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Lecture no 8

Content: • Calibration of partial safety factors

– Partial safety factor method – relation to FORM– Design value format in Eurocodes– Determination of partial safety factors

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IntroductionApplication of probabilistic methods - examples:• Offshore structures:

– fixed and floating platforms – ships– coastal structures

• Bridges & tunnels• Wind turbines• Buildings – reliability-based code calibration• Existing structures

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Building codes

„Normal structures“ are designed according to structural design codes

Design codes: reliability-based calibration of partial factors

• Normal purposes• Common design• Well known materials• Well tested maintenance

No design codes (Exceptional Structures) – probabilistic design:• New purposes• Unusual designs• New materials• New maintenance

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Reliability based code calibration

Examples:• US, Canadian, UK, … building and bridge structural codes• Denmark:

– DS409: 1998– DS409: 2006– EN1990 – National Annex (2006)

• Eurocode – EN1990 / ISO 2394– Design value format

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Reliability based code calibration

Optimality and Target Reliabilities• Acceptance criteria may be established on the basis of

– cost benefit considerations economic optimum reliability level– LQI (Life Quality Index) lower limit on reliability level

• JCSS minimum reliabilities for ULS verification (1 year reference period)

• Eurocode minimum reliabilities:

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Code based design

Standard Code Format – Component based- Safety format- Design equations- Enveloping loads- Load combinations- Material characteristics- Characteristic values / partial safety factors- etc.

Robustness requirements – system based

Quality control requirements - human errorsInspection & maintenance - deterioration

System aspects

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Overview Eurocodes

• EN 1990 Eurocode 0: Basis of Structural Design• EN 1991 Eurocode 1: Actions on structures• EN 1992 Eurocode 2: Design of concrete structures• EN 1993 Eurocode 3: Design of steel structures• EN 1994 Eurocode 4: Design of composite steel and

concrete structures• EN 1995 Eurocode 5: Design of timber structures• EN 1996 Eurocode 6: Design of masonry structures• EN 1997 Eurocode 7: Geotechnical design• EN 1998 Eurocode 8: Design of structures for earthquake

resistance• EN 1999 Eurocode 9: Design of aluminum structures

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Limit state designLimit states:

• Ultimate (ULS)– safety of people, and/or– safety of the structure

• Serviceability (SLS)– functioning of the structure or structural members under

normal use– comfort of people– appearance of the construction works,

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Limit state designUltimate limit states:

• Persistent design situations - normal use

• Transient design situations - e.g. execution or repair

• Accidental design situations - unusual conditions – e.g. fire, explosion, impact or consequences of local failure

• Seismic design situations - horizontal mass load

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Basic variables - loadsCharacteristic values

Permanent loads: Gk• If variation of G is small (COV < 5-10%) Gk = mean value• If variation of G is large, use two values:

– Upper value Gk,sup (95% fractile) – Lower value Gk,inf (5% fractile)

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Basic variables - loadsVariable loads:• Characteristic value Qk (98% fractile in distribution of annual max

load – 50 år return period)Other representative values:• Combination value 0Qk

• Frequent value 1Qk (exceeded in 1% af reference period)• Quasi-permanent value 2Qk (exceeded in 50% af reference period)

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Ultimate Limit States (ULS) - DKCombination of loads – persistent or transient design situationsSTR/GEO:

(6.10b)

(6.10a)

EQU:(6.10)

"...""""""""" 3,3,02,2,01, 321 kQkQkQkGd QQQGS

kGd GS ""

"...""""""""" 3,3,02,2,01, 321 kQkQkQkGd QQQGS

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Reliability level – DK National annexULS 1 year reference period

NKB: 1975 β = 4.3 (loads: Normal distributed)JCSS β = 4.2EN 1990:2002 β = 4.7DS 409:1998 β = 4.8

DS 409:2006 β = 4.3EN 1990 Nat. Annex β = 4.3

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Eurocode – National Annex: 2007

Load bearing capacity

M = m R

wherem partial factor for strength parameterR partial factor for computational model

R = 1 2 3 1 partial factor for failure mode2 partial factor for computational model3 partial factor for control

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Eurocode – National Annex: 2007

Uncertainty and partial factors (0 = 1 1 = 1 3 = 1)

index 0 : uncertainty related to production test data / laboratory testsindex p: uncertainty related to difference between production / laboratory

conditions and real structure

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2202

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tor Partialfac

y Uncertaint

capacity bearing Load model nalComputatio parameter Strength

mMm

mMpmpmm VVVVVVVVV

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Eurocode – National Annex: 2007Computational model uncertainty - examples

small bias: 1.06small COV: V20 =12%

large bias: 2.5large COV: V20 =25%

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Experimental capacity [kN]

Calc

ulat

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apac

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N]

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Experimental capacity [kNm]

Calc

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apac

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Eurocode – National Annex: 2007Material partial factors

Partial factor M is calibrated to the reliability index β = 4.3

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1,1

1,2

1,3

1,4

1,5

1,6

1,7

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4

V_M

gam

ma_

M

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Lecture no 8

Content: • Calibration of partial safety factors

– Partial safety factor method – relation to FORM– Design value format in Eurocodes– Determination of partial safety factors