferential throughwall cracks subjected to in-plane closing bending

Abstract A comparative study of postulated cross sections for failure analysis of 90°structurally deformed pipe bends with critical circumferential throughwall cracks was performed. Elliptical and semi-oval cross sections were assumed to determine the collapse loads under in-plane closing bending moment. Finite element analysis was conducted based on elastic-perfectly-plastic material considering geometric nonlinearity and twice-elastic-slope method was used to obtain collapse loads for each model. The influence of pipe ratio and bend radius in the presence of ovality and thinning were also investigated for the postulated cross sections. The results indicated a pronounced effect of ovality on collapse loads of throughwall circumferentially cracked pipe bends, primarily with elliptic cross sections whereas the thinning effect is significantly lower for both the cross sections. The present study provided a better estimation of the plastic loads and elliptic cross sections were found to be ideal in the analysis of cracked pipe bends for the present geometries and across the boundary conditions considered.

Limit Load Analysis of Elbow with Local Wall Thinning under Combined Loads

The local wall thinning(LWT) is a kind of common volume defect in pressure pipe. The limit loads of elbows with LWT under pressure, bending moment, torque and their combined loads have been studied in detail by orthogonal experimental design and finite element method. The results have shown that the influence of depth and circumferential length of LWT on the limit load is more obvious compared to that of axial length when an elbow is under pressure, bending moment or torque. The change of limit bending moment and torque with the depth of LWT and circumferential length is significant for an elbow under combined bending moment and torque. At last, the safety assessment equations for elbow under combined in-plane closing bending moment and torque were proposed by regression analysis.

Analysis and Experiments on the Plastic Limit Load of Elbows under Combined Pressure and In-Plane Closing Bending Moment

This paper discusses the plastic limit load of elbows without defects and with local thinned area (LTA) in the extrados under combined pressure and in-plane closing bending moment. Finite element analysis (FEA) and experiments have been used. The results of FEA show that, for the elbows without defects, when the ratio of pressure to the limit pressure (P/PL) is smaller than 0.469, the limit moment of elbows increases with the increasing pressure; when the ratio (P/PL) is bigger than 0.469, the limit moment of elbow decreases with the increasing pressure. For the elbows with LTA, the FEA results show that with different LTA the variation of the limit load of elbows to the pressure is different. Perhaps, the limit moment of elbows always decreases with the increasing pressure. It is also likely that the limit moment of elbows increases with the increasing pressure and then decreases with the increasing pressure. The results of FEA are consistent with the experimental results. By fitting the results of FEA, the safety assessment figure for elbows under combined pressure and in-plane closing bending moment is drawn.

Determination of Shakedown Limit Load for a 90-Degree Pipe Bend Using a Simplified Technique

In this paper a simplified technique is presented to determine the shakedown limit load of a 90-degree pipe bend subjected to constant internal pressure and cyclic in-plane closing bending moment using the finite element method. The simplified technique determines the shakedown limit load without performing time consuming full elastic-plastic cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit load is determined by performing two finite element analyses namely; an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown limit load is determined through the calculation of the residual stresses developed in the pipe bend. In order to gain confidence in the simplified technique, the output shakedown limit moments are used to perform full elastic-plastic cyclic loading simulations to check for shakedown behavior of the pipe bend. The shakedown limit moments output by the simplified technique are used to generate the shakedown diagram of the pipe bend for a range of constant internal pressure magnitudes. The maximum moment carrying capacity (limit moment) the pipe bend can withstand and the elastic limit are also determined and imposed on the shakedown diagram of the pipe bend. In order to get acquainted with the simplified technique, it is applied beforehand to a bench mark shakedown problem namely, the Bree cylinder (Bree, J., 1967, J. Strain Anal., 3, pp. 226–238) problem. The Bree cylinder is subjected to constant internal pressure and cyclic high heat fluxes across its wall. The results of the simplified technique showed very good correlation with the analytically determined Bree diagram of the cylinder.

Simplified, Detailed, and Isochronous Analysis and Test Results for the In-Plane Elastic-Plastic and Creep Behavior of an Elbow

Abstract Predictions obtained from simplified and detailed MARC analyses are compared with experimental results for the elastic-plastic and creep behavior of a 16-in-dia 304 stainless steel piping structure subjected to an in-plane closing bending moment. The piping structure is composed of a 90-deg elbow and two straight tangent pipes. The simplified analysis is found to considerably overestimate the measured results, especially for the case of creep behavior. The correlation of detailed analysis predictions with measured results is satisfactory for the elastic-plastic behavior of the structure, and inconclusive for the creep behavior, since the creep predictions are based on a commonly used creep law rather than on the actual (but unmeasured) creep properties. The paper also shows that predictions of creep deformation obtained from the relatively inexpensive time-independent isochronous method of analysis agree well with results given by a “complete” and more costly time-dependent creep analysis.

The Southwell Method for Predicting Plastic Buckling Loads for Elbows

The Southwell method for the prediction of buckling loads is applied to results obtained from tests of two 16-in-dia Type 304 stainless steel elbows loaded by an in-plane closing bending moment M. The basis of the method is discussed, and it is shown that proper application of the method requires that the nonlinear component of the deformation, δnl, be used in the Southwell plot. Predicted buckling loads determined from four experimental M-δnl curves for each test are found to be consistent and accurate, with an average value that is only slightly above the experimental plastic buckling load. The major conclusion of this paper is that the Southwell method based on δnl is valid for elbows loaded by an in-plane closing bending moment, and for a certain broader class of elastic or plastic nonlinear buckling (geometric collapse) problems for imperfection-insensitive structures. Consequently, tests and analyses of such structures need not be carried out to buckling to determine buckling loads. Practical advantages of such nonbuckling tests and analyses are discussed.

Effect of cross section on collapse load in pipe bends subjected to in-plane closing moment

A comparison between pipe bends with assumed cross sections, namely elliptic and semi oval to include ovality along with wall thinning, was performed to determine the plastic collapse load under in-plane closing bending moment using finite element limit analysis based on an elastic-perfectly plastic material considering geometric nonlinearity. Twice-elastic-slope method was used to obtain collapse load from the moment-rotation curve drawn for each pipe bend model considered. The effect of ovality on collapse load is significant and higher for elliptic cross sections for almost all cases while the thinning effect is negligible for both the cross sections. The study concludes that the use of elliptic cross section is suitable for analyzing pipe bend with ovality. Therefore, a closed-form solution is proposed to determine collapse load of pipe bend based on the finite element results of elliptic cross sections.