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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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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

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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



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



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.



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



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



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



Oceanographic Center ValenciaArchitect/Engineer: Santiago Calatrava



Tempodrom Berlin 2001

Architect: GMP

Photo: Tomas Schmidt

Concrete folded plate, designed to

represent a tent, as the originaltent 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 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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