Structural Design I Philippe Block · Joseph Schwartz 2 3 Arch-Cable Structures

http://www.block.arch.ethz.ch/eq/ 1

Structural Design I Philippe Block · Joseph Schwartz 2 3 Arch-cable structures

>> Structural behavior of simple arch-cable structures Support reactions External load distribution to arch and cable Cantilever-like arch-cable structures Geometric variations Combined arch-cable structures Constant-force gable truss Cable-stayed structures Tree structures Structural behavior of simple arch-cable structures 4

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN R

q R

A B Structural behavior of simple arch-cable structures 5

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN R

A q R

A B Structural behavior of simple arch-cable structures 6

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

A B

B A B Structural behavior of simple arch-cable structures 7

Eugène Freyssinet: Pont Albert Louppe, Bretagne, 1930 Structural behavior of simple arch-cable structures 8

Eugène Freyssinet: Pont Albert Louppe, Bretagne, 1930 Structural behavior of simple arch-cable structures 9

Eugène Freyssinet: Pont Albert Louppe, Bretagne, 1930 Structural behavior of simple arch-cable structures 10

Eugène Freyssinet: Pont Albert Louppe, Bretagne, 1930 Structural behavior of simple arch-cable structures 11

R. Brosi & Obrist and Partner, Peter Rice: Bus station Chur, 1992 Structural behavior of simple arch-cable structures 12

R. Brosi & Obrist and Partner, Peter Rice: Bus station Chur, 1992 Structural behavior of simple arch-cable structures 13

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

A B

R Structural behavior of simple arch-cable structures 14

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

A B

B R A

R Structural behavior of simple arch-cable structures 15

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN A B B

A B B R A

q 16 Arch-cable structures

Structural behavior of simple arch-cable structures >> Support reactions External load distribution to arch and cable Cantilever-like arch-cable structures Geometric variations Combined arch-cable structures Constant-force gable truss Cable-stayed structures Tree structures Support reactions 17 Support reactions 18 Support reactions 19 Support reactions 20 Support reactions 21 22 Arch-cable structures

Structural behavior of simple arch-cable structures Support reactions >> External load distribution to arch and cable Cantilever-like arch-cable structures Geometric variations Combined arch-cable structures Constant-force gable truss Cable-stayed structures Tree structures External load distribution to arch and cable 23

Eugène Freyssinet: Pont Albert Louppe, Bretagne, 1930 External load distribution to arch and cable 24

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN External load distribution to arch and cable 25

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN External load distribution to arch and cable 26

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN External load distribution to arch and cable 27

G.H. Lohse: New Elbbridge, Hamburg, 1868 External load distribution to arch and cable 28

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN External load distribution to arch and cable 29

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN External load distribution to arch and cable 30

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F A

F F F F F F

F B A B F External load distribution to arch and cable 31

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

I F II

F F F F F

A B

II External load distribution to arch and cable 32

Robert Maillart: Magazzini Generali, Chiasso, 1924 External load distribution to arch and cable 33

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F F F F F F F

B A B External load distribution to arch and cable 34

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F1 F2 External load distribution to arch and cable 35

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

R F1 F2

F1 R

F2 External load distribution to arch and cable 36

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

R A B B External load distribution to arch and cable 37

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F1 F2

h1 A F1

A B B F2

H1 External load distribution to arch and cable 38

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

h1 H2 =

F1 F2 h2 H1

h2 h1 A F1

A B B F2

H1 39 Arch-cable structures

Structural behavior of simple arch-cable structures Support reactions External load distribution to arch and cable >> Cantilever-like arch-cable structures Geometric variations Combined arch-cable structures Constant-force gable truss Cable-stayed structures Tree structures Cantilever-like arch-cable structures 40

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

B F F

A Cantilever-like arch-cable structures 41

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN Cantilever-like arch-cable structures 42

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN Cantilever-like arch-cable structures 43

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN Cantilever-like arch-cable structures 44

Norman Foster, Ove Arup: Honkong and Shanghai Banking Coorp., Hongkong, 1979 Cantilever-like arch-cable structures 45

B 3 B2 B1

+ + A1 A 2 A 3

F1 F2 F3

B 3 B B 3 2 F3

B2 F2

A B1 F1

F1 F2 F3

A Cantilever-like arch-cable structures 46

Norman Foster, Michel Virlogeux: Viaduct de Millau, Aveyon, 2004 Cantilever-like arch-cable structures 47

Christian Menn: Sunnibergbrücke, Klosters, 1998 Cantilever-like arch-cable structures 48

Christian Menn: Ganterbrücke, Brig, 1980 Cantilever-like arch-cable structures 49

F F F F Cantilever-like arch-cable structures 50

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F F F F

F F R F F Cantilever-like arch-cable structures 51

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

B B

R A

A Cantilever-like arch-cable structures 52

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

B B F F F F F A F F F A Cantilever-like arch-cable structures 53

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

R q

B B

R A

A Cantilever-like arch-cable structures 54

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

R 100% q

R A A Cantilever-like arch-cable structures 55

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

R1 25% q

B R1

R 2 A A

R 2 75% q Cantilever-like arch-cable structures 56

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

R1 50% q

B R1

A R 2 A

R 2 50% q Cantilever-like arch-cable structures 57

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

R1 75% q

B R1 A

R 2 A R 2 25% q Cantilever-like arch-cable structures 58

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

R 100% q

B R A

A Cantilever-like arch-cable structures 59

P.L. Nervi: Paperfactory Burgo, Manuta, Italy, 1962 Cantilever-like arch-cable structures 60

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN Q 6

Q 5

Q 4

Q 3 A

Q 2

Q1 Q1 Q 2 Q 3 Q 4 Q 5 Q 6

A B

Maurice Koechlin, Gustave Eiffel: La Tour Eiffel, Paris, 1889 Cantilever-like arch-cable structures 61

eQ: Eiffel Tower

http://www.block.arch.ethz.ch/eq/drawing/view/31 62 Arch-cable structures

Structural behavior of simple arch-cable structures Support reactions External load distribution to arch and cable Cantilever-like arch-cable structures >> Geometric variations Combined arch-cable structures Constant-force gable truss Cable-stayed structures Tree structures Geometric variations 63

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

B F

A B Geometric variations 64

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

B F

A B Geometric variations 65

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

B F

A B Geometric variations 66

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

B F

A B Geometric variations 67

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

B F

A B Geometric variations 68

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

B F

A B Geometric variations 69 70 Arch-cable structures

Structural behavior of simple arch-cable structures Support reactions External load distribution to arch and cable Cantilever-like arch-cable structures Geometric variations >> Combined arch-cable structures Constant-force gable truss Cable-stayed structures Tree structures Combined arch-cable structures 71

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F1 F2 F3 Combined arch-cable structures 72

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

R F1 F2 F3

R F2

F3 Combined arch-cable structures 73

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

R B

A B Combined arch-cable structures 74

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F1 F2 F3

A F1

F2 B

A B Combined arch-cable structures 75

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

A F1 F2 F3 F1

F2 B A B F3

F3 B B F2

A F F F F 1 2 3 1 A Combined arch-cable structures 76

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F1 F2 F3 F 1 A

B A B F3

F3 B B

F2 F1 F2 F3 A A F1 Combined arch-cable structures 77

l ' = 0

l Combined arch-cable structures 78

l ' : l = 0.2

0.16 f

0.84 f

l ' l l ' Combined arch-cable structures 79

l ' : l = 0.35

0.5 f

l ' l l ' Combined arch-cable structures 80

Sir John Fowler, Sir Benjamin Baker: Forth Bridge, South Quennsferry, 1890 Combined arch-cable structures 81

l ' : l = 0.4

0.67 f

0.33 f

l ' l l ' Combined arch-cable structures 82

l ' : l = 0.5

l ' l l ' Combined arch-cable structures 83

A. Fried: Rip-Bridge, Woy-Woy, Australia, 1971 Combined arch-cable structures 84

Image by D‘Arcy W. Thomson Combined arch-cable structures 85 Combined arch-cable structures 86

Train bridge, Riga, Lettland, 1914 Combined arch-cable structures 87 Combined arch-cable structures 88

Heinrich Gerber: Hassfurt Bridge, Hassfurt, 1867 Combined arch-cable structures 89 90 Arch-cable structures

Structural behavior of simple arch-cable structures Support reactions External load distribution to arch and cable Cantilever-like arch-cable structures Geometric variations Combined arch-cable structures >> Constant-force gable truss Cable-stayed structures Tree structures Constant-force gable truss 91

Robert Maillart: Warehouse Magazzini Generali, Chiasso, 1925 Constant-force gable truss 92

Robert Maillart: Warehouse Magazzini Generali, Chiasso, 1925 Constant-force gable truss 93

Robert Maillart: Warehouse Magazzini Generali, Chiasso, 1925 Constant-force gable truss 94

F F F F F F F

A B

F F F F F F F

B A B Constant-force gable truss 95

eQ: Constant-force gable truss

http://www.block.arch.ethz.ch/eq/drawing/view/26 Constant-force gable truss 96

eQ: Freeform truss

http://www.block.arch.ethz.ch/eq/drawing/view/52 Constant-force gable truss 97

Robert Maillart: Warehouse Magazzini Generali, Chiasso, 1925 Constant-force gable truss 98

Robert Maillart: Warehouse Magazzini Generali, Chiasso, 1925 Constant-force gable truss 99

Robert Maillart: Sihlhölzli gymnasium, Zurich, 1932 Constant-force gable truss 100

Robert Maillart: Sihlhölzli gymnasium, Zurich, 1932 Constant-force gable truss 101

Robert Maillart: Sihlhölzli gymnasium, Zurich, 1932 Constant-force gable truss 102

Robert Maillart: Sihlhölzli gymnasium, Zurich, 1932 103 Arch-cable structures

Structural behavior of simple arch-cable structures Support reactions External load distribution to arch and cable Cantilever-like arch-cable structures Geometric variations Combined arch-cable structures Constant-force gable truss >> Cable-stayed structures Tree structures Cable-stayed structures 104

Foster+Partners, Michel Virlogeux: Millau Viaduct, near Montpellier, France, 2004 Cable-stayed structures 105

Foster+Partners, Michel Virlogeux: Millau Viaduct, near Montpellier, France, 2004 Cable-stayed structures 106

Foster+Partners, Michel Virlogeux: Millau Viaduct, near Montpellier, France, 2004 Cable-stayed structures 107

Foster+Partners, Michel Virlogeux: Millau Viaduct, near Montpellier, France, 2004 Cable-stayed structures 108 Cable-stayed structures 109

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F1 F6 F5 F4 F3 F2 F1

A Cable-stayed structures 110

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F1 F6 F5 F4 F3 F2 F1 F2

A Cable-stayed structures 111

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F1 F6 F5 F4 F3 F2 F1 F2

A Cable-stayed structures 112

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F A 3

F6 F5 F4 F3 F2 F1

A Cable-stayed structures 113

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F6 A F1 F F F F F F 6 5 4 3 2 1 F2

A Cable-stayed structures 114

eQ: Fan-harp bridge

http://www.block.arch.ethz.ch/eq/drawing/view/21 Cable-stayed structures 115

Christian Menn: Ganter Bridge, Brig, 1980 Cable-stayed structures 116

Christian Menn: Sunniberg Bridge, between Klosters and Serneus, 2005 Cable-stayed structures 117 Cable-stayed structures 118

eQ: Cantilevered fan bridge

http://www.block.arch.ethz.ch/eq/drawing/view/22 Cable-stayed structures 119

Santiago Calatrava: Alamillo Bridge, Sevilla, 1992 Cable-stayed structures 120

Santiago Calatrava: Alamillo Bridge, Sevilla, 1992 Cable-stayed structures 121

Santiago Calatrava: Alamillo Bridge, Sevilla, 1992 Cable-stayed structures 122 Cable-stayed structures 123

Nicholas Grimshaw: Newport City Footbridge, UK, 2006 Cable-stayed structures 124

Ben Van Berkel: Alamillo Bridge, Sevilla, 1992 Cable-stayed structures 125

eQ: Cable-stayed bridge

http://www.block.arch.ethz.ch/eq/drawing/view/23 Cable-stayed structures 126

Santiago Calatrava: Trinity Footbridge, Salford UK, 1995 Cable-stayed structures 127

Santiago Calatrava: Trinity Footbridge, Salford UK, 1995 Cable-stayed structures 128

Santiago Calatrava: Trinity Footbridge, Salford UK, 1995 Cable-stayed structures 129 Cable-stayed structures 130

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F6 A F6 F5 F4 F3 F2 F1 F1

A Cable-stayed structures 131

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F2 Cable-stayed structures 132

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN

F3 Cable-stayed structures 133

Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN Cable-stayed structures 134

Lord Richard Rogers: Newport Factory, Wales UK, 1982 Cable-stayed structures 135

Lord Richard Rogers: Newport Factory, Wales UK, 1982 Cable-stayed structures 136

Lord Richard Rogers: Newport Factory, Wales UK, 1982 Cable-stayed structures 137

Lord Richard Rogers: Fleetguard Factory, Quimper, France, 1981 Cable-stayed structures 138

Lord Richard Rogers: Fleetguard Factory, Quimper, France, 1981 Cable-stayed structures 139

Lord Richard Rogers: Fleetguard Factory, Quimper, France, 1981 Cable-stayed structures 140

Samuel Marx, Skidmore, Owings & Merrill: Baxter Laboratories, Deerfield, IL, USA, 1975 Cable-stayed structures 141

Samuel Marx, Skidmore, Owings & Merrill: Baxter Laboratories, Deerfield, IL, USA, 1975 Cable-stayed structures 142

Samuel Marx, Skidmore, Owings & Merrill: Baxter Laboratories, Deerfield, IL, USA, 1975 Cable-stayed structures 143

Samuel Marx, Skidmore, Owings & Merrill: Baxter Laboratories, Deerfield, IL, USA, 1975 Cable-stayed structures 144

Philip Cox: Sydney Exhibition Center, Australia, 1988 Cable-stayed structures 145

Philip Cox: Sydney Exhibition Center, Australia, 1988 Cable-stayed structures 146

Philip Cox: Sydney Exhibition Center, Australia, 1988 Cable-stayed structures 147

Nicholas Grimshaw: Igus Factory, Köln, 2001 Cable-stayed structures 148

Nicholas Grimshaw: Igus Factory, Köln, 2001 Cable-stayed structures 149

Nicholas Grimshaw: Igus Factory, Köln, 2001 Cable-stayed structures 150

Foster+Partners: Renault Distribution Center, Swindon UK, 1983 Cable-stayed structures 151

Foster+Partners: Renault Distribution Center, Swindon UK, 1983 Cable-stayed structures 152

Foster+Partners: Renault Distribution Center, Swindon UK, 1983 Cable-stayed structures 153

Foster+Partners: Renault Distribution Center, Swindon UK, 1983 Cable-stayed structures 154

Lord Richard Rodgers: PAT Center, Princeton NJ, USA, 1982 Cable-stayed structures 155

Lord Richard Rodgers: PAT Center, Princeton NJ, USA, 1982 Cable-stayed structures 156

Lord Richard Rodgers: PAT Center, Princeton NJ, USA, 1982 157 Arch-cable structures

Structural behavior of simple arch-cable structures Support reactions External load distribution to arch and cable Cantilever-like arch-cable structures Geometric variations Combined arch-cable structures Constant-force gable truss Cable-stayed structures >> Tree structures Tree structures 158 Tree structures 159

Daniel Bonilla: Colombia Pavilion, Hannover Expo 2000 Tree structures 160

Christian Menn: Ganter Bridge, Brig, 1980 Tree structures 161

Robert Maillart: Simme River Bridge, Garstatt, 1940 Tree structures 162

Jürg Conzett: Glenner Bridge, Peiden Bad, 2002 Tree structures 163

Jürg Conzett: Glenner Bridge, Peiden Bad, 2002 Tree structures 164

Jürg Conzett: Glenner Bridge, Peiden Bad, 2002 Tree structures 165

Alvar Aalto: Säynätsalo Town Hall, Finland, 1993 Tree structures 166

Alvar Aalto: Säynätsalo Town Hall, Finland, 1993 Tree structures 167

Alvar Aalto: Säynätsalo Town Hall, Finland, 1993 Tree structures 168

Alvar Aalto: Säynätsalo Town Hall, Finland, 1993 Tree structures 169

Gerkan, Mark & Partner, Schlaich Bergermann: Stuttgart Airport Terminal 3, 2004 Tree structures 170

Gerkan, Mark & Partner, Schlaich Bergermann: Stuttgart Airport Terminal 3, 2004 Tree structures 171

A R

A Tree structures 172

R / 2 R / 2

R / 2 A

R / 2

A Tree structures 173

R / 4 R / 4 R / 4 R / 4 R / 4 R / 4 A

R / 4

A Tree structures 174

eQ: Tree structure

http://www.block.arch.ethz.ch/eq/drawing/view/25 Tree structures 175

Gerkan, Mark & Partner, Schlaich Bergermann: Stuttgart Airport Terminal 3, 2004 Tree structures 176

Gerkan, Mark & Partner, Schlaich Bergermann: Stuttgart Airport Terminal 3, 2004 Tree structures 177

Gerkan, Mark & Partner, Schlaich Bergermann: Stuttgart Airport Terminal 3, 2004