This study uses a three-dimensional nonlinear finite-element method to investigate the effects of bend angle () 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.
Chattopadhyay,JTomarAKS. New plastic collapse moment equations of defect-free and through wall circumferentially cracked elbows subjected to combined internal pressure and in-plane bending moment. Eng Fract Mech2006; 73: 829–854.
2.
KaramanosSA. Mechanical behavior of steel pipe bends: An overview. J Press Vessel Technol Trans ASME 2016; 138: PVT-15–1165.
3.
CalladineCR. Limit analysis of curved tubes. J Mech Eng Sci1974; 16: 85–87.
4.
KitchingRZarrabiK. Limit moment for a smooth pipe bend under in-plane bending. Int J Mech Sci1979; 21: 731–738.
5.
GreenstreetWL. Experimental study of plastic responses of pipe elbows. ORNL/NUREG1978; 9: 59.
6.
HilsenkopfPBonehBSollogoubP. Experimental study of behavior and functional capability of ferritic steel elbows and austenitic stainless steel thin-walled elbows. Int J Press Vessel Pip1988; 33: 111–128.
7.
TouboulFBenDAckerD. Design criteria for piping components against plastic collapse: Application to pipe bend experiments. J Press Vessel Technol1988; 319: 73–84.
8.
KirkwoodMGMoffatDG. Plastic loads for piping branch junctions subjected to combined pressure and in-plane moment loads. Proc IMechE Part E: J Process Mechanical Engineering1994; 208: 31–43.
9.
YahiaouiKMoffatDGMoretonDN. Pressurized piping elbows under simulated seismic bending: Design code implications. Proc IMechE Part E: J Process Mechanical Engineering1996; 210: 159–170.
10.
ShalabyMAYounanMYA. Limit loads for pipe elbows with internal pressure under in-plane closing bending moments. J Press Vessel Technol Trans ASME1998; 120: 35–42.
11.
ChattopadhyayJNathaniDKDuttaBK,et al.Closed-form collapse moment equations of elbows under combined internal pressure and in-plane bending moment. J Press Vessel Technol Trans ASME2000; 122: 431–436.
12.
RobertsonALiHMackenzieD. Plastic collapse of pipe bends under combined internal pressure and in-plane bending. Int J Press Vessel Pip2005; 82: 407–416.
13.
VeerappanARShanmugamS. Analysis for flexibility in the ovality and thinning limits of pipe bends. ARPN J Eng Appl Sci2008; 3: 31–41.
14.
VeerappanARShanmugamSSoundrapandianS. The accepting of pipe bends with ovality and thinning using finite element method. J Press Vessel Technol Trans ASME2010; 132: 0312041–0312049.
15.
Dan. The influence of the initial ovality tolerance on the nonlinear cycling analysis of piping bends. J Press Vessel Technol Trans ASME2009; 131: 1–7.
16.
Christo MichaelTVeerappanARShanmugamS. Comparison of plastic limit and collapse loads in pipe bends with shape imperfections under in-plane bending and an internal pressure. Int J Press Vessel Pip2012; 99–100: 23–33.
17.
CollieGJBlackI. An experimental evaluation of induction bending as a method for producing pipe bends with radii ≤2.5D. Proc IMechE Part E: J Process Mechanical Engineering2008; 222: 103–114.
18.
KimY-JKimN-HOhC-Y,et al.A method to estimate plastic loads for elbows with non-uniform thicknesses. Fatigue Fract Eng Mater Struct2008; 31: 822–837.
19.
Christo MichaelTVeerappanARShanmugamS. Effect of internal pressure and shape imperfections on plastic loads of pipe bends under in-plane closing moment. Eng Fract Mech2013; 105: 1–15.
20.
KrishnaLAVeerappanARShanmugamS. Effect of shape imperfections on elastic stresses of U-bends subjected to in-plane moment. Int J Struct Integr2020; 12: 388–407.
21.
AthanasopoulosN. Prediction of pipeline collapse due to hydrostatic pressure. Int J Struct Integr 2019; 10: 55–66
22.
BuckshumiyanAVeerappanARShanmugamS. Plastic collapse loads in shape-imperfect pipe bends under in-plane opening bending moment. Int J Press Vessel Pip2013; 111–112: 21–26.
23.
KimYJLeeKHOhCS,et al.Effect of bend angle on plastic loads of pipe bends under internal pressure and in-plane bending. Int J Mech Sci2007; 49: 1413–1424.
24.
MinSHJeonJYLeeKH,et al.Limit and plastic collapse loads for un-reinforced mitred bends under pressure and bending. Int J Press Vessel Pip2011; 88: 482–494.
25.
LiSZhouCLiJ,et al.Effect of bend angle on plastic limit loads of pipe bends. In: Proceeding of ASME 2016 pressure vessels and piping conference 2016, July 17-21, Vancouver, British Columbia, Canada. 3: pp. 1–8.
26.
LiSJZhouCYLiJ,et al.Effect of bend angle on plastic limit loads of pipe bends under different load conditions. Int J Mech Sci2017; 131–132: 572–585.
27.
SilambarasanRVeerappanARShanmugamS. Effect of structural deformations and bend angle on the collapse load of pipe bends subjected to in-plane closing bending moment. World J Eng2021; 19: 594–603.
28.
MooreCV. ASME boiler and pressure vessel code short courses. J Press Vessel Technol Trans ASME1975; 97: 123.
29.
NeilsonRWoodJHamiltonR,et al.A comparison of plastic collapse and limit loads for single mitred pipe bends under in-plane bending. Int J Press Vessel Pip2010; 87: 550–558.
30.
SumeshSVeerappanARShanmugamS. Determination of critical angle of circumferential throughwall crack for structurally distorted 90° pipe bends under bending moment with and without internal pressure. Proc IMechE Part L: J Material Design and Applications2019; 233: 817–830.
31.
BalakrishnanSVeerappanARShanmugamS. Determination of ovality and wall thinning effects on B 2 stress indices for pipe bends under in-plane closing bending moment. Simulation2019; 95: 185–192.
32.
BalakrishnanSVeerappanARShanmugamS. B2 stress index for structurally distorted pipe bends under in-plane opening bending moment. Int J Press Vessel Pip2019; 176: 103957.
33.
BalakrishnanSVeerappanARShanmugamS. Determination of plastic, shakedown and elastic limit loads of 90°pressurized pipe bends with shape imperfections.Int J Press Vessel Pip2019; 175: 103925.
34.
SumeshSVeerappanARShanmugamS. Evaluation of postulated cross sections with ovality and thinning for 90° pipe bends with circumferential throughwall cracks subjected to in-plane closing bending. Eng Fail Anal2017; 75: 82–91.
35.
SumeshSVeerappanARShanmugamS. Assessment of plastic loads of critical throughwall circumferentially cracked pipe bends with structural distortions under in-plane bending. Thin-Walled Struct2016; 104: 144–151.
36.
VeerappanARShanmugamS. Stress analysis of pipe bends subjected to internal fluid pressure using the finite element technique. J Strain Anal Eng Des2006; 41: 561–573.
37.
ABAQUS. Dassault Systèmes Simulia Corp., USA.
38.
ChattopadhyayJTomarAKSDuttaBK,et al.Closed-form collapse moment equations of throughwall circumferentially cracked elbows subjected to in-plane bending moment. J Press Vessel Technol Trans ASME2004; 126: 307–317.
39.
Christo MichaelTVeerappanARShanmugamS. Effect of ovality and variable wall thickness on collapse loads in pipe bends subjected to in-plane bending closing moment. Eng Fract Mech2012; 79: 138–148.
40.
KimYJJeJHOhCS, et al.Plastic loads for 90° thick-walled elbows under combined pressure and bending. J Strain Anal Eng Des2010; 45: 115–127.
41.
AbdallaHFMegahedMMYounanMYA. Shakedown limits of a 90-degree pipe bend using small and large displacement formulations. J Press Vessel Technol Trans ASME2007; 129: 287–295.
42.
LiJZhouCYCuiP, et al.Plastic limit loads for pipe bends under combined bending and torsion moment. Int J Mech Sci2015; 92: 133–145.
43.
Data fit version 9.0. Oakdale Engineering, Oakdale.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
