9.

Large-span structures
Rigid 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.

planar systems (2D),

space systems (3D).

material
usage

Generally:

support
demands

plate girder
truss and lattice girder

frame
stayed structure
suspension structure
OK3

Prof. Ing. Josef Machek, DrSc.

ascend

descends

arch

1. Structures with rigid members

Planar systems
Plate girder
Drawbacks: heavy, rarely use.

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

Exception: girders with predeformed thinwalled webs

t = 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:
Vtkovice stadium L = 100 m
Amsterdam stadium L = 177 m
(with movable roof)
OK3

Prof. Ing. Josef Machek, DrSc.

Arches (plate, truss)

Drawbacks: curvature may cause problems to roofing.
(hence often polygonal shape). See Olymp. stadium Sydney L = 300 m
Olymp. stadium Athens L = 304 m

Statics:
M
H= v
f

v
f
L

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).

Arch stability:
a) Approximate check in buckling for Nx = L/4 :
)
l/2

)
l
Lcr =
2

in-plane buckling:
N
L

out-of-plane buckling for:

- length of trans. supports
- or

Lcr = 1 2 L

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

OK3

Prof. Ing. Josef Machek, DrSc.

= 0,7
= 1,0
= 1,15

1, 2 given in standards acc. to

geometry and loading)
3

Olympic stadium in Athens

arches with L = 304 m, polycarbonated roofing
(Spanish architect Santiago Calatrava)

OK3

Prof. Ing. Josef Machek, DrSc.

Portal frames
Various types of supports, haunches etc. For stability see chapter 8 (Classification of
frames).
connection with friction-grip bolts
(to restrict deformations)
Detail of the pin"
(fixing requires
too large bases):

L up to 70 m

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.
OK3

Prof. Ing. Josef Machek, DrSc.

Grids

plate girders
girders:

bidirectional

lattice girders
(supports usually along perimeter)

three-way grids

in plan may become skew

necessary bracing in both directions !!!

- these are rigid, no bracing necessary.

Truss plates (usually from tubes)

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

the structure has 1 of internal freedom

min. 4 vertical simple supports !!!

OK3

Prof. Ing. Josef Machek, DrSc.

 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
t
d
~ 2d

d
40

- pieces are pressed while warm,

- one tube is continuous,
- other tubes are welded in the space to sphere by
butt weld V.
OK3

Prof. Ing. Josef Machek, DrSc.

b) Patented joints
Mero system Germany

Analogy: KT-I Jap.:

(polyhedron up to 18 tubes may be connected)

hexagonal cover
spring
nut
cover nut
bolt

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)

OK3

Prof. Ing. Josef Machek, DrSc.

S. Jordi (1992)
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clamping bolt

Triodetic system
Canada
flattened tube,
hooked
Outstanding structures:

Glasshouse in Vancouver (1969)

Nodus system
GB

Toronto IMAX (1971)

Hawaii Energy Center (2004)

high-strength bolt
parted joint
RHS (rectangular
hollow section)
lugs for pins of tube
diagonals
OK3

Prof. Ing. Josef Machek, DrSc.

Cylindrical vaults and shells

plated

usually orthotropic (stiffened for local rigidity)

Example:

Prague fairground stadium (1962)

L= 64 m, t = 4 mm

single-layered

trussed

double-layered

Example: lamellar structures of ice-hockey

stadiums Kladno, Prostjov

236

112

Lab in Moscow
(collapsed in about 1985)

Static analysis (see EN 1993-1-6)

a) Strength analysis:

- bending theory
6 internal resultants

moment disturbance
at gable Mx

beam force Nx

arch force N
+ shear force Nx
OK3

Prof. Ing. Josef Machek, DrSc.

(Nx, N, Nx, Mx, M, Mx)

- membrane theory
3 membrane forces only (Nx, N, Nx).
Necessary to take into account
moment effects (namely at gables, Mx).
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a) Stability analysis ( incl. snap through" of the shell):

- global instability

w0

- local instability

Spherical domes
parallel force N
meridian force N

membrane
theory

+ shear force N

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

Example: latticed Z pavillion in Brno

93 m (tubes 602 up to 1026)
compression tube 33017
OK3

Prof. Ing. Josef Machek, DrSc.

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 Double-layer domes
2,5 m

Stadium in Detroit (1979)

266
36 truss girders

135

ties 100 mm (S460)

Sazka Arena in Prague (2004)

simillar to hall in Anaheim LA
L=101133 m
hall in Chicago L = 115 159 m

Glasshouses Eden (GB, 2000)

Globe Arena (Stockholm, 1987)

History: Schwedlers domes, Zimmermans cupolas.

New trends: geodetic dome (icosahedron) - 12 peaks, 20 plates, 30 equal members.
OK3

Prof. Ing. Josef Machek, DrSc.

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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).

OK3

Prof. Ing. Josef Machek, DrSc.

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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,

shape depends on loading, i.e.:

- 2nd order theory analysis,
- high roofing requirements.

M(x) = 0
great horizontal reactions.

f
L

H=

q L2
8f

OK3

Prof. Ing. Josef Machek, DrSc.

- 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)

open strand

locked strand

gaps filled up by
galvanized wax, polyurethane,
zinc dust + oil
wires
Zn95Al5
(300g/m2)
plastic

plastic
tubes

Sockets:

filling: resin,
polymers,
cements.

open, filled with zinc

cylindrical, filled with metal or epoxy:
can be supplied with outer/inner thread, or lug for joint

fork swaged socket

aluminium or steel
swaged thimble
OK3

Prof. Ing. Josef Machek, DrSc.

U clamp

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

Plane cable structures (cylindrical roofs)

a) Single-layer

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

For wind suction the roof need to be stabilized by:

heavy dead load (ballast),
stiffening (stiff elements),
prestressing (two-layer structures,
see further).

change of the shape

and vibration

OK3

Prof. Ing. Josef Machek, DrSc.

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b) Double-layer
connecting
tension ties

prestressed
bearing cable
and tension
cable

Jawerths truss
(all members are ropes in tension)

connecting
compression
props

Examples:
ice stadium in Johannesburg (Stockholm)
15 800

auditorium of Utica (USA) university

75 000

82 800

OK3

Prof. Ing. Josef Machek, DrSc.

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 Space cable structures

a) With radial cables (usually circular in plan)
1.

2.

3.

plan

cable couple

outer
compression
ring

section

inner tension ring

Example:
USA pavillion in Brussels,
EXPO 1958 (104 m)

b) Geigers cable domes

upper tension ring
prestressed radials

compression ring
compression posts
great span (up to 250 m)

tension rings

OK3

Prof. Ing. Josef Machek, DrSc.

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

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Geigers system
Static behaviour
P

Execution

P/2

P/2

P/2

P/2

P/4

tension
rings

P/4

P
P/4
P/2

P/4
P/2

compression ring

Erection
prestressing 1
compression ring
prestressing 2
etc.

OK3

Prof. Ing. Josef Machek, DrSc.

supply tension rings

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c) Cable meshes
2 cable warps

concave

- load bearing

convex

- prestressing

1. Straight peripheral members

great bending
moments

2. Arched peripheral members

Examples:
. Budjovice,
Bratislava Pasienky, 1962 (72x66 m)

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

OK3

Prof. Ing. Josef Machek, DrSc.

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Membrane suspension structures

Load bearing membrane may form roofing at the same time.
Types of structures:

cylindrical,
circular, elliptic.

keeps the shape

during wind suction
t = 5 mm + stiffeners for fastening of soffit

Example:
Moscow (ellipse 224x183 m):

224 x 183

tension ring

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).

OK3

Prof. Ing. Josef Machek, DrSc.

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Example of textile membranes (PTFE)

peripheral cables

cable anchorage

OK3

Prof. Ing. Josef Machek, DrSc.

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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:
Example:
Ruzyn hangar
outside anchoring
(plot requirements)

anchored into
column base

48

Stayed suspension roof structure:

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

textile, plastic
OK3

Prof. Ing. Josef Machek, DrSc.

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4. Pneumatic structures stabilized by cables

Textile structures with inner overpressure of approx. 0,003 at (= 0,0003 MPa = 0,3
kN/m2).
Examples:
Stadium in Vancouver (1983)
textile
ropes 80 mm

Dimensions: 232 x 190 m

pressure 0,003 at

Big Egg Tokio (1988)

ropes 80 8,5 m
textile 0,8 mm
pressure 0,003 at
201 m
Stadium for baseball,
55000 spectators,
deflated in typhoons
OK3

Prof. Ing. Josef Machek, DrSc.

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5. Structures with tension rods and glass

Esthetic 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

OK3

Prof. Ing. Josef Machek, DrSc.

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").

OK3

Prof. Ing. Josef Machek, DrSc.

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Large-sized glass faade (Munich)

OK3

Prof. Ing. Josef Machek, DrSc.

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