Folded Plate
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 2
Fo
lded Plate
1 Beam compression/tension
2 Buckling
3 Ribs resist buckling
4 Edge buckling
5 Curbs resist edge buckling
Linear compositions
1 One-edge fold
2 Two-edge fold
3 Twin fold
4 Folded roof and wall
Other compositions
1 Triangular unit / composition
2 Square unit / composition
3 Hexagonal unit / composition
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 4
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
Mining shelter Pomezia Italy
Architect: 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 lighting
to save energy.
Triangular windows at the base provide additional
Lighting as and view to the outside.
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 6
Air force Chapel, Colorado Springs
Architect/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
Portable exhibit hall
Architect/ Engineer: Santiago Calatrava
The roof and wall of folded plate plywood was
designed for easy assemblage. The parabolic
form implies constant bending stress.
Assume:
½” plywood glued to ribs
DL = 10 psf
LL = 20 psf
= 30 psf
Uniform load
w = 30 psf x (50”/12)
w = 125 plf
Bending moment
M = w L
2
/8 = 125x 41
2
/8 M = 26,266 #’
Moment of Inertia
I ~ (BD
3
-bd
3
)/36
I ~ (50x24
3
-47.2x22.8
3
)/36 I ~ 3360 in
4
Top panel stress
(most relevant effects full top panel)
f
b
=M c1/I=26266x12x8/3360 f
b
= 750 psi
Extreme fiber stress @ bottom
f
=M c2/I=26266x12x16/3360 f
= 1500 psi
L=41’
b=50”
d=24”
C1=8”
C2=16”
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 8
Train station Savona, Italy
Architect: Antonio Nervi
Engineer: Pier Luigi Nervi
The 38x75m folded 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.
Assume:
0.6”
tendons, design load
P = 35 k
DL = 68 psf (average)
LL = 12 psf
= 80 psf
Uniform load per unit (see A-A)
w = 80 psf x7.5’/1000
w = 0.6 klf
Reactions
R
l
= 0.6x120x30/90
R
l
= 24 k
R
r
= 0.6x120x60/90
R
r
= 48 k
X = R
ll
/ w = 24/0.6
X = 40’
Max. bending moment
Max. M = R
a
X/2 =24x40/2
M = 480 k’
Z = 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 =2.86
Use 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
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 10
Assume:
0.6”
tendons, design load
P = 35 k
DL = 81 psf (concrete + roofing)
LL = 12 psf
= 93 psf
Uniform load per shell
w = 93 psf x21.5’/1000
w = 2 klf
Max. bending (at mid support)
M = w L
2
/12 = 2x71
2
/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 Angeles
Architect: California State Architect Office
Engineer: T Y Lin
Z
d
Concrete compression
Tendon tension
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, 30’x100’ each
• Cycloid cross-sections (point on moving wheel)
• Post-tensioned cast-in-place concrete
• Inverted U’s between cycloids for ducts & pipes
• Linear skylight with deflectors to project
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 12
Oceanographic Center Valencia
Tempodrom Berlin 2001
Architect: GMP
Photo: Tomas Schmidt
Concrete folded plate, designed to
represent a tent, as the original
tent structure of 1980 it replaced
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 14
Yokohama Terminal
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 16
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 18
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 20
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 and cylindrical shell structures Copyright Prof Schierle 2012 22
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 24
Force scale
Assume: model concrete = original concrete
Geometric scale
S
g
= 1:50
E
m
(steel wire)
E
m
= 30,000ksi
E
o
(strand)
E
o
= 22,000 ksi
Force scale
S
f
= (1/50)
2
(E
m
/E
o
) = (1/50)
2
(30/22)
S
f
= 1:4167
3 tendons
0.6” 70% metallic
3 tendons A = 3(.7)
(0.3)
2
A = 0.5938 in
2
Assume single wire in model
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
S
f
= (1/50)
2
(0.2)/(0.174)
S
f
= 1: 2175
Original load
P
o
= 0.6 klf (120’)
P
o
=72,000 #
Model load
P
m
= P
o
/ S
f
= 72,000 / 2175
P
m
= 33.1 #
Use 30 cups, each 33.1 / 30
P
= 1.1 #
L=90’
C=30’
w=0.6 klf
a
b=7.5’
z=4.8’
d=6’
X=40’
Section A-A
Folded plate and cylindrical shell structures Copyright Prof Schierle 2012 26