brussels, 18-20 february 2008 – dissemination of...

Brussels, 18-20 February 2008 – Dissemination of information workshop 1

EUROCODESBackground and Applications

Eurocode – EN 1990 Basis of Structural Design

Structural Analysisand

Design by Testing

Gerhard SedlacekChristian MüllerRWTH Aachen


EUROCODESBackground and Applications Contents EN 1990 – Section 5

SECTION 5 STRUCTURAL ANALYSIS ANDDESIGN ASSISTED BY TESTING

5.1 STRUCTURAL ANALYSIS 5.1.1 Structural modelling5.1.2 Static actions 5.1.3 Dynamic actions5.1.4 Fire design

5.2 DESIGN ASSISTED BY TESTING


EUROCODESBackground and Applications Contents Section 5

for calculation Appropriate structural models

predicting structural behaviour at limit state 5.1.1(2)

involving relevant variables5.1.1(1)

acceptable accuracy5.1.1(2)

established engineering theory and practice, where necessary verified experimentally

Design assisted by testing

Design may be based on combination of calculations and tests see Annex D [5.2(1)]The limited number of tests to be considered in the reliability required [5.2(2)]

Partial factors should be as inEN 1991 - 1999 [5.2(3)]

Modelling

For static or equivalent static actions For dynamic actions For fire design

Modelling based on appropriate choice offorce-deformation relationshipof [5.1.2]

and[5.12(2)]

members connections ground boundary conditions intended

Modelling based on [5.13(1)]- masses- stiffness- damping characteristic- boundary conditions as intended [5.13(2)]- strengthsfor all structural and non-structural members

Contribution of soil modelled by equivalent springs and dash pots [5.1.3(4)]

Where relevant (for wind and seismic actions) actions from modal analysis or where the fundamental mode is relevant from equivalent static forces [5.1.3(5)]

Dynamic actions also expressed as time histories or in the frequency domain to be dealt with by appropriate methods [5.1.3(6)]

Where relevant dynamic analysis also for SLS [5.1.3(7)] see Annex A, EN 1992 - 1999

In case of determination of equivalent static action dynamic parts either included implicitely or by magnification factors

2nd order theory [5.1.2(3)]when increase of action effects significant see => EN 1990 - 1999

Indirect actions to be introduced in

linear elastic analysis directly or by equivalent forces

non-linear analysis as imposed deformations

Structural fire design analysis based on fire scenarios considering models for [5.1.4(1)]- temperature evolution in the structure- mechanical non-linear behaviour of [5.1.4(6)] structure at elevated temperature (see EN 1992-1999) [5.1.4(4)]

Fire exposure as- nominal fire exposure (5.1.4(3))- modelled fire exposure

Verification of the required performance by either - global analysis - analysis of subassemblies or member analysisor by tabulated data or test results

Specific assessment methods within- uniform or non uniform temperature with cross-section and along members

- analysis of individual members and interaction of members



deflection

test load Rstatic

linear behaviour

time

deformation controlled

Product Resistance

Basis assumptions for static analysis


EUROCODESBackground and Applications Basis assumptions for static analysis

Actions

G permanent

ψ2Qqp quasi permanent

ψ1Qk frequentψ0γqQk combination

Qk characteristic

γqQk extreme

Verification: ULS (static)

{ }M

kddd

RRQGEEγ

=≤+=


EUROCODESBackground and Applications Code for type of static analysis

GMNIAGMNAMNA

non-linear

GNIAGNALA

linear

imperfectionincluded

non-linearlinear

Geometry

Material

σ

ε

σ

ε


EUROCODESBackground and Applications Action effects in static analysis

γF

over

linea

r linear

underlinear

load amplification γ

γNγNγF

γFγNγN

action effect


EUROCODESBackground and Applications Substructuring for static analsysis


EUROCODESBackground and Applications Consideration of stiffness of connections


EUROCODESBackground and Applications Dynamic actions and response


EUROCODESBackground and Applications Static and dynamic actions for traffic loads


EUROCODESBackground and Applications Contents Annex D

ANNEX D (INFORMATIVE) DESIGN ASSISTED BY TESTING

D1 SCOPE AND FIELD OF APPLICATION D2 SYMBOLS D3 TYPES OF TESTSD4 PLANNING OF TESTS D5 DERIVATION OF DESIGN VALUESD6 GENERAL PRINCIPLES FOR STATISTICAL EVALUATIONSD7 STATISTICAL DETERMINATION OF A SINGLE PROPERTY

D7.1 GeneralD7.2 Assessment via the characteristic value D7.3 Direct assessment of the design value for ULS verifications

D8 STATISTICAL DETERMINATION OF RESISTANCE MODELS D8.1 GeneralD8.2 Standard evaluation procedure (Method (a))

D8.2.1 General D8.2.2 Standard procedure

D8.3 Standard evaluation procedure (Method (b))D8.4 Use of additional prior knowledge


EUROCODESBackground and Applications Contents of Annex D

Types of tests (D3)a) to determine ultimate resistance or serviceability propertiesb) to determine material properties with standardized testing proceduresc) to reduce parameters in load and load effect modelsd) to reduce parameters in resistance modelse) to check identity or quality of delivered productsf) to obtain information for executiong) to check the behaviour of an actual structure

Planing of tests in agreement with test organisation covering- objectives and scopes- prediction of test results- specification of test specimens and sampling- loading specification- testing arrangement- measurements- evaluation and reporting of tests [D4]

Evaluation of tests for single material properties and for resistances [D.5, D.6]

for presentation of resistance [6.3.5(2)] for presentation of resistance [6.3.5(4)]

}{1d

Rdd XRR

γ= }{1

KKM

d XRRγ

=

Determination of the single material property XK and Xd from tests Xi [D.7]

Determination of resistance RK(XK) and Rd {XK} form tests Rei [D8]

Test valuation according to

[D.5-D8]

Test evaluation

according to [D5-D8]



Procedure via XK: [D.7.2]

kn from table D1mx and Vx from

Procedure via RK: [D.8.2]

1. theoretical deterministic function Rt

2. Comparison Rexp - Rt to improve Rt

3. Probabilistic function

4. Mean value deviation

5. Coefficient of variation vδ for error terms δi

6. Inclusion of vxi for variables Xi

)1( xnxKn VkmX −=

nxmx1Σ

=

x

xx m

SV =

22 )(11

xi mxn

Sx

−Σ−

=

m

Kdd

nXXγ

η )(=

ti

eii Rb

R=δ 22 )1(

11

−Σ−

≈ inS δ

δ

22δδ

SV ≈

222ixR VVV Σ+=

δ

δfRbR=

ti

ei

RR

nb Σ≈

1



7.

kn, k from table D1

8.

25.0)( QQkQkmK

nrtrteXgrtbR −−− ∞= δδαα

2ixrt VQ Σ≈

2δδ VQ ≈

2RVQ≈

QQrt

rt ≈α

QQδ

δα ≈

M

Kd

RRγ

≈

Procedure via Xd: [D 7.3]

kdn from table D2

Procedure via Rd: [D 8.3]

kdn, kd from table D2

)1( xdnxd vkmX −=η25.0)( QQkQk

mddnrtrtdeXgrtbR −−− ∞= δδαα


EUROCODESBackground and Applications Procedure to obtain reliable values Rk

excluded by appropriate choice of

material

Failure modesfracture

Brittle failure Ductile failure

fractureyielding

1. Mode 0excessive deformation by yieldinge.g. tension bar

Mode 1member failure by instabilitye.g. column buckling

Mode 2fracture after yieldinge.g. bolt

4. Characteristic value Rk = γM Rd

3. Recommended values

γM1 = 1,10 γM2 = 1,25

2. Test evaluation

( )0M

ykd

fRR

γ=

( )1M

ykd

,fRR

γ

λ=

( )2M

ukd

fRRγ

=

γM0 = 1,00

( ) 80,3;5,08,0expmR 2RRRd =βσ−σβ=



Reliability links between Product Standard, Execution Standanrd and Eurocode 3

Requirements for quality

Tests with memberscomplying with

Product Standards and Execution

Standards

Evaluationof Rexp acc. to EN 1990

Design standardcharacteristic resistance

Rk = Rnom χ(e0)for Rd = Rk / γM

where γM = 1,10 recom. value

Product Standards

- dimensions- tolerances of

dimensions- lower limits for

material properties (fu, fy)

fu ,fy

f

Execution Standardminimum executionquality:- straightness- tolerances- flawsLe

e

f

S

Rexp

Rcalc

γM

Rm

Rd

Rk }



Determination of characteristic values Rk and γMvalues from tests

Conditions for numerical value of γM

Product standards for materials and semi-fabricated products

EN 10025

Execution standardEN 1090 – Part 2

Design standard Eurocode 3

Prefabricated steel componentfor component testing

Component tests to determine Rexp

Engineering model to determine Rcalc

Rk = γMi Rd

Classification accord. to γMi (1,0; 1,10; 1,25)

γMi = Rk / Rd

S

Rexp

Rcalc

γM

Rm

Rd

Rk }

Test evaluation accord. to

EN1990- Annex D

1,0

Rexp/Rcalc

Parameter X1

O O O O O OO

O O

Rexp/Rcalc

OO

O OO

OO

OO

Parameter X2

1,0


EUROCODESBackground and Applications Probability distribution of experimental data



Use of test evaluation method for various regulatory routes

R & D Unique Verification

Technical Approval

Standardisation

Product Innovation

Time

Practical Application

proving satisfactory

Acknowledged state of the art



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_λ

a0

ab

cd

0,00

0,20

0,40

0,60

0,80

1,00

1,20

0 0,5 1 1,5 2 2,5 3_λ

ab

cd

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_λp [-]

χ p [-

]

a0

b

EN 1993-1-5

M

kult

M

kd 1RE

γχα

≤γχ

≤ ,

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

( )λχ=χαα

==λ=α=α

crit

kult

crit

k

critdcrit

kdkult

RR

RERE ,,

skEd Ed

r

tEd EdEd/2

a

Ed

b

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



Test evaluation for buckling curves and γM-values

Column buckling Lateral torsional buckling Plate buckling

0,0

0,2

0,4

0,6

0,8

1,0

1,2

0 0,5 1 1,5 2 2,5 3_λ [-]

χ [-]

KSL a0

KSL a

KSL b

KSL c

KSL d

Euler

A5.1: IPE160, S235

A5.2: IPE160, S235

A5.3: IPE160, S235

A5.4: IPE160, S235

A5.5: IPE160, S235

A5.6: IPE160, S235

A5.7: IPE160, S235

A5.10: HEM340, S235

A5.11: HEM340, S235

KSL bα=0,34

0,0

0,2

0,4

0,6

0,8

1,0

1,2

0 0,4 0,8 1,2 1,6 2 2,4 2,8_λ [-]

χ [-]

KSL a0KSL aKSL bKSL cKSL dEulerABDFGHIJZ

A

C

B

D

E

F

G

H

I

JZ

KSL aα=0,21

0

0,2

0,4

0,6

0,8

1

1,2

0 0,5 1 1,5 2 2,5 3_λ [-]

χ [-]

VBK a0VBK bBeulkurve für lok. Lasteinl. nach ENV 1993-1-5KarmanEinseitige Lasteinleitung a)Zweiseitige Lasteinleitung b)Einseitige Lasteinleitung am Trägerende c)

Fall b) Fall a) Fall c)

VBK bαp=0,34

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