Design rules for bridges in Eurocode 3

Gerhard Sedlacek Christian Müller

2

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

3

Cross section of a box girder bridge with an orthotropic deck

4

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

5

Single span bridge K210 and tied arch bridge K138

K 210 K 138

6

Safety indices b for various structural elements of the reference

bridge K210 and K138

7

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

8

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

9

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

10

Fatigue details – welded attachments and stiffeners

11

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]

12

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

13

Hanger connection for arch bridges

1

2

4

3

14

Standard orthotropic steel deck with continuous stringers with

cope holes in the web of the cross beam

15

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

16

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

17

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

18

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

19

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

20

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

21

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)

22

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

23

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

24

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

.

25

Choice of material to EN 1993-1-10

26

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

27

Choice of material to EN 1993-1-10

Olympic stadium in Berlin

28

Bridge St. Kilian

29

Bridge St. Kilian

30

Cast node for the bridge St. Kilian

31

Cast node for the bridge St. Kilian

32

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

33

Modelling of plate buckling

F

Rult

yield plateau

effective crosssection

limit y

Rel

gross crosssection

slimit slimit

fyfy

fy

fyslimit

fy

slimit

fy

34

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

35

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 ,,

36

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