Tensile Structures. Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 1
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1 Tensile Structures Stayed Suspended Anticlastic Pneumatic Cable truss Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 1
2 Stayed Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 2
3 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 Copyright G G Schierle, Press Esc to end, for next, for previous slide 3
4 Imos factory, Newport, UK Architect: Richard Rogers Engineer: Anthony Hunt Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 4
5 Patscenter Princeton Architect: Richard Rogers Engineer: Ove Arup Stays resist both gravity load and wind uplift Design alternates Lines meet = concentric joints Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 5
6 Renault Center Swindon, UK Architect: Norman Foster Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 6
7 Suspended Golden Gate Bridge, photo courtesy Peter Craig Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 7
8 Suspension span/sag ratios: Small sag = large stress Large sag = small stress but tall supports Optimal span/sag ratio = 10 Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 8
9 New York bridges: George Washington Bridge, top Brookline Bridge, bottom & left (diagonal hangers resist deformation) Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 9
10 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 is efficient to resist lateral thrust 6 Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 10
11 Oakland Coliseum (1967) Architect: SOM Engineer: 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 load Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 11
12 Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 12
13 Dulles Airport Terminal Washington, DC (1963) Architect: Eero Saarinen Engineer: Ammann & Whitney Initial size: 150 x600 street side: 105 runway side: 65 Roof features: Concrete deck Steel strands φ 1 Edge beams ~ 50 (lean back to counteract roof thrust) Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 13
14 Dulles Airport Terminal Left: Initial structure Below: 1990 expansion Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 14
15 Lufthansa aircraft hanger, Frankfurt Architect: Beckert & Beckert Engineer: Bomhard The maintenance hanger houses up to six 747 jets in a 100x270 m area Pre-stressed suspended oncrete bands Linear skylights Only 10 m sag (span/depth ratio 13.5 due to flight safety height limit) Inclined ballasts resist roof trust Straight strands restrain ballasts Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 15
16 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 Copyright G G Schierle, Press Esc to end, for next, for previous slide 16
17 Anticlastic Anticlastic = saddle shape, inverse curvatures Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 17
18 Anticlastic Surface 1 Opposing strings stabilize a point in space 2 Several opposing strings stabilize several points 3 Anticlastic curvature stabilizes a membrane 4 Membrane shear causes wrinkles in fabric 5 Stress without wrinkles 6 HP-surface Quadratic equation 7 Minimal surface Differential equation Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 18
19 Minimal Surface Criteria: Minimum surface area Equal stress throughout Equal curvature at any point Governing Equations (Schierle 1977*) F1/F2 = A/B Y = F1(X/S1) K/F1 + X tan φ Y = F2(Z/S2) K/F2 * First published in Journal of Optimization Theory and Applications, September 1977 Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 19
20 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 Test model Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 20
21 Edge Conditions 1, 2 Edge Cable 3, 4 Edge Arch 5, 6 Edge Frame Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 21
22 Edge Cable Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 22
23 Edge Arch Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 23
24 Edge Frame Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 24
25 Surface Conditions Saddle shapes Arch shapes Wave shapes Point shapes Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 25
26 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 Copyright G G Schierle, Press Esc to end, for next, for previous slide 26
27 Saddle Shapes Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 27
28 Expo 64 Lausanne Architect: Saugey / Schierle Engineer: Froadvaux et Weber 26 restaurants featured regional cuisines Symbolized sailing and mountain peaks Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 28
29 Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 29
30 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 Copyright G G Schierle, Press Esc to end, for next, for previous slide 30
31 Arch Shapes Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 31
32 Skating rink Munich Architect: Ackermann Engineer: Schlaich / Bergermann Prismatic steel truss arch, 100 m span Anticlastic cable nets Wood slats Translucent fabric Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 32
33 Wave Shapes 1 Ridge/valley cables, cable edge 2 Ridge/valley cables, beam edge 3 Ridge/valley beams, beam edge 4 Ridge beam/valley cable beam edge Ridge/valley cables, closed end 6 Ridge/valley cables, circular plan Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 33
34 Wave Shapes Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 34
35 Circular Wave Shapes Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 35
36 Point Shapes 1 Mast punctures fabric 2 Radial cables 3 Ring with radial cables 4 Loop cable 5 Dish top 6 Eye cable 7 Twin mast rows 8 Three mast rows 9 Suspension cables 10 Supporting cables Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 36
37 Point Shapes Sea World Africa USA Architect: Schierle Engineer: ASI Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 37
38 German Pavilion, Montreal Expo 1967 Architect: Rolf Gutbrot / Frei Otto Engineer: Fritz Leonhard Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 38
39 German Pavilion Montreal Expo 67 Cable net of 75x75 cm meshes Translucent membrane suspended from cable net Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 39
40 Retractable roof Bad Hersfeld Architect: Frei Otto Retractable umbrellas Riyadh Architect: Bodo Rush Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 40
41 Design Process Stretch fabric models Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 41
42 Design Process computer models Cutting patterns by triangulation Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 42
43 Design optimization Edge and surface curvature (Schierle, 1971) Usual optimum L/f = 10 L = span f = sag L f Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 43
44 Erection Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 44
45 Details Edge cable Prestress turn buckle Fabric holder webbing Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 45
46 Balance Forces Balanced Unbalanced Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 46
47 Balance Forces Balanced tension ring Unbalanced Tension ring requires costly footings Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 47
48 Olympic facilities Munich Architect: Guenter Behnisch / Frei Otto Engineer: Fritz Leonhard Design competition model Design metaphor: Spider web over landscape Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 48
49 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 Copyright G G Schierle, Press Esc to end, for next, for previous slide 49
50 Stretch fabric model Piano wire model Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 50
51 Cable net of 75 cm (2.5 ft) square mesh (flat squares formed anticlastic rhomboids) edge cable edge cable soil anchor Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 51
52 Cable net lifted into space Flat squares meshes deformed into rhomboids to assume anticlastic curvature Twin cables facilitate the deformation Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 52
53 Cable net assumed anticlastic shape Anticlastic net with acrylic glass roof Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 53
54 Arena roof Translucent skin below cable net: Two layers of translucent fabric 4 thermal insulation between fabric Glass wall with cantilever trusses Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 54
55 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 Copyright G G Schierle, Press Esc to end, for next, for previous slide 55
56 Acrylic panels of 3x3m (10 x10 ) with neoprene joints are supported by 75x75 cm (2.5 x2.5 ) net of twin cables Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 56
57 Cable details Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 57
58 Mast details Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 58
59 Pneumatic Air Supported Air Inflated Fuji pavilion Osaka Expo 1970 Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 59
60 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 Copyright G G Schierle, Press Esc to end, for next, for previous slide 60
61 US Pavilion Expo Osaka (1970) Architect: Davis Brody Engineer: Geiger, Berger Size: 465 x 265 ft Steel cables Teflon-coated fiberglass fabric Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 61
62 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 hp fans hp fans 50 revolving doors 93 pressure balance doors Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 62
63 Cable Truss G G Schierle & UC Berkeley students Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 63
64 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 Copyright G G Schierle, Press Esc to end, for next, for previous slide 64
65 Auditorium Utica, NY Architect: Gehron & Seltzer Engineer: Lev Zetlin Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 65
66 Cable truss test models Left top: Left bottom: Below: 2-way lintel truss Flat truss Truss dome Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 66
67 Flat chord truss load bearing mode 1 Four-bay cable truss 2 Polygon supporting P1, P2 3 Polygons supporting P1, P2, P3 4 Externally stabilized truss 5 Internally stabilized truss Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 67
68 Olympic pool 4 multipurpose gyms Cable trusses, 120 span Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 68
69 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 Copyright G G Schierle, Press Esc to end, for next, for previous slide 69
70 Watts Tower Crescent Architect: Ado / Schierle Engineer: ASI Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 70
71 Stadium roof Oldenburg, Germany Engineer: Schlaich Bergermann Cable truss & anticlastic membrane panels Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 71
72 Tensile structures are fun Tensile structures Copyright G G Schierle, Press Esc to end, for next, for previous slide 72
Type of Force 1 Axial (tension / compression) Shear. 3 Bending 4 Torsion 5 Images 6 Symbol (+ -)
Cause: external force P Force vs. Stress Effect: internal stress f 05 Force vs. Stress Copyright G G Schierle, 2001-05 press Esc to end, for next, for previous slide 1 Type of Force 1 Axial (tension /
Thermal Stress & Strain. 07 Thermal Stress and Strain Copyright G G Schierle, 2001-05 press Esc to end, for next, for previous slide 3
Thermal Stress & Strain 07 Thermal Stress and Strain Copyright G G Schierle, 2001-05 press Esc to end, for next, for previous slide 3 Thermal Stress & Strain 07 Thermal Stress and Strain Copyright G G
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