Tension Structures Form and behaviour

Contents Preface vii
Acknowledgements ix
About the author xi
1 Introduction 1
1.1 Definitions and classifications 2
1.2 Strength and stiffness of architectural fabrics 3
1.3 Types of architectural fabrics 4
1.4 Boundary tensioned membranes 4
1.5 Pneumatic structures 10
1.6 Pre-stressed cable nets and beams 12
1.7 Design process of tension membranes 16
1.8 Main features of tension membranes 18
1.9 Conventional roofing forms versus tension
membranes 19
1.10 Closing remarks 20
References 21
2 Form-finding 23
2.1 General concepts. Nature’s ‘secrets’ 23
2.2 Concept of a ‘minimal surface’: historical
background 26
2.3 Form-finding methodologies 28
References 35
3 Geometrically nonlinear behaviour: solutions
using commonly used numerical methods 37
3.1 Geometric nonlinearity 37
3.2 Commonly used computational methods
for the analysis of geometrically nonlinear
behaviour 39
3.3 Transient stiffness method 39
3.4 Force density method (original formulation) 48
3.5 Dynamic relaxation method 54
3.6 Computational static analysis versus
Form-finding 54
References 55
4 Dynamic relaxation method 57
4.1 Dynamic relaxation method with viscous
damping 58
4.2 Dynamic relaxation method with kinetic
damping 63
4.3 Application of dynamic relaxation to cable
networks 67
4.4 Evaluation of the dynamic relaxation method 73
References 74
5 Cable roof structures. Case studies 75
5.1 Introduction 75
5.2 Case studies 76
References 99
6 Tension cables in suspension bridges.
A case of form-finding 101
6.1 ‘Shape’ equation for an inextensible
suspension cable 103
6.2 ‘Shape’ equation for an extensible
suspension cable 109
6.3 Numerical modelling of shape of
suspension bridge cables 111
6.4 Form-finding of suspension bridge cables:
practical aspects 126
6.5 Form-finding, or form-dictating? 127
6.6 Relevance of ‘shape’ equations to
form-finding of arch structures 130
References 133
7 Modelling of tension membranes 135
7.1 Introduction 135
7.2 Surface discretisation 135
7.3 Surface discretisation for use with the
transient stiffness method: limitations of
the approach 136
7.4 Surface discretisations used with the
Dynamic relaxation method 144
7.5 Line elements in modelling of stable
minimal surface membranes 152
7.6 Application of triangular elements to modelling
of stable minimal surface membranes 154
7.7 Mesh control – implications for design 156
7.8 Patterning of membranes 160
7.9 Numerical accuracy and criteria used for
convergence 167
7.10 Data processing 169
References 172
Appendix 1 Architectural fabrics 175
Appendix 11 Cables for tension structures 183
Appendix 111 Minimal surfaces 185
Appendix 1V Viscous damping in dynamic relaxation 193
Appendix V Finite-difference analysis of inextensible
cable. Load case 1: deck weight only 195
Index 199