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Research Papers: Operations, Applications and Components

Shakedown Limits for Hillside Nozzles in Cylindrical Vessels

[+] Author and Article Information
Ahmed K. Bakry

Faculty of Engineering,
Cairo University,
Orman, Giza 12613, Egypt
e-mail: ahmed.bakry@enppi.com

Chahinaz A. Saleh

Associate Professor
Solid Mechanics,
Faculty of Engineering,
Cairo University,
Orman, Giza 12613, Egypt
e-mail: chahinaz@eng.cu.edu.eg

Mohammad M. Megahed

Professor
Solid Mechanics,
Faculty of Engineering,
Cairo University,
Orman, Giza 12613, Egypt
e-mail: mmegahed@eng.cu.edu.eg

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received September 25, 2017; final manuscript received February 25, 2018; published online April 10, 2018. Assoc. Editor: Steve J. Hensel.

J. Pressure Vessel Technol 140(3), 031601 (Apr 10, 2018) (8 pages) Paper No: PVT-17-1193; doi: 10.1115/1.4039503 History: Received September 25, 2017; Revised February 25, 2018

This research paper is concerned with the mechanical behavior of the cylindrical vessels with hillside nozzles when subjected to both pressure and nozzle bending loads in cyclic forms. The influence of hillside angle on shakedown (SD) limits of the connection under cyclic pressure and combined steady pressure with cyclic nozzle bending is investigated. A shell finite element analysis model is built for the assembly using five different hillside angles ranging from 0 deg to 40 deg. Shakedown limits are determined by a direct technique known as the nonlinear superposition method (NSM). Bree diagrams for cyclic out of plane opening (OPO)/in plane (IP) nozzle moments combined with steady internal pressure are determined. The results show an increase in both OPO and IP shakedown moments as the hillside angle is increased. In addition, the OPO shakedown limit moments for all hillside angles were found to be insensitive to the level of internal pressure; this differs from the IP shakedown moment which starts to decrease with pressure for the high pressures.

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References

Wichman K. R, M. J. L. , and Hopper, A. G. , 1979, “Local Stresses Spherical Cylindrical Shells Due to External Loadings,” Welding Research Council, New York, Report No. 107.
Mershon, J. L. , Mokhtarian, K. , Ranjan, G. V. , and Rodabaugh, E. C. , 1987, “Local Stresses in Cylindrical Shells Due to External Loadings on Nozzles-Supplement to WRC Bulletin No. 107 (Revision I),” Welding Research Council, New York, Report No. WRC 297.
ASME, 2015, ASME B&PVC, Section VIII, Division 2, Rules for Construction of Pressure Vessels—Alternative Rules, American Society of Mechanical Engineers, New York.
Mershon, J. L. , 1970, “Part 1: Interpretive Report on Oblique Nozzle Connections in Pressure Vessel Heads and Shells Under Internal Pressure Loading,” Welding Research Council, New York, Report No. 153.
Wang, H. F. , Sang, Z. F. , Xue, L. P. , and Widera, G. E. O. , 2006, “Elastic Stresses of Pressurized Cylinders With Hillside Nozzle,” ASME J. Pressure Vessel Technol., 128(4), pp. 625–631. [CrossRef]
Hazlett, T. , 1990, “Three Dimensional Parametric Finite Element Analyses of Hillside Connections in Cylinders Subject to Internal Pressure,” ASME Pressure Vessels & Piping Conference, Nashville, TN, June 17–21, pp. 141–145.
Skopinsky, V. N. , 1993, “Numerical Stress Analysis of Intersecting Cylindrical Shells,” ASME J. Pressure Vessel Technol., 115(3), pp. 275–282. [CrossRef]
Rodabaugh, E. C. , 2000, “Part 1: Internal Pressure Design of Isolated Nozzles in Cylindrical Vessels With d/D up to and Including 1.00: Report No. 1: Code Rules for Internal Pressure Design of Isolated Nozzles in Cylindrical Vessels,” Welding Research Council, New York, Report No. WRC 451.
Fang, J. , Li, N. , Sang, Z. F. , and Widera, G. E. O. , 2009, “Study of Elastic Strength for Cylinders With Hillside Nozzle,” ASME J. Pressure Vessel Technol., 131(5), p. 051202. [CrossRef]
Bree, J. , 1967, “Elastic-Plastic Behaviour of Thin Tubes Subjected to Internal Pressure and Intermittent High-Heat Fluxes With Application to Fast-Nuclear-Reactor Fuel Elements,” J. Strain Anal. Eng. Des., 2(3), pp. 226–238. [CrossRef]
Megahed, M. M. , 1981, “Influence of Hardening Rule on the Elasto-Plastic Behaviour of a Simple Structure Under Cyclic Loading,” Int. J. Mech. Sci., 23(3), pp. 169–182. [CrossRef]
Mackenzie, D. , and Boyle, J. T. , 1992, “A Method of Estimating Limit Loads by Iterative Elastic Analysis—I: Simple Examples,” Int. J. Pressure Vessels Piping, 53(1), pp. 77–95. [CrossRef]
Nadarajah, C. , Mackenzie, D. , and Boyle, J. T. , 1992, “A Method of Estimating Limit Loads by Iterative Elastic Analysis—II: Nozzle Sphere Intersections With Internal Pressure and Radial Load,” Int. J. Pressure Vessels Piping, 53(1), pp. 97–119. [CrossRef]
Shi, J. , Mackenzie, D. , and Boyle, J. T. , 1992, “A Method of Estimating Limit Loads by Iterative Elastic Analysis—III: Torispherical Heads Under Internal Pressure,” Int. J. Pressure Vessels Piping, 53(1), pp. 121–142. [CrossRef]
Melan, E. , 1936, “Theorie Statisch Unbestimmter Systeme Aus Ideal-Plastichem Baustoff,” Sitzungsber. Kais. Akad. Wiss. Wien, 2A(145), pp. 195–218.
Ponter, A. R. S. , Fuschi, P. , and Engelhardt, M. , 2000, “Limit Analysis for a General Class of Yield Conditions,” Eur. J. Mech.-A/Solids, 19(3), pp. 401–421. [CrossRef]
Chen, H. F. , and Ponter, A. R. S. , 2001, “Shakedown and Limit Analyses for 3-D structures Using the Linear Matching Method,” Int. J. Pressure Vessels Piping, 78(6), pp. 443–451.
Ure, J. , Chen, H. , and Tipping, D. , 2015, “Verification of the Linear Matching Method for Limit and Shakedown Analysis by Comparison With Experiments,” ASME J. Pressure Vessel Technol., 137(3), p. 031003. [CrossRef]
Muscat, M. , and Mackenzie, D. , 2003, “Elastic-Shakedown Analysis of Axisymmetric Nozzles,” ASME J. Pressure Vessel Technol., 125(4), pp. 365–370. [CrossRef]
Abdalla, H. F. , Megahed, M. M. , and Younan, M. Y A. , 2006, “Determination of Shakedown Limit Load for a 90-Degree Pipe Bend Using a Simplified Technique,” ASME J. Pressure Vessel Technol., 128(4), pp. 618–624. [CrossRef]
Oh, C.-S. , Kim, Y.-J. , and Park, C.-Y. , 2008, “Shakedown Limit Loads for Elbows Under Internal Pressure and Cyclic In-Plane Bending,” Int. J. Pressure Vessels. Piping, 85(6), pp. 394–405. [CrossRef]
Vermaak, N. , Valdevit, L. , Evans, A. G. , Zok, F. W. , and Mcmeeking, R. M. , 2011, “Implications of Shakedown for Design of Actively Cooled Thermostructural Panels,” J. Mech. Mater. Struct., 6(9–10), pp. 1313–1327. [CrossRef]
Abdalla, H. F. , Megahed, M. M. , and Younan, M. Y. A. , 2009, “Comparison of Pipe Bend Ratchetting/Shakedown Test Results With the Shakedown Boundary Determined Via a Simplified Technique,” ASME Paper No. PVP2009-77403.
Abdalla, H. F. , Megahed, M. M. , and Younan, M. Y. A. , 2011, “A Simplified Technique for Shakedown Limit Load Determination of a Large Square Plate With a Small Central Hole Under Cyclic Biaxial Loading,” Nucl. Eng. Des., 241(3), pp. 657–665. [CrossRef]
Abdalla, H. F. , 2014, “Shakedown Limit Load Determination of a Cylindrical Vessel–Nozzle Intersection Subjected to Steady Internal Pressures and Cyclic in-Plane Bending Moments,” ASME J. Pressure Vessel Technol., 136(5), p. 051602. [CrossRef]
Abdalla, H. F. , 2014, “Elastic Shakedown Boundary Determination of a Cylindrical Vessel-Nozzle Intersection Subjected to Steady Internal Pressures and Cyclic Out-of-Plane Bending Moments,” Nucl. Eng. Des., 267, pp. 189–196. [CrossRef]
ANSYS, 2012, “ANSYS Mechanical APDL Element Reference,” ANSYS Inc., Canonsburg, PA, pp. 724–746.
Wang, H. F. , Sang, Z. F. , Xue, L. P. , and Widera, G. E. O. , 2009, “Burst Pressure of Pressurized Cylinders With Hillside Nozzle,” ASME J. Pressure Vessel Technol., 131(4), p. 041204. [CrossRef]
Wu, B. H. , Sang, Z. F. , and Widera, G. E. O. , 2010, “Plastic Analysis for Cylindrical Vessels Under In-Plane Moment on the Nozzle,” ASME J. Pressure Vessel Technol., 132(6), p. 061203. [CrossRef]
Sang, Z. F. , Wang, Z. L. , Xue, L. P. , and Widera, G. E. O. , 2005, “Plastic Limit Loads of Nozzles in Cylindrical Vessels Under Out-of-Plane Moment Loading,” Int. J. Pressure Vessels Piping, 82(8), pp. 638–648. [CrossRef]
Oda, A. A. , Megahed, M. M. , and Abdalla, H. F. , 2015, “Effect of Local Wall Thinning on Shakedown Regimes of Pressurized Elbows Subjected to Cyclic In-Plane and Out-of-Plane Bending,” Int. J. Pressure Vessels Piping, 134, pp. 11–24. [CrossRef]
Abdalla, H. F. , Younan, M. Y. A. , and Megahed, M. M. , 2011, “Shakedown Limit Load Determination for a Kinematically Hardening 90 Deg Pipe Bend Subjected to Steady Internal Pressures and Cyclic Bending Moments,” ASME J. Pressure Vessel Technol., 133(5), p. 051212. [CrossRef]

Figures

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Fig. 1

Elastic and elastic-plastic analysis in the NSM: (a) elastic analysis and (b) elastic-plastic analysis

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Fig. 2

Master model dimensions used in current research similar to Wang et al. [28]

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Fig. 3

FE model of Wang et al. [28] intersection of hillside nozzle with cylindrical vessel adopted in the present work

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Fig. 4

Comparison of the predicted elastic and shakedown limit moments for combined sustained P and cyclic IP nozzle moment with Abdalla prediction [25]: d/D = 0.25, t/T = 0.5, and D/T = 63.5

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Fig. 5

Comparison of the predicted elastic and shakedown limit moments for combined sustained P and cyclic OP nozzle moment with Abdalla prediction [26]: d/D = 0.25, t/T = 0.5, and D/T = 63.5

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Fig. 6

Elastic and shakedown pressures for hillside nozzle intersections with cylindrical vessels under condition of cyclic pressure only for various values of hillside angle (β)

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Fig. 7

Residual stress distribution showing the location of SD critical element for β = 40 deg model under cyclic internal pressure

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Fig. 8

Comparison of elastic limit boundaries for different hillside angle (d/D = 0.32, t/T = 0.8, and D/T = 75.1)

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Fig. 9

Comparison of OPO shakedown load boundaries for different hillside angle (β) (d/D = 0.32, t/T = 0.8, and D/T = 75.1)

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Fig. 10

Effect of hillside angle on the pressure-independent OPO shakedown limit

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Fig. 11

Location for SD critical element for β = 10 deg model and cyclic moment

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Fig. 12

Comparison of elastic limit boundaries for different hillside angle (β) for IP moment loading

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Fig. 13

Comparison of IP shakedown load boundaries for different hillside angle (β)

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Fig. 14

Location for SD critical element for β = 10 deg model and steady pressure + cyclic IP moment

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Fig. 15

Comparison of elastic limit boundaries for different hillside angle (β) for IP and OPO moment loading

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Fig. 16

Comparison of shakedown boundaries for different hillside angle (β) for IP and OPO moment loading

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Fig. 17

Cyclic elastic-plastic verification points

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Fig. 18

Pattern for moment and pressure loading in cyclic analysis

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Fig. 19

Point 1a shakedown behavior due to cyclic loading

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Fig. 20

Point 1b plastic cycling behavior due to cyclic loading including zooming the cyclic portion

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Fig. 21

Point 4b ratcheting behavior due to cyclic loading including zooming the cyclic portion

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