NON LINEAR ANALYSIS FOR PIPE BENDS DUE TO PLASTIC LOAD MASTER THESIS KHAMTANH SANTISOUK NIM: Mechanical Engineering Department

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1 NON LINEAR ANALYSIS FOR PIPE BENDS DUE TO PLASTIC LOAD MASTER THESIS In Partial Fulfillment of the Requirement for the Degree of Master in Engineering by KHAMTANH SANTISOUK NIM: Mechanical Engineering Department INSTITUT TEKNOLOGI BANDUNG 2007

2 NON LINEAR ANALYSIS FOR PIPE BENDS DUE TO PLASTIC LOAD by KHAMTANH SANTISOUK NIM: Mechanical Engineering Institut Teknologi Bandung Approved by Date: 1 st, October, 2007 Advisor Dr. IGN. Wiratmaja Puja Prof.Dr.Ir. Djoko SUHARTO NIP NIP

3 Bandung Institute of Technology Abstract Nonlinear Analysis for Pipe Bends Due to Plastic Load Khamtanh Santisouk Chair of the Supervisory Committee: Dr. Ir. IGN. Wiratmaja Puja Department of Mechanical Engineering Pipe bends are very important components used in a piping system. So that it is important to understand the behavior of pipe bends. This paper presents the behaviors of pipe bends under a variety of loading conditions. The pipe bend used in this study is mildsteel that nominal size outside diameter of 2 inches, standardized in schedule 5, 10, 20, 40, and 80. Pipe bends angles, 90, geometry and material properties of pipes are main parameters in this analysis. The plastic finite element analysis has been carried out to evaluate plastic collapse loads of pipe bends. Three types of load were used in the simulations, internal pressure loading, in-plane and out-plane bending moment loading, and combined loading. Empirically, a pipe bend is made from three piping systems, a 90 bend and two equal length of straight pipe run terminating at stiff flanges. Each spacemen was loaded with an external load of sufficient magnitude to produce predominantly plastic collapse response. In-plane and out-plane loading were applied and the effect of internal pressure on the response was studied. The results of these analyses have been presented in the form of normalize pressure versus normalize moment plots, for each load case belonging to each model. The limit load of each case are obtained by normalize pressure-normalize moment curves. The effects of modeling parameters are also studied. The results obtained from

4 small and large deformation are compared. A good agreement is obtained in an adequate manner by comparing theoretical, numerical, and experimental results.

5 TABLE OF CONTENTS Table of Contents... i List of Figures... iv List of Tables... ix List of Nomenclatures... x CHAPTER 1. INTRODUCTION Introduction Objectives Scope of Work... 6 CHAPTER 2. LITERATURE REVIEW Theoretical Investigation of Pipe Bends Minimum Potential Energy Approach Mechanics of Materials Approach Inelastic Analysis of Pipe Bends Numerical Analysis of Pipe Bends Numerical Analysis Using the Finite Element Method Experimental Investigation of the Behavior of Pipe Bends Limit Load Analysis Limit Load Analysis of Pipe Bends Definition of Limit Moment Method for Determining the Plastic Collapse Load i

6 CHAPTER 3. NON LINEAR ANALYSIS OF PIPE BEND UNDER COMBINED INTERNAL PRESSURE, IN- PLANE, AND OUT-OF-PLANE BENDING MOMENT Finite Element Modelling and Analysis Material Model Element Selection and Meshing Boundary Condition Pressure only Loading Bending only Loading Out-of-plane Bending only Loading Combined Loading Limit Loads Combined Loading Instability Loads Combined Loading Plastic Loads Load-Deflection Behavior Effect of Internal Pressure on the Load-Deflection Behavior CHAPTER 4. EXPERIMENTAL ANALYSIS FOR A 2 IN, SCHEDULE 10 PIPE Tension Test Experiment and Equipment Selection Load Cell Calibration Load Cell Calibration Setup Test Rigs of Pipe Bends Spacemen Modelling Non-Pressurized Pipes Test Out-of-Plane Bending Moment In-Plane Opening Bending Moment In-Plane Closing Bending Moment ii

4.4.3. Pressurized Pipes Test... 97 4.4.3.1.

7 Pressurized Pipes Test Pressure-in plane Bending Moment CHAPTER 5. CONCLUSION REFERENCES APPENDIX A iii

8 List of Figures Figure.1.1. Piping Accident in Ohio, USA (1994)... 1 Figure.2.1. Cross-sectional deformations of a pipe bend under in-plane and outof-plane loading... 9 Figure.2.2. Pipe bend cross-section geometry (MSC.NASTRAN) Figure.2.3. In-plane, out-of-plane, and torsional moment loading of pipe bend (ASME B 31.3) Figure.2.4. Comparison between numerical and experimental load-deflection results (Sobel and Newman, 1986) Figure.2.5. Limit load, plastic instability load and plastic load surfaces compared with Shalaby and Younan and Chattopadhyay et al: (a) h=0.18, (b) h=0.24, (c) h= Figure.2.6. Overall Spacemen Dimension (James Kevin Wilkins) Figure.2.7. Elbows Measurement Location and Terminology (James Kevin Wilkins) Figure.2.8. Test Setup for Closing Mode (James Kevin Wilkins) Figure.2.9. Pined End Assembly (James Levin Wilkins) Figure Diagram of Test Setup (Greenstreet) Figure Simple of the Load-Strain Response, Obtain by Greenstreet, Test PE-3 (Out-of-Plane Loading, Without Pressure) Figure Load-Deflection Curve Obtained by Hilsenkopf et al, at Thinwalled Austenite Stainless Steel Elbow Under Out-of Plane Loading (Test 15) Figure Axial Stress Distribution in the Mid-Section of the First Bend Tested by Smith and Ford, Out-of-Plane Loading Figure True Stress- True strain curves of material model used throughout this Figure (a) twice-elastic-slope, criterion, TES, (b) tangent-intersection, criterion, TI Figure.3.1. Pipe bend connected with flanges subject to in-plane, out-of-plane, and torsional moment loading Figure.3.2. Finite element mesh iv

9 Figure.3.3. a.) Internal pressure acted on the element, b.) Constraint and location of moment application Figure.3.4. von Mises equivalent plastic strain distribution at failure: (a) pressure only limit analysis, (b) pressure only large deformation analysis, (c) in-plane bending-only limit analysis, (d) in-plane bending-only large deformation analysis, (e) out-of-plane bendingonly limit analysis, (f) out-of-plane bending-only large deformation analysis Figure.3.5. von Mises equivalent stress distribution at failure: (a) pressure only limit analysis, (b) pressure only large deformation analysis, (c) inplane bending-only limit analysis, (d) in-plane bending-only large deformation analysis, (e) out-of-plane bending-only limit analysis, (f) out-of-plane bending-only large deformation analysis Figure.3.6.a.) Limit load surface for the h = bend evaluated by proportional and sequential loading, b.) von Mises stress distribution at P-M limit loading Figure.3.7. Plastic instability load surfaces for the h = 0.327, b.) h = 0.462, c.) h = Figure.3.8. Typical pressure-rotation curve from moment-pressure large deformation analysis Figure.3.9. Plastic loads for large deformation proportional and pressuremoment loading. Limit and plastic instability loads shown for comparison Figure Limit load, plastic instability load and plastic load surfaces compared with (15) and (17) h = 0.327, h= Figure Displacement of a pipe bend with h = at moment bending M = 500N.m. a.) In-plane closing bending, b.) In-plane opening bending, c.) Out-of-plane bending Figure Variation of moment with end-rotation of pipe bend in case of inplane closing bending moment with h=0.462, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of inplane opening bending moment with h=0.462, without internal pressure v

10 Figure Variation of moment with end-rotation of pipe bend in case of out-of-plane bending moment with h=0.462, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of closing bending moment with h=0.327, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of in-plane opening bending moment with h=0.327, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of out-of-plane bending moment with h=0.327, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of closing bending moment with h=0.654, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of in-plane opening bending moment with h=0.654, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of out-of-plane bending moment with h=0.654, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of closing bending moment with h=1.029, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of opening bending moment with h=1.029, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of out-of-plane bending moment with h=1.029, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of closing bending moment with h=1.029, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of opening bending moment with h=1.029, without internal pressure Figure Variation of moment with end-rotation of pipe bend in case of out-of-plane bending moment with h=1.029, without internal pressure Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure 1 MPa Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure 2 MPa Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure 3 MPa Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure 4 MPa vi

11 Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure 5 MPa Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure range 0-5 MPa Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure range MPa Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure range 0-70 MPa Figure Variation of moment with end rotation for a pipe bend with h = and internal pressure range MPa Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure range MPa Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure range MPa Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure range MPa Figure Variation of moment with end-rotation for a pipe bend with h = and internal pressure range MPa Figure Tension test equipment Figure Location of longitudinal tension test specimens in rings cut from pipe and guideline dimension of coupon (standard test methods and definitions for mechanical testing of steel product, A 370) Figure Dimension of specimen used for tension test according to ASTM guideline Figure Tension test setup Figure Tension test process Figure Tension test results Figure Stress-strain and load-displacement curve obtained from tension test of specimen Figure Stress-strain and load-displacement curve obtained from tension test of specimen Figure Stress-strain and load-displacement curve obtained from tension test of specimen Figure Comparison of Stress-Strain diagram obtained from three-tension test of mild-steel vii

12 Figure Comparison of Load-Displacement diagram obtained from three-tension test of mild-steel Figure gage length of strain Figure Wheatstone bridge schematic Figure Bridge box Figure Wiring to the bridge box Figure Wheatstone circuit with compensation Figure Strain amplifier DPM-611 auto-balancing type Figure NI-USB 6211 and its components Figure USB-6211 Block diagram Figure Load cell calibration setup Figure Load-Strain behavior of load cell obtained from the load cell calibration Figure Geometry and dimension of specimen, unit in mm Figure Out-of-plane bending moment experimental setup Figure Straingauges location Figure Photo of out-of-plane bending moment test setup Figure Load Displacement curve in case of out-of-plane bending moment Figure In-plane opening bending moment experimental setup Figure Photo of experimental setup Figure Load Displacement curve in case of opening bending moment Figure Test setup in case of in-plane closing bending moment Figure Photo of in-plane closing test setup Figure Load Displacement curve in case of closing bending moment viii

13 List of Tables Table 2.1. Pipe-1 and 2 Measured Thicknesses (James Kevin Wilkins) Table.2.2. Summary of Properties and Loading Conditions of Specimens Used in the Tests Conducted by Greenstreet Table.3.1. pipe bend geometry parameters ix

14 Nomenclature r m M i M 0 t M L M p My Mc M I h P 0 σ 0 R b E m L P p φ ν M-P P-M mean pipe radius limit out-plane moment of pipe bend limit out-plane moment of pipe bend wall thickness of pipe limit out-plane of a straight pipe limit moment full plastic moment first-yield moment collapse moment instability moment bend characteristic limit pressure of pipe bend yield strength limit pressure of straight pipe limit moment for the straight pipe bend radius Young modulus normalized moment length of the straight pipe applied pressure normalized pressure angle around circumference Poisson s ratio moment-pressure pressure-moment MTS material test system λ the flexibility characteristic σ 0 the limiting stress of an elastic-perfectly-plastic material x

15 ACKNOWLEDGEMENTS I am immensely indebted to my parents for their inspiration and encouragement throughout the course of my education including this Mater Degree. I am grateful to my advisor, Dr. IGN. Wiratmaja Puja who always helps me in every possible way to complete my Master Degree and his efforts for interaction on my thesis. I am also grateful to my helpful co-advisor, Prof. Dr. Djoko SUHARTO for his good advices and giving me permission to use load cell in his laboratory. Furthermore, I am grateful to my friends, Mr. CHAN Sarin, Miss. Kinnaleth VONGCHANH, Mr. Aung Tanhsin, Mr. NGOUN Kollika, and Mr. Thein Minhtike for their help when I conducted the experimental work. Since some parts of my experimental work have done in cooperation with other laboratories, therefore, I am grateful to all lecturers and staffs in those laboratories for their supportive helps. These include head of the Dynamics and control laboratory, Dr. Ir. Zainal ABIDIN for giving me permission to calibrate load cell in his laboratory. I also thank to Mr. Luffi Hasanudin, technician, and his co-worker in Dynamic laboratory PRI-ITB for their help during the load cell calibration. Moreover, I am thankful to the Production laboratory for allowing me to borrow some components for my experimental setup. I would like to thank the technicians in Solar Energy laboratory that help me to make some necessary components for the experiment. I am grateful to all of the lecturers in Mechanical Engineering Department, especially, in the Engineering Design Centre Laboratory for giving me a change to join their important and interesting courses. Their helpful discussion enables me to overcome the problems relating to coursework. I thank to the technicians, and all friends in the Engineering Design Centre Laboratory for their continuous helps. Finally, I would like to express my gratitude to the AUN/SEED-Net-JICA for giving me the scholarship and research fund. Without the support, my Master Degree would never be possible.

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