six cables & arches Cables Cables Cables simple uses have same tension all along can t stand compression struts do

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1 APPLIED ARCHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS FALL 2017 lecture six cables & arches Cables & 1 Applied Architectural Structures Millennium Bridge in Newcastle, UK Cables simple uses suspension bridges roof structures transmission lines guy wires, etc. have same tension all along can t stand compression struts do Cables & 2 nisee.berkeley.edu/godden 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 Cables & 3 Cables & 4 1

2 Cables equilibrium: not enough to solve, we have slopes X component the same everywhere Cable Loads straight line between forces A 4 m 6 m B 2 m C 45 kn 45 kn Cables & 5 Cables & 6 Cable Loads shape directly related to the distributed load Cable Loads trig: T x T cos T y T sin parabolic (catenary) distributed uniform load y 2 2 4h( Lx x ) / L 2 L( 1 8 h 3 2 L L 32 4 total 5 4 h L ) x y L h Cables & 7 Cables & 8 2

3 Cables & Tension Elements typical cross sections Multi-wire strand Cable Structures categories single drape double different curvature same plane or different cases Brooklyn Bridge Dulles Terminal Cables & 9 Cables & 10 Brooklyn Bridge, Roebling 1883 Brooklyn Bridge, Roebling 1883 Cables & 11 nisee.berkeley.edu/godden Cables & 12 3

4 Dulles Terminal, Saarinen 1962 Dulles Terminal, Saarinen 1962 Cables & 13 Cables & 14 Cable-Stayed Structures diagonal cables support horizontal spans typically symmetrical cases Patcenter Alamillo Bridge Patcenter, Rogers 1986 Cables & 15 Cables &

5 Patcenter, Rogers 1986 Patcenter, Rogers 1986 dashes cables pulling Cables & 17 Cables & 18 Alamillo Bridge, Calatrava 1992 Alamillo Bridge, Calatrava 1992 concrete mast parallel cable stays steel box beam spine in deck Cables & 19 Cables & 20 5

6 Tensegrities 3D frame discontinuous struts continuous cables Olympic Gymnastics Stadium Geiger Free Ride Home Kenneth Snelson Cables & 21 Cables & 22 Olympic Gymnastics Stadium Geiger 1988 Florida Suncoast Dome, HOK 1989 Cables & 23 Cables & 24 6

7 Florida Suncoast Dome, HOK 1989 Georgia Dome, Stainback 1992 Cables & 25 Cables & 26 Georgia Dome, Stainback 1992 curvilinear form efficient in compression minimal bending stress Cables & 27 Cables & 28 7

8 ancient stone masonry ancient stone masonry Packhorse Bridge, UK Rainbow Bridge National Monument Cables & 29 Lions Gate Cables & 30 Roman Aquaducts terminology arch axis crown rise extrados intrados depth spring line span skewback soffit behavior stabilization resist thrust materials stone masonry concrete laminated wood steel Cables & 31 Cables & 32 8

9 behavior thrust related to height to width common forms Cables & 33 Cables & 34 common variations two hinged three hinged statically determinate requires lateral bracing lateral ties diagonal ties Cables & 35 Cables & 36 nisee.berkeley.edu/godden 9

10 ... bracing lamellas Vaults Cables & 37 nisee.berkeley.edu/godden Cables & 38 Vaults Crypt of the Colonia Güell - Gaudi Domes arch of revolutionary design resists compressive forces Cables & 39 Cables & 40 10

11 Domes materials & forms concrete masonry steel Pantheon Domes materials & forms concrete masonry steel Union Station Rotunda, Pittsburg Cables & 41 Cables & 42 Domes stresses and displacements Harvard GSD Domes Palazzetto dello Sport -Nervi Cables & 43 Cables & 44 11