The document discusses the design and construction of steel arches. It notes several advantages of steel arches including large spans of 80-100 meters, low weight for economy, and aesthetics in modern architecture. Some challenges in design include a lack of specific rules in codes and instability being a major criteria. Common structural systems for arches include free-standing, doubly articulated, and encased in foundations. Steel arches can have parabolic, circular, or polygonal shapes and use cross sections like beams, boxes, or lattice designs. Bracing systems provide stability and connections transfer loads between the arch and other structures like purlins.

1. ARCHES IN STEEL
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2. GENERALFEATURES.
STRUCTURALSYSTEMSADOPTEDINARCHDESIGN
A. IMPORTANT ADVANTAGES OF ARCHES
•Large spans – in average 80...100 m;
•Low weight- economy in the steel
consumption;
•Appreciated aesthetics in modern
architecture;
•Favorable mechanism;
•Efficient production-use of standard
sections on large scale;
•Large possibilities of using advanced
computer aided design tools.
B. DIFFICULTIES IN THE DESIGN
•Lack of specific rules for design in the
international steel codes;
•The instability may be a major criteria
in arches design.
Olyimpic Stad-Athens Hassel Ethias
Santiago Calatrava’s Bilbao footbridge, Bilbao
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3. Implications of the static system adopted
Free standing arch: bigger deformations; intricate constructive details for the arch and for the roof in
the crown of the arch (rarely used).
Doubly articulated arch: simple execution; not influenced by the variations of temperature and the
sunk of the supports; the disadvantage is related to un-rational distribution of bending moments along
the arch line.
Arch encased in the foundations: increased stiffness; more rational distribution of the bending
moments along the arch line; needs stronger foundations and the whole system is sensible to ground
sinking (settlements at the foundation level); a solution for weak soils- arch with sag-rod.
Static structures adopted:
a- static determinate: free standing arch;
b- hyper-static structures:
1) double hinged arch;
2) fully restraint ;
3) rigid connections in foundations and articulation at the key stone;
4) fixed or doubly hinged with sag-rod.
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4. SOLUTIONSADOPTEDFORTHEDESIGNOFSTEELARCHES
Various systems of lattice systems adopted for the cross section of arches
Solutions for arches in steel with great spans and heights
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5. SHAPESOFTHEARCHES
xpy  22
chx
ee
y
xx




2
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6. • Parabola - drawn on the coincidence curved line of the uniform distributed load acting on a
horizontal line.
• A very small ratio between the deflection and the span - parabola replaced by an arc of circle
without a significant modification on the internal efforts (mostly the bending moments). Arc of
circle is preferred from the point of view of assembling and mounting.
• Stability criteria: The neutral axis of the arch must be situated between the two pressure curves
modeled by wind pressure; otherwise special measures to insure the stability of the arch must be
provided (both extreme fibers are in compression).
The deformations of N. A. of arches under wind pressure
SHAPESOFTHEARCHES
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7. In the figure above:
a - hot-rolled cross section, beam or box;
b – lattice beam, simply or double walled
Cross section is constant; variation is adopted in the case of very important spans. Shape of the arch is
rarely designed in a continuous line; generally is a polygonal line (several linear prefabricated units
assembled in site of 6…9 m length).
Heights of the cross section of arches depend on the solution adopted:
-arches with beam cross section: h= (1/50....1/80)l
-arches made of lattice systems: h= (1/30....1/60)l; the internal system adopted is triangular with or
without struts with the angle between the ties and the chord 400...500
Plate girder is a solution sensitive to local buckling of the web under big axial efforts – thick webs and
transversal stiffeners.
Steel sections used for arches
Geometry of the internal members f the arches; a)- triangular system; b)- triangular system with struts
CONSTRUCTIVE DETAILS
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8. Classic solution:
The roof cladding lays directly on the top chord of arches (LT=4...6 m) or on purlins
(LT=6...12 m);.
Longitudinal and transversal bracing insure the collaboration between arches for the
effects of wind action and a general stiffness against lateral instability;
Purlins: hot-rolled sections, Castella beams, lattice girders; braces connected between the
bottom flanges or bottom chords of purlins and bottom flanges or bottom chords of laced
arches insure lateral stability.
Connections between the purlins and the arch elements:
a)- arches made of trusses; b)- arches made of plate girder sections
Purlins placed normal to the axis or the arch: they must
be interconnected with diagonals when the roof cover is
not rigid enough or not fixed continuously
CONSTRUCTIVE DETAILS
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9. POSSIBILITIESOFPLACINGTHEPURLINSINTHECLASSICSOLUTION
Position of purlins in the roof: a)- in vertical plane; b)- normal to the axis of the arch
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10. SOLUTIONOFPURLINSWITHRIBS
• Purlins placed normal to the N.A.:
I - weight of the roof cladding and snow transferred to purlins and to the structure of arch;
II- the tangent force in the plane of the roof (from self-weight and snow action) is taken by the ribs.
• Ribs are multi-hinged arches; they collect the transversal forces from the crown of the arch to the
supports and sometimes the ribs have their own foundations.
•The force normal to the plane of the roof is taken by the purlins.
•Purlins placed gravitational:
•Very difficult details of supports and fixing;
•Difficult laying the roofing.
Forces transmitted to the ribs
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11. The two arches and the transversal bracing act as space rigid frames.
MODERN SOLUTIONS: COUPLED ARCHES BRACED TRANSVERSALLY
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12. MODERNSOLUTIONS:COUPLEDARCHESANDCANTILEVEREDPURLINS
The end parts of the purlins are knee braced and they are parts of the longitudinal
bracing in the plane of the roof.
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13. BRACINGSYSTEMOFARCHES
Bracing system for the
classic solution adopted
for the structure of
arches
Bracing system for the solution
with coupled arches
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14. DESIGNOFTHEHINGESONTHESUPPORTSANDINAPEX
Hinges in the supports of arches:
a)- with plates; b), c)- knee; d)- swing support
Hinges in the apex: a), b)- with plates; c)-
bolted; d)- with splices; e)- swing support
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15. SPECIFICPROBLEMSINTHESTRUCTURALCOMPUTATIONOFARCHES
Coefficients of the snow deposit on the roof and
wind pressure on the structure of an arch
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16. DOUBLEHINGEDARCH-MOSTFREQUENTSOLUTION
Equilibrium of forces in hyper-static arches: a)- double hinge arch; b)- double hinged with tie-rod
Arch with parabolic shape
Variation of temperature in the N. A of the arch
01  PX


cos1;1
22
1




 
nym
EA
dsn
EI
dsm





EA
dsnN
EI
dsmM
P
00
iiA PxVM  0
 sinsin0   iA PVNcos0
0


XNN
yXMM
01 



t
P
AE
lX
X
0
cos8cos
8
2
2







M
f
lqX
N
f
lq
X



 l
ds
EI
y
tl
X
0
2




 l
l
ds
EI
y
ds
EI
yM
X
0
2
0
0
h
t
IEEIM 1
0

 
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17. AXIALFORCESINTHEMEMBERSOFTHELACEDARCH
Arch Values of  for l/f equal with
0.05 0.2 0.3 0.4 0.5
With 3 hinges 1.2 1.2 1.22 1.35 1.48
With 2 hinges 1.00 1.10 1.22 1.35 1.48
Fully restraint 0.70 0.75 0.80 0.85 0.90
Axial forces in the internal members of the arch
Instability patterns of arches
The verifications regarding instability are:
-verifications for lateral or flexural-torsional buckling;
-verifications for overall buckling.
critical axial force (Euler):
 22
/ sEINcr  
s- equal with half of the arch length; in the case when the
ratio l/f<5 (l, the span of the arch and f, the height), s will be
considered equal with l.
- - tabulated values depending on the end restraints of the
arch (see table) and also on the ratio l/f.
Table 6. Values of the amplifying factor 



cos
T
D
h
M
h
NN
h
M
h
NN
i
i
s
s



2
sin


 d
is
is
A
AA
NN
D
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18. AXIALFORCESINTHETRANSVERSALBRACING
Forces in the internal members of the transversal bracing (wind on the gable)
iiiiii
i
i
iiii
tgTDNN
T
DTD





 sin
cos
1
111
11
coscos 



iiiiiii
iii
WDDTT
WTT

 
i
ji WWT
1
2/
 

 
1
1
1 2/
i
ji WWT
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19. DETAILSOFCONSTRUCTION-ARCHESWORLDWIDE
Foot springs
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20. Archesofsmallerdimensionswithdifferentdestinations:agriculture,
commerce,lightindustry
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21. OlympicSportsStructures-Athens
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22. Roofsforgreatstadiums
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23. Churches
Airport Terminal Chek Lap Kok-Corea
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24. ChicagoRailwayStationTerminal
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