04 Tensile

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Tensile Structure

Text of 04 Tensile

  • Tensile structures Copyright Prof Schierle 2012 1

    Pneumatic TrussedAnticlasticStayed Suspended

    Tensile structures

  • Tensile structures Copyright Prof Schierle 2012 2

    Stayed

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    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

  • 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

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    Renault Center Swindon, UKArchitect: Norman Foster

  • Tensile structures Copyright Prof Schierle 2012 7

    Golden Gate Bridge, photo courtesy Peter Craig

    Suspended

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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

    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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    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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  • 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

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    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)

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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

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    Edge Conditions

    1, 2 Edge Cable

    3, 4 Edge Arch

    5, 6 Edge Frame

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    Edge Cable

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    Edge Arch

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    Edge Frame

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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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    Saddle Shapes

  • Tensile structures