Photo: Michael Bodycomb, © 1977 Kimbell Art Museum, reproduced with permission
Folded Plate 1 2 3 4 5
Beam compression/tension Buckling Ribs resist buckling Edge buckling 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
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.
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 tetrahedrons
Portable exhibit hall Architect/ Engineer: Santiago Calatrava
b=50”
C1=8” C2=16”
” 4 2 = d
’ 1 4 = L
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 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) f b=M c1/I=26266x12x8/3360 f b = 750 psi Extreme fiber stress @ bottom f b=M c2/I=26266x12x16/3360 f b = 1500 psi
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.
w=0.6 klf
L=90’
C=30’
X=40’
b=7.5’ a ’ ’ 8 . 6 4 = = d z
Section A-A
Assume: 0.6” tendons, design load DL= 68 psf (average) LL = 12 psf = 80 psf Uniform load per unit (see A-A) w = 80 psf x7.5’/1000 Reactions Rl = 0.6x120x30/90 Rr = 0.6x120x60/90 X = Rll / w = 24/0.6 Max. bending moment Max. M = RaX/2 =24x40/2 Z = 0.8d ~0.8(6’) Tendon tension T = M/Z = 480/4.8 Number of tendons required # = T/P= 100/35 =2.86 Use 3 tendons Note: a Concrete compression block d Effective depth (rebar center to top) Z Lever arm of resisting moment
P= 35 k
w = 0.6 klf Rl = 24 k Rr = 48 k X = 40’ M = 480 k’ z ~ 4.8’ T = 100 k
3 0.6”
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
Yokohama Terminal Architect: 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
Folded plate dome
w=0.6 klf
L=90’
C=30’
X=40’
3 tendons A= 3(.7)(0.3)2
b=7.5’ a ’ ’ 8 . 6 4 = = d z
Section A-A
Force scale Assume: model concrete = original concrete Geometric scale Sg= 1:50 Em (steel wire) Em= 30,000ksi Eo (strand) Eo = 22,000 ksi Force scale Sf = (1/50)2 (Em/Eo) = (1/50)2 (30/22) Sf = 1:4167 3 tendons 0.6” 70%metallic Assume single wire in model Equiv. original = 2(0.5938/)0.5 Model = 0.87/50 = 0.0174 Use model diameter Adjust force scale Sf = (1/50)2 (0.2)/(0.174) Original load Po = 0.6 klf (120’) Model load Pm = Po / Sf = 72,000 / 2175 Use 30 cups, each 33.1 / 30
A= 0.5938 in2 = 0.87 in = 0.02 in
Sf = 1: 2175 Po =72,000 # Pm = 33.1 # Pcup =1.1#
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
Science & Industry Museum Los Angeles Architect: California State Architect Office Engineer: T Y Lin
Science & Industry Museum Los Angeles Architect: California State Architect Office Engineer: T Y Lin
Assume: 0.6” tendons, design load DL= 81 psf (concrete + roofing) LL = 12 psf = 93 psf
P= 35 k
Uniform load per shell w = 93 psf x21.5’/1000 Max. bending (at mid support) M = w L2/12 = 2x712/12 Lever arm Z ~ 0.85 d ~ 0.85x7’ Tendon tension T = M / Z = 840 / 6 Number of tendons required # = T / P = 140 / 35 = 4 Use 4 tendons
w = 2 klf M = 840 k’ Z ~ 6’ T = 140 k
4 0.6
Tendon tension
Z
d Concrete compression
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 daylight onto the cycloids
Photos: Michael Bodycomb, © 1977 Kimbell Art Museum, reproduced with permission
Oceanographic Center Valencia Architect/Engineer: Santiago Calatrava
Cylindrical shells are strong and efficient
Museum of Science and Industry
Photo: Michael Bodycomb, © 1977 Kimbell Art Museum, reproduced with permission
