Upload
phamanh
View
227
Download
0
Embed Size (px)
Citation preview
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
Brussels, 18-20 February 2008 – Dissemination of information workshop 2
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
Brussels, 18-20 February 2008 – Dissemination of information workshop 3
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
Brussels, 18-20 February 2008 – Dissemination of information workshop 4
EUROCODESBackground and Applications
deflection
test load Rstatic
linear behaviour
time
deformation controlled
Product Resistance
Basis assumptions for static analysis
Brussels, 18-20 February 2008 – Dissemination of information workshop 5
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
=≤+=
Brussels, 18-20 February 2008 – Dissemination of information workshop 6
EUROCODESBackground and Applications Code for type of static analysis
GMNIAGMNAMNA
non-linear
GNIAGNALA
linear
imperfectionincluded
non-linearlinear
Geometry
Material
σ
ε
σ
ε
Brussels, 18-20 February 2008 – Dissemination of information workshop 7
EUROCODESBackground and Applications Action effects in static analysis
γF
over
linea
r linear
underlinear
load amplification γ
γNγNγF
γFγNγN
action effect
Brussels, 18-20 February 2008 – Dissemination of information workshop 8
EUROCODESBackground and Applications Substructuring for static analsysis
Brussels, 18-20 February 2008 – Dissemination of information workshop 9
EUROCODESBackground and Applications Consideration of stiffness of connections
Brussels, 18-20 February 2008 – Dissemination of information workshop 10
EUROCODESBackground and Applications Dynamic actions and response
Brussels, 18-20 February 2008 – Dissemination of information workshop 11
EUROCODESBackground and Applications Dynamic actions and response
Brussels, 18-20 February 2008 – Dissemination of information workshop 12
EUROCODESBackground and Applications Static and dynamic actions for traffic loads
Brussels, 18-20 February 2008 – Dissemination of information workshop 13
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
Brussels, 18-20 February 2008 – Dissemination of information workshop 14
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]
Brussels, 18-20 February 2008 – Dissemination of information workshop 15
EUROCODESBackground and Applications Contents of Annex D
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
Brussels, 18-20 February 2008 – Dissemination of information workshop 16
EUROCODESBackground and Applications Contents of Annex D
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
Brussels, 18-20 February 2008 – Dissemination of information workshop 17
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=
Brussels, 18-20 February 2008 – Dissemination of information workshop 18
EUROCODESBackground and Applications
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 }
Brussels, 18-20 February 2008 – Dissemination of information workshop 19
EUROCODESBackground and Applications
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
Brussels, 18-20 February 2008 – Dissemination of information workshop 20
EUROCODESBackground and Applications Probability distribution of experimental data
Brussels, 18-20 February 2008 – Dissemination of information workshop 21
EUROCODESBackground and Applications
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
Brussels, 18-20 February 2008 – Dissemination of information workshop 22
EUROCODESBackground and Applications
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
Brussels, 18-20 February 2008 – Dissemination of information workshop 23
EUROCODESBackground and Applications
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