1Prof. G G Schierle, PhD, FAIADesign of Fabric StructuresSession T33, Thursday, 04/30, 2 – 3:30 PMAcknowledgements/CreditsThis presentation includes book excerpts ofStructure and Designhttp://www.universityreaders.com/titles/schierle/Design of Fabric StructuresSaddle shapeWave shapeArch shapePont shape2Anticlastic Stability• Two stressed strings stabilize a point in space• Two sets of strings form a stable surface• Without prestress, convex fiber gets slack, causing instability• Flat fiber deform greatly under load, causing instability• Triangular panels are flat & unstable (AVOID)Prestress Prestress (PS) effect on a stringF = force, P = load,  = deflection 1 Without prestress top link resists all Assume:  = 12 With prestress  = 1/2Top link increase: F=PS+P/2Lower link decrease: F=PS–P/23 Stress / strain diagram f/A without prestressB with prestressC Prestress reduced to PS = 0D Prestressed string after PS = 0Cable nets need about 50% prestressFabric structures need about 30% prestresshttp://www-classes.usc.edu/architecture/structures/papers/GGS-Yin.pdfMinimal SurfaceCriteria:• Minimum surface area• Equal stress throughout• Equal +- curvature at any pointGoverning Equations (Schierle 1977*)*First published 1977 inJournal of Optimization Theory and ApplicationsF1/F2 = A/BY = F1(X/S1)K/F1+ X tan Y = F2(Z/S2)K/F2K= F1+F233: small deflection Principal curvature 4: large deflection Straight generating lineFiber orientationGood Flawed Fabric PropertiesType Makeup Common use Tensile strengthCoated fabric*Polyester fabric PVC coatingPermanent + mobile Internal + external40 to 200 kN/m228 to 1142 lb/inCoated fabric* Glass fiber fabric PTFE coatingPermanentInternal + external20 to 160 kN/m114 to 914 lb/inCoated fabric Glass fiber fabricSilicone coatingPermanentInternal + external20 to 100 kN/m114 to 571 lb/inLaminated fabric* Fine mesh fabricLaminated with PTFE filmPermanent Internal + external50 to 100 kN/m286 to 571 lb/inFoil PVC foil Permanent internalTemporary external6 to 40 kN/m34 to 228 lb/inFoil* Flouro-polymer foilETFEPermanentInternal + external6 to 12 kN/m34 to 69 lb/inCoated or uncoated fabric*PTFE fabric(good qualities for sustainability)Permanent + mobileInternal + external40 to 100 kN/m228 to 571 lb/inCoated or uncoated fabric*Flouro-polymer fabricPermanent + mobileInternal + external8 to 20 kN/m46 to 114 lb/in* Self-cleaning Fire rating++ incombustible+ low flammability0 noneUV light resistance++ very good+ goodTranslucency Durability+ + 0 to 25 % 15 to 20 years++ ++ 4 to 22 % > 25 years++ ++ 10 to 20 % > 20 years++ ++ 35 to 55 % > 25 years0 + Up to 90 % 15 to 20 yearsinternally++ ++ Up to 96 % > 25 years++ ++ 15 to 40 % > 25 years++ ++ Up to 90 % > 25 yearsMaximum spansAssuming:Live load LL = 20 psfSafety factor Sf = 4Span/sag ratio L/f = 10Fabric breaking strength Max. span600 pli (lb/in) ~ 60 ft800 pli (lb/in) ~ 80 ftDesign stress (tensile strength / 4)Tensile strength Design stress400 pli 100 pli600 pli 150 pli800 pli 200 pliCosts Type Cost / sq. ftPrefab PVC $15 to $20Custom PVC $30 to $60PTFE Teflon-coated fiberglass $60 to $180Note: costs exclude foundationsStructure4RLRRHTRTLW= w Lwh RLRRL/2L f f HSymmetric suspensionHorizontal reaction H = w L2/(8f)Vertical reaction R = w L/2Max fabric tension T = 1.35 w LAsymmetric suspensionVector methodTotal load W = w LFabric tensions TRTLHorizontal reaction HVertical reactions RLRRwDesign / AnalysisRadial loadEdge cable tension T = R pLateral LoadSeismic (not critical)V = Cs WV = seismic base shearCs = Seismic coefficient W = mass (dead load)Example (V / ft2, Cs = 0.2, w = 1 psf)V = 0.2 x1 V = 0.2 psfLDG: Lateral Design Graph Sample: 100’ x 50’ x 20’Wind (critical)Velocity• 90 mph (most USA)• 150 mph (Golf coast)Gust factors (G= 0.85 for rigid structures)G ~ 1.5 for fabric structuresExample (V per ft2, p = 20 psf)V = p G = 20 x 1.5 V = 30 psfAcoustics• Thin fabric provides little sound insulation • Micro-perforated foils absorb sound(suspended under structural fabric) • Form may be used to control acoustics• Anticlastic forms disperse sound• Synclastic forms focus soundLightingDaylight sunny days ~75000 luxDaylight overcast ~25000 lux10% translucent fabric ~2500 - 7500 luxTypical office lighting ~1000 luxThermalWhile fabric has low R-valuesThermal reflection is very good5Surface conditionsPoint shape Arch shape Wave shape Saddle shape Edge conditionsEdge beam Edge arch Edge cableEdge ConditionsEdge Cable (tension)Edge Arch (compression)Edge Beam (bending)UCB CanopyStage canopyEdge Cable – tension6Raleigh Arena North Carolina (1953)Architect: Novicki and DeitrickEngineer: Severud Elstad KruegerEdge arch / cable roofEFL portable classroom (1968)Architect: G G SchierleEngineer: Nick ForellEdge arch / anticlastic Fabric Sony Center BerlinArchitect: Helmut JahnEngineer: Ove ArupEdge ring / radial cables and fabricEdge Arch / Ring – compression Horticultural CenterGallaway Gardens, GeorgiaBy ODC Dining Pavilion Saddlebrook FloridaBy Helios IndustriesNote:Edge beams facilitate groupings Edge Beam – bending Saddle shapes Wave shapesSurface conditions7Arch shapesStayed Masts Dish Ring PuncturePropped Masts Eye Loop Radial Point shapesSaddle shapesExpo ‘64 LausanneArchitect: Saugey / SchierleEngineer: Froidevaux et Weber26 restaurant pavilions: - Featured Swiss regional cuisines- Symbolizing sailing and mountains8L=120’ f=12’AABBSection B-BDesign exampleAssume:Wind pressure p = 30 psfAllowable fabric stress Fa= 200 pliAvailable canvass stress Fa= 50 pliWind load (normal to fabric) T = p R = (30)(100) T = 3000 #Fabric stress per inch f = 3000/12 f = 250 pliFabric NOT OK 250 > 200 > 50Cable net was required Assume: Same allowable stressGravity load w = 20 psfGraphic methodTotal LoadW = w L = 20 (120’) W = 2400 #Horizontal reaction H = 3000 #Vertical reaction RL= 2400 #Fabric tension T T = 3720 #Fabric stress (#/in)f = 3720#/12” f = 310 pliGravity load not OK 310>200>50Cable net was requiredL=120’ f=12’AABBh=40’HRLfRL=2400#H=3000#W= 2400#T=3720#w = 20 psf9Wave shapes Computer modelSan Diego Convention CenterArchitect: Arthur EricksonEngineer: Horst BergerFabric design: Horst BergerConcrete pylons at 60’ supportridge, valley, and guy cables thatspan 300’ between pylonsTranslucent