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Research Papers: Theoretical Applications

Ratchet Limit Solution of a Beam With Arbitrary Cross Section

[+] Author and Article Information
R. Adibi-Asl

AMEC NSS Ltd.,
393 University Avenue,
Toronto, ON M5G 1E6, Canada
e-mail: reza.adibiasl@amec.com

W. Reinhardt

Candu Energy,
Mississauga, ON L5K 1B2, Canada

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received May 3, 2014; final manuscript received September 1, 2014; published online March 23, 2015. Assoc. Editor: David L. Rudland.

J. Pressure Vessel Technol 137(3), 031004 (Jun 01, 2015) (11 pages) Paper No: PVT-14-1076; doi: 10.1115/1.4028514 History: Received May 03, 2014; Revised September 01, 2014; Online March 23, 2015

The classical approaches in shakedown analysis are based the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. In recent years, the “noncyclic method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure by generalizing the static shakedown theorem (Melan's theorem). The fundamental idea behind the proposed method is to (conservatively) determine the stable and unstable boundary without going through the cyclic history. The method is used to derive the interaction diagrams for a beam subjected to primary membrane and bending with secondary bending loads. Various cross-sections including rectangular, solid circular and thin-walled pipe are investigated.

Copyright © 2015 by ASME
Topics: Stress , Membranes
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References

Figures

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Fig. 1

Application of noncyclic method to a beam subjected to cyclic linear variation of temperature through the thickness and sustained axial mechanical load, (a) elastic thermal stress, (b) elastic–plastic thermal stress, and (c) mechanical membrane stress

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Fig. 2

Beam at ratchet boundary with given (secondary) cyclic load, shaded areas indicate stress available to support a time-invariant primary load. (a) Primary membrane with cyclic load below yield, (b) primary membrane with cyclic load exceeding yield, (c) primary bending with cyclic load below yield, and (d) primary bending with cyclic load exceeding yield [12].

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Fig. 3

A beam cross section that is symmetric about the neutral axis and about the bending plane

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Fig. 4

Beam subjected to cyclic secondary bending load and sustained axial and bending mechanical loads (a) elastic thermal stress and (b) elastic–plastic thermal stress

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Fig. 5

Analyzed cross-sections, (a) rectangular, (b) solid circular, and (c) thin-walled pipe

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Fig. 6

Ratchet boundary for a rectangular cross section subjected to cyclic secondary bending coincident with constant primary membrane and with constant level of primary bending stress

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Fig. 7

Ratchet boundary for a rectangular cross section subjected to cyclic secondary bending coincident with constant primary bending and with constant level of primary membrane stress

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Fig. 8

Ratchet boundary for a rectangular beam subjected to cyclic secondary bending coincident with constant primary membrane and with constant primary bending stress

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Fig. 9

Ratchet boundary for a solid circular beam subjected to cyclic secondary bending coincident with constant primary membrane and with constant level of primary bending stress

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Fig. 10

Ratchet boundary for a solid circular beam subjected to cyclic secondary bending coincident with constant primary bending and with constant level of primary membrane stress

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Fig. 11

Ratchet boundary for a solid circular beam subjected to cyclic secondary bending coincident with constant primary membrane and with constant primary bending stress

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Fig. 12

Ratchet boundary for a thin pipe beam subjected to cyclic secondary bending coincident with constant primary membrane and with constant level of primary bending stress

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Fig. 13

Ratchet boundary for a thin pipe beam subjected to cyclic secondary bending coincident with constant primary bending and with constant level of primary membrane stress

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Fig. 14

Ratchet boundary for a thin pipe beam subjected to cyclic secondary bending coincident with constant primary membrane and with constant primary bending stress

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Fig. 15

Comparison of ratchet boundaries for a case with cyclic secondary bending load coincident with constant primary membrane load

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Fig. 16

Comparison of Ratchet boundaries for a case with cyclic secondary bending load coincident with constant primary bending load

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Fig. 17

Comparison of limit load for a case with constant primary membrane load coincident with constant primary bending load

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