1.General features. Structural systems used in arch design 2. Solutions adopted for the design of arches3. Shapes of the arches4. Constructive details 5. Usual systems adopted6. Design of the hinges on the supports and in apex –crown of the arch7. Specific problems in the structural computation of arches

1. General features. Structural systems adopted in arch design

A. IMPORTANT ADVANTAGES OF ARCHESLarge 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 DESIGNLack of specific rules for design in the international steel codes;The instability may be a major criteria in arches design

Santiago Calatrava’s Bilbao footbridge

Olyimpic Stad-Athens Hassel Ethias

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.

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.

2. Solutions adopted for the design of arches

Various systems of lattice systems adopted for the cross section of arches

Solutions for arches in steel with great spans and heights

3. Shapes of the arches

xpy 22

chxee

yxx

2

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

4. Constructive details 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

4. Constructive details A. Classic solution: 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; connections with the bottom chord insure lateral stability of the arch.

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

Possibilities of placing the purlins in the classic solution

Position of purlins in the roof: a)- in vertical plane; b)- normal to the axis of the arch

Solution of purlins with ribs

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.

Modern solutions: coupled arches transversally braced

The two arches and the transversal bracing act as space rigid frames.

Modern solutions: coupled arches and cantilevered purlins The end parts of the purlins are knee braced and they are parts of the longitudinal bracing

in the plane of the roof

Bracing system of arches

Bracing system for the classic solution adopted for the

structure of arches

Bracing system for the solution with coupled arches

5. Design of the hinges on the supports and in apex

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

7. Specific problems in the structural computation of arches

Coefficients of the snow deposit on the roof and wind pressure on the structure of

an arch

Double hinged arch-most frequent solution

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

nymEA

dsn

EI

dsm

EA

dsnN

EI

dsmMP

00

iiA PxVM 0

sinsin0 iA PVN

cos0

0

XNN

yXMM01

t

P AE

lXX

0

cos8cos

82

2

M

f

lqXN

f

lqX

l

dsEI

y

tlX

0

2

l

l

dsEI

y

dsEI

yM

X

0

2

0

0

h

tIEEIM 1

0

Axial efforts in the members of the arch

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 efforts 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 / sEIN cr -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

TD

h

M

hNN

h

M

hNN

ii

ss

2sin

dis

is AAA

NND

Axial efforts in the transversal bracing

Efforts in the internal members of the transversal bracing (wind on the gable)

iiiiii

i

iiiii

tgTDNN

TDTD

sin

cos

1

111

11

coscos

iiiiiii

iii

WDDTT

WTT

i

ji WWT1

2/

1

11 2/

i

ji WWT

Details of construction-arches worldwide

Foot springs

Arches of smaller dimensions with different destinations agriculture, commerce, light industry

Olympic Sports Structures-Athens

Roofs for great stadiums

Churches

Airport Terminal Chek Lap Kok-Corea

Chicago Railway Station Terminal