13-Folded Plate PPt Design Example

Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 1

Folded Plate

Cylindrical ShellPhoto: Michael Bodycomb, 1977 Kimbell Art Museum, reproduced with permission


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1 Beam compression/tension2 Buckling 3 Ribs resist buckling4 Edge buckling5 Curbs resist edge buckling

Linear compositions1 One-edge fold2 Two-edge fold3 Twin fold4 Folded roof and wall

Other compositions1 Triangular unit / composition 2 Square unit / composition 3 Hexagonal unit / composition

Folded Plate


Structural action1-3 Bending/shear patterns4-5 Bending/shear stress6-7 Buckling 8-9 Buckling resisting walls/ribs

Skylight integration1 Slanted skylights2 Top skylights3 Vertical skylight

Examples1 Shells with skylight ends2 Shells cantilever from beam3 Shells of two-way cantilever

Cylindrical Shell


Mining shelter Pomezia ItalyArchitect: Renzo Piano

This shelter for sulfur mining was designed to allow moving it along with mining progress.

A folded plate vault of reinforced polyester provides light weight to facilitate movement.

Folding thin sheets of polyester provides strength, stiffness, and stability with minimum weight.

Translucent polyester also provides natural lightingto save energy.

Triangular windows at the base provide additionalLighting as and view to the outside.


Air force Chapel, Colorado SpringsArchitect/Engineer: Skidmore Owings and Merill

The air force chapel features: A folded plate of tubular steel A dramatic space of vertical dominance Two inclined triple tetrahedrons Concrete buttresses support gravity load and

lateral thrust The tetrahedrons are glad with aluminum Stain glass windows close gaps between

tetrahedrons


Portable exhibit hallArchitect/ Engineer: Santiago Calatrava

The roof and wall of folded plate plywood wasdesigned for easy assemblage. The parabolicform implies constant bending stress.Assume: plywood glued to ribsDL = 10 psfLL = 20 psf = 30 psf

Uniform loadw = 30 psf x (50/12) w = 125 plfBending momentM = w L2/8 = 125x 412/8 M = 26,266 #Moment of InertiaI ~ (BD3-bd3)/36 I ~ (50x243-47.2x22.83)/36 I ~ 3360 in4Top panel stress (most relevant effects full top panel)fb=M c1/I=26266x12x8/3360 fb = 750 psiExtreme fiber stress @ bottomfb=M c2/I=26266x12x16/3360 fb = 1500 psi

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Train station Savona, ItalyArchitect: Antonio NerviEngineer: Pier Luigi Nervi

The 38x75m folded plate roof provides column-free spaceInclined rebars resist longitudinal shear stress andplate bending stress.Folded plates stabilize adjacent plates against buckling.Tendons at the folded plate base resist bending stress.Tendons on top resist overhang bending stress.


Assume:0.6 tendons, design load P = 35 kDL = 68 psf (average)LL = 12 psf = 80 psfUniform load per unit (see A-A)w = 80 psf x7.5/1000 w = 0.6 klfReactionsRl = 0.6x120x30/90 Rl = 24 kRr = 0.6x120x60/90 Rr = 48 kX = Rll / w = 24/0.6 X = 40Max. bending momentMax. M = RaX/2 =24x40/2 M = 480 kZ = 0.8d ~0.8(6) z ~ 4.8 Tendon tensionT = M/Z = 480/4.8 T = 100 kNumber of tendons required# = T/P= 100/35 =2.86Use 3 tendons 3 0.6Note:a Concrete compression blockd Effective depth (rebar center to top) Z Lever arm of resisting moment

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Section A-A


Assume:0.6 tendons, design load P = 35 kDL = 81 psf (concrete + roofing)LL = 12 psf = 93 psfUniform load per shellw = 93 psf x21.5/1000 w = 2 klfMax. bending (at mid support)M = w L2/12 = 2x712/12 M = 840 kLever arm Z ~ 0.85 d ~ 0.85x7 Z ~ 6Tendon tensionT = M / Z = 840 / 6 T = 140 kNumber of tendons required# = T / P = 140 / 35 = 4Use 4 tendons 4 0.6

Science & Industry MuseumLos AngelesArchitect: California State Architect OfficeEngineer: T Y Lin

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Concrete compression

Tendon tension


Photos: Michael Bodycomb, 1977 Kimbell Art Museum, reproduced with permission

Kimbell Art Museum, Fort WorthArchitect: Louis KahnEngineer: Kommendant

The Kimbell Art Museum features: Recessed main entrance Two gallery wings, one on each side of entry Atriums within gallery wings 16 modules, 30x100 each Cycloid cross-sections (point on moving wheel) Post-tensioned cast-in-place concrete Inverted Us between cycloids for ducts & pipes Linear skylight with deflectors to project

daylight onto the cycloids


Oceanographic Center ValenciaArchitect/Engineer: Santiago Calatrava


Tempodrom Berlin 2001Architect: GMP

Photo: Tomas Schmidt

Concrete folded plate, designed torepresent a tent, as the original tent structure of 1980 it replaced


Yokohama TerminalArchitect: Moussavi & Zaera-Polo


Yokohama Terminal


Industrial building in Villanueva, Honduras


Factory in San Pedro Sula, Honduras


Folded plate gymnasium roof


Folded plate gymnasium cafeteria roof, two spans 50 & 60 feet


Folded plate church roof/wall


Folded plate roof

Church building. Designed as a folded plate concrete shell, structurally this building can be compared with the A-frame or the 3-hinged arch as the bending stiffness approaches zero at the apex and at the supports. (Las Vegas, Nevada)


Folded plate vault


Folded plate dome


Force scaleAssume: model concrete = original concreteGeometric scale Sg= 1:50Em (steel wire) Em= 30,000ksiEo (strand) Eo = 22,000 ksiForce scaleSf = (1/50)2 (Em/Eo) = (1/50)2 (30/22) Sf = 1:41673 tendons 0.6 70% metallic3 tendons A = 3(.7)(0.3)2 A = 0.5938 in2Assume single wire in modelEquiv. original = 2(0.5938/)0.5 = 0.87 inModel = 0.87/50 = 0.0174Use model diameter = 0.02 inAdjust force scaleSf = (1/50)2 (0.2)/(0.174) Sf = 1: 2175Original loadPo = 0.6 klf (120) Po =72,000 #Model loadPm = Po / Sf = 72,000 / 2175 Pm = 33.1 #Use 30 cups, each 33.1 / 30 Pcup = 1.1 #

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Section A-A


Folded Plate

Cylindrical ShellPhoto: Michael Bodycomb, 1977 Kimbell Art Museum, reproduced with permission

Study the cylindrical shell across the Rose Garden

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13-Folded Plate PPt Design Example