Tensile structures Pneumatic Trussed Anticlastic Stayed Suspended Tensile structures
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Transcript of Tensile structures Pneumatic Trussed Anticlastic Stayed Suspended Tensile structures
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
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Imos factory, Newport, UKArchitect: Richard Rogers Engineer: Anthony Hunt
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Patscenter PrincetonArchitect: Richard RogersEngineer: Ove ArupStays resist both gravity load and wind uplift
Design alternates Lines meet = concentric joints
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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
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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
6
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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
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• Dulles Airport Terminal• Left: Initial structure • Below: 1990 expansion
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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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Min
imal
Su
rfac
eMinimal 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
Test
mod
el
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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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Expo 64 LausanneArchitect: Saugey / SchierleEngineer: Froadvaux et Weber
• 26 restaurants featured regional cuisines• Symbolized sailing and mountain peaks
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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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Skating rink MunichArchitect: AckermannEngineer: Schlaich / Bergermann
• Prismatic steel truss arch, 100 m span• Anticlastic cable nets• Wood slats• Translucent fabric
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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
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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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Ge
rma
n P
avi
lion
, M
on
tre
al
Exp
o 1
967
Arch
itect:
Rolf
Gutb
rot /
Frei
Otto
Engin
eer:
Fritz
Leon
hard
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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
Retra
ctable
umbr
ellas
Med
ina
A
rchite
ct: B
odo R
ush
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Design Process computer models Cutting patterns by triangulation
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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
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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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Cable net of 75 cm (2.5 ft) square mesh(flat squares formed anticlastic rhomboids)
edge
cable
edge
cable
soil a
ncho
r
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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
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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 (10’x10’) with neoprene joints are supported by75x75 cm (2.5’x2.5’) net of twin cables
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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
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US Pavilion Expo Osaka (1970)Architect: Davis Brody Engineer: Geiger, Berger• Size: 465 x 265 ft• Steel cables• Teflon-coated fiberglass fabric
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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
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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
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Auditorium Utica, NYArchitect: Gehron & SeltzerEngineer: Lev Zetlin
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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
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Stadium roof Oldenburg, GermanyEngineer: Schlaich BergermannCable truss & anticlastic membrane panels