PROBLEMS IN THE CURRENT EUROCODE Tikkurila 5.5.2011 T. Poutanen.
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Transcript of PROBLEMS IN THE CURRENT EUROCODE Tikkurila 5.5.2011 T. Poutanen.
![Page 1: PROBLEMS IN THE CURRENT EUROCODE Tikkurila 5.5.2011 T. Poutanen.](https://reader036.fdocuments.net/reader036/viewer/2022062515/56649f525503460f94c75e94/html5/thumbnails/1.jpg)
PROBLEMS IN THE CURRENT EUROCODE
Tikkurila
5.5.2011
T. Poutanen
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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
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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:
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Thank you for your attention