Design of Plated Structures. E-Book

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 220

Veröffentlichungsjahr: 2012

Beschreibung

The main aim of this book is to provide practical advice to designers of plated structures for correct and efficient application of EN 1993-1-5 design rules. In chapter 1 the purpose, the scope and the structure of the book is explained. In chapter 2 a rather detailed and commented overview of EN 1993-1-5 design rules is given following the structure of the standard. Shear lag effect as well as plate buckling problems due to direct stresses, shear forces, transverse forces and interactions of these effects are covered. This chapter also includes a reduced stress method and a finite element analysis approach to plate buckling problems. A large number of design examples illustrate the proper application of individual design rules. Chapter 3 and 4 bring two complete design examples on a crane runway and a box-girder bridge.

Leseprobe

TABLE OF CONTENTS

FOREWORD

PREFACE

SYMBOLS

Chapter 1 INTRODUCTION

1.1 Plate buckling in steel structures

1.2 Purpose of this book

1.3 Structure of this book

Chapter 2 OVERVIEW OF DESIGN RULES

2.1 Introduction

2.2 Basis of design and modelling

2.3 Shear lag in member design

2.4 Plate buckling effects due to direct stresses (including annexes A and E where applicable)

2.5 Resistance to shear (including annex A where applicable)

2.6 Resistance to transverse loading

2.7 Interaction

2.8 Flange induced buckling

2.9 Stiffeners and detailing

2.10 Reduced stress method (including Annexes A and B where applicable)

2.11 FEM

Chapter 3 CRANE RUNWAY BEAM EXAMPLE

3.1 Description of the crane

3.2 Description of the crane runway beam

3.3 Actions and load partial factors

3.4 Internal forces and stresses

3.5 Verifications in general

3.6 Buckling verifications according to sections 4 to 7, EN 1993-1-5

3.7 Buckling verifications according to section 10, EN 1993-1-5

3.8 Flange induced buckling verification

3.9 Stiffener verifications 3.9.1. Bearing stiffeners

Chapter 4 BOX-GIRDER BRIDGE EXAMPLE

4.1 Description of the bridge

4.2 Internal forces and moments, Stresses

4.3 Web buckling verification for the launching phase

4.4 Effective cross section of the stiffened bottom flange at internal support P1 (uniform compression)

4.5 Effective cross section of the stiffened web at internal support (bending)

4.6 Checking of the box-girder section under bending at support P1

4.7 Shear resistance of the stiffened web panel closest to the internal support P1

4.8 Interaction between bending and shear at support P1

4.9 Intermediate transverse stiffener design

4.10 Buckling verifications at internal support P1 according to section 10, EN 1993-1-5

REFERENCES

Design of Plated Structures

1st Edition, 2010

Published by:

ECCS – European Convention for Constructional Steelwork

[email protected]

www.steelconstruct.com

Sales:

Wilhelm Ernst & Sohn Verlag für Architektur und technische Wissenschaften

GmbH & Co. KG, Berlin

All rights reserved. No parts of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner.

ECCS assumes no liability with respect to the use for any application of the material and information contained in this publication.

Copyright © 2010 ECCS – European Convention for Constructional Steelwork

ISBN (ECCS): 978-92-9147-100-3

ISBN (Ernst & Sohn): 978-3-433-02980-0

Legal dep.: - Printed in Multicomp Lda, Mem Martins, Portugal

Photo cover credits: Vincent de Ville de Goyet

Foreword

Plated structures are large steel structures commonly made from steel plates welded together. A typical use is for bridge girders and girders for heavy overhead cranes. Compared to steel structures of rolled profiles, plated structures are more prone to local buckling and therefore require design rules to cover such phenomena. In Eurocode 3 such rules are collected in Part 1-5 “Plated structures”, EN 1993-1-5. I was the convener of the project team that wrote the standard, and this team was made up of some very knowledgeable specialists. We spent many years on comparing and finding the best methods of dealing with the most common buckling phenomena. These have attracted a lot of research efforts not only due to some spectacular bridge failures, but also because buckling of plates, and particularly stiffened plates, are scientifically interesting and have attracted the attention of many sharp brains. The result of our efforts was published as a standard in 2006, but the implementation in the different member countries of CEN follows different time tables.

Already before the standard was published we had many requests for background information. The reason was probably that the project team had collected design rules from different sources and chosen the ones that best fitted available information. Some of those were unfamiliar to many engineers and the requests of background information were reasonable. The contract with the EU commission did not include the task of delivering background documents but the academic participants in the project team decided to write one on their own expense. This document can be found on the ECCS web site with the URL http://www.steelconstruct.com/. It is described as a commentary to EN 1993-1-5 and includes background to the design rules and some explanations. There are also some design examples.

As a third step, ECCS has taken on the task of publishing the present manual that you have in your hands. It is intended for engineers who shall apply the rules of EN 1993-1-5 and I have to admit that it is needed. That does not mean that I think we did a bad job with the standard but that the text in the standard is quite brief and in order to interpret it correctly one needs experience and insight in the problems to be dealt with. This manual will be of great importance for engineers to aid them to apply the standard correctly thanks to its explanations and design examples. The authors have done a very good job and after reviewing the text I fully support it as a proper interpretation of the standard.

Bernt Johansson

Professor Emeritus Steel Structures

Preface

Plate buckling related problems in steel structures are inherently linked to complex solution strategies and design procedures. They involve stability analysis in the post-critical state, interaction of different failure modes, imperfection sensitivity, etc.

Eurocode standard EN 1993-1-5 gives a unique opportunity to deal with these problems, at least for typical geometrically more or less regular structural components, by means of fairly simple and consistent set of design procedures, suitable for hand calculations. The main advantage of these design procedures is that generally they were derived from available test results and despite their relative simplicity very often they can be more reliable than advanced numerical simulations. The latter heavily depend on the quality of the applied software tool, the way of modelling, experience of the user, correct interpretation of the results, etc. But even when an experienced design engineer applies advanced numerical simulations for plate buckling problems, a check by means of EN 1993-1-5 design procedures provides comfort and confidence in the results.

The main aim of this Design Manual is to provide practical advice to designers of plated structures for correct and efficient application of EN 1993-1-5 design rules, including several design examples. No deeper theoretical background is given and in this respect the reader is directed to other literature.

The initiative for this Design Manual came from the ECCS that included this Manual into the comprehensive action of preparing the ECCS Eurocode Design Manuals.

The four authors: Darko Beg (University of Ljubljana, Slovenia), Laurence Davaine (SNCF – French National Railway Service), Ulrike Kuhlmann and Benjamin Braun (University of Stuttgart, Germany) worked in close cooperation helping each other and carefully proof-reading parts of the text prepared by other authors. Nonetheless, the leading authors of individual chapters are:

Chapters 2.2, 2.4, 2.9 and all short numerical examples in Chapter 2: Darko Beg

Chapters 1, 2.5, 2.6, 2.10, 3: Ulrike Kuhlmann and Benjamin Braun

Chapters 2.3, 2.7, 2.8, 2.11: Laurence Davaine

Chapter 4: Laurence Davaine and Benjamin Braun

It should be mentioned that Franci Sinur and Blaž ermelj helped in the preparation of the short numerical examples of Chapter 2 and Primož Može and Mojca Jelani helped at the final editing of the text, all four coming from the University of Ljubljana.

At the end of this short Preface it is important to express strong wishes and expectations of the authors that this Manual will find a place on the working desks of design engineers helping them design excellent plated structures. In the authors’ opinion the manual will also be helpful to students of structural engineering on their way of getting familiar with plated structures.

Darko Beg

Ulrike Kuhlmann

Laurence Davaine

Benjamin Braun

Symbols

alength of a stiffened or unstiffened platebwidth of a stiffened or unstiffened platebfflange widthbc,loc,iwidth of the compressed part of each individual sub-panel ibeffeffective width (for elastic shear lag or local plate buckling)b1height of the loaded sub-panel taken as the clear distance between the loaded flange and the longitudinal stiffenerbwclear width between weldsCdistance between plastic hinges in the flangesemaxmaximum distance from the edge of the stiffener to the centroid of the stiffenerfyyield strength of steelfyfflange yield strengthfywweb yield strengthhfdistance between mid-planes of flangeshwclear web depth between flangeshwiclear height of sub-panel ikFbuckling coefficient for transverse loadingkσ,pplate buckling coefficientkτshear buckling coefficient of the web between flangeskτ,ishear buckling coefficient of sub-panel ikτslshear buckling coefficient of a web stiffened with longitudinal stiffenersyeffective loaded lengthsslength of stiff bearingTthickness of the platetfflange thicknesstwweb thicknesswelelastic deflection of the stiffenerw0equivalent geometric imperfection of the stiffenerAsgross cross sectional area of the stiffenerAsltotal area of all the longitudinal stiffeners of a stiffened plateAstgross cross sectional area of one transverse stiffenerAeffeffective cross sectional areaAc,effeffective area of the compression zone of the stiffened orunstiffened plateAc,eff,loceffective section areas of all the stiffeners and sub-panelsthat are fully or partially in the compression zoneAsl,effsum of the effective sections of all longitudinal stiffenerswith gross area Asl located in the compression zoneAsl,1gross cross sectional area of the stiffener and the adjacentparts of the plateAsl,1,effeffective cross sectional area of the stiffener and adjacentparts of the plate with due allowance for plate buckling ofsub-panelsEelastic modulus of steelFEddesign transverse forceFRddesign resistance to transverse loadingFcrelastic critical load at transverse loadingFyyield load at transverse loadingGshear elastic modulusIppolar second moment area of the stiffener alone around the edge fixed to the plateIstminimum required second moment of the area of a transverse stiffener to be considered as rigidItSt. Venant torsional constant of the stiffener alone (without contributing plating)Iwwarping cross section constant of the stiffener alone around the edge fixed to the plateLeffeffective length for resistance to transverse forcesIssum of the second moment of area of all longitudinal stiffenersIs,1second moment of area of the gross cross section of the stiffener and the adjacent parts of the plate, relative to the out-of-plane bending of the plateIstsecond moment of the area of a stiffener for a cross section for the axis parallel to the web plateIst,actactual second moment of area of the transverse stiffenerMEdapplied design bending momentMpl,Rddesign plastic moment resistance of the cross section (irrespective of cross section class)Mf,Rddesign plastic moment resistance of a cross section consisting of the flanges onlyNEddesign axial forceNst,tenaxial force in the intermediate stiffener imposed by the tension field actionNcrEuler elastic critical forceNcr,stEuler elastic critical force of the stiffenerVEddesign shear force including shear from torqueVbw,Rdcontribution from the web to the design shear resistanceVbf,Rdcontribution from the flanges to the design shear resistanceVb,Rddesign shear resistanceWeffeffective elastic section modulusαult,kminimum load amplifier for the design loads to reach the characteristic value of the resistanceαcrminimum load amplifier for the design loads to reach the elastic critical value of the plateβeffective width factor for elastic shear lagβlteffective width factor for the effect of shear lag at the ultimate limit stateχcreduction factor due to column bucklingχFreduction factor for transverse loadingχwreduction factor for shear bucklingγMpartial safety factorηfactor depending on the steel gradeη 1utilisation level of the design resistance to direct stressesη 2utilisation level of the design resistance to transverse loadingη3utilisation level of the design shear resistanceslenderness for transverse loading (in EN 1993-1-5 the term “modified slenderness” is used according the Corrigendum (April 2009). In this document a shorter version, i.e. “slenderness”, is systematically used for the sake of simplicity)plate slendernessreduced plate slendernessweb slenderness for shearVPoisson coefficient of steelρplate buckling reduction factorρx; ρzreduction factorsρloc,ireduction factor for each sub-panel iσcr,pelastic critical plate buckling stressσcr,celastic critical column buckling stressσcr,slelastic critical column buckling stress of a single stiffenerσcom,Edmaximum design compressive stressσeq,Edequivalent design stressσEEuler stressσcr,x; σcr,z; τcrelastic critical buckling stressσx,Ed; σz,Ed; τEddesign stressesτcrelastic critical shear buckling stressψstress ratio along edges

Chapter 1

INTRODUCTION

1.1 PLATE BUCKLING IN STEEL STRUCTURES

State-of-the-art steel structures are characterised by a lightweight, slender and fabrication-optimised design. Especially the progress in welding technology since the 1930s has facilitated the increased application of steel plated structures, see Figure 1.1. The significant knowledge gained since then has clearly influenced the design as well as the development of the design standards. With the Eurocodes, harmonised European rules have been established of which standard EN 1993-1-5 “Design of steel structures – Plated structural elements” (CEN, 2006a) deals with the design of plated structural elements in steel structures.

Figure 1.1: Assembly of Haseltal road bridge near Suhl, Germany

Based on EN 1993-1-5 the designer can choose, considering national allowance, mainly between two different types of design methods according to Fig. 1.2. The effective width method, also comprising resistance models for shear force and transverse force, is very efficient for standard geometries because it accounts not only for the post-critical reserve in a single plate element but also for load shedding between cross sectional elements. The reduced stress method abstains from load shedding between cross sectional elements, but it fully accounts for the post-critical reserve in a single plate element. Beyond that, its general format facilitates its use for serviceability verifications and for the design of non-uniform members such as haunched beams, beam webs with openings and plates with non-orthogonal stiffeners. In addition, a verification methodology based on the finite element method is given in section 2.11. It is the most versatile verification method, however, it requires a lot of experience. It can be used for the determination of the “real” buckling resistance by means of a nonlinear analysis considering imperfections and for the calculation of elastic critical stress values by means of a linear bifurcation analysis.

Figure 1.2: Overview of design methods in EN 1993-1-5 and their references to the sections in this book

1.2 PURPOSE OF THIS BOOK

This book intends to provide the designer of steel plated structures with a practically oriented guide to assess EN 1993-1-5 (CEN, 2006a). This design manual is part of a comprehensive series of ECCS publications dealing with accompanying documentation to the Eurocodes. Its aim is to complement the comprehensive theoretical background given in the Commentary to EN 1993-1-5 (Johansson et al, 2007) with practical knowledge for daily usage. Nevertheless, fundamental knowledge of structural mechanics is expected.

This book gives explanations and examples, advice and warnings, all of which intend to give the user considerably more insight and confidence in applying the rules of EN 1993-1-5. In order not to prejudice the use of EN 1993-1-5 where national choices are possible, Eurocode recommendations have been adopted throughout. This has to be kept in mind and, if required, the nationally determined parameters have to be adjusted when applying EN 1993-1-5 in the various member states.

1.3 STRUCTURE OF THIS BOOK

The layout of this book deliberately follows the layout of EN 1993-1-5 in order to allow for easy navigation and reference.

Chapter 2 gives a concise overview of the stability behaviour of plates in steel structures and the corresponding design rules in EN 1993-1-5. Relevant knowledge and terms about load-carrying mechanisms in plates and plated structures under direct stress, shear stress and transverse stress are introduced in order to ease the understanding of the design rules. The main components of Chapter 2 are the explanations of the verification methods which correspond to sections in this book as shown in Figure 1.2. In this book, small design examples in each section address specific issues of these design rules.

In addition, chapters 3 and 4 present two comprehensive design examples of a crane runway beam and a box-girder bridge. In both examples not only the verification methods are illustrated, but also the big picture of the whole design is given. Besides general information on geometry and material properties, firstly loads and governing internal forces are determined. Based on cross section classification, and while adhering to the objective of this book, the examples finally focus on the plate buckling verifications.