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RESEARCH PAPERS

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

[+] Author and Article Information
Hany F. Abdalla

Department of Mechanical Design and Production, Faculty of Engineering, Cairo University, Cairo, 11511 Egypthany_f@aucegpyt.edu

Mohammad M. Megahed

Department of Mechanical Design and Production, Faculty of Engineering, Cairo University, Cairo, 11511 Egyptmmegahed47@yahoo.com

Maher Y. A. Younan

Chair, Mechanical Engineering Department,The American University in Cairomyounan@aucegypt.edu

J. Pressure Vessel Technol 128(4), 618-624 (Feb 09, 2006) (7 pages) doi:10.1115/1.2349575 History: Received October 27, 2005; Revised February 09, 2006

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.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Cyclic loading pattern

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Figure 2

Schematic diagram showing meshing and loading of the thin strip across the Bree cylinder thickness

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Figure 3

The analytically determined Bree diagram of the cylinder

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Figure 4

Schematic of the connected pipe bend

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Figure 5

Finite element meshing of the pipe bend and the connected straight pipes in addition to a zoomed view of the pipe bend meshing

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Figure 6

Normalized limit, shakedown, and elastic moments of the pipe bend subjected to in-plane closing bending loading

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Figure 7

Shakedown behavior of the pipe bend for the 0.3PY case (element at crown of pipe bend middle section-SP1)

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Figure 8

Reversed plasticity behavior of the pipe bend for the 0.3PY case (element at crown of pipe bend middle section-SP1)

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Figure 9

Shakedown behavior of the pipe bend for the 0.6PY case (element at crown of pipe bend middle section-SP5)

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Figure 10

Ratcheting behavior of the pipe bend for the 0.6PY case (element at crown of pipe bend middle section-SP4)

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