Table Of ContentNoel W. Murray· Georg Thierauf
Tables for the Design and Analysis
of Stiffened Steel Plates
Entwurfs- und Berechnungstabellen
fur ausgesteifte Stahlplatten
Noel W. Murray· Georg· Thierauf
Tables for the Design
and Analysis
of Stiffened Steel Plates
Entwurfs-
und Berechnungstabellen
fOr ausgesteifte Stahlplatten
Friedr. Vieweg & Sohn Braunschweig/Wiesbaden
CIP-Kurztitelaufnahme der Deutschen Bibliothek
MurnlY, Noel W_:
Tables for the design and analysis of stiffened steel
plates = Entwurfs-und Berechnungstabellen fur
ausgesteifte Stahlplatten I Noel W. Murray; Georg
Thierauf. - Braunschweig; Wiesbaden: Viewag, 19B1.
ISBN-13: 978-3-528-08673-2 e-ISBN-13: 978-3-322-86307-2
001: 10.1007/978-3-322-86307-2
NE: Thierauf, Georg:
Noel W. Murray ist Professor of Civil Engeneering an der Monash University
in Clayton, Victoria / Australia
Georg Thierauf ist Professor an der Gesamthochschule Essen / Bundesrepublik
Deutschland
Aile Rechte vorbehalten
© Friedr. Vieweg & Sohn Verlagsge ..l lschaft mbH, Braunschweig 1981
Softcover reprint of the hardcover 1st edition 1981
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Umschlagentwurf: Peter Neitzke, Koln
Buchbinderische Verarbeitung: W. Langeluddecke, Braunschweig
ISBN-13: 978-3-528-08673-2
5
Contents· Inhalt
Part/Teil Page/Seite
A : Theory 7
General Background and Use of the
Tables
B Theorie 67
Allgemeine Grundlagen und Gebrauch
der Tabellen
(German Translation . Deutsche Ubersetzung)
c
Tables • Tabellen 129
References • Literaturnachweis 197
7
A Theory
General Background and Use of the Tables
8
Table of Contents· Part A
Page
Preface 10
1. Introduction 12
2. Theoretical background 17
2.1 Geometry 17
2.2 Potential energy 18
2.3 Orthogonality of assumed displacements 21
3. Element matrices 24
3.1 First order in-plane stiffness matrix 25
3.2 First order out-of-plane stiffness matrix 25
3.3 Second order in-plane stiffness matrix 26
3.4 Second order out-of-plane stiffness matrix 26
3.5 Complete element matrices in local coordinates 26
3.6 Coordinate transformation to global coordinates 29
4. Assembly of elements 29
5. The eigenvalue problem 31
5.1 General form 31
5.2 Critical stress and first Euler length 32
6. Some remarks on the numerical solution 36
6.1 Iterative solution (Program PLATE 1) 36
6.2 Solution by bisection (PLATE 2) 36
7. The programs PLATE 1, PLATE 2 and PLATE 3 37
7.1 Sample problems 37
8. The use of the tables 45
8.1 Information listed in the tables 45
8.2 Scaling results for stiffened plates with plate 46
thickness t1 ~ 1
9
Page
8.3 Standardization of cross-sections 46
8.4 Use of tables with design rules 54
9. List of symbols 60
10
Preface
Stiffened steel plates have been used for many years
especially in the fields of bridges, ships and towers.
They are very efficient components of a structure, having
both a high strength - to -weight ratio and a pleasing
appearance. However, in some cases they have a tendency to
buckle in one mode or even two simultaneous modes. In
existing codes of practice designers have been supplied
with many comprehensive rules so that they can
calculate failure loads (collapse conditions) and the loads
at which first yield occurs (serviceability conditions).
A key calculation in each of these determinations is
that which gives the critical stress. However, the
critical stress depends upon many features such as the
boundary conditions along the sides and at the ends and the
geometry of the cross-section. A short stiffened plate may
buckle locally whereas a longer panel with the same
cross-section may buckle as a wide Euler column.
The labour involved in checking individual trial designs is
often formidable. It is the aim of this book to try to ease
this burden for designers. They will find that it is a
simple matter to use this book as if it were a catalogue of
sectional properties. Indeed the tables contained herein
present the usual section properties but they also indicate
the stresses at which local buckling occurs and the panel
length beyond which global (i.e. Euler type) buckling
governs.
The design data presented here has been derived from a
finite element program which uses the finite strip method
of analysis. Details of this method are presented here for
the sake of completeness. It is not necessary for designers
to understand all of these details but Sections 1, 5.2 and
7 to 8.4 should be read so that the tables can be more
fully understood.
11
Although it is difficult to compare results from a computer
which are based upon purely theoretical considerations and
those from a code of practice, where of necessity there
must be some empiricism, nevertheless this has been
attempted in Examples 8.1 and 8.2. The first shows how the
tables of this book may be used in conjunction with a code
of practice and the second gives a comparison between a
theoretical critical stress from the tables of this book
and that obtained from a code of practice. Not only are
the results of that comparison interesting but readers will
see that the amount of calculation is many times less in
the former case.
The authors would especially like to thank Frau Christel
Hausmann for the meticulous manner in which she has carried
out the work of data preparation and the presentation of
results. Frau Monika Mehl is thanked for her work
preparing the diagrams. Thanks are also due to Herr Artur
Senftleben for checking the manuscript and to Frau Ulrike
Riewe and Mrs. Pam Smith for preparing the manuscript. The
authors and collaborators have carefully checked the
information contained in this book but there may still be
errors in it. The authors and the publisher cannot accept
responsibili ty for any losses incurred by users of this
book, either through errors or interpretation of the
information. The work described has been sponsored in part
by Deutsche Forschungsgemeinschaft. All numerical results
have been obtained using the computers at Universitat
Dusseldorf, Germany and Monash University, Australia.
Noel W. Murray.
Georg Thierauf.
12 1 Introduction
1 Introduction
The problem of the elastic stability of stiffened plates
has many special features which do not occur in the sta
bility of struts and frameworks. The differences can be
summarized by referring to Fig. 1. In the latter cases
it is found from first order theory (second order theory
gives almost the same result) that there is a horizontal
asymptote at the buckling load and the behaviour of a strut
with some initial imperfection 00 closely follows the
hyperbola shown in Fig.1(a).
axial axial
stress stress
a a
--H- central deflection Ii --H- central deflectIon Ii
0 (0) 0 (b)
0 0
Fig. Comparison of strut and plate behavi our
The value of the critical stress, in this case the Euler
stress, 0e ' and the mode of buckling can be found by
solving the eigenvalue problem
(~ + a eK-G) r o (1 )
where K is the usual stiffness matrix, ~G is the geometric
stiffness matrix (1) and E is a vector which defines the
geometry of the buckling mode. One must be careful to en
sure that the smallest value of a which satisfies equation
e
(1) is obtained. The buckling shape of the strut (or
structure) is obtained as part of the solution of equation
(1) but the magnitude of the buckles cannot be evaluated
