Steel Structures - Design Using Fem

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 the future.
This book has evolved within the teaching activities of the authors in the lecture Computer-oriented Design of Steel Structures on the Masters Programme 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.

University-Professor Dr.-Ing. Rolf Kindmann studied civil engineering at the University of Bochum. Between 1974 and 1989 he worked at the university for six years as a researcher and then for ten years at Thyssen Engineering in different positions, lastly as division manager of all engineering departments. In 1990 he was appointed to a full professorship and to the head if the Institute of Steel and Composite Structures at the University of Bochum. In 1991 he founded Schurmann - Kindmann and partners, Consulting Engineers in Dortmund. Professor Dr. Kindmann is a licensed checking engineer for steel and concrete structures and of design in railway engieneering.
Dr.-Ing. Matthias Kraus studied civil engineering at the Technical University of Darmstadt. In 2001 he changed to the University of Bochum as researcher, where he received his doctoral degree in 2005 and then worked as chief engineer at the Institute of Steel and Composite Structures. Since 2010 Dr. Kraus has worked at Schurmann - Kindmann and Partners, Dortmund, as chief engineer. He also has adjunct lecturships at the University of Bochum.

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 250

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.

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 Examples.

References.

Index.