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Tensile Structure
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Tensile structures Copyright Prof Schierle 2012 1
Pneumatic TrussedAnticlasticStayed Suspended
Tensile structures
Tensile structures Copyright Prof Schierle 2012 2
Stayed
Tensile structures Copyright Prof Schierle 2012 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 Copyright Prof Schierle 2012 4
Imos factory, Newport, UKArchitect: Richard Rogers Engineer: Anthony Hunt
Tensile structures Copyright Prof Schierle 2012 5
Patscenter PrincetonArchitect: Richard RogersEngineer: Ove ArupStays resist both gravity load and wind uplift
Design alternates Lines meet = concentric joints
Tensile structures Copyright Prof Schierle 2012 6
Renault Center Swindon, UKArchitect: Norman Foster
Tensile structures Copyright Prof Schierle 2012 7
Golden Gate Bridge, photo courtesy Peter Craig
Suspended
Tensile structures Copyright Prof Schierle 2012 8
Suspension span/sag ratios:
Small sag = large stress
Large sag = small stress but tall supports
Optimal span/sag ratio = 10
Tensile structures Copyright Prof Schierle 2012 9
New York bridges:
George Washington Bridge, top
Brookline Bridge, bottom & left
(diagonal hangers resist deformation)
Tensile structures Copyright Prof Schierle 2012 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 Copyright Prof Schierle 2012 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 Copyright Prof Schierle 2012 12
Tensile structures Copyright Prof Schierle 2012 13
Dulles Airport Terminal Left: Initial structure Below: 1990 expansion
Tensile structures Copyright Prof Schierle 2012 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
Tensile structures Copyright Prof Schierle 2012 15
Anticlastic
Anticlastic = saddle shape, inverse curvatures
Tensile structures Copyright Prof Schierle 2012 16
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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)
Tensile structures Copyright Prof Schierle 2012 17
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
Tensile structures Copyright Prof Schierle 2012 18
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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Tensile structures Copyright Prof Schierle 2012 19
Edge Conditions
1, 2 Edge Cable
3, 4 Edge Arch
5, 6 Edge Frame
Tensile structures Copyright Prof Schierle 2012 20
Edge Cable
Tensile structures Copyright Prof Schierle 2012 21
Edge Arch
Tensile structures Copyright Prof Schierle 2012 22
Edge Frame
Tensile structures Copyright Prof Schierle 2012 23
Surface Conditions
Saddle shapes
Arch shapes
Wave shapes
Point shapes
Tensile structures Copyright Prof Schierle 2012 24
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
Tensile structures Copyright Prof Schierle 2012 25
Saddle Shapes
Tensile structures Copyright Prof Schierle 2012 26
Expo 64 LausanneArchitect: Saugey / SchierleEngineer: Froadvaux et Weber
26 restaurants featured regional cuisines Symbolized sailing and mountain peaks
Tensile structures Copyright Prof Schierle 2012 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
Tensile structures Copyright Prof Schierle 2012 28
Arch Shapes
Tensile structures Copyright Prof Schierle 2012 29
Skating rink MunichArchitect: AckermannEngineer: Schlaich / Bergermann
Prismatic steel truss arch, 100 m span Anticlastic cable nets Wood slats Translucent fabric
Tensile structures Copyright Prof Schierle 2012 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
5 6
Tensile structures Copyright Prof Schierle 2012 31
Wave Shapes
Tensile structures Copyright Prof Schierle 2012 32
Circular Wave Shapes
Tensile structures Copyright Prof Schierle 2012 33
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
Tensile structures Copyright Prof Schierle 2012 34
Point ShapesSea World Africa USAArchitect: SchierleEngineer: ASI
Tensile structures Copyright Prof Schierle 2012 35
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Tensile structures Copyright Prof Schierle 2012 36
German Pavilion Montreal Expo 67
Cable net of 75x75 cm meshes Translucent membrane
suspended from cable net
Tensile structures Copyright Prof Schierle 2012 37
Retractable roof Bad Hersfeld Architect: Frei Otto
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Tensile structures Copyright Prof Schierle 2012 38
Design Process
Stretch fabric models
Tensile structures Copyright Prof Schierle 2012 39
Design Process computer models Cutting patterns by triangulation
Tensile structures Copyright Prof Schierle 2012 40
Erection
Tensile structures Copyright Prof Schierle 2012 41
Edge cablePrestress turn buckle
Fabric holder webbing
Details
Tensile structures Copyright Prof Schierle 2012 42
Balance Forces
Balanced Unbalanced
Tensile structures Copyright Prof Schierle 2012 43
Balance Forces
Balanced tension ring
UnbalancedTension ringrequirescostly footings
Tensile structures Copyright Prof Schierle 2012 44
Olympic facilities MunichArchitect: Guenter Behnisch / Frei OttoEngineer: Fritz Leonhard
Design competition model
Design metaphor:Spider web over landscape
Tensile structures Copyright Prof Schierle 2012 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
Tensile structures Copyright Prof Schierle 2012 46
Stretch fabric model
Piano wire model
Tensile structures Copyright Prof Schierle 2012 47
Cable net of 75 cm (2.5 ft) square mesh(flat squares formed anticlastic rhomboids)
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Tensile structures Copyright Prof Schierle 2012 48
Cable net lifted into space
Twin cables facilitate the deformation
Flat squares meshes deformed into rhomboids to assume anticlastic curvature
Tensile structures Copyright Prof Schierle 2012 49
Cable net assumed anticlastic shape
Anticlastic net with acrylic glass roof
Tensile structures Copyright Prof Schierle 2012 50
Arena roof Translucent skin below cable net:
Two layers of translucent fabric 4 thermal insulation between fabric
Glass wall with cantilever trusses
Tensile structures Copyright Prof Schierle 2012 51
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
Tensile structures Copyright Prof Schierle 2012 52
Acrylic panels of 3x3m (10x10) with neoprene joints are supported by75x75 cm (2.5x2.5) net of twin cables
Tensile structures Copyright Prof Schierle 2012 53
Cable details
Tensile structures Copyright Prof Schierle 2012 54
Mast details
Tensile structures Copyright Prof Schierle 2012 55
Pneumatic
Air Supported Air InflatedFuji pavilion Osaka Expo 1970
Tensile structures Copyright Prof Schierle 2012 56
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 Copyright Prof Schierle 2012 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 Copyright Prof Schierle 2012 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 Copyright Prof Schierle 2012 59
Cable TrussG G Schierle & UC Berkeley students
Tensile structures Copyright Prof Schierle 2012 60
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 Copyright Prof Schierle 2012 61
Auditorium Utica, NYArchitect: Gehron & SeltzerEngineer: Lev Zetlin
Tensile structures Copyright Prof Schierle 2012 62
Olympic pool 4 multipurpose gyms Cable trusses, 120 span
Tensile structures Copyright Prof Schierle 2012 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 Copyright Prof Schierle 2012 64
Watts Tower CrescentArchitect: Ado / SchierleEngineer: ASI
Tensile structures Copyright Prof Schierle 2012 65
Stadium roof Oldenburg, GermanyEngineer: Schlaich BergermannCable truss & anticlastic membrane panels
Tensile structures Copyright Prof Schierle 2012 66
Tensile structures are fun