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Folded plate and cylindrical shell structures Prof Schierle 1
Folded Plate
ylindrical Shell Photo: Michael Bodycomb, 1977 Kimbell Art Museum, reproduced with permission
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Folded plate and cylindrical shell structures Prof Schierle 2
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1 Beam compression/tension
2 Buckling
3 Ribs resist buckling4 Edge buckling
5 Curbs resist edge buckling
Linear compositions
1 One-edge fold
2 Two-edge fold3 Twin fold
4 Folded roof and wall
Other compositions
1 Triangular unit / composition
2 Square unit / composition3 Hexagonal unit / composition
Folded Plate
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Structural action
1-3 Bending/shear patterns
4-5 Bending/shear stress
6-7 Buckling
8-9 Buckling resisting walls/ribs
Skylight integration
1 Slanted skylights
2 Top skylights
3 Vertical skylight
Examples
1 Shells with skylight ends
2 Shells cantilever from beam
3 Shells of two-way cantilever
ylindrical Shell
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Mining shelter Pomezia Italy
Architect: Renzo Piano
This shelter for sulfur mining was designed toallow 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 additional
Lighting as and view to the outside.
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Air forceChapel, ColoradoSprings
Architect/Engineer: SkidmoreOwingsandMerill
Theair forcechapel 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
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Portable exhibit hall
Architect/ Engineer: Santiago Calatrava
The roof and wall of foldedplate plywood was
designed for easy assemblage. The parabolicform implies constant bending stress.
Assume:
plywood glued to ribs
DL = 10 psfLL = 20 psf
= 30 psf
Uniform load
w = 30 psf x (50/12) w = 125 plf Bending moment
M = w L2/8 = 125x 412/8 M = 26,266 #
Moment of Inertia
I ~ (BD3-bd3)/36
I ~ (50x243-47.2x22.83)/36 I ~ 3360 in4
Top panel stress
(most relevant effects full top panel)
fb=M c1/I=26266x12x8/3360 fb = 750 psi
Extreme fiber stress @ bottomfb=M c2/I=26266x12x16/3360 fb = 1500 psi
L
=41
b=50
d=
24C1=8
C2=16
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Train station Savona, Italy
Architect: Antonio Nervi
Engineer: Pier Luigi Nervi
The 38x75mfolded plate roof provides column-free space
Inclined rebars resist longitudinal shear stress and
plate 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.
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Assume:
0.6 tendons, design load P=35k
DL=68psf (average)
LL=12psf
= 80psf
Uniform load per unit (see A-A)
w = 80 psf x7.5/1000 w = 0.6 klf
Reactions
Rl = 0.6x120x30/90 Rl = 24 kRr= 0.6x120x60/90 Rr= 48 k
X = Rll / w = 24/0.6 X = 40
Max. bending moment
Max. M = RaX/2 =24x40/2 M = 480 kZ = 0.8d ~0.8(6) z ~ 4.8
Tendon tension
T = M/Z = 480/4.8 T = 100 k
Number of tendons required
# = T/P= 100/35 =2.86Use 3 tendons 3 0.6
Note:
a Concrete compression block
d Effective depth (rebar center to top)Z Lever arm of resisting moment
L=90 C=30
w=0.6 klf
a
b=7.5
z=4.8
d=6
X=40
Section A-A
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Assume:
0.6 tendons, design load P=35k
DL=81psf (concrete+roofing)
LL=12psf
= 93psf
Uniform load per shell
w = 93 psf x21.5/1000 w = 2 klf
Max. bending (at mid support)M = w L2/12 = 2x712/12 M = 840 k
Lever arm
Z ~ 0.85 d ~ 0.85x7 Z ~ 6
Tendon tension
T = M / Z = 840 / 6 T = 140 k
Number of tendons required
# = T / P = 140 / 35 = 4
Use 4 tendons 4 0.6
Science & Industry Museum
Los AngelesArchitect: California State Architect Office
Engineer: T Y Lin
Zd
Concrete compression
Tendon tension
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Photos: Michael Bodycomb, 1977 Kimbell Art Museum, reproduced with permission
Kimbell Art Museum, Fort Worth
Architect: Louis Kahn
Engineer: 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 projectdaylight onto the cycloids
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Oceanographic Center ValenciaArchitect/Engineer: Santiago Calatrava
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Tempodrom Berlin 2001
Architect: GMP
Photo: Tomas Schmidt
Concrete folded plate, designed to
represent a tent, as the originaltent structure of 1980 it replaced
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Yokohama TerminalArchitect: Moussavi & Zaera-Polo
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Yokohama Terminal
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Industrial building in Villanueva, Honduras
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Factory in San Pedro Sula, Honduras
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Folded plate gymnasium roof
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Folded plate gymnasium cafeteria roof, two spans 50 & 60 feet
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Folded plate church roof/wall
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Folded plate roof
Church building. Designed as a folded plateconcrete shell, structurally this building can
be compared with the A-frame or the
3-hinged arch as the bending stiffnessapproaches zero at the apex and at
the supports. (Las Vegas, Nevada)
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Folded plate vault
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Folded plate dome
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Folded plate dome
Forcescale
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Forcescale
Assume: model concrete=original concrete
Geometric scale Sg=1:50
Em (steel wire) Em=30,000ksiEo (strand) Eo =22,000 ksi
Forcescale
Sf=(1/50)2 (Em/Eo) = (1/50)
2 (30/22) Sf=1:4167
3 tendons 0.6 70%metallic
3 tendonsA=3(.7)(0.3)2 A=0.5938 in2
Assumesinglewire inmodel
Equiv. original =2(0.5938/)0.5 =0.87 in
Model =0.87/50 =0.0174
Use model diameter = 0.02 in
Adjust force scale
Sf=(1/50)2
(0.2)/(0.174) Sf=1: 2175Original load
Po =0.6klf (120) Po =72,000#
Model load
Pm =Po / Sf=72,000 / 2175 Pm =33.1 #Use30cups, each33.1 / 30 Pcup =1.1#
L=90 C=30
w=0.6 klf
a
b=7.5
z=4.8
d=6
X=40
Section A-A
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Folded Plate
ylindrical Shell
Photo: Michael Bodycomb, 1977 Kimbell Art Museum, reproduced with permission
Study the cylindrical shell across the Rose Garden
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