Tensile structures Prof Schierle 1Tensi l e St r uc t ur esStayed Pneumatic Cable truss AnticlasticSuspendedTensile structures Prof Schierle 2St ayedTensile structures Prof Schierle 3McCormick 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 upliftTensile structures Prof Schierle 4Imos factory, Newport, UKArchitect: Richard Rogers Engineer: Anthony HuntTensile structures Prof Schierle 5Patscenter PrincetonArchitect: Richard RogersEngineer: Ove ArupStays resist both gravity load and wind upliftDesign alternates Lines meet = concentric jointsTensile structures Prof Schierle 6Renault Center Swindon, UKArchitect: Norman FosterTensile structures Prof Schierle 7Golden Gate Bridge, photo courtesy Peter Craig SuspendedTensile structures Prof Schierle 8Suspension span/sag ratios:Small sag = large stressLarge sag = small stress but tall supportsOptimal span/sag ratio = 10Tensile structures Prof Schierle 9New York bridges: George Washington Bridge, top Roebling Bridge, bottom & left (diagonal hangers resist deformation)http://en.wikipedia.org/wiki/John_A._RoeblingTensile structures Prof Schierle 10Stability 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, BrusselsCircular compression ring isefficient to resist lateral thrust 6Tensile structures Prof Schierle 11Oakland 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 seismic loadTensile structures Prof Schierle 12Tensile structures Prof Schierle 13Dulles Airport TerminalWashington, DC (1963)Architect: Eero SaarinenEngineer: Ammann & WhitneyInitial size: 150x600Height @ street side:105Height @ runway side: 65Roof features: Concrete deck Steel strands 1 Edge beams Pylons @ ~ 50 (lean back to counteract roof thrust)Tensile structures Prof Schierle 14 Dulles Airport Terminal Left:Initial structure Below:1990 expansionTensile structures Prof Schierle 15Lufthansa aircraft hanger, FrankfurtArchitect: Beckert & BeckertEngineer: Bomhard The maintenance hanger houses up tosix 747 jets in a 100x270 m area Pre-stressed suspended oncrete bands Linear skylights Only 10 m sag(span/depth ratio 13.5due to flight safety height limit) Inclined ballasts resist roof trust Straight strands restrain ballasts Tensile structures Prof Schierle 16Exhibit Hall HanoverArchitect: Thomas HerzogEngineer: Schlaich BergermannRoof 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 ofmullions due to roof deflectionTensile structures Prof Schierle 17Ant i c l ast i cAnticlastic = saddle shape, inverse curvaturesTensile structures Prof Schierle 18Anticlastic Surface1 Opposing strings stabilize a point in space2 Several opposing stringsstabilize several points3 Anticlastic curvaturestabilizes a membrane4 Membrane shear causes wrinkles in fabric5 Stress without wrinkles6 HP-surface Quadratic equation7 Minimal surfaceDifferential equationTensile structures Prof Schierle 19Minimal 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 Applicationhttp://link.springer.com/article/10.1007/BF00932303The 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 Paraboloid1 Minimal surfaceof squareplan2 HyperbolicParaboloidof squareplan3 Minimal surfaceof rhomboidplan(membranecenter belowmid-height)4 HyperbolicParaboloidof rhomboidplan(membrane center at mid-height) Tensile structures Prof Schierle 20Fiber 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 orientationTest modelTensile structures Prof Schierle 21Edge Conditions1, 2 Edge Cable3, 4 Edge Arch5, 6 Edge FrameTensile structures Prof Schierle 22Edge CableTensile structures Prof Schierle 23Edge ArchTensile structures Prof Schierle 24Edge FrameTensile structures Prof Schierle 25Surface Conditions Saddle shapes Arch shapes Wave shapes Point shapesTensile structures Prof Schierle 26Saddle Shapes1 Square / cable edge2 Hexagon / cable edge3 Square / arch edge4 Oval / arch edge5 Square / beam edge6 Hexagon / beam edgeTensile structures Prof Schierle 27Saddl e ShapesTensile structures Prof Schierle 28Expo 64 LausanneArchitect: Saugey / SchierleEngineer: Froadvaux et Weber 26 restaurants featured regional cuisines Symbolized sailing and mountain peaksTensile structures Prof Schierle 29Tensile structures Prof Schierle 30Arch Shapes1, 2 Single arch / edge cable3, 4Twin arch / edge cable5 Twin arch / edge arch6 Single arch / edge archTensile structures Prof Schierle 31Ar c h ShapesTensile structures Prof Schierle 32Skating rink MunichArchitect: AckermannEngineer: Schlaich / Bergermann Prismatic steel truss arch, 100 m span Anticlastic cable nets Wood slats Translucent fabricTensile structures Prof Schierle 33Wave Shapes1 Ridge/valley cables,cable edge2 Ridge/valley cables,beam edge3 Ridge/valley beams,beam edge4 Ridge beam/valley cablebeam edge5 Ridge/valley cables,closed end6 Ridge/valley cables,circular plan56Tensile structures Prof Schierle 34Wave ShapesTensile structures Prof Schierle 35Circular Wave ShapesTensile structures Prof Schierle 36Point Shapes1 Mast punctures fabric2 Radial cables3 Ring with radial cables4 Loop cable5 Dish top6 Eye cable7 Twin mast rows8 Three mast rows9 Suspension cables10 Supporting cablesTensile structures Prof Schierle 37Point ShapesSea World Africa USAArchitect: SchierleEngineer: ASITensile structures Prof Schierle 38German Pavilion, Montreal Expo 1967Architect: Rolf Gutbrot / Frei OttoEngineer: Fritz LeonhardTensile structures Prof Schierle 39German Pavilion Montreal Expo 67Architect: Rolf Gutbrod & Frei OttoEngineer: Leonhard & Andrea Cable net of 75x75 cm meshes Translucent membranesuspended from cable netTensile structures Prof Schierle 40Retractable roof Bad Hersfeld Architect: Frei OttoRetractable umbrellas Medina Architect: Bodo RushTensile structures Prof Schierle 41Desi gn Pr oc essStretch fabric modelsTensile structures Prof Schierle 42Desi gn Pr oc ess computer modelsCutting patterns by triangulationTensile structures Prof Schierle 43Desi gn opt i mi zat i onEdge and surface curvature(Schierle, 1971)Usual optimumL/f = 10L = spanf = sagLfTensile structures Prof Schierle 44Er ec t i onTensile structures Prof Schierle 45Edge cablePrestress turn buckleFabric holder webbingDet ai l sTensile structures Prof Schierle 46Balance ForcesBalanced UnbalancedTensile structures Prof Schierle 47Balance ForcesBalanced tension ringUnbalancedTension ringrequirescostly footingsTensile structures Prof Schierle 48Olympic facilities MunichArchitect: Guenter Behnisch / Frei OttoEngineer: Fritz LeonhardDesign competition modelDesign metaphor:Spider web over landscapeTensile structures Prof Schierle 49Olympic Stadium MunichArchitect: Guenter BehnischEngineer: Leonhardt und AndraeThe roof consists of 7 saddle-shape cable netsAnticlastic curvature provides stability: Concave cables support gravity Convex cables resist wind uplift Cable net supported by: Masts at rear Ring cable Flying buttressTensile structures Prof Schierle 50Stretch fabric modelPiano wire modelTensile structures Prof Schierle 51Cable net of 75 cm (2.5 ft) square mesh(flat squares formed anticlastic rhomboids)edge cableedge cable soil anchorTensile structures Prof Schierle 52Cable net lifted into spaceTwin cables facilitate the deformationFlat squares meshesdeformed into rhomboids to assume anticlastic curvatureTensile structures Prof Schierle 53Cable net assumed anticlastic shapeAnticlastic net with acrylic glass roofTensile structures Prof Schierle 54Arena roof Translucent skin below cable net: Two layers of translucent fabric 4 thermal insulation between fabric Glass wall with cantilever trussesTensile structures Prof Schierle 55Swim 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 supportTensile structures Prof Schierle 56Acrylic panels of 3x3m (10x10) with neoprene joints are supported by75x75 cm (2.5x2.5) net of twin cablesTensile structures Prof Schierle 57Cable detailsTensile structures Prof Schierle 58Mast detailsTensile structures Prof Schierle 59Pneumat i cAir SupportedAir InflatedFuji pavilion Osaka Expo 1970Tensile structures Prof Schierle 60Pneumatic structure types:Left: Air inflatedRight: Air supported1Air inflated cushion 2Air inflated vault3Air inflated dome 4Air inflated dome grid5Air supported dome 6Air supported vault7Air supported vault with cables8Air supported dome gridTensile structures Prof Schierle 61US 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 62Silverdome Pontiac, MI (1975)Architect: O'Dell Hewlett & Luckenbach Engineer: Geiger/BergerBuilding 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 doorsTensile structures Prof Schierle 63Cabl e Tr ussG G Schierle & UC Berkeley studentsTensile structures Prof Schierle 64Cable trusses1Lintel trusses2Concave trusses3Lintel truss with compression braces4Lintel truss with compression struts5Concave truss with tension braces6Concave truss with tension struts7Concave/lintel truss with braces8Concave/lintel truss with struts9 Gable truss with radial strut10 Gable truss with center compression struts11 Radial brace truss12 Flat chord truss with compression strutsTensile structures Prof Schierle 65Auditorium Utica, NYArchitect: Gehron & SeltzerEngineer: Lev ZetlinTensile structures Prof Schierle 66Cable truss test modelsLeft top: 2-way lintel trussLeft bottom: Flat trussBelow: Truss domeTensile structures Prof Schierle 67Fl atchor d t r uss l oad bear i ng mode1 Four-bay cable truss2 Polygon supporting P1, P23 Polygons supporting P1, P2, P3 4 Externally stabilized truss5 Internally stabilized trussTensile structures Prof Schierle 68 Olympic pool 4 multipurpose gyms Cable trusses, 120 spanTensile structures Prof Schierle 69Loyola University PavilionArchitect: Kahn, Kappe, Lottery, BoccatoEngineer: Reiss and Brown Consultant: DrSchierleSpanning the long way provides openings to join outdoor seating for large eventsTensile structures Prof Schierle 70Watts Tower CrescentArchitect: Ado / SchierleEngineer: ASITensile structures Prof Schierle 71Stadium roof Oldenburg, GermanyEngineer: Schlaich BergermannCable truss & anticlastic membrane panelsTensile structures Prof Schierle 72Tensi l e st r uc t ur es ar e f un