9. large-span structures - fsv Čvut --...

© 9 Prof. Ing. Josef Macháček, DrSc. 1

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9. Large-span structuresRigid element structures, suspension structures, stayed structures, pneumatic structures reinforced by cables.

Distribution chosen according to the main load-carrying elements:(complete with cladding, bracing, side walls etc.)

structures with rigid members,suspension structures,stayed structures,pneumatic structures with ropes.

• plate girder

• truss and lattice girder

• arch

• frame

• stayed structure

• suspension structure

materialusage

supportdemands

desc

ends

asce

nd

planar systems (2D),space systems (3D).

Generally:


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1. Structures with rigid membersPlanar systemsPlate girderDrawbacks: heavy, rarely use. Example:

Prague Wilson station, upper flange orthotropic, L = 45 m

Exception: girders with predeformed thinwalled webst = 2 ÷ 4 mm, L up to 50 m

Truss (or lattice girder with parallel chords) Drawbacks: great height (up to L/10), instability of compression chord.Modification: space truss (Lcr between nodes only)

Example:Vítkovice stadium L = 100 mAmsterdam stadium L = 177 m(with movable roof)


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L

v

ffMH v=

Two-pinned arch (or fixed arch):- compression of centre line (→ lower H),- sensitive to settling of support and temperature,- convenient to use ties in floor (to carry H).

• in-plane buckling:

• out-of-plane buckling for:- length of trans. supports

- or β1, β2 given in standards acc. to geometry and loading)

Arch stability:a) Approximate check in buckling for Nx = L/4 :

NL

2/l)

2crl)

β=L β = 0,7

β = 1,0

β = 1,15

LL 21cr ββ=

b) 2nd order theory with imperfections (GNIA).

Arches (plate, truss)Drawbacks: curvature may cause problems to roofing.

(hence often polygonal shape). See Olymp. stadium Sydney L = 300 mOlymp. stadium Athens L = 304 m

Statics:


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Olympic stadium in Athensarches with L = 304 m, polycarbonated roofing(Spanish architect Santiago Calatrava)


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Portal framesVarious types of supports, haunches etc. For stability see chapter 8 (Classification of frames). connection with friction-grip bolts

(to restrict deformations)

L up to 70 m

Detail of the “pin"(fixing requirestoo large bases):

bolts in column perimeter

Space systems• grids,• truss plates,• cylindrical (wagonhead) vaults and shells,• spherical domes.

In space design:- the material (steel) is better used,- design rigidity of the structure is greater,- however, the fabrication is more laborious and assembly

more difficult.


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Grids• bidirectional

Truss plates (usually from tubes)

Differ from grids by shifting of bottom flanges for ½ of truss panel:

plate girdersgirders:

lattice girders

(supports usually along perimeter)

in plan may become skew⇒ necessary bracing in both directions !!!

• three-way grids

- these are rigid, no bracing necessary.

• bidirectional the structure has 1º of internal freedom⇒ min. 4 vertical simple supports !!!


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• three-way

Advantages of space truss plates• supports may be placed acc. to need (solved by member dimensions - “hidden

primary beams"),• all plan shapes available,• some members may be omitted (e.g. parts of bottom flanges, diagonals, etc.).

Drawbacks of space truss plates• complicated joints (usually patented),• material usage is high (due to requirement of minimum member size).

Joints of space truss plates

a) Welded piece of pressed hemispheres

d

~ 2d

40dt ≈ - pieces are pressed while warm,

- one tube is continuous, - other tubes are welded in the space to sphere by

butt weld ½ V.


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b) Patented joints

Mero system Germany Analogy: KT-I Jap.:(polyhedron – up to 18 tubes may be connected)

Family of modifications, e.g.:• cylindrical joint (carries M),• plate joint (for singlelayer structures)

Outstanding structures:

Globe Arena (1987) Eden projekt (2000) Singapore Art C. (2002) S. Jordi (1992)

hexagonal coverspring

nut

cover nutbolt


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Triodetic systemCanada

Outstanding structures:

Hawaii Energy Center (2004)Toronto IMAX (1971)Glasshouse in Vancouver (1969)

Nodus systemGB

clamping bolt

flattened tube,hooked

high-strength boltparted joint

RHS (rectangularhollow section)

lugs for pins of tubediagonals


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Cylindrical vaults and shells• plated usually orthotropic (stiffened for local rigidity)

Example: Prague fairground stadium (1962)L= 64 m, t = 4 mm

• trussed

Lab in Moscow(collapsed in about 1985)

236 112

Static analysis (see EN 1993-1-6)

a) Strength analysis:- bending theory

6 internal resultants (Nx, Nϕ, Nxϕ, Mx, Mϕ, Mxϕ)

- membrane theory3 membrane forces only (Nx, Nϕ, Nxϕ). Necessary to take into account moment effects (namely at gables, Mx).

moment disturbanceat gable ⇒ Mx beam force Nx

+ shear force Nxϕϕ

arch force Nϕ

single-layereddouble-layered Example: lamellar structures of ice-hockey

stadiums Kladno, Prostějov


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a) Stability analysis ( incl. “snap through" of the shell):

- global instability

- local instabilityw0

Spherical domes

membrane theory

parallel force Nϑ

meridian force Nϕ

+ shear force Nϑϕ

− in bottom there is a tension ring (or the horizontal forces are anchored),− at top there is concentration of members ⇒ insert compression ring.

• Single-layer domes

compression tube ∅ 330×17

Example: latticed Z pavillion in Brno∅ 93 m (tubes 60×2 up to 102×6)


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• Double-layer domes2,5 m

266

135

36 truss girders

ties ∅ 100 mm (S460)

Stadium in Detroit (1979)

Sazka Arena in Prague (2004)

simillar to hall in Anaheim LAL=101×133 mhall in Chicago L = 115 ×159 m

Glasshouses Eden (GB, 2000)

Globe Arena (Stockholm, 1987)

History: Schwedler’s domes, Zimmerman’s cupolas.New trends: geodetic dome (icosahedron) - 12 peaks, 20 plates, 30 equal members.


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Sazka Arena (2004)

- 18 000 spectators,- diameter 135 m, height 9 m,- 36 stayed trusses with ties of ∅ 98 mm (S460),- middle tube ∅ 18 m weighing 170 t (another 30 t may be suspended).


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2. Suspension structures (use of tension suspended elements)

- cable structures,- membrane structures.

Advantages:• small material usage,• great shape possibilities (architectonic diversity).

Drawbacks:• shape lability,

M(x) = 0

shape depends on loading, i.e.:- 2nd order theory analysis,- high roofing requirements.

• great horizontal reactions.

L

ffLqH

8

2=

- great requirements on supports.


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Ropes(see Seidel „Tensile surface structures“: spiral ropes, compound from parallel wires, one-strand ropes, more-strand ropes, open and locked ropes)

aluminium or steelswaged thimble U clampfork swaged socket clamps

open strand locked strand

galvanizedwiresZn95Al5(300g/m2)

gaps filled up bywax, polyurethane,

zinc dust + oil

plastic

Sockets:

open, filled with zinccylindrical, filled with metal or epoxy:

can be supplied with outer/inner thread, or lug for joint

plastictubes filling: resin,

polymers,cements.


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Cable structures• plane (2D),• space (3D).

• Plane cable structures (cylindrical roofs)

a) Single-layer

For wind suction the roof need to be stabilized by:

change of the shapeand vibration

• heavy dead load (ballast),• stiffening (stiff elements),• prestressing (two-layer structures,

see further).

circumferential cable

anchored into foundation or into ring-beam/circumferential cable:


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b) Double-layer

connectingtension ties

connecting compressionprops

prestressedbearing cableand tensioncable

Jawerth’s truss(all members are ropes in tension)

Examples:auditorium of Utica (USA) university ice stadium in Johannesburg (Stockholm)

82 800

15 8

00

75 000


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• Space cable structures

a) With radial cables (usually circular in plan)

1. 3.2.

cable couple

plan

section inner tension ringouter compressionring

Example: USA pavillion in Brussels, EXPO 1958 (104 m)b) Geiger’s cable domes

upper tension ringprestressed radials

compression ring

tension ringscompression posts

great span (up to 250 m)

Example: Olympic stadium in Seul, 1988(textile covering)


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Geiger’s system

Static behaviour Execution

Erection

compression ring

tensionrings

prestressing 1compression ring

supply tension rings

P P

P PP/2P/2

P/2 P/2

P/2 P/2

P/4 P/4

P/4 P/4

prestressing 2etc.


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c) Cable meshes

2 cable warps concave - load bearingconvex - prestressing

Festival complex in Tartu (53,3x42,6 m): assembly and final form.

1. Straight peripheral members 2. Arched peripheral members

Examples: • Č. Budějovice, • Bratislava Pasienky, 1962 (72x66 m)

great bendingmoments


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Membrane suspension structuresLoad bearing membrane may form roofing at the same time. Types of structures:

• cylindrical,• circular, elliptic.

Example:Moscow (ellipse 224x183 m):

t = 5 mm + stiffeners

tension ring

keeps the shape during wind suction

for fastening of soffit

224 x 183

Material of membranes in general:• stainless steel (sheets t = 4 ÷ 5 mm),• alloys of Al (up to 70 m only t ≈ 2 mm),• textile, plastic foils (today mostly ETFE, PTFE).


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Example of textile membranes (PTFE)

peripheral cables cable anchorage


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3. Stayed structures (use of stiff or flexible stay elements)Stays create additional supports, which are flexible. Their positions need to be optimized. The stays are:

• stiff (rods, tubes), provided they are in compression under wind suction, • flexible (cables), which may be prestressed to exclude compression.

Stayed rigid roof structures:

Stayed suspension roof structure:

anchored intocolumn base

outside anchoring(plot requirements)

48

Example:Ruzyně hangar

textile, plastic

Example:• Olympic stadium in Munich, 1972• Airport Jeddah (for pilgrims to Mecca),405000 m2, 1980


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4. Pneumatic structures stabilized by cablesTextile structures with inner overpressure of approx. 0,003 at (= 0,0003 MPa = 0,3 kN/m2).

Examples:

• Stadium in Vancouver (1983)

Stadium for baseball, 55000 spectators,deflated in typhoons

pressure 0,003 at

textileropes ∅ 80 mm

Dimensions: 232 x 190 m

• Big Egg Tokio (1988)

ropes ∅ 80 ā 8,5 m

201 m

pressure 0,003 at

textile 0,8 mm


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5. Structures with tension rods and glassEsthetic new structures (e.g. passenger terminals / entrance halls) are more and more using tensioned rods and glass sheets:

DETAN system MACALLOY system

Examples:

Expo Lisbon 1998 Granada Airport 1998 Madrid Barajas 2006 Senftenberg 1998


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Glass facades supported by rope prestressed girders

Structures formed from prestressed rods and compressed posts. The tube posts support glass panes with help of rectified point fixings (“spiders").


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Large-sized glass façade (Munich)

9. large-span structures - fsv Čvut --...

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