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Tensile structures Copyright Prof Schierle 2012 1

Pneumatic TrussedAnticlasticStayed Suspended

Tensile structures


Stayed


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


Imos factory, Newport, UKArchitect: Richard Rogers Engineer: Anthony Hunt


Patscenter PrincetonArchitect: Richard RogersEngineer: Ove ArupStays resist both gravity load and wind uplift

Design alternates Lines meet = concentric joints


Renault Center Swindon, UKArchitect: Norman Foster


Golden Gate Bridge, photo courtesy Peter Craig

Suspended


Suspension span/sag ratios:

Small sag = large stress

Large sag = small stress but tall supports

Optimal span/sag ratio = 10


New York bridges:

George Washington Bridge, top

Brookline Bridge, bottom & left

(diagonal hangers resist deformation)


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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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


Dulles Airport Terminal Left: Initial structure Below: 1990 expansion


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


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)


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


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


Edge Cable


Edge Arch


Edge Frame


Surface Conditions

Saddle shapes

Arch shapes

Wave shapes

Point shapes


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


Saddle Shapes


Expo 64 LausanneArchitect: Saugey / SchierleEngineer: Froadvaux et Weber

26 restaurants featured regional cuisines Symbolized sailing and mountain peaks


Arch Shapes

1, 2 Single arch / edge cable

3, 4 Twin arch / edge cable

5 Twin arch / edge arch

6 Single arch / edge arch


Arch Shapes


Skating rink MunichArchitect: AckermannEngineer: Schlaich / Bergermann

Prismatic steel truss arch, 100 m span Anticlastic cable nets Wood slats Translucent fabric


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


Circular Wave Shapes


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


Point ShapesSea World Africa USAArchitect: SchierleEngineer: ASI


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German Pavilion Montreal Expo 67

Cable net of 75x75 cm meshes Translucent membrane

suspended from cable net


Retractable roof Bad Hersfeld Architect: Frei Otto

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Design Process

Stretch fabric models


Design Process computer models Cutting patterns by triangulation


Erection


Edge cablePrestress turn buckle

Fabric holder webbing

Details


Balance Forces

Balanced Unbalanced


Balance Forces

Balanced tension ring

UnbalancedTension ringrequirescostly footings


Olympic facilities MunichArchitect: Guenter Behnisch / Frei OttoEngineer: Fritz Leonhard

Design competition model

Design metaphor:Spider web over landscape


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


Stretch fabric model

Piano wire model


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


Cable net assumed anticlastic shape

Anticlastic net with acrylic glass roof


Arena roof Translucent skin below cable net:

Two layers of translucent fabric 4 thermal insulation between fabric

Glass wall with cantilever trusses


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


Acrylic panels of 3x3m (10x10) with neoprene joints are supported by75x75 cm (2.5x2.5) net of twin cables


Cable details


Mast details


Pneumatic

Air Supported Air InflatedFuji pavilion Osaka Expo 1970


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


US Pavilion Expo Osaka (1970)Architect: Davis Brody Engineer: Geiger, Berger Size: 465 x 265 ft Steel cables Teflon-coated fiberglass fabric


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


Cable TrussG G Schierle & UC Berkeley students


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


Auditorium Utica, NYArchitect: Gehron & SeltzerEngineer: Lev Zetlin


Olympic pool 4 multipurpose gyms Cable trusses, 120 span


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


Watts Tower CrescentArchitect: Ado / SchierleEngineer: ASI


Stadium roof Oldenburg, GermanyEngineer: Schlaich BergermannCable truss & anticlastic membrane panels


Tensile structures are fun