problems in the current eurocode tikkurila 5.5.2011 t. poutanen
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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
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