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Tensile structures Prof Schierle 1
Pneumatic TrussedAnticlasticStayed Suspended
Tensile structures
Tensile structures Prof Schierle 2
Stayed
Tensile structures Prof Schierle 3
McCormick exhibit hall ChicagoArchitect/Engineer: SOMTo span railroad trucks underneath, the truss roof issuspended by stay cables from concrete pylons.1 Axon2 Section3 Center joint4 Exterior jointA Pylon topB Stay cableC Truss web barD Stay bracketE Edge stay, resists wind uplift
Tensile structures Prof Schierle 4
Imos factory, Newport, UKArchitect: Richard Rogers Engineer: Anthony Hunt
Tensile structures Prof Schierle 5
Patscenter PrincetonArchitect: Richard RogersEngineer: Ove ArupStays resist both gravity load and wind uplift
Design alternates Lines meet = concentric joints
Tensile structures Prof Schierle 6
Renault Center Swindon, UKArchitect: Norman Foster
Tensile structures Prof Schierle 7
Golden Gate Bridge, photo courtesy Peter Craig
Suspended
Tensile structures Prof Schierle 8
Suspension span/sag ratios:
Small sag = large stress
Large sag = small stress but tall supports
Optimal span/sag ratio = 10
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New York bridges:
George Washington Bridge, top
Roebling Bridge, bottom & left
(diagonal hangers resist deformation)
http://en.wikipedia.org/wiki/John_A._Roebling
Tensile structures Prof Schierle 10
Stability issues:1 Point load deformation2 Wind deformation3 Stabilizing cable to resist wind uplift4 Dead load to resist wind uplift
(increases seismic load)6 US pavilion Expo 57, Brussels
Circular compression ring resistslateral thrust effectively
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Tensile structures Prof Schierle 11
Oakland Coliseum (1967)Architect: SOMEngineer: Ammann and Whitney
Diameter 400 ft Outer concrete compression ring Inner steel tension ring Steel strands for main support Concrete ribs resist unbalanced load X-columns resist lateral seismic load
Tensile structures Prof Schierle 12
Tensile structures Prof Schierle 13
Dulles Airport Terminal Left: Initial structure Below: 1990 expansion
Tensile structures Prof Schierle 14
Exhibit Hall HanoverArchitect: Thomas HerzogEngineer: Schlaich Bergermann
Roof features: 3x40 cm steel suspender band Prefab wood panels with ballast gravel Skylights provide lighting and ventilation
(prevent balanced suspender support) Prestressed glass wall avoids buckling of
mullions due to roof deflection
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Anticlastic
Anticlastic = saddle shape, inverse curvatures
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Minimal surface equations (Schierle, 1977 *)Y= f1(X/S1)(f1+f2)/f1 + X tan Y= f2 (Z/S2)(f1+f2)/f2
* Published in Journal of Optimization Theory and Application
The minimal surface conditions: Minimum surface area between any boundary Equal and opposite curvature at any point Uniform stress throughout the surface f1/f2 = A/B (Schierle, 1977 *)
Minimal surface vs. Hyperbolic Paraboloid
1 Minimal surface of square plan2 Hyperbolic Paraboloid of square plan3 Minimal surface of rhomboid plan
(membrane center below mid-height)4 Hyperbolic Paraboloid of rhomboid plan
(membrane center at mid-height)
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Anticlastic Surface1 Opposing strings
stabilize a point in space2 Several opposing strings
stabilize several points
3 Anticlastic curvaturestabilizes a membrane
4 Membrane shear causes wrinkles in fabric
5 Stress without wrinkles
6 HP-surface Quadratic equation
7 Minimal surface
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Fiber Orientation (Schierle, 1968)1 Orthogonal (causes shear stress)2 Principal curvature (avoids shear stress)3 Principal curvature vs.4 Generating lines5 Principal curvature orientation (small deflections)6 Generating line orientation (large deflections)Lesson: Orient fibers in principal curvature Avoid generating line orientation
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Edge Conditions
1, 2 Edge Cable
3, 4 Edge Arch
5, 6 Edge Frame
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Edge Cable
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Edge Arch
Tensile structures Prof Schierle 22
Edge Frame
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Surface Conditions
Saddle shapes
Arch shapes
Wave shapes
Point shapes
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Saddle Shapes
1 Square / cable edge
2 Hexagon / cable edge
3 Square / arch edge
4 Oval / arch edge
5 Square / beam edge
6 Hexagon / beam edge
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Saddle Shapes
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Expo 64 LausanneArchitect: Saugey / SchierleEngineer: Froadvaux et Weber
26 restaurants featured regional cuisines Symbolized sailing and mountain peaks
Tensile structures Prof Schierle 27
Arch Shapes
1, 2 Single arch / edge cable
3, 4 Twin arch / edge cable
5 Twin arch / edge arch
6 Single arch / edge arch
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Arch Shapes
Tensile structures Prof Schierle 29
Skating rink MunichArchitect: AckermannEngineer: Schlaich / Bergermann
Prismatic steel truss arch, 100 m span Anticlastic cable nets Wood slats Translucent fabric
Tensile structures Prof Schierle 30
Wave Shapes
1 Ridge/valley cables,cable edge
2 Ridge/valley cables,beam edge
3 Ridge/valley beams,beam edge
4 Ridge beam/valley cablebeam edge
5 Ridge/valley cables,closed end
6 Ridge/valley cables,circular plan
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Wave Shapes
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Circular Wave Shapes
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Point Shapes1 Mast punctures fabric2 Radial cables
3 Ring with radial cables4 Loop cable
5 Dish top6 Eye cable
7 Twin mast rows8 Three mast rows
9 Suspension cables10 Supporting cables
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Point ShapesSea World Africa USAArchitect: SchierleEngineer: ASI
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German Pavilion Montreal Expo 67Architect: Rolf Gutbrod & Frei OttoEngineer: Leonhard & Andrea
Cable net of 75x75 cm meshes Translucent membrane
suspended from cable net
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Retractable roof Bad Hersfeld Architect: Frei Otto
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Design Process
Stretch fabric models
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Design Process computer models Cutting patterns by triangulation
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Erection
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Edge cablePrestress turn buckle
Fabric holder webbing
Details
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Balance Forces
Balanced Unbalanced
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Balance Forces
Balanced tension ring
UnbalancedTension ringrequirescostly footings
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Olympic facilities MunichArchitect: Guenter Behnisch / Frei OttoEngineer: Fritz Leonhard
Design competition model
Design metaphor:Spider web over landscape
Tensile structures Prof Schierle 45
Olympic Stadium MunichArchitect: Guenter BehnischEngineer: Leonhardt und Andrae
The roof consists of 7 saddle-shape cable nets Anticlastic curvature provides stability: Concave cables support gravity Convex cables resist wind uplift Cable net supported by:
Masts at rear Ring cable Flying buttress
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Stretch fabric model
Piano wire model
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Cable net of 75 cm (2.5 ft) square mesh(flat squares formed anticlastic rhomboids)
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Cable net lifted into space
Twin cables facilitate the deformation
Flat squares meshes deformed into rhomboids to assume anticlastic curvature
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Cable net assumed anticlastic shape
Anticlastic net with acrylic glass roof
Tensile structures Prof Schierle 50
Arena roof Translucent skin below cable net:
Two layers of translucent fabric 4 thermal insulation between fabric
Glass wall with cantilever trusses
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Swim arena
Point shape cable net (high and low points) Translucent skin below net consists of:
Two layers of translucent fabric 4 thermal insulation between fabric
External mast support
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Acrylic panels of 3x3m (10x10) with neoprene joints are supported by75x75 cm (2.5x2.5) net of twin cables
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Cable details
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Mast details
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Pneumatic
Air Supported Air InflatedFuji pavilion Osaka Expo 1970
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Pneumatic structure types:
Left: Air inflated
Right: Air supported
1 Air inflated cushion
2 Air inflated vault
3 Air inflated dome
4 Air inflated dome grid
5 Air supported dome
6 Air supported vault
7 Air supported vault with cables
8 Air supported dome grid
Tensile structures Prof Schierle 57
US Pavilion Expo Osaka (1970)Architect: Davis Brody Engineer: Geiger, Berger Size: 465 x 265 ft Steel cables Teflon-coated fiberglass fabric
Tensile structures Prof Schierle 58
Silverdome Pontiac, MI (1975)Architect: O'Dell Hewlett & Luckenbach Engineer: Geiger/Berger
Building data: Capacity: 90,000 Size: 770 x 600 Air pressure: 5 psf 10 - 75 hp fans 15 - 100 hp fans 50 revolving doors 93 pressure balance doors
Tensile structures Prof Schierle 59
Cable TrussG G Schierle & UC Berkeley students
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Cable trusses
1 Lintel trusses
2 Concave trusses
3 Lintel truss with compression braces
4 Lintel truss with compression struts
5 Concave truss with tension braces
6 Concave truss with tension struts
7 Concave/lintel truss with braces
8 Concave/lintel truss with struts
9 Gable truss with radial strut
10 Gable truss with center compression struts
11 Radial brace truss
12 Flat chord truss with compression struts
Tensile structures Prof Schierle 61
Auditorium Utica, NYArchitect: Gehron & SeltzerEngineer: Lev Zetlin
Tensile structures Prof Schierle 62
Olympic pool 4 multipurpose gyms Cable trusses, 120 span
Tensile structures Prof Schierle 63
Loyola University PavilionArchitect: Kahn, Kappe, Lottery, BoccatoEngineer: Reiss and Brown Consultant: Dr SchierleSpanning the long way provides openings to join outdoor seating for large events
Tensile structures Prof Schierle 64
Watts Tower CrescentArchitect: Ado / SchierleEngineer: ASI
Tensile structures Prof Schierle 65
Stadium roof Oldenburg, GermanyEngineer: Schlaich BergermannCable truss & anticlastic membrane panels
Tensile structures Prof Schierle 66
Tensile structures are fun