PROBLEMS IN THE CURRENT EUROCODE

Tikkurila

5.5.2011

T. Poutanen

Summary

1. In the current EUROCODE loads are combined in three contradicting ways (error …-20 %) : a:Dependently, permanent loads, loads are at the target reliability values,b:Independently, G, Q, M, loads have random values (Borges-Cashaheta), c:Semi-dependently, 0, one load has random the other the target value (Turkstra)

loads must always be combined dependently

2. Variation of variable load is assumed constant VQ = 0.4 (error -10…+40 %) :

3. Material safety factors M are assumed constant (error …+20 %):

4. Load factors are non-equal G ≠ Q , Q = Q = 1 results in the same outcome with less effort

Basic assumptions:• Permanent load G:

normal distribution, design point value: 0.5, VG = 0.0915 (corresponding to G=1.35)

• Variale load Q:Gumbel distribution, design point value: 50 year value i.e. 0.98-value, VQ = 0.4 (in reality 0.2-0.5)

• Materiat M:Log-normal distribution, design point value: 0.05-value, VMsteel 0.1, Vmglue-lam 0.2, VMtimber 0.3

• Code, design, execution and use variabilities are usually included in the V-values

Comparison of distributions, = 1, = 0.2

Permanent load Solid line NormalCariable load Dashed line GumbelMaterial Dotted line Log-normal

0.5 1 1.5 20

0.2

0.4

0.6

0.8

11

0

pnorm z 1 .2( )

FQ z 1 .2( )

FL z 1 0.2( )

2.2 z0.5 1 1.5 2

0

0.5

1

1.5

2

2.5

33

0

dnorm z 1 .2( )

fQ z 1 .2( )

fL z 1 0.2( )

2.2 z

fN x 1

2 e

x 2

2 2

Distributions:

• Normal

• Gumbel

• Log-normal

FN x 1

2

x

xe

x 2

2 2

d

FN x 1

2

x

xe

x 2

2 2

dfG x

6 e

6 x

0.577216 6

e

6 x

0.577216 6

fL x 1

x 2 ln 1

2

e

ln

x 1

2

2

2 ln 1

2

FL x

0

x1

x 2 ln 1

2

e

ln

x 1

2

2

2 ln 1

2

d

Basic equations:

F x( )

rfG x( ) FQ x r( )

d

1

rfQ r Q

Q

Q V Q

Q

FG x ref r1

G

V G 1

G

d

P fref

1

0

x

rfQ r Q

Q M

Q V Q

Q M

FG x r1

G M

V G 1

G M

d fL x M M

d P f

F x( )

rFG x( ) fQ x r( )

dF x( )

rfG x r( ) FQ x( )

d

F x( )

rFG x r( ) fQ x( )

d

0

xf x

M

M

FM x M M

d P f

0

xf x

FM x M M M M

d P f

0

xf x

M

M

FM x M M

d P f

0

xf x FM x M M M M

d P f

1

0

xF x

M

M

fM x M M

d P f

1

0

xF x

fM x M M M M

d P f

1

0

xF x

M

M

fM x M M

d P f

1

0

xF x fM x M M M M

d P f

EC distributions assigned to the design point 1

The design point is selected at unity i.e. 1Permanent load VG=0.091, solid lineVariable load VQ=0.4 dash-dotted line, VQ=0.2,0.5 dot lineMaterial VM=0.1, 0.2, 0.3, dashed line

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

11

0

pnorm z 1 V G135 1

FQ z Q04 0.4 Q04 FQ z Q02 0.2 Q02 FQ z Q05 0.5 Q05 FL z 10 0.1 10 FL z 20 0.2 20 FL z 30 0.3 30

2.50.0100 z

0 0.5 1 1.5 2 2.50

1

2

3

4

55

0

dnorm z 1 V G135 fQ z Q04 0.4 Q04 fQ z Q02 0.2 Q02 fQ z Q05 0.5 Q05 fL z 10 0.1 10 fL z 20 0.2 20 fL z 30 0.3 30

2.50.0100 z

EC distributions at failure state (Finland)

Permanent load VG=0.091, G = 1.35 , solid lineVariable load VQ=0.4,Q = 1.5, dash-dotted lineMaterial VM=0.1, 0.2, 0.3, M ≈ 1.0, 1.2, 1.4, dashed line

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

11

0

pnorm z1

1.35 V G135

1

1.35

1

FQ z1

1.5 Q04 0.4

1

1.5 Q04

FL z 10 0.1 10 FL z 20 1.2 0.2 20 1.2 FL z 30 1.4 0.3 30 1.4

2.50 z

0 0.5 1 1.5 2 2.50

1

2

3

4

5

66

0

dnorm z1

1.35 V G135

1

1.35

1

fQ z1

1.5 Q04 0.4

1

1.5 Q04

fL z 10 0.1 10 fL z 20 1.2 0.2 20 1.2 fL z 30 1.4 0.3 30 1.4

2.50 z

EC M-values if G = 1.35, Q = 15, calculated - dependently, thick solid line fractile sum method, thin solid line normalized convolution equation- independently, dotted line, convolution equation, Borges-Castanheta-method- Semi-dependently, Tursktra’s method , dashed line

VM = 0.3

(Sawn timber)VM = 0.2(Glue lam)

VM = 0.1(Steel)

(load ratio,variable load/total load)

0 0.2 0.4 0.6 0.8 10.9

1

1.1

1.2

1.3

1.4

1.5

.9

E230us02

E230u02

E230v02

turk03GQ02

10 02100

0 0.2 0.4 0.6 0.8 10.9

1

1.1

1.2

1.3

1.4

1.5

.9

E220us02

E22002

E220v02

turk02GQ02

10 02100

0 0.2 0.4 0.6 0.8 10.9

1

1.1

1.2

1.3

1.4

1.5

.9

E210us01

E21001

E210v01

turk01GQ01

10 01100

0 0.2 0.4 0.6 0.8 10.9

1

1.1

1.2

1.3

1.4

1.5

0.9147

1 E200100 1 100

E200

E200v

turk00GQ

10 100

VM = 0 (Ideal material)

EC M-values, independent combination

Permanent load VG=0.091, G = 1.35Variable load VQ=0.2, 0.4,G = 1.5MaterialVM = 0.1 (≈steel), 0.2 (≈glue lam), 0.3 (≈sawn timber)Dotted lines denote VQ=0.2 calculation, solid lines to VQ=0.4 calculation

VM = 0.3

(Sawn timber)

VM = 0.2(Glue lam)

VM = 0.1(Steel)

Permanent load

Variable load

(load ratio, variable load/total load)

0 0.2 0.4 0.6 0.8 1

0.8

1

1.2

1.4

1.5

.7

E230v

E220v

E210v

eueo0230FNI

eueo0220FNI

eueo0210FNI

10

100

EC M-values, dependent combination

Permanent load VG=0.091, G = 1.35Variable load VQ=0.2, 0.4,G = 1.5MaterialVM = 0.1 (≈steel), 0.2 (≈glue lam), 0.3 (≈sawn timber)Dotted lines denote VQ=0.2 calculation, solid lines to VQ=0.4 calculation

VM = 0.3

(Sawn timber)

VM = 0.2(Glue lam)

VM = 0.1(Steel)

Permanent load

Variable load

(load ratio, variable load/total load)

0 0.2 0.4 0.6 0.8 10.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.51.5

.7

eueo0430

eueo0230F

eueo0420

eueo0220F

eueo0410

eueo0210F

10

100

Independent GQ,-calculation when M-values are known: Dashed lines denote Finnish GQ–values: G = 1.15, 1.35, Q = 1.5

(load ratio, variable load/total load)

Ideal material, V = 0

Glue lam, V = 0.2, M = 1.2

Sawn timber, V = 0.3, M = 1.4

Steel, V = 0.1, M = 1.0

Rule 6.10a,mod

Dependent GQ,-calculation when M-values are known: Dashed lines denote Finnish GQ–values: G = 1.15, 1.35, Q = 1.5

(load ratio, variable load/total load)

Ideal material, V = 0

Glue lam, V = 0.2, M = 1.2

Sawn timber, V = 0.3, M = 1.4

Steel, V = 0.1, M = 1.0

Rule 6.10a,mod

0 0.2 0.4 0.6 0.8 1

1.2

1.4

1.6

1.8

1.9

1.1

E330

E320

E310

E300

N a( )

10

100

100

100

100

a

100

Partial factor design code can be converted into a permissible stress /total safety factor code in three optional ways:

1.35 X G 1.5 X Q50X M

M

1.35 X G 1.351.5

1.35 X Q50

X M

M

X G X Q103X M

1.35 M

1.35 X G 1.35 X Q103X M

M

1.5

1.35X Q50 X Q103

Option 2

X G X Q50X M

T

X G X Q50 X P

Option 1 Option 3

G X G Q X Q kx M

M

X Q

X G X Q

X G X Q kx M

M G 1 Q

X G X Q kx M

M 1.35 0.15

Safety factors are not imperative

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

11

0

FN z1

1.35

V G135

1.35

FG z Q04

1.5

0.4 Q04

1.5

FL z 10 1.09 0.1 10 1.09 FL z 20 1.17 0.2 20 1.17 FL z 30 1.4 0.3 30 1.4

2.50 z

G Q M01 M02 M03

1 1.35 1.5 1.08 1.15 1.39char.1 0.5 0.98 0.05 0.05 0.052 1 1 1 1 1

char.2 0.99993496 0.99922904 0.02219741 0.00937230 0.003053173 1 1 1.61 1.60 1.88

char.3 0.5 0.98 0.05 0.05 0.05

EC Serviceability EC Failure

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

11

0

FN z1

1.

V G135

1.

FG z Q04

1.

0.4 Q04

1.

FL z 10 1.4 0.1 10 1.09 FL z 20 1.5 0.2 20 1.17 FL z 30 1.9 0.3 30 1.4

2.50 z

A new(old) method

0.99922904 1297 years

G: solidQ: dashed VQ = 0.4M: dotted, M- values are selected in a way the target reliability is obtained if the load combination has more than 10 % G or Q

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

11

0

FN z 1 V G135 FG z Q04 0.4 Q04 FL z 10 0.1 10 FL z 20 0.2 20 FL z 30 0.3 30

2.50 z

EC T-values if G = 1, Q = 1, calculated dependently

VM = 0.3

(Sawn timber)

VM = 0.2(Glue lam)

VM = 0.1(Steel)

Permanent load

Variable load (load ratio, variable load/total load)

VM = 0.1: TC.0.1 = 1.4 + *0.35 (1.4…1.74)

VM = 0.2: TC.0.2 = 1.64

VM = 0.3: TC.0.3 = 1.99 - * 0.33, 0 < 0.6, 1.8, 0.6 1 (1.99…1.66)

Permanent load VG=0.091, G = 1Variable load VQ = 0.2, dp = 0.96, Q = 1VQ = 0.4, dp = 0.98, Q = 1Material VM = 0.1 (≈steel), 0.2 (≈glue lam), 0.3 (≈sawn timber)

0 0.2 0.4 0.6 0.8 11.3

1.4

1.5

1.6

1.7

1.8

1.9

22

1.3

US0430a

US0230a

US0420a

US0220a

US0410a

US0210a

y30a ( )

1.64

y10a ( )

10

100

How time is considered in design

Current snow code

Current wind code

Correct equation

Time is considered in the variable load safety factor Q only :

s n s k

1 V Q6

ln ln 1 P n 0.57722

1 2.5923 V Q

c prob1 K ln ln 1 p( )( )1 K ln ln 0.98( )( )

n

n 50 n

50

Time Q1 day 0.301 week 0.541 month 0.721 year 1.0310 years 1.3120 years 1.3950 years 1.50100 years 1.59150 years 1.64200 years 1.68500 years 1.791000 years 1.88

Load factors should be removed G = Q = 1, accuracy remains

Material factors M should be set variable, accuracy inceases by ca 20 %

The design point value of the variable load should be set variable ca 25…50 years, accuracy increases by ca 40 %

Combination factors 0 should be updated

The reliability error of the modified eurocode is 0…10 % with less calculation work (current eurocode -20…+60 %)

Eurocode should have a compatibility condition

A MODIFIED EUROCODE:

Thank you for your attention