Sako Report

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NKB Committee and Work Reports

1999:01 E

S A K O; Joint Committee of NKB and INSTA-B

Nordic Committee on Building Regulations, NKB

Nordic Standardization in the Construction Field, INSTA-B

BASIS OF DESIGN OF STRUCTURES

Proposals for Modification of Partial Safety Factors

in Eurocodes


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(blank page)


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mailto:%[email protected]:%[email protected]


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Figure 2.1-1 Section of a) concrete, b) welded steel and c) gluelam timber

beam

Figure 2.1-2 Section of a) concrete, b) welded steel and c) gluelam timber

column

b c


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Table 2.3-1 Statistical distributions and coefficients of variation used for the

Base Case

Table 2.3-2 Statistical distributions and coefficients of variation used for sensi-

tivity studies


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(blank page)


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Table 3.2-1 Average reliability indices for

,

and calibrated

partial safety factors

for environmental load with V = 40 % for

the variable action


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Figure 3.2-1 Variation of the reliability indices around the target index

for

,

and calibrated partial safety factors

E[ ] = 4,57, D[ ] = 0,25, V[ ] = 5,5 %

Figure 3.2-2 Reliability indices as a function of

for target

reliability = 4,7, = 1,35, = 1,5 and calibrated partial safety

factors


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Table 3.2-2 Calibrated partial safety factors

for = 4,7 based on

= 1,35 and = 1,50 using one design equation


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Table 3.3-2 Dominating action: permanent (P) or variable (V) for load combina-

tions with imposed action as variable action


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Table 3.3-3 Partial safety factors calibrated to a target reliability index

= 4,7.

The partial factor used as a starting premise is indicated by boxing

the fixed values


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Figure 3.3-1 Variation of the reliability indices,

E[ ] = 4,69, D[ ] = 0,05, i.e. V[ ] = 1,1 %.

The graph applies to all three cases in Table 3.3-3 and includes

both imposed and environmental actions


for cali-

brated

and

. Environmental action is used as variable action.

The graph applies to all three cases in Table 3.3-3

E[ ] = 4,69, D[ ] = 0,05, i.e. V[ ] = 1,1 %


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for cali-

brated

and

. Imposed action is used as variable action

E[ ] = 4,69, D[ ] = 0,05, i.e. V[ ] = 1,1 %.

The graph applies to all three cases in Table 3.3-3


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Table 3.3-4 Results of sensitivity study for load and material parameters


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Table 3.4-1 Partial safety factors

calibrated to a target reliability level

= 4,7. The boxed values are prescribed partial factors


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Environmental action as variable action.

Imposed action as variable action.


for op-

tion 1 in Table 3.4-1, = 4,7.

E[ ] = 4,68, D[ ] = 0,06, i.e. V[ ] = 1,3 %


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for

option 2 in Table 3.4-1, = 4,7.

E[ ] = 4,71, D[ ] = 0,07, i.e. V[ ] = 1,5 %


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for op-

tion 3 in Table 4.4-1, = 4,7.

E[ ] = 4,64, D[ ] = 0,12, i.e. V[ ] = 2,6 %


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Table 3.4-2 Partial safety factors

calibrated to a target reliability level

= 3,7. The boxed values are prescribed partial factors


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, for op-

tion 1 in Table 3.4-2, = 3,7.

E[ ] = 3,79, D[ ] = 0,15, i.e. V[ ] = 4,0 %


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, for op-

tion 2 in Table 4.4-2, = 3,7.

E[ ] = 3,77, D[ ] = 0,10, i.e. V[ ] = 2,7 %


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for op-

tion 3 in Table 3.4-2, = 3,7.

E[ ] = 3,72, D[ ] = 0,08, i.e. V[ ] = 2,2 %


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T a b l e 4

. 1 - 1

S u m m a r y o f t h e r e s u l t s . P

r e s c r i b e d

F - a n d

M

- v a l u e s a r e

w r i t t e n i n b o l d t y p e s

C o l .

1

2

3

4

5

6

7

8

9

1 0

1 1

1 2

1 3

1 4

1 5

1 6

1 7

R o w

S e c -

t i o n

t

T a r -

g e t

) ( E M

e a n

) (

) (

E D %

m i n

P G

P E

P I

VG

V E

V I

M

R e i n f .

M

C o n c .

M S t e e l

M

G l u e -

l a m

N o . o f

e q . 1

)

C o m m e n t s

1

3 . 1

-

4 , 7 7

9 , 9

3 , 7

1 ,

3 5

1 ,

5

1 ,

5

1 ,

3 5

1 ,

5

1 ,

5

1 ,

1 5

1

, 5

1 ,

1

1 ,

3

1

D

e s i g n a c c o r d i n g t o

E N V - E u r o c o d e s

2

3 . 2

4 , 7

4 , 5 7

5 , 5

3 , 9

1 ,

3 5

1 ,

5

1 ,

5

1 ,

3 5

1 ,

5

1 ,

5

1 , 0 5

1 , 2 7

1 , 1 3

1 , 3 0

1

3

3 . 3

4 , 7

4 , 6 9

1 , 1

4 , 2

1 , 0 7

1 ,

3 5

1 , 2 6

0 4 0

0 , 5 1

0 , 4 7

0 , 6 2

0 , 7 8

0 , 7 2

0 , 8 5

1 , 0 8

1 ,

0

1 ,

5 0

1 , 9 0

1 , 7 6

1 , 2 4

1 , 5 7

1 , 4 6

1 , 3 7

1 , 0 8

1 , 1 7

1 , 6 5

1 , 3 0

1 , 4 0

1 , 4 2

1 , 1 3

1 , 2 1

1 , 6 3

1 , 2 9

1 , 3 9

2

C a s e I

C a s e I I

C a s e I I I

4

3 . 4

4 , 7

4 , 6 8

1 , 3

4 , 2

1 ,

2

1 ,

0

1 ,

0

1 ,

0

1 ,

7

1 ,

4

1 , 1 9

1 , 4 3

1 , 2 4

1 , 4 2

2

O

p t i o n 1

5

3 . 4

4 , 7

4 , 7 1

1 , 5

4 , 2

1 ,

3

1 ,

0

1 ,

0

1 ,

1

1 ,

9

1 ,

6

1 , 0 9

1 , 3 1

1 , 1 3

1 , 2 9

2

O

p t i o n 2

6

3 . 4

4 , 7

4 , 6 4

2 , 6

4 , 0

1 ,

3 5

0

0

1 ,

0

1 ,

7

1 ,

4

1 , 1 4

1 , 3 9

1 , 2 1

1 , 3 9

2

O

p t i o n 3

7

3 . 4

3 , 7

3 , 7 9

4 , 0

2 , 9

1 ,

1

1 ,

0

1 ,

0

1 ,

0

1 ,

5

1 ,

3

1 , 1 4

1 , 3 1

1 , 1 3

1 , 2 2

2

O

p t i o n 1

8

3 . 4

3 , 7

3 , 7 7

2 , 7

3 , 1

1 ,

2

1 ,

0

1 ,

0

1 ,

0

1 ,

6

1 ,

4

1 , 0 7

1 , 2 3

1 , 0 6

1 , 1 5

2

O

p t i o n 2

9

3 . 4

3 , 7

3 , 7 2

2 , 2

2 , 9

1 ,

3

0

0

1 ,

0

1 ,

5

1 ,

3

1 , 0 7

1 , 2 5

1 , 0 8

1 , 1 7

2

O

p t i o n 3

1 ) O n e e

q u a t i o n r e p r e s e n t s a f o r m a t a c c o r d i n g t o e q . ( 9 . 1 0 ) a n d t w o e q u a t i o n s a f o r m a t a c c

o r d i n g t o ( 9 . 1 0 a ) a n d ( 9 . 1 0 b ) i n E N V 1 9 9 1 - 1 .


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Figure 4.3-1 Reliability level as a function of

for con-

crete beams designed according to ENV-Eurocodes (Figure 3.1-2)

and the best choice of partial safety factors for

= 4,7

(Figures 3.3-2 and 3.3-3)


for con-

crete columns designed according to ENV-Eurocodes

(Figure 3.1-2) and the best choice of partial safety factors for

= 4,7 (Figures 3.3-2 and 3.3-3)

Concrete Beams, ENV-Eurocode

Concrete Beams, imposed action

Concrete Beams, environmental action

7,0

6,5

6,0

5,5

5,0

4,5

4,0

3,5

3,0

0,0

R e l i a b i l i t y l e v e l ,

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Concrete Columns, ENV-Eurocode

Concrete Columns, imposed action

Concrete Columns, environmental action

7,0

6,5

6,0

5,5

5,0

4,5

4,0

3,5

3,0

0,0


0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0


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for steel

beams designed according to ENV-Eurocodes (Figure 3.1-2) and

the best choice of partial safety factors for

= 4,7 (Figures 3.3-2

and 3.3-3)


for steel

columns designed according to ENV-Eurocodes (Figure 3.1-2) and

the best choice of partial safety factors for

= 4,7 (Figures 3.3-2

and 3.3-3)

3,0

3,5

4,0

4,5

5,0

5,5

6,0

6,5

7,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Steel Beams, environmental action

Steel Beams, imposed action

Steel Beams, ENV-Eurocode


3,0

3,5

4,0

4,5

5,0

5,5

6,0

6,5

7,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Steel Columns, ENV-Eurocode

Steel Columns, imposed action

Steel Columns, environmental action



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for gluelam

timber beams designed according to ENV-Eurocodes (Figure 3.1-2)

and the best choice of partial safety factors for

= 4,7 (Figures

3.3-2 and 3.3-3)


for gluelam

timber columns designed according to ENV-Eurocodes (Figure 3.1-

2) and the best choice of partial safety factors for

= 4,7 (Figures

3.3-2 and 3.3-3)

3,0

3,5

4,0

4,5

5,0

5,5

6,0

6,5

7,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Gluelam Beams, environmental action

Gluelam Beams, imposed action

Gluelam Beams, ENV-Eurocode


3,0

3,5

4,0

4,5

5,0

5,5

6,0

6,5

7,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

Gluelam Columns, ENV-Eurocode

Gluelam Columns, imposed action

Gluelam Columns, environmental action



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(blank page)


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Table A.1-1 Material parameters for concrete and reinforcement

Table A.1-2 Material parameters for structural steel


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Table A.1-3 Material parameters for gluelam timber


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Table A.2-1 Concrete beam,

= 25 MPa,

= 1,5, steel B500B,

= 500 MPa,

= 1,15 and = 1,0.

is the self weight of the beam and

represents other per-

manent actions.

Table A.2-2 Welded steel beam, S235,

= 235 MPa,

= 1,1.


represents other per-

manent actions.


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Table A.2-3 Gluelam timber beam, GL32,

= 32 MPa,

= 1,0,

= 1,0 and

= 1,3.


represents

other permanent actions.


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L 12 G k1 3.6 Q k 6 k 3 n 1.431 γ s 1.1 [ 5.1.1(1)]

t f b( ) b

20t w b( )

b

20 nh b( ) k b

D b( ) h b( ) 2 t f b( ) Physical web height

d b( ) h b( ) 2 t f b( ) Web height when calculating web slenderness.The same in this case

A w b( ) D b( ) t w b( )A f b( ) b t f b( )

W pl b( ) b t f b( ) h b( ) t f b( )t w b( ) D b( )

2.

4A b( ) A w b( ) 2 A f b( )

f sk 235 f yk for steel S235 f sdf sk

γ s

b .3 Start value

b root f sd W pl b( )1.35 G k1 A b( ) 76.5 1.5 Q k L

2. 10 3.

8 b,

root( ) solves the equation (the part within the brackets left of ",b" =0)and returns the web width b.

Gk2 = Self-weight of the beam based on the density 76,5 kN/m

3

.


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b 0.17688= d b( ) 0.5129= h b( ) 0.53063= c b

2c 0.0884=

tf b( ) 8.843875 10 3

= t w b( ) 6.1802 10 3

=

c

tf b( )10=


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G k1 3.6 Q k 6 L 12 k 5 h b( ) k b

γ 1.3 [ 2.3.3.2]

Gluelam class: GL32, according to prEN 1194:1995

f k 32 prEN 1194:1995 k h b( ) 1.0 h b( ) . 6if

.6

h b( )

.2

otherwise k h b( ) 1.15

W b( ) b h b( )( )

2.

6

k m 1 kmod was chosen to 1,0. A b( ) b h b( ) b 0.2 Start value

b root W b( )k m f k

γ

k h b( )..

1.35 G k1 A b( ) 4.2 1.5 Q k L2. 10( )

3.

8

b,

b 0.1362= h b( ) 0.681= k h b( ) 1=

root( ) solves the equation (the part within the brackets left of ",b" =0)and returns the width b.

Gk2

= Self-weight of the beam based on the density 4.2 kN/m3 .

G k2 b h b( ) 4.2 G k2 0.3896= G k G k1 G k2 G k 3.9896=

νQ k

G k Q k

ν 0.6006= I b( ) b h b( )3.

12

SLS, check of deformation, Total load Pd. P d G k Q k P d G k Q k

P d 9.9896= E d 13300 δ5 P d L

4.

384 E d I b( )δ 56.5761= mm

δ

L 1000

4.7147 10 3

= 1000 L

δ

212.1037=


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Figure A.3.2.1-1 Assumed section

Table A.3.2.1-1 Actions and corresponding sectional area for concrete columns


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Table A.3.2.2-1 Actions and corresponding sectional area for steel columns

a

a

t

t t

t


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Table A.3.2.3-1 Actions and corresponding sectional area for timber columns


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(blank page)


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Table B.1.2-1 Imposed actions in apartment, hotel, hospital, office and schoolbuildings. Action from persons - if included - is the temporally

arbitrary live load, i.e. the measured or calculated load from per-

sons during the investigation. From [10].


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Table B.1.3-1 Some statistical values of snow load on the ground in Sweden


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Table B.1.3-1 Coefficient of variation for different threshold values in Göteborg.

The characteristic value – given with two significant numbers –

is the same, 1,1 kN/m2


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Figure B.1.4-1 Sketch showing the statistical wind load distribution as well as

the statistical distribution off the individual parameters

q, q

q

C e C, e

C e C pe

C pe C, pe J w J, w

J w

W , W

W q C C J = e pe w

W


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Figure B.2.2.1-1 Experimental and fitted probability distribution function (Lognor-

mal) of material strength. Tests carried out in August

Figure B.2.2.1-2 Experimental and fitted probability distribution function (Weibull)

of material strength. Tests carried out in August


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mal) of material strength. Tests carried out in November


of material strength. Tests carried out in November


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mal) of material strength. All data


of material strength. All data


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Figure B.2.2.2-1 Tensile test results of EN 10025+A1–S235,

= 914 test

pieces

0

50

100

150

200

265 275 285 295 305 315 325 335 345 355 365 375 385 395 (MPa)

R eH


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Figure B.2.2.2-2 Empirical, normal and log normal distribution functions

0

0,1

0,2

0,3

0,4

0,5

0,7

0,6

0,8

0,9

1,0

260 270 280 290 300 310 320 330 340 350 360 370 380 390


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Table B.2.2.3 Mean values and coefficients of variation for conversion factor

result from Swedish investigations [16]


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Table B.2.2.4.1-1 Yield strength values from the production of producer (I) (1994)


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Table B.2.2.4.1-2 Yield strength values from the production of producer (II) ( 1995)


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The figures represent the number of specimens

Figure B.2.2.4.3-1 Upper yield strength,

, for reinforcing steel with a

characteristic value

equal to 500

6


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Table B.2.3.2-1 Tolerances on thickness according to EN 10 029


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Table B.2.3.2-2 Tolerances on thickness according to EN 10 029, continued


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Figure B.2.3.2-1 Permitted deviations for welded I-sections and box-sections according to ENV 1090-1

Table B.2.3.2-3 Coefficients of variation for welded I- and box-sections


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Table B.2.3.3-1 Tolerances – requirements versus measured values

Table B.2.3.3-2 Tolerances – requirements versus measured values


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