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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

  • Tensile structures Prof Schierle 9

    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

    6

  • 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

  • Tensile structures Prof Schierle 15

    Anticlastic

    Anticlastic = saddle shape, inverse curvatures

  • Tensile structures Prof Schierle 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 Prof Schierle 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 Prof Schierle 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 Prof Schierle 19

    Edge Conditions

    1, 2 Edge Cable

    3, 4 Edge Arch

    5, 6 Edge Frame

  • Tensile structures Prof Schierle 20

    Edge Cable

  • Tensile structures Prof Schierle 21

    Edge Arch

  • Tensile structures Prof Schierle 22

    Edge Frame

  • Tensile structures Prof Schierle 23

    Surface Conditions

    Saddle shapes

    Arch shapes

    Wave shapes

    Point shapes

  • Tensile structures Prof Schierle 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 Prof Schierle 25

    Saddle Shapes

  • Tensile structures Prof Schierle 26

    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

  • Tensile structures Prof Schierle 28

    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

    5 6

  • Tensile structures Prof Schierle 31

    Wave Shapes

  • Tensile structures Prof Schierle 32

    Circular Wave Shapes

  • Tensile structures Prof Schierle 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 Prof Schierle 34

    Point ShapesSea World Africa USAArchitect: SchierleEngineer: ASI

  • Tensile structures Prof Schierle 35