Full plastic resistance of tubes under bending and axial force: exact treatment and approximations
File(s)
Author(s)
Rotter, JM
Sadowski, AJ
Type
Journal Article
Abstract
The full plastic resistance under a combination of
bending and axial force of tubes of
all possible wall thicknesses, from thin cylinders
to circular solid sections, does not
ever seem to have been thoroughly studied, despite
the fact that this is a relatively
simple analysis. The first part of this paper pres
ents a formal analysis of the state of
full plasticity under longitudinal stresses in a ri
ght circular tube of any thickness free
of cross-section distortions. The derivation leads
to relatively complicated algebraic
expressions which are unsuitable for design guides
and standards, so the chief purpose
of this paper is to devise suitably accurate but si
mple empirical descriptions that give
quite precise values for the state of full plastici
ty whilst avoiding the complexity of a
formal exact analysis. The accuracy of each approx
imation is demonstrated. The two
limiting cases of a thin tube (cylindrical shell) a
nd circular solid section are shown to
be simple special cases.
The approximate expressions are particularly useful
for the definition of the full
plastic condition in tension members subject to sma
ll bending actions, but also
applicable to all structural members and steel buil
ding structures standards, as well as
to standards on thin shells where they provide the
full plastic reference resistance.
These expressions are also useful because they give
simple definitions of the
orientation of the plastic strain vector, which can
assist in the development of analyses
of the plastic collapse of arches and axially restr
ained members under bending.
bending and axial force of tubes of
all possible wall thicknesses, from thin cylinders
to circular solid sections, does not
ever seem to have been thoroughly studied, despite
the fact that this is a relatively
simple analysis. The first part of this paper pres
ents a formal analysis of the state of
full plasticity under longitudinal stresses in a ri
ght circular tube of any thickness free
of cross-section distortions. The derivation leads
to relatively complicated algebraic
expressions which are unsuitable for design guides
and standards, so the chief purpose
of this paper is to devise suitably accurate but si
mple empirical descriptions that give
quite precise values for the state of full plastici
ty whilst avoiding the complexity of a
formal exact analysis. The accuracy of each approx
imation is demonstrated. The two
limiting cases of a thin tube (cylindrical shell) a
nd circular solid section are shown to
be simple special cases.
The approximate expressions are particularly useful
for the definition of the full
plastic condition in tension members subject to sma
ll bending actions, but also
applicable to all structural members and steel buil
ding structures standards, as well as
to standards on thin shells where they provide the
full plastic reference resistance.
These expressions are also useful because they give
simple definitions of the
orientation of the plastic strain vector, which can
assist in the development of analyses
of the plastic collapse of arches and axially restr
ained members under bending.
Date Issued
2016-11-25
Date Acceptance
2016-11-22
Citation
Structures, 2016, 10, pp.30-38
ISSN
2352-0124
Publisher
Elsevier
Start Page
30
End Page
38
Journal / Book Title
Structures
Volume
10
Copyright Statement
© 2016 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Publication Status
Published