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Description
“Its carefully constructed content successfully redresses the imbalance in risk between the finite element process based around generally determinate calculation output which has itself been derived from a possibly non-determinate understanding of the actual modelling process.
In the Introduction, the author suggests that all structural engineers and all civil engineers who use structural analysis will find the contents of the book to be useful. I think that he is right.”
Michael Dickson FIStructE
Director, Design and Technology Board, Buro Happold
President, Institution of Structural Engineers 2005-06
This book is essential reading for 21st century practitioners and students who need to do structural analysis. It contains a great deal of information that is not available in any other book on the subject. This is because the conventional view of structural analysis is rooted in the early part of the 20th century in the pre-computer era rather than present time. A main feature of this text is the information on modelling process, which is omitted in traditional books. Another important feature is the inclusion of what the author calls validation information, which is used to assess whether a model is capable of satisfying the objectives of the analysis.
The author reveals how the emphasis for the structural engineer has changed radically from analysis to model synthesis, from contexts where the outcomes are unique to contexts where uncertainty plays a dominant role. The paradigm shift has not been identified in education and hence it is not well understood in practice.
This book:
- Deals with structural analysis in a way that addresses the needs of structural design engineers
- Focuses more on processes for using software than on the solution process used by the software
- Shows how an understanding of behaviour can be significantly improved by a reflective approach to the analysis modelling process
- Details issues for basic and intermediate level analysis modelling - with emphasis on the modelling of skeletal frames
The risk of a disaster causing serious harm due to inadequate modelling cannot be eliminated; it can only be minimised. But for it to be minimised, the modelling process discussed within this book needs to be formally adopted.
While there is a significant danger that software can be used in the absence of competence, the reality of computer use for modelling is that it has made the work more intellectually challenging. Iain MacLeod states that to operate successfully in environments of significant uncertainty requires intellectual power of the highest order. This is the realm of modern structural analysis, the realm of the professional engineer.
Iain MacLeod has worked as a design engineer and consultant in the UK and Canada and in design research with the Portland Cement Association in Illinois, USA.
He was Professor of Structural Engineering at the University of Strathclyde in Glasgow for 23 years and Professor and Head of Department at Paisley University. He is a former Lecturer at the University of Glasgow and now has an appointment as Emeritus Professor at the University of Strathclyde.
His research work has spanned a range of topics in the design of buildings, including the analysis of tall buildings, the use of IT in design and studies in design process. Contents
- Chapter 1 Introduction
1.1 Scope and definitions
1.2 Why 'Modern' Structural Analysis?
1.3 Issues for practice
1.4 Issues for education
1.5 Finite elements
1.6 Accuracy of the information provided in the text
1.7 Website
- Chapter 2 Basic principles in modelling 2.1 Managing the analysis process
2.1.1 Quality management system
2.1.2 Use the modelling process
2.1.3 Competence
2.2 Modelling principles
2.2.1 Use the simplest practical model
2.2.2 Estimate results before you analyse
2.2.3 Increment the complexity
2.2.4 When you get results assume that they may be errors
2.2.5 Trouble shooting
2.2.6 Relationship between the analysis model and the design code of practice
2.2.7 Case Study - The Ronan Point Collapse
2.3 Principles in the use of structural mechanics
2.3.1 Local and resultant stresses - the St Venant Principle
2.3.2 Principle of superposition
2.3.3 Lower bound theorem in plasticity
2.4 Understanding structural behaviour
2.4.1 General
2.4.2 Model Validation
2.4.3 Results verification/ Checking models
2.4.4 Sensitivity analysis
2.4.5 Solution comparisons
2.4.6 Convergence analysis
2.4.7 Identify patterns
2.4.8 Mathematics
2.4.9 Physical modelling, Testing
- Chapter 3 The Modelling process
3.1 Overview of the process
3.1.1 General
3.1.2 Representations of the modelling process
3.1.3 Validation and verification
3.1.4 Error and uncertainty
3.2 Defining the system to be modelled
3.3 The model development process
3.3.1 Conceptual and computational Models
3.3.2 Model options
3.4 Validation of the analysis model
3.4.1 Validation process
3.4.2 Validating the conceptual model
3.4.3 Validating the computational model
3.5 The solution process
3.5.1 Selecting Software
3.5.2 Software Validation and Verification
3.5.3 Truncation error, ill-conditioning
3.6 Verifying the results
3.6.1 Acceptance criteria for results
3.6.2 Verification process
3.6.3 Checking models
3.6.4 Checking loadcase
3.7 The Modelling review
3.7.1 Sensitivity analysis
3.7.2 Overall acceptance of the results
3.7.3 The modelling review document
3.8 Case studies
3.8.1 The Tay Rail Bridge disaster
3.8.2 The Hartford, Connecticut roof collapse
3.8.3 Case Study - the Sleipner Platform collapse
- Chapter 4 Modelling with finite elements
4.1 Introduction
4.2 Elements
4.2.1 Constitutive relationships
4.2.2 Line elements
4.2.3 Surface elements
4.2.4 Volume elements
4.2.5 Joint elements
4.2.6 Basic principles for the derivation of finite element stiffness matrices
4.3 Mesh refinement
4.3.1 Discretisation error
4.3.2 Convergence
4.3.3 Singularities
4.3.4 Benchmark tests
4.3.5 Case Study - Mesh layouts for a cantilever bracket
4.3.6 Meshing principles
4.4 Case Study - Convergence analysis of a plane stress cantilever beam model
4.4.1 General
4.4.2 The context
4.4.3 Elements used in the convergence analysis
4.4.4 Reference solution
4.4.5 Convergence parameters
4.4.6 Meshes
4.4.7 Results
4.4.8 Overview
4.5 Constraints
4.5.1 General
4.5.2 Rigid constraint conditions
4.5.3 Constraint equations
4.6 Symmetry
4.6.1 General
4.6.2 Mirror Symmetry
4.6.3 Symmetry checking
- Chapter 5 Skeletal frames - Modelling with line elements
5.1 General
5.2 Bending
5.2.1 Background
5.2.2 Behaviour
5.2.3 Basic relationships for bending
5.2.4 Symmetric and asymmetric bending
5.2.5 Shear in bending
5.2.6 Combined bending and shear
5.2.7 Validation information for Engineer's Theory of Bending
5.3 Axial effects
5.3.1 Behaviour
5.3.2 Basic relationships
5.3.3 Validation information
5.4 Torsion
5.4.1 Behaviour
5.4.2 Basic relationships for shear torsion
5.4.3 Basic relationships for bending torsion
5.4.4 Combined torsion
5.4.5 Validation information for torsion
5.5 Beam elements and bar elements
5.5.1 Bar elements
5.5.2 Engineering beam elements
5.5.3 Higher order beam elements
5.6 Connections
5.6.1 Basic connection types
5.6.2 Treatment of the finite depth of a beam using beam elements
5.6.3 Modelling beam to column connections in steelwork
5.6.4 Connections in concrete
5.6.5 Eccentricity of members at a joint
5.7 Distribution of load in skeletal frames
5.7.1 Vertical load in beam systems
5.7.2 Distribution of lateral load
5.8 Modelling curved and non-uniform members
5.8.1 Curved members
5.8.2 Case study - Modelling of curved beams
5.8.3 Modelling members with non-uniform cross section
5.8.4 Case study - Tapered cantilever
5.8.5 Cantilever with a tapered soffit
5.8.6 Haunched beams
5.9 Triangulated frames
5.9.1 Modelling issues
5.9.2 Euler buckling effect of members
5.10 Equivalent beam model for parallel chord trusses
5.10.1 General
5.10.2 Definitions
5.10.3 Behaviour
5.10.4 Equivalent beam model
5.11 Vierendeel frames
5.11.1 Definitions
5.11.2 Behaviour
5.11.3 Equivalent beam model
5.12 Grillage models
5.13 3D Models
5.14 Plastic collapse of frames
5.14.1 Prediction of collapse loads - limit analysis
5.14.2 Prediction of plastic collapse using an iterated elastic analysis
5.14.3 Prediction of plastic collapse using a finite element solution 40
5.14.4 Validation information
- Chapter 6 Plates in bending, slabs
6.1 Introduction
6.2 Plate bending elements
6.2.1 Plate bending element basics
6.2.2 Validation information for biaxial plate bending
6.2.3 Output stresses and moments
6.2.4 Checking models for plates in bending
6.3 Concrete slabs
6.3.1 General
6.3.2 Element models for slab analysis
6.3.3 Reinforcing moments and forces for concrete slabs
6.3.4 Beam supported slabs - Basic modelling principles
6.3.5 Modelling the effect of eccentricity of beams in relation to the slab centreline
6.3.6 Shear lag effect
6.3.7 Plate grillage models for concrete slabs
6.3.8 Ribbed Slabs
6.3.9 Plastic Collapse of Concrete Slabs - The Yield line method
- Chapter 7 Material models
7.1 Introduction
7.2 Linear elastic behaviour
7.2.1 General
7.2.2 Types of elastic behaviour
7.2.3 Values of elastic constants
7.2.4 Validation information for linear elastic materials
7.3 Non-linear material behaviour
7.3.1 Plasticity
7.3.2 Other non-linear constitutive relationships
- Chapter 8 Support models
8.1 Introduction
8.2 Modelling support fixity
8.2.1 General
8.2.2 Support requirements
8.2.3 Roller supports
8.2.4 Pin supports
8.2.5 Rotational restraint at a cantilever support
8.2.6 Rotational restraints at column bases
8.2.7 Slab supports
8.3 Modelling the ground
8.3.1 General
8.3.2 The Winkler model for soil behaviour
8.3.3 Half space models
8.3.4 Finite element models
8.4 Foundation structures
8.4.1 Ground beams
8.4.2 Raft foundations
8.4.3 Piles
- Chapter 9 Loading
9.1 Introduction
9.2 Dead Loading
9.3 Live loading
9.4 Wind loading
9.5 Earthquake loading
9.6 Fire
9.7 Temperature
9.7.1 General
9.7.2 Basic relationships
9.8 Influence lines for moving loads
9.8.1 General
9.8.2 Basic concept
9.8.3 Using influence lines
9.8.4 Defining influence lines
9.8.5 Validation information for the use of the Mueller-Breslau method for defining influence lines
9.9 Prestressing
9.10 Impact loading
9.11 Gravity impact
- Chapter 10 Non-linear geometry
10.1 Introduction
10.1.1 Basic behaviour
10.1.2 Cantilever strut example - the P-D effect
10.2 Modelling for geometric non-linearity
10.2.1 Using the non-linear geometry option in FE packages
10.2.2 Use of the critical load ratio magnification factor
10.2.3 Case study - Non-linear geometry analysis of a cantilever
10.2.4 Validation information for non-linear geometry effects
10.3 Critical load analysis of skeletal frames
10.3.1 The Euler critical load for single members
10.3.2 No-sway instability of a column in a frame
10.3.3 The critical load ratio for an axially loaded member of a frame
10.3.4 Estimation of critical loads using eigenvalue extraction
10.3.5 Case study - Eigenvalue analysis of a cantilever strut
10.4 Global critical load analysis of building structures
- Chapter 11 Dynamic behaviour
11.1 General
11.2 Dynamic behaviour of a single mass and spring system
11.2.1 Governing equation
11.2.2 Validation information for Equation (14.1)
11.2.3 Free undamped vibration
11.2.4 Damping
11.3 Multi-degree of freedom systems
11.3.1 Basic behaviour
11.3.2 Governing equation for multi-degree of freedom systems
11.3.3 Modelling for dynamic eigenvalue extraction
11.3.4 Verification of output for dynamic models
11.4 Resonance
11.5 Transient load
11.6 Checking models for natural frequencies
11.6.1 Single span beams
11.6.2 The maximum deflection formula
11.6.3 Case study - use of Equation (11.11)
11.6.4 Single mass and spring
11.6.5 Combinations of Frequencies
- Chapter 12 Case studies
12.1 Vierendeel frame
12.1.1 General
12.1.2 Definition of the system to be modelled - the engineering model
12.1.3 Model development
12.1.4 The Analysis model
12.1.5 Model validation
12.1.6 Results verification
12.1.7 Sensitivity analysis
12.1.8 Overall acceptance
12.1.9 Modelling review document
12.2 Example 2 Four storey building
12.2.1 General
12.2.2 Definition of the system to be modelled - the Engineering Model
12.2.3 Model development
12.2.4 Model validation
12.2.5 Results Verification
12.2.6 Sensitivity analysis
12.2.7 Model Review
- Appendix A Appendix A
Table A1 Areas and second moments of area of standard shapes
Table A2 Shear areas for beams
Table A3 J values and shear stress formulae for shear torsion of different cross sections
Table A4 Deflection formulae for beams
Table A5 End displacement of axially loaded members
Table A6 Typical physical properties for structural materials
Table A7 Typical values of Winkler stiffness for soils
Table A8 Typical values for modulus of elasticity for soils - Es
Table A9 Typical Poisson's ratios for soils
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