six Cables & Arches 1 APPLIED ACHITECTURAL STRUCTURES: DR. ANNE NICHOLS SPRING 2019 lecture STRUCTURAL ANALYSIS AND SYSTEMS ARCH 631

Transcription

1 APPLIED ACHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 2019 lecture six cables & arches Millennium Bridge in Newcastle, UK Cables & Arches 1

2 Cables simple uses suspension bridges roof structures transmission lines guy wires, etc. have same tension all along can t stand compression struts do nisee.berkeley.edu/godden Cables & Arches 2

3 Cables use high-strength steel need towers anchors stiffeners (hangers) have spans & sag don t want movement dynamic effects of wind resonance nisee.berkeley.edu/godden Cables & Arches 3

4 Cables Cables & Arches 4

5 Cables equilibrium: not enough to solve, we have slopes X component the same everywhere A 4 m 6 m B 2 m C 45 kn 45 kn Cables & Arches 5

6 Cable Loads straight line between forces Cables & Arches 6

7 Cable Loads shape directly related to the distributed load Cables & Arches 7

8 Cable Loads trig: T x = Tcos T y = Tsin parabolic (catenary) distributed uniform load y = 4h(Lx x 2 ) / L 2 y h L total = L( h 2 L h 4 L4) x L Cables & Arches 8

9 Cables & Tension Elements typical cross sections Multi-wire strand Cables & Arches 9

10 Cable Structures categories single drape double cases different curvature same plane or different Brooklyn Bridge Dulles Terminal Cables & Arches 10

11 Brooklyn Bridge, Roebling 1883 Cables & Arches 11 nisee.berkeley.edu/godden

12 Brooklyn Bridge, Roebling 1883 Cables & Arches 12

13 Dulles Terminal, Saarinen 1962 Cables & Arches 13

14 Dulles Terminal, Saarinen 1962 Cables & Arches 14

15 Cable-Stayed Structures diagonal cables support horizontal spans typically symmetrical cases Patcenter Alamillo Bridge Cables & Arches 15

16 Patcenter, Rogers 1986 Cables & Arches 16

17 Patcenter, Rogers 1986 Cables & Arches 17

18 Patcenter, Rogers 1986 dashes cables pulling Cables & Arches 18

19 Alamillo Bridge, Calatrava 1992 Cables & Arches 19

20 Alamillo Bridge, Calatrava 1992 concrete mast parallel cable stays steel box beam spine in deck Cables & Arches 20

21 Tensegrities 3D frame discontinuous struts continuous cables Free Ride Home Kenneth Snelson Cables & Arches 21

22 Olympic Gymnastics Stadium Geiger Cables & Arches 22

23 Olympic Gymnastics Stadium Geiger 1988 Cables & Arches 23

24 Florida Suncoast Dome, HOK 1989 Cables & Arches 24

25 Florida Suncoast Dome, HOK 1989 Cables & Arches 25

26 Georgia Dome, Stainback 1992 Cables & Arches 26

27 Georgia Dome, Stainback 1992 Cables & Arches 27

28 Arches curvilinear form efficient in compression minimal bending stress Cables & Arches 28

29 Arches ancient stone masonry Rainbow Bridge National Monument Cables & Arches 29 Lions Gate

30 Arches ancient stone masonry Packhorse Bridge, UK Cables & Arches 30 Roman Aquaducts

31 Arches terminology arch axis crown rise extrados intrados depth spring line span skewback soffit Cables & Arches 31

32 Arches behavior stabilization resist thrust materials stone masonry concrete laminated wood steel Cables & Arches 32

33 Arches behavior thrust related to height to width Cables & Arches 33

34 Arches common forms Cables & Arches 34

35 Arches common variations two hinged three hinged statically determinate Cables & Arches 35

36 Arches requires lateral bracing lateral ties diagonal ties Cables & Arches 36 nisee.berkeley.edu/godden

37 Arches... bracing lamellas Cables & Arches 37

38 Vaults nisee.berkeley.edu/godden Cables & Arches 38

39 Vaults Crypt of the Colonia Güell - Gaudi Cables & Arches 39

40 Domes arch of revolutionary design resists compressive forces Cables & Arches 40

41 Domes materials & forms concrete masonry steel Pantheon Cables & Arches 41

42 Domes materials & forms concrete masonry steel Union Station Rotunda, Pittsburg Cables & Arches 42

43 Domes stresses and displacements Harvard GSD Cables & Arches 43

44 Domes Palazzetto dello Sport -Nervi Cables & Arches 44