Introduction to EN 1990 – Section 6

1

EUROCODESA tool for building safety andreliability enhancement

Introduction to EN 1990 – Section 6

Workshop on Eurocodes: Training the trainersMoscow - 09 December - 10 December, 2010

Section 6: Verification by the partial factor method

Annex B: Management of structural reliability for construction works

Jean-Armand CalgaroJean-Armand CalgaroChairman of CEN/TC250Chairman of CEN/TC250

TC250TC250

2


Section 6 - Section 6 - Verification by the partial factor Verification by the partial factor methodmethod

6.1 General6.2 Limitations and

simplifications6.3 Design values6.3.1 Design values of

actions6.3.2 Design values of the

effects of actions6.3.3 Design values of

material properties6.3.4 Design values of

geometrical data6.3.5 Design resistance

6.4 Ultimate limit states6.4.1 Verifications : General

6.4.2 Verifications of static equilibriumand resistance

6.4.3 Combination of actions6.4.4 Partial factors for actions and

combinations of actions6.4.5 Partial factors for materials

6.5 Serviceability limit states6.5.1 Verifications of serviceability6.5.2 Performance criteria6.5.3 Combination of actions6.5.4 Partial factors for actions6.5.5 Partial factors for materials


3


Turkstra’s Rule (1972) Turkstra’s Rule (1972)

In the set of variable actions In the set of variable actions to be applied to a to be applied to a construction works, construction works, one of one of these variable actions is these variable actions is selected and considered as selected and considered as the leading action the leading action and the and the other actions are other actions are accompanying actionsaccompanying actions; they ; they are taken into account in are taken into account in calculations with their calculations with their combination value.combination value.

The set including permanent actions, the leading variable action and The set including permanent actions, the leading variable action and the variable accompanying actions form a combination of actions.the variable accompanying actions form a combination of actions.

COMBINATIONS OF ACTIONS : PRINCIPLECOMBINATIONS OF ACTIONS : PRINCIPLE


4


FFii FFk,ik,i FFd,id,i = = f,if,iFFk,ik,i E(FE(Fd,id,i ; a ; add))

EEdd = = SdSdE(FE(Fd,id,i ; a ; add)) EEdd = E( = E(F,iF,iFFk,ik,i ; a ; add))

F,iF,i = = f,if,i

SdSd

ActionAction

Characteristic Characteristic value of the value of the

actionaction

Design value of Design value of the actionthe action

Effect of Effect of actionsactions

Design value of Design value of action effectaction effect Design value of action Design value of action

effect (simplified effect (simplified expression)expression)

ACTIONSACTIONS


5


Key :Key :

aadd Design value of geometrical data

ff Partial factor for actions, which takes account of the possibility of unfavourable deviations of the action values from the representative values

SdSd Partial factor associated with the uncertainty of the action and/or action effect model

is 1,00 or 0, 1, or 2


6


XXii XXk,ik,i XXd,id,i = ( = (ii//m,im,i)X)Xk,ik,i R(XR(Xd,id,i ; a ; add))

RRdd = (1/ = (1/RdRd)R(X)R(Xd,id,i ; a ; add)) RRdd = R(( = R((ii//M,iM,i)X)Xk,ik,i; a; add))

M,iM,i = = m,im,i

RdRd

Material Material propertyproperty

Characteristic Characteristic value of the value of the

material material propertyproperty

Design value of Design value of the material the material

propertyproperty

Structural Structural resistanceresistance

Design value of Design value of the structural the structural

resistanceresistanceDesign value of the Design value of the

structural resistance structural resistance (simplified expression)(simplified expression)

RESISTANCESRESISTANCES


7


Key

ad Design value of geometrical data

m Partial factor for a material property

Rd Partial factor associated with the uncertainty of the

resistance model

Conversion factor taking account of :

- volume and scale effects,

- effects of temperature and moisture,

- and any other appropriate factor.


8


6.46.4 Ultimate limit statesUltimate limit states


9


Ultimate Limit-StatesUltimate Limit-States

EQU – STR – GEO EQU – STR – GEO


10


FAFATT

EQUEQU STRSTR

GEOGEO


11


6.4.2 Verifications of static equilibrium and resistance6.4.2 Verifications of static equilibrium and resistance

Ultimate limit states of static equilibrium (EQU) :Ultimate limit states of static equilibrium (EQU) :

EEd,dstd,dst E Ed,stbd,stb

Ultimate limit states of resistance (STR/GEO) :Ultimate limit states of resistance (STR/GEO) :

EEdd R Rdd

6.5 Serviceability limit states 6.5 Serviceability limit states EEdd C Cdd

CCdd is the limiting design value of the relevant is the limiting design value of the relevant

serviceability criterion.serviceability criterion.EEdd is the design value of the effects of actions specified is the design value of the effects of actions specified

in the serviceability criterion, determined on the basis in the serviceability criterion, determined on the basis of the relevant combination.of the relevant combination.


12


1 1

,,0,1,1,,, """"""j i

ikiiQkQPjkjG QQPG

Expression (6.10)

Expressions (6.10a) and (6.10b)

1,,0,1,1,

1,,

1,,0,

1,,

""""""

""""

iikiiQkQP

jjkjGj

iikiiQP

jjkjG

QQPG

QPG

Ultimate limit states of STR/GEO - Fundamental combination for persistent and transient design situations

0,85 1,001,00


13


EN 1990 - ULS Verification (Persistent and Transient Design Situations)

Ed = E { j≥1G,jGk,j “+” pP “+” Q,1Qk,1 “+” i>1Q,i ψ0,iQk,i }

Ed ≤ Rd

Applying Equation 6.10 from EN1990:


14


EN 1990 - ULS Verification (Persistent and Transient Design Situation)


Design effect or design value of action effects


15



Designeffect

Effect of



16



Designeffect

Effect of

Permanentactions



17



Designeffect

Effect of

Permanentactions

Combinedwith



18



Designeffect

Effect of

Permanentactions

Prestress

Combinedwith



19



Designeffect

Effect of

Permanentactions

Prestress

Leadingvariableaction

Combinedwith



20



Designeffect

Effect of

Permanentactions

Prestress

Leadingvariableaction

AccompanyingvariableactionsCombined

with



21


EN 1990: Table A1.1 -

Recommended values of factors for buildings


22


EN 1990: Table A1.1 -

Recommended values of factors for

road bridges


Action Symbol 0 1 2

gr1a (LM1+pedestrian or cycle-track loads) 1)

TS 0,75 0,75 0 UDL 0,40 0,40 0 Pedestrian+cycle-track loads 2) 0,40 0,40 0

gr1b (Single axle) 0 0,75 0 Traffic loads gr2 (Horizontal forces) 0 0 0 (see EN 1991-2, Table 4.4)

gr3 (Pedestrian loads) 0 0,40 0

gr4 (LM4 – Crowd loading)) 0 0 0 gr5 (LM3 – Special vehicles)) 0 1,0 0 Wind forces

WkF

- Persistent design situations - Execution

0,6 0,8

0,2 -

0 0

Thermal actions Tk 0,6 3) 0,6 0,5 Snow loads QSn,k (during execution) 0,8 - - Construction loads Qc 1,0 - 1,0 1) The recommended values of 0, 1 and 2 for gr1a and gr1b are given for road traffic corresponding to adjusting factors Qi, qi, qr and Q equal to 1. Those relating to UDL correspond to common traffic

scenarios, in which a rare accumulation of lorries can occur. Other values may be envisaged for other classes of routes, or of expected traffic, related to the choice of the corresponding factors. For example, a value of 2 other than zero may be envisaged for the UDL system of LM1 only, for bridges supporting severe continuous traffic. See also EN 1998. 2) The combination value of the pedestrian and cycle-track load, mentioned in Table 4.4a of EN 1991-2, is a “reduced” value. 0 and 1 factors are applicable to this value. 3) The recommended 0 value for thermal actions may in most cases be reduced to 0 for ultimate limit states EQU, STR and GEO. See also the design Eurocodes.

23


1 1

,,0,1,1,,, """"""j i

ikiiQkQPjkjG QQPG

Expression (6.10) in EN 1990

Expressions (6.10a) and (6.10b) in EN 1990

1,,0,1,1,

1,,

1,,0,

1,,

""""""

""""

iikiiQkQP

jjkjGj

iikiiQP

jjkjG

QQPG

QPG

Ultimate limit states of STR/GEO - Fundamental combination for persistent and transient design situations

0,85 1,00


24


R

E

Q

W

(6.10)

(6.10)

(6.10a)(6.10b)

(6.10b)(6.10a)

G

mod (6.10a)

mod (6.10a)

Variation of the reliability index for one variable action

forEN 1990

kkk

kk

WQG

WG


25


0 0.2 0.4 0.6 0.8 1 3

3.5

4

4.5

5

5.5

6

A = 0,95 = 0,90 = 0,85

B B = 3,8


26


APPROACH 1APPROACH 1



TABLESTABLES

A1.2(A) A1.2(B) A1.2(C)A1.2(A) A1.2(B) A1.2(C)

ULS EQUULS EQU

ULS STRULS STRwithout geotechnicalwithout geotechnical

actionsactions

ULS STRULS STRwith geotechnical with geotechnical

actionsactionsULS GEOULS GEO


27



k )(, kaFda FFa

d )(, dada FF

Safety in geotechnical design

28


Approach 1: Applying in separate calculations design values from Table A1.2(C) and Table A1.2(B) to the geotechnical actions as well as the other actions on/from the structure. In common cases, the sizing of foundations is governed by Table A1.2(C) and the structural resistance is governed by Table A1.2(B) ;NOTE In some cases, application of these tables is more complex, see EN

1997.Approach 2 : Applying design values from Table A1.2(B) to the

geotechnical actions as well as the other actions on/from the structure ;

Approach 3 : Applying design values from Table A1.2(C) to the geotechnical actions and, simultaneously, applying partial factors from Table A1.2(B) to the other actions on/from the structure,NOTE The use of approaches 1, 2 or 3 is chosen in the National annex.


29


Accidental design situations : expression 6.11b

1 1

,,21,1,21,1, "")(""""""j i

ikikdjk QQorAPG

Seismic design situations : expression 6.12b

1 1

,,2, """"""j i

ikiEdjk QAPG


30


EN 1990: Design values of actions for use in accidental and seismic combinations of actions

for both buildings and bridges


31


Serviceability limit states

It shall be verified that :

Ed Cd (6.13)

where :

Cd is the limiting design value of the relevant serviceability criterion

Ed is the design value of the effects of actions

specified in the serviceability criterion, determined on the basis of the relevant combination


32


Serviceability limit states : combinations of actions

For function and damage to structural and non-structural elements (e.g. partition walls etc) the Characteristic

Combination (irreversible SLS) should be used

1 1

,,01,, """"""j i

ikikjk QQPG


33



For comfort to user, use of machinery, avoiding ponding of water etc. the Frequent Combination (reversible SLS)

should be used

1 1

,,21,1,1, """"""j i

ikikjk QQPG


34



For appearance of the structure, the Quasi-permanent Combination (reversible SLS) should be used

1 1

,,2, """"j i

ikijk QPG


35


wc Precamber in the unloaded structural member

w1 Initial part of the deflection under permanent loads of the relevant

combination of actions according to expressions (6.14a) to (6.16b)

w2 Long-term part of the deflection under permanent loads

w3 Additional part of the deflection due to the variable actions of the relevant combination of actions according to expressions (6.14a) to (6.16b)

wtot Total deflection as sum of w1 , w2 , w3

wmax Remaining total deflection taking into account the precamber

Vertical deflections


36


Horizontal displacements


37


Thank you for your attention


Documents

Introduction to EN 1990 – Section 6