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 A q R B 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 B A B Structural behavior of simple arch-cable structures 6 Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN q A B A B A 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 B R A q 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 q 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 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 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 I 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 A 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 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 H2 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 B F F A 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 B1 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 R 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 R 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 B B 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 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 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 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 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 B 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 F A B F A B Geometric variations 64 Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN F A B F A B Geometric variations 65 Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN F A B F A B Geometric variations 66 Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN F A B F A B Geometric variations 67 Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN F A B F A B Geometric variations 68 Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN F A 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 F1 R F2 F3 Combined arch-cable structures 73 Form diagram Force diagram Scale 1 : 100 Scale 1 cm ≙ 1 kN R A 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 F3 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 F2 B A B F3 F3 B B F2 F1 F2 F3 A A F1 Combined arch-cable structures 77 l ' = 0 f 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 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 f l ' l l ' Combined arch-cable structures 83 A.