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RESEARCH PAPERS

Ultimate Bending Capacity and Buckling of Pressurized 90 deg Steel Elbows

[+] Author and Article Information
S. A. Karamanos

Department of Mechanical and Industrial Engineering, University of Thessaly, Volos 38334, Greeceskara@mie.uth.gr

D. Tsouvalas

Department of Mechanical and Industrial Engineering, University of Thessaly, Volos 38334, Greece

A. M. Gresnigt

Faculty of Civil Engineering and Geosciences, Delft University of Technology, 2600 GA Delft, The Netherlandsa.m.gresnigt@citg.tudelft.nl

J. Pressure Vessel Technol 128(3), 348-356 (Jul 07, 2005) (9 pages) doi:10.1115/1.2217967 History: Received March 24, 2004; Revised July 07, 2005

The paper examines the nonlinear elastic-plastic response of internally pressurized 90 deg pipe elbows under in-plane and out-of-plane bending. Nonlinear shell elements from a general-purpose finite element program are employed to model the inelastic response of steel elbows and the adjacent straight parts. The numerical results are successfully compared with real-scale experimental measurements. The paper also presents a parametric study, aimed at investigating the effects of diameter-to-thickness ratio and moderate pressure levels on the ultimate bending capacity of 90 deg elbows, focusing on the failure mode (local buckling or cross-sectional flattening) and the maximum bending moment. Special attention is given to the response of 90 deg elbows under out-of-plane bending moments.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 5

Out-of-plane loading of specimen 80 under external pressure p=0.0981MPa; (a) force Q versus cross-sectional flattening at cross-section F and (b) deformed shape of specimen

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Figure 1

Experimental setup for specimen 80, tested at TNO (4)

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Figure 2

Schematic representation of 90deg specimen 80 and elbows used in the parametric study; geometry and boundary conditions

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Figure 3

(a) Devices for measuring rotations and ovalization of specimen 80, subjected to out-of-plane bending loading (4). Note the 45deg orientation of the ovalization devises with respect to the pipe axis, so that the maximum ovalization of the cross section is measured. (b) Deformed shape of specimen 80 after the out-of-plane bending test (4); ovalization of the elbow is oriented at 45deg with respect to pipe axis.

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Figure 4

Elastic flexibility of specimen 80 under in-plane closing bending moments; comparison between numerical and experimental results (values of pressure p are in MPa)

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Figure 10

Response of Elbow II (D∕t=55) under in-plane opening bending and three levels of internal pressure: (a) moment–rotation diagram and (b) ovalization–rotation diagram

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Figure 11

Response of Elbow III (D∕t=20) under in-plane opening bending and three levels of internal pressure: (a) moment–rotation diagram and (b) ovalization–rotation diagram

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Figure 12

Buckles in elbows under in-plane opening bending moments for zero internal pressure: (a) Elbow I (D∕t=90) and (b) Elbow II (D∕t=55)

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Figure 13

Buckles in elbows under in-plane opening bending moments for internal pressure 20% of py (“bulging buckle”): (a) Elbow I (D∕t=90) and (b) Elbow II (D∕t=55)

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Figure 14

Elbow I (D∕t=90) response under out-of-plane bending moments and three levels of internal pressure (0, 20%, and 40% of py)

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Figure 15

Buckled shapes of thin-walled Elbow I (D∕t=90) under out-of-plane bending moments: (a) for zero pressure, (b) for pressure level 20% of py, and (c) for pressure level 40% of py

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Figure 16

(a) Deformation of a 90deg elbow under out-of-plane bending. Note the deformation of the straight pipe portion. (b) Schematic representation of the state of stress on an arbitrary location at the “intrados” of the curved pipe portion due to out-of-plane torque.

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Figure 17

Elbow cross-section F under out-of-plane bending; post-buckling shape

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Figure 18

Response of Elbows I, II, and III under out-of-plane bending moments for zero internal pressure: (a) moment–rotation and (b) ovalization–rotation

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Figure 19

Response of Elbows I, II, and III under out-of-plane bending moments for internal pressure 20% of py: (a) moment–rotation and (b) ovalization–rotation

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Figure 20

Buckled shapes of elbows under out-of-plane bending moments for zero pressure: (a) Elbow II (D∕t=55), (b) Elbow III (D∕t=20)

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Figure 6

Elbow response under in-plane closing bending moments and three levels of internal pressure: (a) Elbow I (D∕t=90) and (b) Elbow III (D∕t=20)

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Figure 7

Ovalization of cross-section F of thick-walled Elbow III (D∕t=20) for three different pressure levels; closing bending moments

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Figure 8

Deformed three-dimensional elbow shapes: cross-sectional shapes and spread of plastic deformation under in-plane closing bending moments for zero pressure: (a) thin-walled Elbow I (D∕t=90), (b) thick-walled Elbow III (D∕t=20)

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Figure 9

Response of Elbow I (D∕t=90) under in-plane opening bending and three levels of internal pressure: (a) moment–rotation diagram and (b) ovalization–rotation diagram

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