Transparent Shells

Foreword 6

Preface 6

Acknowledgements 8

About the Author 9

With the collaboration of 10

1 Introduction to shells 13

1.1 Designing shells 14

2 History 19

2.1 Historical examples 20

3 Design principle of grid shells 31

3.1 Development of the design principle 32

3.2 Construction of the grid shells in Neckarsulm 40

4 Graphic design principles for grid shells with flat quadrilateral meshes 49

4.1 Graphic design principles for translational surfaces 51

4.2 The barrel vault as simplest translational surface 53

4.2.1 Optimum section curve 55

4.2.2 Bracing of barrel vaults 56

4.2.3 The barrel-vault according to the Zollinger construction method 63

4.3 Surface of revolution 64

4.3.1 Array of surfaces of revolution 67

4.3.2 One-dimensional scaling and rotation 70

4.4 Domes as translational surfaces 72

4.4.1 Optimum rise of domes 73

4.4.2 Examples on dome-like translational surfaces 74

4.4.3 Arrayed translational surfaces 79

4.5 Hyperbolic paraboloid with flat quadrilateral meshes 80

4.5.1 On the load bearing behaviour of hypar-shells with straight edges 82

4.5.2 The hypar as translational surface with flat quads 84

4.5.3 The hypar as ruled surface with flat quadrangles 87

4.5.4 Equation of the hypar at given 4 straight edges 91

4.5.5 Cut-outs from the hypar surface along the generating lines 94

4.5.6 Array of hypar surfaces 101

4.5.7 Rain water drainage of âflatâ surfaces 112

4.6 âSkewâ translation 113

4.7 Graphic design principle for scale-trans surfaces 122

4.7.1 Scaling of spatial curves 122

4.7.2 Scale-trans surfaces 124

4.8 Lamella surfaces with flat quadrangular meshes 132

4.8.1 The regular lamella surface 135

4.8.2 Cut-outs from lamella surfaces 136

4.9 Scaling of double-curved surfaces with flat quadrangular meshes 137

4.10 Application for spatial sheet metal constructions 140

4.11 Application for formwork in concrete construction 142

5 Free formed grid shells 147

5.1 Grid shells with flat quadrangular meshes based on free-forms 149

5.2 Grid shells with warped quadrangular meshes 150

5.3 Combination of flat quadrangular and triangular meshes 154

6 Form-finding and optimisation of grid shells 161

6.1 Form-finding on the inverted hanging model 163

6.2 Form-finding with membrane elements 165

6.3 Form-finding based on dynamic relaxation and the force density method 168

6.4 Holistic âform-findingâ using shape optimisation 175

7 On the structural design of grid shells 185

7.1 Structural analysis of glazing 186

7.2 Analysis of the structure 186

8 Built examples 189

8.1 List of glazed shells 190

8.2 Node connections 208

8.2.1 Introduction 208

8.2.2 Bolted nodes 214

8.2.3 Welded nodes 229

9 Holistic design â" developments and outlook 239

Bibliography 250

Bibliography on projects 251

List of projects 252

Picture credits 254

Imprint 256