Steel Structures E-Book

Rolf Kindmann

• Herausgeber: Ernst, Wilhelm & Sohn
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2012

Seitenzahl: 645

Beschreibung

This book presents the design of Steel Structures using finite element methods (FEM) according to the current state of the art in Germany and the rest of Europe. After a short introduction on the basics of the design, this book illustrates the FEM with a focus on internal forces, displacements, critical loads and modal shapes. Next to finite element procedures for linear calculations considering the stress states of normal force, biaxial bending and warping torsion, non-linear calculations and the stability cases of flexural buckling, lateral torsional buckling and plate buckling are concentrated on significantly. In this context, design procedures for stability according to the standard Eurocode 3 is introduced and discussed. In addition, important fundamental issues are covered, such as the determination of cross-section properties as well as the elastic and plastic cross-section resistance. Complementary, finite element procedures for cross sections are dealt with, which will have an increasing importance in future. This book has evolved within the teaching activities of the authors in the lecture Computer-oriented Design of Steel Structures on the Master?s Program Computational Engineering at the University of Bochum. It covers the total variety of demands needed to be discussed for the safe, economic and modern design of Steel Structures.

Leseprobe

Contents

1 Introduction

1.1 Verification Methods

1.2 Methods to Determine the Internal Forces and Moments

1.3 Element Types and Fields of Application

1.4 Linear and Nonlinear Calculations

1.5 Designations and Assumptions

1.6 Fundamental Relationships

1.7 Limit States and Load Combinations

1.8 Introductory Example

1.9 Content and Outline

1.10 Computer Programs

2 Cross Section Properties

2.1 Overview

2.2 Utilisation of Symmetry Properties

2.3 Standardisation Part I: Centre of Gravity, Principal Axes and Moments of Inertia

2.4 Calculation of Standardised Cross Section Properties Part I

2.5 Standardisation Part II: Shear Centre, Warping Ordinate and Warping Constant

2.6 Warping Ordinate

2.7 Shear Centre M

3 Principles of FEM

3.1 General Information

3.2 Basic Concepts and Methodology

3.3 Progress of the Calculations

3.4 Equilibrium

3.5 Basis Functions for the Deformations

4 FEM for Linear Calculations of Beam Structures

4.1 Introduction

4.2 Beam Elements for Linear Calculations

4.3 Nodal Equilibrium in the Global Coordinate System

4.4 Reference Systems and Transformations

4.5 Systems of Equations

4.6 Calculation of the Deformations

4.7 Determination of the Internal Forces and Moments

4.8 Determination of Support Reactions

4.9 Loadings

4.10 Springs and Shear Diaphragms

4.11 Hinges

5 FEM for Nonlinear Calculations of Beam Structures

5.1 General

5.2 Equilibrium at the Deformed System

5.3 Extension of the Virtual Work

5.4 Nodal Equilibrium with Consideration of the Deformations

5.5 Geometric Stiffness Matrix

5.6 Special Case: Bending with Compression or Tension Force

5.7 Initial Deformations and Equivalent Geometric Imperfections

5.8 Second Order Theory Calculations and Verification Internal Forces

5.9 Stability Analysis / Critical Loads

5.10 Eigenmodes / Buckling Shapes

5.11 Plastic Hinge Theory

5.12 Plastic Zone Theory

6 Solution of Equation Systems and Eigenvalue Problems

6.1 Equation Systems

6.2 Eigenvalue Problems

7 Stresses According to the Theory of Elasticity

7.1 Preliminary Remarks

7.2 Axial Stresses due to Biaxial Bending and Axial Force

7.3 Shear Stresses due to Shear Forces

7.4 Stresses due to Torsion

7.5 Interaction of All Internal Forces and Verifications

7.6 Limit Internal Forces and Moments on the Basis of the Theory of Elasticity

8 Plastic Cross Section Bearing Capacity

8.1 Effect of Single Internal Forces

8.2 Limit Load-Bearing Capacity of Cross Sections

8.3 Limit Load-Bearing Capacity of Doubly-Symmetric I-Cross Sections

8.4 Computer-Oriented Methods

9 Verifications for Stability and according to Second Order Theory

9.1 Introduction

9.2 Definition of Stability Cases

9.3 Verification according to Second Order Theory

9.4 Verifications for Flexural Buckling with Reduction Factors

9.5 Calculation of Critical Forces

9.6 Verifications for Lateral Torsional Buckling with Reduction Factors

9.7 Calculation of Critical Moments

9.8 Verifications with Equivalent Imperfections

9.9 Calculation Examples

10 FEM for Plate Buckling

10.1 Plates with Lateral and In-Plane Loading

10.2 Stresses and Internal Forces

10.3 Displacements

10.4 Constitutive Relationships

10.5 Principle of Virtual Work

10.6 Plates in Steel Structures

10.7 Stiffness Matrix for a Plate Element

10.8 Geometric Stiffness Matrix for Plate Buckling

10.9 Plates with Longitudinal and Transverse Stiffeners

10.10 Verifications for Plate Buckling

10.11 Determination of Buckling Values and Eigenmodes with FEM

10.12 Calculation Examples

11 FEM for Cross Sections

11.1 Tasks

11.2 Principle of Virtual Work

11.3 One-Dimensional Elements for Thin-Walled Cross Sections

11.4 Two-Dimensional Elements for Thick-Walled Cross Sections

11.5 Calculation Procedure

11.6 Calculation Exa mples

References

Index

Prof. Dr.-Ing. Rolf KindmannRuhr-Universität BochumLehrstuhl für Stahl-, Holz-und LeichtbauUniversitätsstraße 15044801 Bochum

Dr.-Ing. Matthias KrausIngenieursozietät SKPPrinz-Friedrich-Karl-Str. 3644135 Dortmund

Language Polishing by Paul Beverley, London

Cover: SIGNAL IDUNA PARK, Dortmund,©Professor Rolf Kindmann

Library of Congress Card No.:applied for

British Library Cataloguing-in-Publication Data

Acatalogue record for this book is available from the BritishLibrary.

Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de.

©2011 Wilhelm Ernst&Sohn, Verlag für Architektur und technische Wissenschaften GmbH&Co. KG,Rotherstraße 21, 10245 Berlin, Germany

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprint, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. usedin this book, even when not specifically marked as such, are nottobe considered unprotected by law.

Coverdesign: Sophie Bleifuß, BerlinHerstellung: pp030 – Produktionsbüro Heike Praetor, BerlinPrinting and Binding: Betz-Druck GmbH, Darmstadt

ISBN978-3-433-02978-7Electronic version available. O-book ISBN 978-3-433-60077-1

Preface

Steel structures are usually beam or plate structures consisting of thin-walled cross sections. For their design, deformations, internal forces and moments as well as stresses are needed, and the stability of the structures is of great importance. Generally, the finite element method (FEM) is used for structural analysis and as a basis for the verification of sufficient load-bearing capacity.

This book presents the relevant procedures and methods needed for calculations, computations and verifications according to the current state of the art in Germany and the rest of Europe. In doing so the following topics are treated in detail:

determination of cross-section properties, stresses and plastic cross section bearing capacityfinite element method for linear and nonlinear calculations of beam structuressolution of eigenvalue problems (stability) for flexural, lateral torsional, torsional and plate bucklingverification of sufficient load-bearing capacityfinite element method for open and hollow cross sections

The basis of the calculations and verifications are the German standard DIN 18800 and the German version of Eurocode 3. They are widely comparable, however, the final version of Eurocode 3 has just been published and the corresponding national annexes have to be considered.

This book has evolved from the extensive experience of the authors in designing and teaching steel structures. It is used as lecture notes for the lecture “Computer-oriented Design of Steel Structures” on the Masters’ programme “Computational Engineering” at the Ruhr-University Bochum, Germany. Large parts of the contents were taken from German books – see [25], [31] and [42] – and therefore, the references at the end of the book contain many publications in the German language. Further information can be found at www.kindmann.de, www.rub.de/stahlbau and www.skp-ing.de.

The authors would like to thank Mr Florian Gerhard for the translations, Mr Paul Beverley for language polishing and Mr Peter Steinbach for the drawing of figures.

Rolf KindmannMatthias Kraus