1. PROBLEMS IN THE CURRENT EUROCODE Tikkurila 5.5.2011 T. Poutanen

2. 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 V Q = 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

3. Basic assumptions: Permanent load G: normal distribution, design point value: 0.5, V G = 0.0915 (corresponding to  G =1.35) Variale load Q: Gumbel distribution, design point value: 50 year value i.e. 0.98-value, V Q = 0.4 (in reality 0.2-0.5) Materiat M: Log-normal distribution, design point value: 0.05-value, V Msteel  0.1, V mglue-lam  0.2, V Mtimber  0.3 Code, design, execution and use variabilities are usually included in the V-values

4. Comparison of distributions,  = 1,  = 0.2 Permanent load Solid lineNormal Cariable load Dashed lineGumbel MaterialDotted lineLog-normal

5. Distributions: Normal Gumbel Log-normal

6. Basic equations:

7. EC distributions assigned to the design point 1 The design point is selected at unity i.e. 1 Permanent load V G =0.091, solid line Variable load V Q =0.4 dash-dotted line, V Q =0.2,0.5 dot line Material V M =0.1, 0.2, 0.3, dashed line

8. EC distributions at failure state (Finland) Permanent load V G =0.091,  G = 1.35, solid line Variable load V Q =0.4,  Q = 1.5, dash-dotted line Material V M =0.1, 0.2, 0.3,  M ≈ 1.0, 1.2, 1.4, dashed line

9. 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 V M = 0.3 (Sawn timber) V M = 0.2 (Glue lam) V M = 0.1 (Steel)  (load ratio, variable load/total load)    V M = 0 (Ideal material)

10. EC  M -values, independent combination  G,Q Permanent load V G =0.091,  G = 1.35 Variable load V Q =0.2, 0.4,  G = 1.5 Material V M = 0.1 (≈steel), 0.2 (≈glue lam), 0.3 (≈sawn timber) Dotted lines denote V Q =0.2 calculation, solid lines to V Q =0.4 calculation V M = 0.3 (Sawn timber) V M = 0.2 (Glue lam) V M = 0.1 (Steel) Permanent load Variable load  (load ratio, variable load/total load)

11. EC  M -values, dependent combination  G,Q Permanent load V G =0.091,  G = 1.35 Variable load V Q =0.2, 0.4,  G = 1.5 Material V M = 0.1 (≈steel), 0.2 (≈glue lam), 0.3 (≈sawn timber) Dotted lines denote V Q =0.2 calculation, solid lines to V Q =0.4 calculation V M = 0.3 (Sawn timber) V M = 0.2 (Glue lam) V M = 0.1 (Steel) Permanent load Variable load  (load ratio, variable load/total load)

12. 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

13. 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

14. Partial factor design code can be converted into a permissible stress /total safety factor code in three optional ways: Option 2 Option 1 Option 3

15. Safety factors are not imperative  G,Q EC ServiceabilityEC FailureA new(old) method 0.99922904  1297 years G: solid Q: dashed V Q = 0.4 M: dotted,  M - values are selected in a way the target reliability is obtained if the load combination has more than 10 % G or Q

16. EC  T -values if  G = 1,  Q = 1, calculated dependently  G,Q V M = 0.3 (Sawn timber) V M = 0.2 (Glue lam) V M = 0.1 (Steel) Permanent load Variable load  (load ratio, variable load/total load)    V M = 0.1:  TC.0.1 = 1.4 +  *0.35 (1.4…1.74) V M = 0.2:  TC.0.2 = 1.64 V M = 0.3:  TC.0.3 = 1.99 -  * 0.33, 0   < 0.6, 1.8, 0.6    1 (1.99…1.66) Permanent load V G =0.091,  G = 1 Variable load V Q = 0.2, d p = 0.96,  Q = 1 V Q = 0.4, d p = 0.98,  Q = 1 Material V M = 0.1 (≈steel), 0.2 (≈glue lam), 0.3 (≈sawn timber)

17. 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 :  G,Q Time QQ 1 day0.30 1 week0.54 1 month0.72 1 year1.03 10 years1.31 20 years1.39 50 years1.50 100 years1.59 150 years1.64 200 years1.68 500 years1.79 1000 years1.88

18. 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:

19. Thank you for your attention