Tensile structures
Stayed
Tensile structures
Suspended
Anticlastic
Prof Schierle
Pneumatic
Trussed
1
Stayed
Tensile structures
Prof Schierle
McCormick exhibit hall Chicago
Architect/Engineer: SOM
To span railroad trucks underneath, the truss roof is
suspended by stay cables from concrete pylons.
1
Axon
2
Section
3
Center joint
4
Exterior joint
A Pylon top
B Stay cable
C Truss web bar
D Stay bracket
E Edge stay, resists wind uplift
Tensile structures
Prof Schierle
Imos factory, Newport, UK
Architect: Richard Rogers
Engineer: Anthony Hunt
Tensile structures
Prof Schierle
Patscenter Princeton
Architect: Richard Rogers
Engineer: Ove Arup
Stays resist both gravity load and wind uplift
Design alternates
Tensile structures
Prof Schierle
Lines meet = concentric joints
Renault Center Swindon, UK
Architect: Norman Foster
Tensile structures
Prof Schierle
Suspended
Golden Gate Bridge, photo courtesy Peter Craig
Tensile structures
Prof Schierle
Suspension span/sag ratios:
Small sag = large stress
Large sag = small stress but tall supports
Optimal span/sag ratio = 10
Tensile structures
Prof Schierle
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
Stability issues:
1 Point load deformation
2 Wind deformation
3 Stabilizing cable to resist wind uplift
4 Dead load to resist wind uplift
(increases seismic load)
6 US pavilion Expo 57, Brussels
Circular compression ring resists
lateral thrust effectively
Tensile structures
Prof Schierle
10
Oakland Coliseum (1967)
Architect: SOM
Engineer: Ammann and Whitney
Tensile structures
Prof Schierle
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
11
Tensile structures
Prof Schierle
12
Dulles Airport Terminal
Left:
Initial structure
Below: 1990 expansion
Tensile structures
Prof Schierle
13
Exhibit Hall Hanover
Architect: Thomas Herzog
Engineer: 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
14
Anticlastic
Anticlastic = saddle shape, inverse curvatures
Tensile structures
Prof Schierle
15
Minimal Surface
Tensile structures
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 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
Minimal surface vs. Hyperbolic Paraboloid
1
2
Minimal surface of square plan
Hyperbolic Paraboloid of square plan
Minimal surface of rhomboid plan
(membrane center below mid-height)
Hyperbolic Paraboloid of rhomboid plan
(membrane center at mid-height)
Prof Schierle
16
Anticlastic Surface
1 Opposing strings
stabilize a point in space
2 Several opposing strings
stabilize several points
3
Anticlastic curvature
stabilizes a membrane
Membrane shear
causes wrinkles in fabric
Stress without wrinkles
5
6
7
Tensile structures
Prof Schierle
HP-surface
Quadratic equation
Minimal surface
17
Test model
Fiber Orientation (Schierle, 1968)
1 Orthogonal (causes shear stress)
2 Principal curvature (avoids shear stress)
3 Principal curvature vs.
4 Generating lines
5 Principal curvature orientation (small deflections)
6 Generating line orientation (large deflections)
Lesson:
Orient fibers in principal curvature
Avoid generating line orientation
Tensile structures
Prof Schierle
18
Edge Conditions
1, 2 Edge Cable
3, 4 Edge Arch
5, 6 Edge Frame
Tensile structures
Prof Schierle
19
Edge Cable
Tensile structures
Prof Schierle
20
Edge Arch
Tensile structures
Prof Schierle
21
Edge Frame
Tensile structures
Prof Schierle
22
Surface Conditions
Tensile structures
Saddle shapes
Arch shapes
Wave shapes
Point shapes
Prof Schierle
23
Saddle Shapes
Tensile structures
Square / cable edge
Hexagon / cable edge
Square / arch edge
Oval / arch edge
Square / beam edge
Hexagon / beam edge
Prof Schierle
24
Saddle Shapes
Tensile structures
Prof Schierle
25
Expo 64 Lausanne
Architect: Saugey / Schierle
Engineer: Froadvaux et Weber
Tensile structures
26 restaurants featured regional cuisines
Symbolized sailing and mountain peaks
Prof Schierle
26
Arch Shapes
1, 2 Single arch / edge cable
3, 4 Twin arch / edge cable
Tensile structures
Twin arch / edge arch
Single arch / edge arch
Prof Schierle
27
Arch Shapes
Tensile structures
Prof Schierle
28
Skating rink Munich
Architect: Ackermann
Engineer: Schlaich / Bergermann
Tensile structures
Prof Schierle
Prismatic steel truss arch, 100 m span
Anticlastic cable nets
Wood slats
Translucent fabric
29
Wave Shapes
1
2
3
4
5
6
5
Tensile structures
Ridge/valley cables,
cable edge
Ridge/valley cables,
beam edge
Ridge/valley beams,
beam edge
Ridge beam/valley cable
beam edge
Ridge/valley cables,
closed end
Ridge/valley cables,
circular plan
Prof Schierle
30
Wave Shapes
Tensile structures
Prof Schierle
31
Circular Wave Shapes
Tensile structures
Prof Schierle
32
Point Shapes
1 Mast punctures fabric
2 Radial cables
3
4
Ring with radial cables
Loop cable
5
6
Dish top
Eye cable
7
8
Twin mast rows
Three mast rows
9 Suspension cables
10 Supporting cables
Tensile structures
Prof Schierle
33
Point Shapes
Sea World Africa USA
Architect: Schierle
Engineer: ASI
Tensile structures
Prof Schierle
34
Tensile structures
Prof Schierle
35
Engineer: Fritz Leonhard
Architect: Rolf Gutbrot / Frei Otto
German Pavilion, Montreal Expo 1967
German Pavilion Montreal Expo 67
Architect: Rolf Gutbrod & Frei Otto
Engineer: Leonhard & Andrea
Cable net of 75x75 cm meshes
Translucent membrane
suspended from cable net
Tensile structures
Prof Schierle
36
Retractable umbrellas Medina
Architect: Bodo Rush
Retractable roof Bad Hersfeld
Architect: Frei Otto
Tensile structures
Prof Schierle
37
Design Process
Stretch fabric models
Tensile structures
Prof Schierle
38
Design Process computer models Cutting patterns by triangulation
Tensile structures
Prof Schierle
39
Erection
Tensile structures
Prof Schierle
40
Details
Edge cable
Prestress turn buckle
Fabric holder webbing
Tensile structures
Prof Schierle
41
Balance Forces
Balanced
Tensile structures
Unbalanced
Prof Schierle
42
Balance Forces
Balanced tension ring
Unbalanced
Tension ring
requires
costly
footings
Tensile structures
Prof Schierle
43
Olympic facilities Munich
Architect: Guenter Behnisch / Frei Otto
Engineer: Fritz Leonhard
Design competition model
Design metaphor:
Spider web over landscape
Tensile structures
Prof Schierle
44
Olympic Stadium Munich
Architect: Guenter Behnisch
Engineer: 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
Tensile structures
Prof Schierle
45
Stretch fabric model
Piano wire model
Tensile structures
Prof Schierle
46
Tensile structures
edge cable soil anchor
edge cable
Cable net of 75 cm (2.5 ft) square mesh
(flat squares formed anticlastic rhomboids)
Prof Schierle
47
Cable net lifted into space
Flat squares meshes deformed into
rhomboids to assume anticlastic curvature
Twin cables facilitate the deformation
Tensile structures
Prof Schierle
48
Cable net assumed anticlastic shape
Anticlastic net with acrylic glass roof
Tensile structures
Prof Schierle
49
Arena roof
Translucent skin below cable net:
Two layers of translucent fabric
4 thermal insulation between fabric
Glass wall with cantilever trusses
Tensile structures
Prof Schierle
50
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
Tensile structures
Prof Schierle
51
Acrylic panels of 3x3m (10x10) with
neoprene joints are supported by
75x75 cm (2.5x2.5) net of twin cables
Tensile structures
Prof Schierle
52
Cable details
Tensile structures
Prof Schierle
53
Mast details
Tensile structures
Prof Schierle
54
Pneumatic
Air Inflated
Fuji pavilion Osaka Expo 1970
Air Supported
Tensile structures
Prof Schierle
55
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
Tensile structures
Prof Schierle
56
US 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
57
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
Tensile structures
Prof Schierle
58
Cable Truss
G G Schierle & UC Berkeley students
Tensile structures
Prof Schierle
59
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
Tensile structures
Prof Schierle
60
Auditorium Utica, NY
Architect: Gehron & Seltzer
Engineer: Lev Zetlin
Tensile structures
Prof Schierle
61
Olympic pool
4 multipurpose gyms
Cable trusses, 120 span
Tensile structures
Prof Schierle
62
Loyola University Pavilion
Architect: Kahn, Kappe, Lottery, Boccato
Engineer: Reiss and Brown
Consultant: Dr Schierle
Spanning the long way provides openings
to join outdoor seating for large events
Tensile structures
Prof Schierle
63
Watts Tower Crescent
Architect: Ado / Schierle
Engineer: ASI
Tensile structures
Prof Schierle
64
Stadium roof Oldenburg, Germany
Engineer: Schlaich Bergermann
Cable truss & anticlastic membrane panels
Tensile structures
Prof Schierle
65
Tensile structures are fun
Tensile structures
Prof Schierle
66
