Limit Load Analysis of Pipe Bend Using the R-Node Method

2005 ◽  
Author(s):  
Ihab F. Z. Fanous ◽  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Closed Form Solution ◽  
Limit Load ◽  
Form Solution ◽  
Collapse Load ◽  
Pipe Bend ◽  
Bending Force ◽  
Multiple Loads ◽  
Plastic Analysis ◽  
Out Of Plane ◽  
Load Analysis

The R-Node method has been developed earlier as a technique to find the limit load using the Elastic Modulus Adjustment Procedures (EMAP). It utilizes the systematic redistribution of the stress to find the load controlled locations in a component to estimate the collapse load. In this paper, the method is shown to be applicable for multiple loads. A simple cantilever beam is analyzed using the R-Node method subjected to both bending force and moment. The results compare well with the closed form solution of the problem. The method is then used to estimate the limit load for an elbow subjected to in-plane and out-of-plane moment. The results compare well with the elastic-plastic analysis.

Limit Load Analysis of Pipe Bend Using the R-Node Method

2005 ◽  
Vol 127 (4) ◽  
pp. 443-448 ◽  
Author(s):  
Ihab F. Z. Fanous ◽  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Closed Form Solution ◽  
Limit Load ◽  
Form Solution ◽  
Collapse Load ◽  
Pipe Bend ◽  
Bending Force ◽  
Multiple Loads ◽  
Plastic Analysis ◽  
Out Of Plane ◽  
Load Analysis

The r-node method has been developed earlier as a technique to find the limit load using the Elastic Modulus Adjustment Procedures. It utilizes the systematic redistribution of the stress to find the load-controlled locations in a component to estimate the collapse load. In this paper, the method is shown to be applicable for multiple loads. A simple cantilever beam is analyzed using the redistribution-node (r-node) method subjected to both bending force and moment. The results compare well with the closed-form solution of the problem. The method is then used to estimate the limit load for an elbow subjected to in-plane and out-of-plane moment. The results compare well with the elastic-plastic analysis.

Effect of Load Angle on Limit Load of Polyethylene Miter Pipe Bends

2010 ◽  
Author(s):  
Tarek M. A. A. EL-Bagory ◽  
Maher Y. A. Younan ◽  
Hossam E. M. Sallam ◽  
Lotfi A. Abdel-Latif
Keyword(s):  
Crack Depth ◽  
Bending Moment ◽  
Limit Load ◽  
Factor H ◽  
Pipe Bend ◽  
Combined Load ◽  
Specific Loading ◽  
Out Of Plane ◽  
Plane Bending ◽  
Load Angle

The aim of this paper is to investigate the effect crack depth a/W = 0 to 0.4 and load angle (30°,45°,and 60°) on the limit load of miter pipe bends (MPB) under out-of-plane bending moment with a crosshead speed 500 mm/min. The geometry of cracked and uncracked multi miter pipe bends are: bend angle, α = 90°, pipe bend factor, h = 0.844, standard dimension ratio, SDR = 11, and three junctions, m = 3. The material of the investigated pipe is a high-density polyethylene (HDPE), which is applied in natural gas piping systems. Butt-fusion welding is used to produce the welds in the miter pipe bends. An artificial crack is produced by a special cracking device. The crack is located at the crown side of the miter pipe bend, such that the crack is collinear with the direction of the applied load. The crack depth ratio, a/W = 0, 0.1, 0.2, 0.3 and 0.4 for out-of-plane bending moment “i.e. loading angle φ = 0°”. For each out-of-plane bending moment and all closing and opening load angles the limit load is obtained by the tangent intersection method (TI) from the load deflection curves produced by the specially designed and constructed testing machine at the laboratory. For each out-of-plane bending moment case, the experimental results reveals that increasing crack depth leads to a decrease in the stiffness and limit load of MPB. In case of combined load (out-of-plane and in-plane opening; mode) higher load angles lead to an increase in the limit load. The highest limit load value appears at a loading angle equal, φ = 60°. In case of combined load (out-of-plane and in-plane closing; mode) the limit load decreases upon increasing the load angle. On the other hand, higher limit load values take place at a specific loading angle equal φ = 30°. For combined load opening case; higher values of limit load are obtained. Contrarily, lower values are obtained in the closing case.

scholarly journals Collapse load analysis for circumferentially cracked cylinder subjected to combined torsion and bending moments

2018 ◽  
Vol 192 ◽  
pp. 02024
Author(s):  
Sutham Arun ◽  
Thongchai Fongsamootr
Keyword(s):  
Finite Element Analysis ◽  
Limit Load ◽  
Failure Strength ◽  
Bending Moments ◽  
Collapse Load ◽  
Welding Zone ◽  
Element Analysis ◽  
Strength Assessment ◽  
Load Analysis ◽  
Cracked Cylinder

Cylinder is one of the most commonly used components which has a risk of having circumferential cracks, especially in the welding zone. When cracks are discovered, it is necessary to perform the failure strength assessment of cracked cylinder and the limit load play an important part as the input of the assessment. At present, the limit load solution for circumferential cracked cylinder under combined bending and torsion can be estimated by using the methods of equivalent moment or biaxial failure parameter. However, these methods still have some limitations. The main aim of this paper is to propose the alternative method for predicting the failure moment of circumferential cracked cylinder under combined bending and torsion. The method used in this paper is based on the modification of biaxial failure parameter and the data from finite element analysis. Details of this method is presented in this paper.

scholarly journals Green's functions for unsymmetric composite laminates with inclusions

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190437
Author(s):  
Chia-Wen Hsu ◽  
Chyanbin Hwu
Keyword(s):  
Composite Laminates ◽  
Green's Functions ◽  
Green’S Functions ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Displacement Discontinuity ◽  
Computational Time ◽  
Out Of Plane ◽  
Logarithmic Functions

It is known that the stretching and bending deformations will be coupled together for the unsymmetric composite laminates under in-plane force and/or out-of-plane bending moment. Although Green's functions for unsymmetric composite laminates with elliptical elastic inclusions have been obtained by using Stroh-like formalism around 10 years ago, due to the ignoring of inconsistent rigid body movements of matrix and inclusion, the existing solution may lead to displacement discontinuity across the interface between matrix and inclusion. Due to the multi-valued characteristics of complex logarithmic functions appeared in Green's functions, special attention should be made on the proper selection of branch cuts of mapped variables. To solve these problems, in this study, the existing Green's functions are corrected and a simple way to correctly evaluate the mapped complex variable logarithmic functions is suggested. Moreover, to apply the obtained solutions to boundary element method, we also derive the explicit closed-form solution for Green's function of deflection. Since the continuity conditions along the interface have been satisfied in Green's functions, no meshes are required along the interface, which will save a lot of computational time and the results are much more accurate than any other numerical methods.

scholarly journals A New Solution to Well-Known Hencky Problem: Improvement of In-Plane Equilibrium Equation

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 653
Author(s):  
Xue Li ◽  
Jun-Yi Sun ◽  
Zhi-Hang Zhao ◽  
Shou-Zhen Li ◽  
Xiao-Ting He
Keyword(s):  
Closed Form ◽  
Equilibrium Equation ◽  
Circumferential Stress ◽  
Closed Form Solution ◽  
Form Solution ◽  
Circular Membrane ◽  
Equilibrium Equations ◽  
Power Series Method ◽  
Out Of Plane ◽  
Plane Equilibrium

In this paper, the well-known Hencky problem—that is, the problem of axisymmetric deformation of a peripherally fixed and initially flat circular membrane subjected to transverse uniformly distributed loads—is re-solved by simultaneously considering the improvement of the out-of-plane and in-plane equilibrium equations. In which, the so-called small rotation angle assumption of the membrane is given up when establishing the out-of-plane equilibrium equation, and the in-plane equilibrium equation is, for the first time, improved by considering the effect of the deflection on the equilibrium between the radial and circumferential stress. Furthermore, the resulting nonlinear differential equation is successfully solved by using the power series method, and a new closed-form solution of the problem is finally presented. The conducted numerical example indicates that the closed-form solution presented here has a higher computational accuracy in comparison with the existing solutions of the well-known Hencky problem, especially when the deflection of the membrane is relatively large.

The Elastic-Plastic Analysis of Tubes—II: Variable Loading

1992 ◽  
Vol 114 (2) ◽  
pp. 222-228 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Closed Form Solution ◽  
Yield Condition ◽  
Complex Loading ◽  
Form Solution ◽  
Stress And Strain ◽  
Variable Loading ◽  
Elastic Plastic ◽  
Incremental Method ◽  
Plastic Analysis ◽  
General Program

This paper is concerned with the elastic-plastic analysis of tubes subjected to variable loads. The yield condition for a material having residual stress and strain is first derived. Then by incremental method, the stresses and strains of the tube at any loading stage can be found. A closed-form solution is achieved as an example of tubes incurring ratchetting, and a general program is developed to make the theory applicable to complex loading situations.

Effect of Load Angle on Limit Load of Polyethylene Miter Pipe Bends1

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Tarek M. A. A. EL-Bagory ◽  
Maher Y. A. Younan ◽  
Hossam E. M. Sallam ◽  
Lotfi A. Abdel-Latif
Keyword(s):  
Crack Depth ◽  
Bending Moment ◽  
Limit Load ◽  
Factor H ◽  
Pipe Bend ◽  
Combined Load ◽  
Specific Loading ◽  
Out Of Plane ◽  
Plane Bending ◽  
Load Angle

The aim of this paper is to investigate the effect of crack depth a/W = 0–0.4 and load angle (30 deg, 45 deg, and 60 deg) on the limit load of miter pipe bends (MPB) under out-of-plane bending moment with a crosshead speed 500 mm/min. The geometry of cracked and un-cracked multi miter pipe bends are: bend angle, α = 90 deg, pipe bend factor, h = 0.844, standard dimension ratio, SDR = 11, and three junctions, m = 3. The material of the investigated pipe is a high-density polyethylene (HDPE), which is applied in natural gas piping systems. Butt-fusion welding is used to produce the welds in the miter pipe bends. An artificial crack is produced by a special cracking device. The crack is located at the crown side of the miter pipe bend, such that the crack is collinear with the direction of the applied load. The crack depth ratio, a/W = 0, 0.1, 0.2, 0.3, and 0.4 for out-of-plane bending moment “i.e., loading angle ϕ = 0 deg”. For each out-of-plane bending moment and all closing and opening load angles the limit load is obtained by the tangent intersection method (TI) from the load deflection curves produced by the specially designed and constructed testing machine at the laboratory (Mechanical Design Department, Faculty of Engineering, Mataria, Helwan University, Cairo/Egypt). For each out-of-plane bending moment case, the experimental results reveals that increasing crack depth leads to a decrease in the stiffness and limit load of MPB. In case of combined load (out-of-plane and in-plane opening; mode) higher load angles lead to an increase in the limit load. The highest limit load value appears at a loading angle equal, ϕ = 60 deg. In case of combined load (out-of-plane and in-plane closing; mode) the limit load decreases upon increasing the load angle. On the other hand, higher limit load values appear at a specific loading angle equal ϕ = 30 deg. For combined load opening case; higher values of limit load are obtained. Contrarily, lower values are obtained in the closing case.

Limit Load Determination and Material Characterization of Cracked Polyethylene Miter Pipe Bends1

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Tarek M. A. A. EL-Bagory ◽  
Maher Y. A. Younan ◽  
Hossam E. M. Sallam ◽  
Lotfi A. Abdel-Latif
Keyword(s):  
Fracture Toughness ◽  
Limit Load ◽  
Factor H ◽  
Thickness Variation ◽  
Pipe Bend ◽  
Manufacturing Defects ◽  
Combined Load ◽  
Crosshead Speed ◽  
Out Of Plane ◽  
Load Angle

The quality of Natural Gas Piping Systems (NGPS), must be ensured against manufacturing defects. The main purpose of the present paper is to investigate the effect of loading mode and load angle (30 deg, 45 deg, and 60 deg) on the limit load of miter pipe bends (MPB), under different crack depths a/W = 0–0.4 at a crosshead speed 500 mm/min. The geometry of cracked and uncracked multi-miter pipe bends are pipe bend angle, α = 90 deg, pipe bend factor, h = 0.844, standard dimension ratio, SDR = 11, and three junctions, m = 3. The material of the investigated pipe is a high-density polyethylene (HDPE), which is commonly used in NGPS. The welds at the miter pipe junction are produced by butt-fusion welding. For all loading modes the limit load is obtained by the tangent intersection (TI) method from the load–deflection curves produced by the specially designed and constructed testing machine at the laboratory5. Tensile tests are conducted on specimens longitudinally extruded from the pipe with thickness, T = 10, 30 mm, at different crosshead speeds (5–500 mm/min), and different gauge lengths (G = 20, 25, and 50 mm) to determine the mechanical properties of welded and unwelded specimens. The fracture toughness is determined on the basis of elastic plastic fracture mechanics (EPFM). Curved three-point bend specimens (CTPB), are used. All specimens are provided with artificial precrack at the crack tip, a/W = 0.5. The effect of specimen thickness variation (B = 10, 15, 22.5, 30, 37.5, and 45 mm) for welded and unwelded specimens is studied at room temperature (Ta = 23 °C) and at different crosshead speeds, VC.H, ranging from 5 to 500 mm/min. The study reveals that increasing the crack depth leads to a decrease in the stiffness and limit load of MPB for both in-plane, and out-of-plane bending moment. In case of combined load (out-of-plane and in-plane opening; mode), higher load angles lead to an increase in the limit load. The highest limit load value occurs at a loading angle, ϕ = 60 deg. In case of combined load (out-of-plane and in-plane closing; mode), the limit load decreases with increasing load angles. At a load angle ϕ = 30 deg, the higher limit load value occurred in both cases. For combined load opening case, higher values of limit load are obtained. The crosshead speed has a significant effect on the mechanical behavior of both welded and unwelded specimens. The fracture toughness, JIC, is greater for unwelded than welded specimen.

Plastic Limit Pressure Solutions for Elbows With Slant Through-Wall Cracks

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Minkyu Kim ◽  
Jaehee Kim ◽  
Moon Ki Kim ◽  
Jae-Boong Choi ◽  
Nam-Su Huh ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Closed Form Solution ◽  
Limit Load ◽  
Form Solution ◽  
Fe Model ◽  
Plastic Limit ◽  
Critical Crack ◽  
Critical Crack Length ◽  
Limit Pressure ◽  
Plastic Limit Pressure

Abstract For leak-before-break (LBB) assessment, an idealized through-wall crack (TWC) is typically postulated to determine the critical crack length of cracked piping. However, such an idealization in terms of crack shape can lead to underestimations of plastic limit pressure. Although many studies have been performed to obtain accurate limit load solutions for cracked straight pipes by considering realistic crack geometries, there is still a lack of information regarding slant TWC at elbow. Therefore, three-dimensional finite element (FE) models of an elbow considering the effects of slant TWC on plastic limit pressure are developed. The proposed FE model and analysis procedure were verified through comparisons to the existing solutions for idealized TWCs in elbow. On this basis, the effect of slant TWC on the plastic limit pressure is analyzed, and a closed-form solution of the plastic limit pressure is proposed, for an elbow containing a longitudinal or a circumferential through-wall crack.

Sign in / Sign up

Export Citation Format

Share Document