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Design rules for bridges in Eurocode 3
Gerhard Sedlacek Christian Müller
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Survey of the Eurocodes
EN 1990
Eurocode: Basis of Design
Eurocode 1: Actions on Structures
1-1 Self weight
1-2 Fire Actions
1-3 Snow
1-4 Wind
1-5 Thermal Actions
1-6 Construction Loads
1-7 Accidential Actions
2 Traffic on bridges
3 Loads from cranes
4 Silo loads
EN 1991
Eurocode 2: Concrete structures
Eurocode 3: Steel structures
Eurocode 4: Composite structures
Eurocode 5: Timber structure
Eurocode 6: Masonry structures
EN 1992 to EN 1996
EN 1997 and EN 1998
Eurocode 7: Geotechnical Design
Eurocode 8: Design in seismic areas
EN 1999Eurocode 9: Aluminium structures
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Cross section of a box girder bridge with an orthotropic deck
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European unified and nationally determinable part of the load
models
MEd
MRd
Ed = gF1Ek1
+ y0 gF2Ek2
Traffic load
Action effect Ed = MEd
Resistance Rd = MRd
European unified
geometrical loading model
with amplitudes Ek
National choices gF, y0, gM
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Single span bridge K210 and tied arch bridge K138
K 210 K 138
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Safety indices b for various structural elements of the reference
bridge K210 and K138
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Determination of gQ by comparing the results of probabilistic design
of single span and continuous span bridges and design with EC 1-2
load model
Probabilistic design EC 1 - Part 2 Load Model
LM
QM
requiredW
35,1
10,1
=
=
-
=
G
M
GG
M
requy
QdM
WfM
g
g
gg
where LM
QQQdMM = g
LM
Q
Qd
QM
M=g
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Fatigue load model specified in EN 1991
Traffic Category Number of heavy vehicles N
1: 2-Lane Highways with a high rate of heavy vehicles
2 • 106 / a
2: Highways and roads with a medium rate of heavy vehicles
0,5 • 106 / a
3: Main roads with a low rate of heavy vehicles
0,125 • 106 / a
4: Country roads with a low rate of heavy vehicles
0,05 • 106 / a
Number of expected trucks
per year for a single lane
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Co
nc
ep
t fo
r fa
tig
ue
as
se
ss
me
nt
wit
h e
qu
iva
len
t
co
ns
tan
t a
mp
litu
de
str
es
s r
an
ge
s
MffatFfgsslg /max
DDj
safety factorfor fatigue strength
safety factorfor fatigue load
damage equivalentimpact factor
damage equivalence factorrepresenting the spectrum
maximum stress range fromEC 1 -2 loadmodel
reference fatigue strength
at 2 10 cycles6
c
crack size a
time
critical
crack
size acrit
detectable
crack
size a0
inspection interval
gFf = 1,00
gMf = 1,00 – 1,15 for damage tolerance
gMf = 1,25 – 1,35 for safe life method
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Fatigue details – welded attachments and stiffeners
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Required moment of inertia from ULS and fatigue design for detail
category 71
α = 1,0
α = 0 , 8
ULS
Fatigue
Span L [m]
Mo
men
t o
f R
esis
tan
ce W
/L [
cm2m
/m]
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Joint for hanger
Alternatives for joints of hangers:
optimised joint:
• continuously increasing stiffness (K90)
low curvature from bending
• end of hanger with hole and inclined
cut
low stresses at end of hanger for
K50
• ratio of inclined cut and connecting
plate
avoiding of stress peak at end of
hanger
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Hanger connection for arch bridges
1
2
4
3
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Standard orthotropic steel deck with continuous stringers with
cope holes in the web of the cross beam
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Steel bridges – serviceability limit state
dis
tan
ce
betw
een
cro
ss g
irde
rs
a [
m]
0
3
4
5
1000 5000 15000 2000010000
AB
second moment of area IB of the stringers including deckplate [m4]
Condition for curve A
1 1,20m
2
IB
1 heavy traffic lane
2 web of main girder or longitudinal girder
Requirements for the minimum stiffness of stringers
depending on the distance between crossbeams
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Structural detailing for deck plate
design life load model 4
without layer < 10 years
asphaltic
sealing
PmB 45
thermosetting
resin
PmB 25
30 - 50 years
70 - 90 years
75
12
Verbindung Längsrippe - Deckblech
300 300 300
HV HV HV
connection of deck plate to troughs
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Structural detailing for cross beams
tLtrough = 6 mm
tweb = 10 - 16 mm; verification of net web section requirded
hcrossbeam 700 mm
tSteg
h
75
12
T
25
> 0,15 hT
hQTr
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Plate buckling
stiffened panel length
sub- panel
longitudinal edge
stif
fen
ed p
an
el w
idth
tra
nsv
erse
ed
ge
y
x
aG
a1 a4 a3 a2
b21
bG
Definition of a plated
element
Verification to web
breathing
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Sta
nd
ard
sys
tem
fo
r
ste
el str
uctu
res
hEN
product
standards for
steel materials,
semi- finished
products etc.
EN 1090 –
Part 2
„Execution of
steel
structures “
EN 1090 – Part 1 „Delivery Conditions for prefabricated steel components“
Eurocode: EN 1990 – „Basis of structural design“
Eurocode 1: EN 1991 – „Actions on structures“
Eurocode 3: EN 1993 – „Design rules for steel structures“
HSS up to
S700
1.12
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Design rules for steel bridges in Eurocode 3
1-11 Rope structures
1-10 Choice of material
1-9 Fatigue
1-8 Connections
1-5 Plate buckling
Annex C Recommendations for orthotropic plates
Annex B Requirements for expansion joints
Annex A Requirements for bearings
EN 1993-Part 2 Steel bridges
EN 1993-Part 1-1 General rules
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Basic features of design rules for bridges
Limit State Concept
ULS Ed Rd
SLS Ed Cd
Fatigue DsE Dsc
Choice of material
based on fracture mechanics
(EN 1993-1-10)
Stability of members and plates
Single l-value for combined
actions,
FEM-methods
(EN 1993-1-1) (EN 1993-1-5)
Fatigue assessments unless
recommended details are used
(EN 1993-2) (EN 1993-1-9)
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Choice of material
Safety assessment based on fracture mechanics
Kappl,d Kmat,d
Kappl,d (member shape, ad, y1·sEd)
Kmat,d (T27J, TEd)
Assumption for a0
design crack
initial crack
fatigue loading
sD=
4
102faa
63c
0d
a0
ad
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Design situation for choice of material in EN 1993-1-10Material toughness
J, CTOD, K
Ti TTmin Troom
J , CTODi i
J -, K -
domainC IC
B1
A1
Tmin Troom T
E (G )K
A2 E (G + K 1y Q )K
E (G +K Q )K
E ( G + g gG K G Q )KB2
sR, R
s s yEd K 1 = (G + Q )K
A3
Rel
fy
B3
MM g
=
g= elpl
d
RRR
y
elasticbehaviour
plasticbehaviour
Action
effect , EsE
curves ofequal densities
E (G + K 2y Q )K
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Safety assessment based on temperature
K*appl,d Kmat,d TEd TRdTransformation
Action side
• lowest air temperature in combination with sEd:
Tmin = -25 °C
• radiation loss:
DTr = - 5 °C
• influence of stress, crack imperfection and member shape and dimension:
• additive safety element:
DTR = +7 °C (with b = 3,8)
]C[70
1025
b20
k
K
ln52T
41
eff
6R
appl
-
-
--=D s
Resistance
• Influence of material toughness
T100 = T27J – 18 [°C]
TEd = DTmin + DTr + DTs + DTR [DT + DTpl ] TRd = T100
TEd TRd
Assessment scheme
.
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Choice of material to EN 1993-1-10
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Example: Thick plates for the composite “Elbebridge Vockerode“
(EN 1993-1-10)
Bridge system and construction
Construction at supports
Cross section
125,28
Span
Upper chord
Bottom plates
Support Support
75
40
30 70 30 7070 95 45 70 95 45
40
50 70 50
40
75 115 135 115 85 85 60 60 60 115 140 145 140 115 60 60 60 85 85 115 135 115 75 75145
70
40
Plate thickness for S355 J2G3
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Choice of material to EN 1993-1-10
Olympic stadium in Berlin
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Bridge St. Kilian
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Bridge St. Kilian
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Cast node for the bridge St. Kilian
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Cast node for the bridge St. Kilian
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Common design rules for column, lateral torsional, plate and shell
buckling
lk
Ed Ed
column buckling lat. tors. buckl. plate buckling shell buckling
0,00
0,20
0,40
0,60
0,80
1,00
1,20
0 0,5 1 1,5 2 2,5 3_
l
a0
a
b
c
d
0,00
0,20
0,40
0,60
0,80
1,00
1,20
0 0,5 1 1,5 2 2,5 3_
l
a
b
c
d
EN 1993-1-1 EN 1993-1-1
0,0
0,2
0,4
0,6
0,8
1,0
1,2
0,0 0,5 1,0 1,5 2,0 2,5 3,0_
lp [-]
p [
-]
a0
b
EN 1993-1-5
M
kult
M
kd 1
RE
g
g
,
0,0
0,2
0,4
0,6
0,8
1,0
1,2
0,0 0,5 1,0 1,5 2,0 2,5 3,0λ
χ
EN 1993-1-6
l=
==l
=
=
crit
kult
crit
k
critdcrit
kdkult
R
R
RE
RE,,
skEd Ed
r
tEd Ed
Ed/2a
Ed
b
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Modelling of plate buckling
F
Rult
yield plateau
effective crosssection
limit y
Rel
gross crosssection
slimit slimit
fyfy
fy
fyslimit
fy
slimit
fy
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Imperfections for members with various boundary conditions
x
EI
CNEdNEd
a1
max,crit
crit
2
crit
Ed
Edd0e
crit
max,crit
2
critd0ini
EI
N1
NeM
e
-
=
=
xsin
N
N1
1NeM
xsine
crit
EdEdd0e
d0ini
-
=
=
x
NEdNEd
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Mechanical background of column- and lateral torsional buckling
Column buckling Lateral torsional buckling
1M
M
N
N
Rky
Ed
Rkpl
Ed =,,
1M
M
N
NFl
Rky
Fl
Edy
Fl
Rkpl
Fl
Ed =,
,
,
1
M
M1
1e
M
N
M
M
M
M
critz
Edz
Fl
Rky
Fl
crit
critz
Edz
Rkz
Edz=
-
,
,
*
,,
,
,
,1
N
N1
1
M
eN
N
N
crit
EdRk,y
*
Ed
Rk,pl
Ed =
-
Fl
Rk,pl
Fl
Rk,yM
*
N
M2,0e
-l=
Rk,pl
Rk,yN
*
N
M2,0e
-l=
11
12,0
*
2
MM
M2
Fl
2
M
MM =l-
-l
=
l
l
1
1
12,0
2
NN
NNN =l-
-l
=
22
1
l-jj
=
2
20150 l-l=j ,,
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Comparison of LTB-curves
0,0
1,0
0,0 1,0 2,0lLT
LT
Lateral torsional buckling
for GIT=oo
Bc b
Lateral torsional
buckling for a beam
HEB 200
Bc a