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Research Papers: Design and Analysis

Shakedown Limit Loads for 90 Degree Scheduled Pipe Bends Subjected to Steady Internal Pressure and Cyclic Bending Moments

[+] Author and Article Information
Hany F. Abdalla

Department of Mechanical Engineering, The American University in Cairo, P.O. Box 74–11835 New Cairo, New Cairo, Egypthany_f@aucegypt.edu

Mohammad M. Megahed

Department of Mechanical Design and Production, Faculty of Engineering, Cairo University, P.O. Box 12613, Giza, Egyptmmegahed47@yahoo.com

Maher Y. A. Younan

Chair, Department of Mechanical Engineering, The American University in Cairo, P.O. Box 74–11835 New Cairo, New Cairo, Egyptmyounan@aucegypt.edu

J. Pressure Vessel Technol 133(3), 031207 (Apr 06, 2011) (12 pages) doi:10.1115/1.4002055 History: Received February 01, 2010; Revised June 09, 2010; Published April 06, 2011; Online April 06, 2011

A simplified technique for determining the shakedown limit load for a long radius 90 deg pipe bend was previously developed (Abdalla, H. F., , 2006, “Determination of Shakedown Limit Load for a 90 Degree Pipe Bend Using a Simplified Technique,” ASME J. Pressure Vessel Technol., 128, pp. 618–624; Abdalla, H. F., , 2007, “Shakedown Limits of a 90-Degree Pipe Bend Using Small and Large Displacement Formulations,” ASME J. Pressure Vessel Technol., 129, pp. 287–295). The simplified technique utilizes the finite element (FE) method and employs the small displacement formulation to determine the shakedown limit load (moment) without performing lengthy time consuming full cyclic loading finite element simulations or utilizing conventional iterative elastic techniques. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure. In the current paper, a parametric study is conducted through applying the simplified technique on three scheduled pipe bends, namely, nominal pipe size (NPS) 10 in. Sch. 20, NPS 10 in. Sch. 40 STD, and NPS 10 in. Sch. 80. Two material models are assigned, namely, an elastic perfectly plastic (EPP) material and an idealized elastic-linear strain hardening material obeying Ziegler’s linear kinematic hardening (KH) rule. This type of material model is termed in the current study as the KH-material. The pipe bends are subjected to a spectrum of steady internal pressure magnitudes and cyclic bending moments. The cyclic bending includes three different loading patterns, namely, in-plane closing, in-plane opening, and out-of-plane bending moment loadings of the pipe bends. The shakedown limit moments outputted by the simplified technique are used to generate shakedown diagrams of the scheduled pipe bends for the spectrum of steady internal pressure magnitudes. A comparison between the generated shakedown diagrams for the pipe bends employing the EPP- and the KH-materials is presented. Relatively higher shakedown limit moments were recorded for the pipe bends employing the KH-material at the medium to high internal pressure magnitudes.

Copyright © 2011 by American Society of Mechanical Engineers
Topics: Pressure , Stress , Pipe bends
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References

Figures

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Figure 3

Schematic diagram of the connected pipe bend for (a) full geometric model and (b) half geometric model

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Figure 4

Normalized limit, shakedown limit, and elastic limit moments of the NPS 10 in. Sch. 20 pipe bend subjected to IPC bending loading employing the EPP- and the KH-materials

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Figure 5

Normalized limit, shakedown limit, and elastic limit moments of the NPS 10 in. Sch. 20 pipe bend subjected to IPO bending loading employing the EPP- and the KH-materials

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Figure 6

Normalized limit, shakedown limit, and elastic limit moments of the NPS 10 in. Sch. 20 pipe bend subjected to OP bending loading employing the EPP- and the KH-materials

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Figure 7

Normalized limit, shakedown limit, and elastic limit moments of the NPS 10 in. Sch. 40 STD pipe bend subjected to IPC bending loading employing the EPP- and the KH-materials

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Figure 8

Normalized limit, shakedown limit, and elastic limit moments of the NPS 10 in. Sch. 40 STD pipe bend subjected to IPO bending loading employing the EPP- and the KH- materials

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Figure 9

Normalized limit, shakedown limit, and elastic limit moments of the NPS 10 in. Sch. 40 STD pipe bend subjected to OP bending loading employing the EPP- and the KH- materials

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Figure 10

Normalized limit, shakedown limit, and elastic limit moments of the NPS 10 in. Sch. 80 pipe bend subjected to IPC bending loading employing the EPP- and the KH- materials

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Figure 18

Normalized shakedown limit moments of Sch. 20, Sch. 40 STD, and Sch. 80 pipe bends determined using the simplified technique employing the KH-material under IPC bending moment loading

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Figure 20

Normalized shakedown limit moments of Sch. 20, Sch. 40 STD, and Sch. 80 pipe bends determined using the simplified technique employing the KH-material under OP bending moment loading

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Figure 19

Normalized shakedown limit moments of Sch. 20, Sch. 40 STD, and Sch. 80 pipe bends determined using the simplified technique employing the KH-material under IPO bending moment loading

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Figure 11

Normalized limit, shakedown limit, and elastic limit moments of the NPS 10 in. Sch. 80 pipe bend subjected to IPO bending loading employing the EPP- and the KH- materials

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Figure 12

Normalized limit, shakedown limit, and elastic limit moments of the NPS 10 in. Sch. 80 pipe bend subjected to OP bending loading employing the EPP- and the KH- materials

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Figure 13

Loading-unloading path of the output critical integration section point of the 0.2PY case of the NPS 10 in. Sch. 40 STD pipe bend employing the KH-material showing translation of the yield surface preserving its initial size (cyclic IPO bending moment loading)

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Figure 14

Loading-unloading path of the output critical integration section point of the 0.2PY case of the NPS 10 in. Sch. 40 STD pipe bend employing the EPP-material showing fixed yield surface preserving its initial size (cyclic IPO bending moment loading)

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Figure 15

Normalized shakedown limit moments of Sch. 20, Sch. 40 STD, and Sch. 80 pipe bends determined using the simplified technique employing the EPP-material under IPC bending moment loading

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Figure 16

Normalized shakedown limit moments of Sch. 20, Sch. 40 STD, and Sch. 80 pipe bends determined using the simplified technique employing the EPP-material under IPO bending moment loading

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Figure 17

Normalized shakedown limit moments of Sch. 20, Sch. 40 STD, and Sch. 80 pipe bends determined using the simplified technique employing the EPP-material model under OP bending moment loading

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Figure 2

Cyclic moment loading pattern employed in the full elastic-plastic cyclic loading finite element simulations

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Figure 1

Stress-strain curve of an elastic-linear strain hardening material

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