Dissemination of information for training – Vienna, 4-6 ... · Dissemination of information for training – Vienna, 4-6 October 2010 2 LIST OF CONTENTS 1. The European Standard

Dissemination of information for training – Vienna, 4-6 October 2010 1

Design of steel-bridgesOverview of key content of EN 1993-Eurocode 3

Illustration of basic element designg

G. Hanswille, W. Hensen, M. Feldmann, G. Sedlacek


LIST OF CONTENTS

1. The European Standard Family and Steel bridges1. The European Standard Family and Steel bridges 2. Load assumptions for steel bridges 3. Modelling of steel bridges 4. Specification of bearings5. Choice of steel 6 D i f b id l t6. Design of bridge elements

6.1. Stability rules 6 2 Fatigue rules6.2. Fatigue rules 6.3. Rope structures


CROSS SECTION OF A BOX GIRDER BRIDGE WITH AN ORTHOTROPIC DECK


HASELTALBRÜCKE SUHL


NAVIGATION THROUGH STANDARDS

actionsEN 1990

Safety aspects

Load combination EN 1991-1-1

EN 1991-2

Self-weight

Traffic actionsactions G/Q-values

y p

EN 1990-A2EN 1991-1-4

EN 1991-1-5

Wind actions

Thermal actions

EN 1993 1 1 f

design

EN 1993-1-1 Imperfections EN 1993-2

EN 1993-1-8

EN 1993-1-11

General

Connections

Ropes

EN 1993-1-5EN 1993-1-5

EN 1993 1 9 Fatigue

Stability of plates

Seismic designEN 1998-3 EN 1337

p

BearingsEN 1993-1-9 Fatigue

MaterialsEN 10025 Prefabrication EN 1090-2

executionWelding

Corrosion protectionEN 1090-2

EN 1090-2 Site work

Tolerances EN 1090-2

EN 1337

productCE-markingEN 1090-2 Inspection EN 1090-2product conformity

CE marking

TraceabilityEN 1337-6

EN 1090 2 Inspection

Maintenance EN 1337-10

EN 1090 2


SURVEY OF THE EUROCODES

EN 1990Eurocode: Basis of Design

Eurocode 1: Actions on Structures1-1 Self weight

EN 1991Eurocode 2: Concrete structuresEurocode 3: Steel structures

EN 1992 to EN 1996

1 1 Self weight1-2 Fire Actions1-3 Snow1-4 Wind1-5 Thermal Actions

Eurocode 3: Steel structuresEurocode 4: Composite structuresEurocode 5: Timber structureEurocode 6: Masonry structures

1 5 Thermal Actions1-6 Construction Loads1-7 Accidential Actions2 Traffic on bridges3 Loads from cranes EN 1997 and EN 19983 Loads from cranes4 Silo loads

EN 1997 and EN 1998Eurocode 7: Geotechnical DesignEurocode 8: Design in seismic areas

EN 1999EN 1999Eurocode 9: Aluminium structures


1. THE EUROPEAN STANDARD FAMILY AND STEEL BRIDGES

hENproduct standards EN 1090 Part 2

EN 1090 – Part 1 „Delivery Conditions for prefabricated steel components“

Eurocode: EN 1990 – „Basis of structural design“product standards for steel materials,

semi- finished products etc.

EN 1090 – Part 2 „Execution of

steel structures “Eurocode 1: EN 1991 – „Actions on structures“

Eurocode 3: EN 1993 – „Design rules for steel structures“

em fo

r re

s HSS up to S7001.12

ard

syst

el s

truct

uS

tand

ast

ee



actions Safety aspects

Load combination Self-weight

Traffic actions

G/Q-valuesWind actions

Thermal actions

Imperfections G ldesigner

design

Imperfections General

Connections

RopesFatigue

Stability of plates

Seismic design BearingsFatigue

tiMaterials Prefabrication

executionWelding

Corrosion protectionSite work

Tolerances

productCE-marking Inspection

contractorproduct

conformity g

Traceability

p

Maintenance

Tasks for designer and contractor



1-5 Plate buckling1-5 Plate buckling

EN 1993-Part 1-1 General rulesEN 1993-Part 1-1 General rules

1-5 Plate buckling

EN 1993-Part 1-1 General rules

1-9 Fatigue1-9 Fatigue

1-8 Connections1-8 Connections

1-9 Fatigue

1-8 Connections

1-11 Rope structures1-11 Rope structures

1-10 Choice of material1-10 Choice of material

1-11 Rope structures

1-10 Choice of material

EN 1993-Part 2 Steel bridgesEN 1993-Part 2 Steel bridgesEN 1993-Part 2 Steel bridges

A C R d ti f th t i l tA C R d ti f th t i l t

Annex B Requirements for expansion jointsAnnex B Requirements for expansion joints

Annex A Requirements for bearingsAnnex A Requirements for bearings

A C R d ti f th t i l t

Annex B Requirements for expansion joints

Annex A Requirements for bearings

Annex C Recommendations for orthotropic platesAnnex C Recommendations for orthotropic platesAnnex C Recommendations for orthotropic plates

Design rules for steel bridges in Eurocode 3



Limit State ConceptULS Ed RdSLS Ed CdSLS Ed CdFatigue E c

Choice of materialb d f t h ibased on fracture mechanics (EN 1993-1-10)

Stability of members and platesSi l l f bi dSingle -value for combined actions,FEM-methods(EN 1993-1-1) (EN 1993-1-5)

Fatigue assessments unlessrecommended details are used

(EN 1993-2) (EN 1993-1-9)

Basic features of design rules for bridges


2. LOAD ASSUMPTIONS FOR STEEL BRIDGES

900 kN

500 kN

2 kN275 kN

11,0 m11,0 m

Load-model LM1



1000 kN12

600 kN

300 kN

6

3

11,0 m

3

Load-model LM1 (draft German NA)



Statistical distribution of characteristics of vehicle



Modelling of vehicles and surfaces



Modelling of bridges



Load-model and simulations



Dynamic effectsDynamic effects



K 210 K 138

Reference bridges for reliability analysis



Definition of target -value



P r o b a b i l i s t i c d e s i g n E C 1 - P a r t 2 L o a d M o d e l

L MMWQre q u ire d

W

GG

req uy

Q dM

WfM

1 0,1M

GG

M

Q d

w h e re L MQQQ d

MM

3 5,1G

L MQ

Q d

Q M

M

Definition of Q-value



Q-values from LM1



Effect of modification: aQ1q1K = 9 8 kN/m²Effect of modification: aQ2q2K = 2,5 5 kN/m²



Forecast of freight-volume



Development of permits for heavy vehicles



Results of WIM-measurements in NL



Fatigue load model specified in EN 1991 480 kN

Traffic Category Number of heavy vehicles N 1: 2-Lane Highways with a high rate of

heavy vehicles 2 • 106 / a

Number of expected trucks per year for a single lane

heavy vehicles2: 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 / aheavy vehicles

Fatigue loading model FLM 3


2. LOAD ASSUMPTIONS FOR STEEL BRIDGESes

M ffa tF f /m ax

c

with es

s ra

nge s a fe ty fa c to r

fo r fa t ig u e s tre n g th

re fe re n c e fa t ig u e s tre n g tha t 2 1 0 c y c le s6

ssm

ent w

litud

e st

re

d a m a g e e q u iv a le n c e fa c to rre p re s e n t in g th e s p e c tru m

m a x im u m s tre s s ra n g e fro mE C 1 -2 lo a d m o d e l

crack size a critical crack size acrit

gue

asse

sta

nt a

mpl

s a fe ty fa c to rfo r fa tig u e lo a d

d a m a g e e q u iv a le n tim p a c t fa c to r

detectable crack size a

pt fo

r fat

igle

nt c

onst

timesize a0

Ff = 1,00Mf = 1,00 – 1,15 for damage toleranceMf = 1,25 – 1,35 for safe life method

Inspection interval

Con

cep

equi

val

Assessment method for FLM 3



Fatigue details – welded attachments and stiffeners

EN 1993-1-9 - Fatigue resistance



Required moment of inertia from ULS and fatigue design for detail category 71

α = 1 ,0 U L S2 m

/m]

α = 0 ,8

U L S

F a tig u e

ista

nce

W/L

[cm

2M

omen

t of R

esi

S p a n L [m ]

Span limits for fatigue design



Joint for hangerAlternatives for joints of hangers:

ti i d j i toptimised joint:• continuously increasing stiffness (K90)

low curvature from bending• end of hanger with hole and inclined cut

l t t d f h f low stresses at end of hanger for K50

• ratio of inclined cut and connecting plate avoiding of stress peak at end of

hhanger

Recommendations for durable detailing



Hanger connection for arch bridges

1

2

3

4

Substitution of fatigue checks for critical details



Standard orthotropic steel deck with continuous stringers with cope holes in the web of the cross beam

Substitution of fatigue checks by structural detailing rulesrules



Structural detailing for deck plate

connection of deck plate to troughsp g75

12HV HV HV

14

300 300 300

design life load model 4without layer < 10 years

asphalticsealingPmB 45

30 - 50 years für t = 12 mm

PmB 45thermosetting

resinPmB 25

70 - 90 years

Recommended details of orthotropic deck



Structural detailing for cross beams

h

75

12T

tSteg

T

25> 0,15 hT hQTr

Steg

tLtrough = 6 mmtweb = 10 - 16 mm; verification of net web section requiredhcrossbeam 700 mmcrossbeam



Potential positions of cracks in the asphalt layer

Durability of asphalt layer



Steel bridges – serviceability limit state

Requirements for the minimum stiffness of stringers gi

rder

s

5

q gdepending on the distance between crossbeams

betw

een

cros

s g

a [m

] 4

AB

dist

ance

b

0

3

1000 5000 15000 2000010000 second moment of area IB of the stringers including deckplate [m4]

Condition for curve A 1 1,20m

IB

2

1 heavy traffic lane 2 web of main girder or

longitudinal girder



Verification to

Plate buckling

longitudinal edge xDefinition of a plated

Verification to web breathing

longitudinal edge

el w

idth

e ed

ge

x

b 21

Definition of a plated element

sub- panel

stiff

ened

pan

e

tran

sver

se

b G

aG a1 a4 a3 a2

stiffened panel length y




3. MODELLING OF STEEL BRIDGES

Shear lag effectb

==+

GS



Subdivision of a moment-distribution to elements with standard shape



-factor for shear lag



Differences in modelling

Modelling for ULS Modelling for fatigue




Fatigue effects on web stiffenersModelling for ULS




Frame and distorsional effectsModelling for ULS


4. SPECIFICATION FOR BEARINGS

Design principles for individual bearings

- Permission of movements minimizing the reaction forces - No tensile forces

N i ifi t di t ib ti f f t th b i- No significant redistribution of forces to other bearingsfrom accomodation to installation tolerances

- Specification of installation conditions with detailspof construction sequence and time variable conditions

- Measure to avoid unforeseen deformation of the bearings(non uniform contact)(non uniform contact)



Construction documents

Bearing plan (drawing of the bearing system) Bearing installation drawing (structural details) Bearing schedule (characteristic values from eachBearing schedule (characteristic values from each

action, design values from combination of action)



sliding rolling deforming

displace-ment

rotation

Functional principles of bearings







No. Action Eurocode

R f t t t T DIN EN 1991 1 5 2004 07

Actions for permanent and transient design situations

Reference to temperature T0 DIN EN 1991-1-5:2004-07

1.11.21.3

1.4

Self-weightDead loads Prestressing

Creep concrete

DIN EN 1991-1-7:2007-02DIN EN 1991-1-7:2007-02DIN EN 1992-1:2005-10 andDIN EN 1994-2:2006-07DIN EN 1992-1:2005-10

1.5 Shrinkage of concrete DIN EN 1992-1:2005-10

2.12.22.32.42.5

Traffic loadsSpecial vehicles Centrifugal forcesNosing forces Brake and acceleration forces

DIN EN 1991-2:2004-05DIN EN 1991-2:2004-05DIN EN 1991-2:2004-05DIN EN 1991-2:2004-05DIN EN 1991-2:2004-05

2.62.72.82.92.102.112 12

Footpath loading Wind on structure without traffic Wind on structure with trafficRange uniform temperature Vertical temperature difference Horizontal temperature differenceSoil Settlements

DIN EN 1991-2:2004-05DIN EN 1991-4:2005-07DIN EN 1991-4:2005-07DIN EN 1991-1-5:2004-07, 6.1.3 and 6.1.5DIN EN 1991-1-5:2004-07, 6.1.4 and 6.1.5DIN EN 1991-1-5:2004-07, 6.1.4 and 6.2DIN EN 1997 1:2009 092.12

2.132.142.152.16

2.17

Soil SettlementsBearing resistance/friction forces Replacement of bearing Pressure and suction from traffic Wind during erection

Construction loads

DIN EN 1997-1:2009-09DIN EN 1337, Part 2 to 8DIN EN 1991-2:2004-05DIN EN 1991-2:2004-05DIN EN 1991-4:2005-07 andDIN EN 1991-1-6:2005-09DIN EN 1991-1-6:2005-09

2.18 Accidental actions DIN EN 1991-1-7:2007-02

For transient design situations reduction of variable actions due to limited duration EN 1991-2, 4.5.3. For steelbridges also actions from installation of hot asphalt according to technical project specifications.



Actions in accidental design situations

• Specifications according to EN 1991-2

• Limitation of bridge movements by structural measuresLimitation of bridge movements by structural measures,e.g. stop devices at abutments

Actions in seismic design situations

Specifications according to EN 1998-1 and EN 1998-2



Determination of design values of movements and bearing forces Principles

C bi i di EN 1990 6 5 3 2 (2) i h i l f di Combination according to EN 1990, 6.5.3.2 (2) with partial factors according toEN 1990, A.2 and particular rules for climatic temperature effects

Movements due to creep and shrinkage by multiplying mean values inMovements due to creep and shrinkage by multiplying mean values inEN 1992-2 and EN 1994-2 by a factor of 1.35

Verification of static equilibrium (uplift of bearings) and anchoring devicesb l i 0 05 G iby applying 0.05 GK spanwise

Consideration of deformations of foundation, piers and bearings in themodelling of the structure, see EN 1991-2, 6.5.4.2g

Use of 2nd order theory for accounting for deformations of piers after installation of bearings if required by EN 1992-1-1, 5.8.2 (6).For calculation of pier deformations k = 0 5 may be applied to geometricFor calculation of pier deformations ky = 0,5 may be applied to geometricmember imperfections in EN 1992-1-1, 5.2.



Determination of design values of movements and bearing forces

Maximum and minimum constant temperature component: Climatic temperature effects

Ted min = T0 - F TN con - T0Ted, min T0 F TN,con T0Ted, max = T0 + F TN,exp + T0

additional safety elementcharact. Values EN 1991-1-5, 6.1.3.3

partial factor F = 1,35partial factor F 1,35

reference temperature during installation of the bearings, e.g. +10°C

Table E.4: Recommended values for T0

T [°C]Case Installation of bearing

T0 [°C]

steel bridges composite bridges concrete bridges

1 Installation with measured Temperature and with correctionResetting with bridge set at T0

0 0 0

2 Installation with estimated T0 and without correction by 10 10 102 0resetting with bridge set T0

10 10 10

3Installation with estimated temperature T0 and without correction by resetting and also one ore more changes in position of the fixed bearing

25 20 20

Td = Ted max - Ted minTd Ted,max Ted,minFor non-linear behaviour stepwise determination

Td = F TN



Reaction forces at fixed points resulting form resistance of the bearing system For sliding bearings:

kiiQikiQkG QQG 01

kGr

kiiQikiQkGakQH G

QQGQF

dinf,

01sup,1

Forces from l ti d

other variable actionsvertical actions of traffic load

self weight, dead loadsacceleration and braking

self weight, dead loadscoefficient of friction according EN 1337-1, 62.For PTFE sliding bearings max = 0,03

For elastomeric bearings

inf,,infinf

sup,,supsup1

dq

dqkQH AG

AGQF

d

Shear deformations of the bearingsforces from acceleration and braking

i l l f h d l

Shear deformations of the bearings according EN 1337-3

plan shear area of bearings

nominal values of shear modulus Gsup = 1,05 N/mm2

Ginf = 0,75 N/mm2


Choice of materialChoice of material 5. CHOICE OF MATERIAL

Assumption for a0

102faa

63c

initial crack

fatigue loading

4

faa 0d

a0

ad

design crack

initial crack

Safety assessment based on fracture mechanics

Kappl d Kmat dappl,d mat,d

Kmat,d (T27J, TEd)

Kappl,d (member shape, ad, 1·Ed)


5. CHOICE OF MATERIAL

Toughness-temperature - Load-strain-diagram

Design situations in the upper-shelf region B and the transition region A of the toughness-temperature diagram



Assessment scheme

K*appl,d Kmat,d TEd TRdTransformationSafety assessment based on temperature

TEd = Tmin + Tr + T + TR [T + Tpl ] TRd = T100

TEd TRd ResistanceAction side

Assessment scheme

Ed min r R [ pl ] Rd 100

• Influence of material toughnessT100 = T27J – 18 [°C]

• lowest air temperature in combination with Ed:

Tmin = -25 °Cmin• radiation loss:

Tr = - 5 °C• influence of stress, crack imperfection

and member shape and dimension:

]C[70

1025b

20kK

ln52T

41eff

6R

appl

• additive safety element:TR = +7 °C (with = 3,8)



Choice of material to EN 1993-1-10



National quality tests

AUBI-test according to SEP 1390 (1996)



trend analysis for the AUBI correlation



Choice of material given in Table 3.1 of EN 1993-2



Example: Thick plates for the composite “Elbebridge Vockerode“ (EN 1993-1-10)

Bridge system and construction

Cross section

SpanUpper chord

Support Support

Plate thickness for S355 J2G3

Upper chord

Bottom plates

75 75 115 135 115 85 85 60 60 60 115 140 145 140 115 60 60 60 85 85 115 135 115 75 75145

Construction at supports125,28

p

40

30 70 30 7070 95 45 70 95 45

40

50 70 50

4070

40

Construction at supports



Bridge St. Kilian



Bridge St. Kilian



Cast node for the bridge St. Kilian



Cast node for the bridge St. Kilian




6. DESIGN OF BRIDGE-ELEMENTS6.1 STABILITY RULES

Ed

Common design rules for column, lateral torsional, plate and shell buckling

lk

Ed Ed

skEd Ed

r

tEd EdEd/2

a

b

column buckling lat. tors. buckl. plate buckling shell buckling

crit

kult

crit

k

critdcrit

kdkult

RR

RERE ,,

Ed/2

0,60

0,80

1,00

1,20

a0

ab

cd

0 60

0,80

1,00

1,20

ab

cd

EN 1993-1-1 EN 1993-1-1

0 6

0,8

1,0

1,2

[-]

a0

EN 1993-1-5

0 6

0,8

1,0

1,2

χ

EN 1993-1-6critcritcritdcrit

0,00

0,20

0,40

0 0,5 1 1,5 2 2,5 3_

0,00

0,20

0,40

0,60

0 0,5 1 1,5 2 2,5 3_

0,0

0,2

0,4

0,6

0,0 0,5 1,0 1,5 2,0 2,5 3,0_p [-]

p

b

0,0

0,2

0,4

0,6

0,0 0,5 1,0 1,5 2,0 2,5 3,0λ

M

kult

M

kd 1RE

,


6.1 STABILITY RULES

Column buckling


6.1 STABILITY RULES

Column buckling curves


6.1 STABILITY RULES

Selection of buckling curves


6.1 STABILITY RULES

Test evaluation – weak axis buckling


6.1 STABILITY RULES

Test evaluation – weak axis buckling


6.1 STABILITY RULES

M-values according to EN 1990 – Annex D


6.1 STABILITY RULES

European buckling curve 2nd order theory with imperfection

d

!

d RE

N

k

!

d RE

lN

crit

dpld N

N ,

dd ,

crit

pl

NN

,

plk N,R

M

pldd

NR

Consequences:EE Option 1:

M

kd

RR

dMd EE .

M

critdcrit

NN

,

0,1M

Option 1:

Option 2:

Option 3:

2

2

0 1

1

M

d ee

Option 4:

Equivalence of buckling curves and 2nd order theory

Md

M *Option 5:


6.1 STABILITY RULES

d d d

dg

M-values for 2nd order analysis

0,5 0,685 0,870 0,477 0,661 0,895 1,03

1,0 1,136 0,597 0,953 1,082 0,627 1,05

1 5 1 846 0 342 1 43 1 734 0 369 1 081,5 1,846 0,342 1,43 1,734 0,369 1,08

2,0 2,806 0,209 1,906 2,605 0,228 1,09

3,0 5,476 0,10 2,859 5,039 0,109 1,09


6.1 STABILITY RULES

Imperfections for members with various boundary conditions

EIC

NEdNEd

a1

x

NEdNEd

x

2x

x

crit

Ed

Edd0e

critmax,crit

critd0ini

NNeM

e

xsinN1

1NeM

xsine

EdEdd0e

d0ini

max,crit2crit

Ed

EIN1

N1

crit

Ed

Use of buckling mode as imperfection


6.1 STABILITY RULES

Example for a column on elastic supportsExample for a column on elastic supports


6.1 STABILITY RULES

Column buckling Lateral torsional buckling

1MM

NN EdEd 1

MM

NN

Fl

FlEdy

Fl

FlEd ,

MN RkyRkpl ,, MN FlRky

FlRkpl ,,

1M

1

1eMN

MM

MM

EdzFl

Rky

Flcrit

critz

Edz

Rkz

Edz

,

*

,,

,

,

,1

NN1

1M

eNNN

EdRk,y

*Ed

Rk,pl

Ed

M critz,Ncrit

FlRk,pl

FlRk,y

M*

NM

2,0e

Rk,pl

Rk,yN

*

NM

2,0e

11

12,0

*

22

2

MM

M

Fl

MMM

1

1

12,0 2NN

NNN

1 MMFl

22

1

2 220150 ,,

Equivalence of flexural and lateral torsional buckling


6.1 STABILITY RULES

Comparison of LTB-curves

1,0

LT

Lateral torsional buckling for GIT=oo

Lateral torsional buckling for a beamHEB 200

B b

Bc a

0 0

Bc b

0,00,0 1,0 2,0LT


6.1 STABILITY RULES

kkult E

R,1. Input parameters:

Procedure for lateral torsional buckling assessments using the buckling curves:

dE

d

critcrit E

R

critt

kult

,

crit

*crit*

2. Modification of imperfection factor:critt

*crit DIG

2* 20150

where is determined without effect of

3. Use of flexural buckling curve:

2,015,0

4 Assessment for design point x

22

1

1, M

kult

4. Assessment for design point xd


6.1 STABILITY RULES

Comparison of laterial torsional buckling curves


6.1 STABILITY RULES

check:

crit

kult

,

,*

check:

Determination of design point xd

1,

M

kult


6.1 STABILITY RULES

Example: Portal frame

1068

knee‐pointLateral support

3 4240∙12

8000

1

2 5

6

240∙15

0

556∙5

240∙12

240∙12

S 355 J2 G3

0

1 6

7

550∙5

240∙15

24420


6.1 STABILITY RULES

1 55Moment distribution [kNm]

ult,k,min=1,55

ult,k (xd)=1,94

Distribution of compression forces [kN]


6.1 STABILITY RULES

Example: Modal out-of-plane deformation crit=1.85

xd


6.1 STABILITY RULES

1. Calculation with extreme value ult,k,min 2. Calculation design point xd

55.1, kult 94.1, kult

85.1crit

84.1* crit

,

915.085.155.1

408.049.085.154.1*

*

crit

crit

05.185.194.1

crit

064.12.015.0 2* LT

50.0622.02

12

225.1LT

50.059.0 22

00.188.010.1

55,1622.0

M

ult

contact splice sufficient

00.104.110.1

94.159.0,

M

kult

contact splice sufficient

M M

Check of out-of-plane stability


6.1 STABILITY RULES

Example: Composite bridge


6.1 STABILITY RULES

Example: Cross-section of the composite bridge


6.1 STABILITY RULES

Example: Moment distribution critical for out-of-plane stability of main girders


6.1 STABILITY RULES

Example: cross-beam at supports


6.1 STABILITY RULES

Example: intermediate cross-beam all 7,50 m


6.1 STABILITY RULES

Example: crit-values and modal out-of-plane deformations

critical area

critical area

critical area


6.1 STABILITY RULES

Example: Input for ult,k-values

295330

250

180

critical areas


6.1 STABILITY RULES

in field at point P1 at support (point P1)

Checks for lateral-torsional buckling

in field at point P1 at support (point P1)

83,1180330

k,ult 184,1250295

k,ult

8576,8crit

45,08576,883,1

489,17crit

26,0489,17

184,1

37,8*crit

72,076,086,837,8*

,

20,15* crit

66,076,0491720,15*

69,0

82,0

49,17554,0

96,0

00,137,110,1

89,182,0

M

k,ult

00,103,110,1

184,196,0

M

k,ult


6.1 STABILITY RULES

Column-like behaviour:

Column buckling and plate buckling

imposed loadson loaded edge

resulting displacements iat loaded edge

Plate-like behaviour:

resulting loadson loaded edge

imposed displacement on loaded edge


6.1 STABILITY RULES

Example: Torsional buckling according to EN 1993-1-1

33

9

33 tbCM

tbIM 34

3

Column:

M 3

12;sin EG

exA

x

byAw sinPlate:

2

2

M

MM

cr i

IGECN

Ncrit

12e b

0 ai

ANcrit

cr

Acrit

cr

161

112 2

22

2

2

2

2 bb

tE

16

112 2

2

2

2

2

2 bb

tE

k

eb 429,0

2

k

eb 429,09,0

2


6.1 STABILITY RULES

Torsional buckling column-like behaviour plate-like behaviour

compression compressioncompressionstress

compressionstrain

AN

N EAN

N

response responseresponse strain

response stress

f1

bending

geometric strain effect:

NN yM f1

2

222

1

2

4

crit

critcritogeom

NN

NN

NN

bs

les


6.1 STABILITY RULES

~2

1k

column buckling plate buckling

yf1 yf1

yfk bendingbending

yf

yf

compression

bending

compression

11

120

*

20*

1

1

bsd 20

bsd 70

assumption: assumption:

11

12.0*

2.00 7.00

1

1

11

12.0 ****

1

* 1

11

12.0 2*

2* 2.015.0

22

2

2.015.0 *


6.1 STABILITY RULES

*

Column buckling curve and plate buckling curve

,,

EulerWinter 2

22.0

21

7.00*

Column buckling


6.1 STABILITY RULES

x

Stress- and strain-controlled plate buckling

x

imperfectx

x xx E perfect

imperfect

imperfectxx E

x


6.1 STABILITY RULES

4 b

Modification of imperfection factor

22

*

1

1

ab

ab

crit

crit

crit *

crit

column plateba


6.1 STABILITY RULES

crit

crit

*

Interaction between column buckling and plate buckling *

crit

platecolumn

column buckling

Winter

ccc 2

10;1,

,

ccr

pcr

*,

,

crit

crit

ccr

pcr


6.1 STABILITY RULES

“Hybrid cross-section” due to different stress-limits

yield plateau

resulting force

yield plateau


6.1 STABILITY RULES

”Yielding effect” in hybrid cross-sections

Method 1

Method 2


6.1 STABILITY RULES

Method 1

”Yielding effect” in bending

Method 2


6.1 STABILITY RULES

Extension of method 2


Choice of materialChoice of material 6.1 STABILITY RULES

Methods in bridge design

Method 1

Use of effective cross-section

Method 2

Use of stress-limit


6.1 STABILITY RULES

Method 1

l t b kli f t t

Method 2

l b l l t b kliplate buckling for stress components global plate buckling

Ed x

critEdEdzEdxEd ,,, ,,

xcrit ,

glob

zzcrit ,

z

,crit


6.1 STABILITY RULES

Method 1 Method 2

Plate-buckling coefficients

Method 1 Method 2

,

for rigidend post

w

13.0*

l kl

p p

x

x

crit

ultx

,

,

z

crit

ultz

,

,

globalcrit

kultglob

,

,

zcrit ,

xcrit

ult

,

,


6.1 STABILITY RULES

Cross-section assessment

Method 1: Effective cross-section for x

0,1f yd

xEd1

ykff 11

Rd

ykyd

ff

1,1Rd

Reduction factor

(for )

0,1

3553,02p

p

Slenderness

Effective web

1b

bb wceff 0

Effective flange

fefft bb ,

Pi,x

ykp

f

Critical stress

effeffeffeff bbbb 6,04,0 2,1,

11112,01

16k2

43,0k 1Critical stress

ePi,x k 22

2st

2

e 1b12tE

11 für für


6.1 STABILITY RULES

rigid end flexible endt

Method 1: Resistance to shear

flexible end post

post post

cr

ykw

f

3

rigid end post

reduction factor

3

fthV yd

wwwRd,bw

EdV

w

83,0w 1.0 1.0

081830 /830 /83,0

Rd,bw

Ed3 V

V08,183,0 w w/83,0 w/83,0

08,1w w7,037,1 w/83,0


6.1 STABILITY RULES

Method 1 Method 2

Assessment for plate buckling

1k,ultglob

Method 1 Method 2Interaction

1M

,g

interaction

1

Ed

11211

12

3,

,1

3

1

Rdpl

Rdf

Rd

Ed

y

MM

VVf


6.1 STABILITY RULES

German National Annex

Method 1 only applicable to girders without longitudinalstiffners

The use of Method 1 should be supplemented by The use of Method 1 should be supplemented bychecking global buckling with Method 2 forcharacteristic load level andkE 10,1M


6.1 STABILITY RULES

Example: cross-section check for a composite bridge

Cross-section at support Cross-section at midspan

stresses

MNm25,107M Ed

MN47,7VEd

stresses

1095,98th

w

w

< 345 MPa

stresses

192151w

w

thMNm1,56M Ed

MN0,1VEd

< 295 MPa

MN31117M

stresses :

78,5k

51598 wh 80,5k

stresses :

MNm31,117M Rd,f

MN14,8V Rd,bw

515,98 wt

MPa6,112cr

33,1w

675,0w

MNm6,135M Rd,pl

MN44,4V Rd,bw

5,044,40,1

3

4,51151w

w

th

MPa2,48w

03,2w 50,0w


6.1 STABILITY RULES

Panel plate buckling check with method 2=83 Mpa

94,03.187

176

13,325608000

MPae 6.19

23k MPacr 8.4506.1923 55,2crit

6k MPacr 6.1176.196 42,1crit

888.01141

411

21

2,

2,

2

,

critcritcritcrcrit

127.1critf

56.13 2

2,

kk EE

ykult

f

18,1crit

k,ult

15.180.013.015.0

00.103.110.1

56.173.0,

M

kultw

73.012

w


6.1 STABILITY RULES

Verification of stiffened web plate for launching, Bridge Oehde


6.1 STABILITY RULES

Stiffened web panel and loading


6.1 STABILITY RULES

Use of method 2 for stress-assessment

kNmM 3,44max MPa24022068152

kNmM 83,2max MPa24024017664

Stiffener :

Webplate:


6.1 STABILITY RULES


6. DESIGN OF BRIDGE-ELEMENTS6.2 FATIGUE RULES

Standardized Wöhler- curve for welded details


6.2 FATIGUE RULES

EinDD

Damage equivalence

Ri

Eii N

DD

63

3EiEI n 63 102C

Damage equivalence:

Ei3EiEi

3e nn

3

1

Ei

Ei3Ei

en

n

Ein


6.2 FATIGUE RULES

Reservoir-counting method


6.2 FATIGUE RULES

Case 1

Various design situations

Case 2

M difi d

Case 3

Modified Wöhler curvefor using theMiner-rule


6.2 FATIGUE RULES

Representations of fatigue spectrum

spectrum for design

after vibrations

cut off

cut off


6.2 FATIGUE RULES

Distribution of weights of heavy vehicles

total weight type 1 total weight type 2total weight type 1 total weight type 2

total weight type 3 total weight type 4


6.2 FATIGUE RULES

Load-models for fatigue checks of road bridges

FLM 3Main structure

Detailed FLM 4


6.2 FATIGUE RULES

Safety-plan for damage tolerant design

153 41

105102 6

3

6

3

Mf

D

EjEjFf

Mf

c

EiEiFf nnD

inspection intervals

41

111

5

nMfFf 145

MfFf

n0 20 40 60 80 100 120 140

ff MfFf

0.1 MfFf 314 nff

15.1 MfFf

35.1 MfFf

1115.14

5 n

0135.14

5 n


6.2 FATIGUE RULES

Mean value m

Characteristic value: m – 1 645 Characteristic value: m – 1,645

Design value:

C t l f ti 15122 5Control of actions

No control of actions

15,122 5 MfN

35,150,45,4 5 MfN


6.2 FATIGUE RULES

Assessment proceduresc

EFf

2

Use of -values

Crossing of FLM3

MfEFf 2

4321

minmax2 E

g

stress history

ti th d

effects of other lanes

counting method

Miner-rule

design life

other lanes2E

span length

traffic composition


6.2 FATIGUE RULES

1 value from simulations with Auxerre traffic


6.2 FATIGUE RULES

Example: Fatigue assessment for a composite bridge = 1.947 = 1.947

= 1.90 = 1.715 = 1.90

31.3

23.61

22

stress ranges (max – min) at lower flangest ess a ges (max min) at o e a ge

Transverse weld from stiffener:12 Butt weld of flange:

MPaE 805.593.319.12

MPaE 778.446.269.12


6.2 FATIGUE RULES


6. DESIGN OF BRIDGE-ELEMENTS6.3 ROPE STRUCTURES

Rope-structures - Stayed cable bridges

Definition

• Any prestress is generated by preloadingy p g y p g

• Preloading is a process to impose• forces or• deformations

• The effects of preloading may be i ti f t ( t )• variations of stresses (prestress)

• variations of deformations• other variations of permanent stage


6.3 ROPE STRUCTURES

1a) Prestressing by internal 1b) Prestressing of trusses by

Examples for preloading processes

1a) Prestressing by internaltendons

1b) Prestressing of trusses bycables in hollow sections

1c) Prestressing by externaltendons

1d) Prestressing of jointssubjected to tension or friction


6.3 ROPE STRUCTURES

2) Prestressing by propping 4) Prestressing by imposed deformation


d

steel

d

steel

cast of concrete cast of concrete

composite composite

phase 1 phase 2 phase 1

3) Prestressing by sequence of casting concrete


6.3 ROPE STRUCTURES

5a) Prestressing of 5b) Prestressing of


) gcable structures

) garches by string-elements

b ow -st rin g

5c) Prestressing of guyedmasts

5d) Prestressing of cablestayed structures


6.3 ROPE STRUCTURES

Principles

f• It is possible to define the preloading or prestressingprocess by all necessary steps including controls

• It is not possible to define “prestress” as an effect of prestressingor preloading in a general way, that covers all cases


6.3 ROPE STRUCTURES

Example for the applicability of “prestress”

stress before prestresses: 0,0 lq

stress immediately after prestressing:

prestress:

lq ,0

00000 llll p es ess 0,0,0,0,0 lqlqllq


6.3 ROPE STRUCTURESof

ca

bilit

y o

n-ap

plic

r the

non

mpl

e fo

rst

ress

”E

xam

“pre

s


6.3 ROPE STRUCTURES

Conclusion

“P” in EN 1990

a) preloading or prestressing process leading to a structural shape or behaviour as required

b) prestress in specific cases where defined


6.3 ROPE STRUCTURES

Treatment of preloading and prestressing processes in the construction phase

Target: attainment of the required structural formand distribution of effects of (G+P)

Conclusion: calculation with characteristic values, linearmaterial law: stress limitations and prestressing of cables.


6.3 ROPE STRUCTURES

Treatment of preloading and prestressing processes in the construction phase


6.3 ROPE STRUCTURES

Treatment of preloading and prestressing processes in the service phase

Target: ULS verification on the basis of:• permanent actions G(G+P)pe a e ac o s G(G )• permanent from resulting from (G+P)• imperfections of the form• variable actions {Q + Q }• variable actions Q{QK1 + 0QQ2}

C l i C l l ti ith th t f i t dConclusion: Calculation with the permanent form associated with the effect from G(G+P)


6.3 ROPE STRUCTURES

Treatment of preloading and prestressing processes in the service phase


6.3 ROPE STRUCTURES

Treatment at counterflexure points

Treatment at counterflexure points, or where the action effects from (G+P) are limited (e g by decompression):effects from (G+P) are limited (e.g. by decompression):

G = G, where 0,05 0,10

applied to influence surfaces.


6.3 ROPE STRUCTURES


7. ASSESSMENT OF EXISTING STEEL BRIDGES

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Dissemination of information for training – Vienna, 4-6 ... · Dissemination of information for training – Vienna, 4-6 October 2010 2 LIST OF CONTENTS 1. The European Standard