Prof. Dr.-Ing. habil. Dr.-Ing. E. h. K. Zilch Dipl.-Ing. S. Grabowski

1. Historical Development and Special Aspects of Reliability Theory Concepts in Design Codes - Past, Present, Future - Prof. Dr.-Ing. habil. Dr.-Ing. E. h. K. Zilch Dipl.-Ing. S. Grabowski The Rackwitz Symposium – a Milestone in Structural Reliability 24.11.06

2. Content • Introduction • Development • Implementation of structural reliability in German standards • Designers questions to be solved • Conclusions

3. Content • Introduction • Development • Implementation of structural reliability in German standards • Designers questions to be solved • Conclusions

4. Introduction Concept of structural concrete design in Germany today semi-probabilistic concept and combination of actions DIN 1055-100 Loadings DIN 1055-series concrete - DIN 1045-2 execution of structures DIN 1045-3 design and construction DIN 1045-1 Reinforcing steels - DIN 488pre-stressing steels - BAZpre-stressing systems - BAZ additional rules for prefabricated elements DIN 1045-4 structural fire design DIN 4102DIN V ENV 1992-1-2

5. Content • Introduction • Development • Implementation of structural reliability in German standards • Designers questions to be solved • Conclusions

6. Development in the first half of 20th century What is the quantity of the probability of failure? Structural Safety – from a point of view of an engineer

7. Development in the first half of 20th century First Standards of Concrete structures Main topics • Inspection • Control / Monitoring • Construction First German standard from 1904 in Prussia "Bestimmungen für die Ausführung von Konstruktionen aus Eisenbeton im Hochbau„ Determination of construction of reinforced concrete in structural engineering (Preußischer Minister der öffentlichen Arbeiten) Volume 10 pages (Content of first German standard of concrete structures)

8. Development in the first half of 20th century Main fields of research at the beginning of the 20th century To expand scope of static analysis • Continuous beam • Structural analysis of slabsand punching • columns with and withoutbuckling risk Scope of structural analysis of DIN 1045 (1915) • Bending with and without axial stress • Shear stress

9. Development in the first half of 20th century Main fields of research at the beginning of the 20th century To enhance concrete technology • Material composition • Execution of workmanship • Strength requirements First ideas of structural reliability Max Meyer, 1926: „Die Sicherheit der Bauwerke und ihre Berechnung nach Grenzkräften anstatt nach zulässigen Spannungen“ (The Safety of Structures and their Design according to Ultimate Forces instead of allowable Stresses)  Rationalizing design • Consider limit states • Idealize the variability of the different quantities(mechanical properties, loads, dimensions) (Jahrhunderthalle, Breslau; year of construction 1910 - 1913)

10. 9 8 Frequency 7 6 5 4 3 2 1 0 22,5 25 27,5 30 32,5 35 Strength [N/mm²] experimental results Development in the first half of 20th century Development in Rüdigers time Definition of material parameters 1925 Definition of compressive strength • testing after 28 days • length of cube 30 cm • mean value ≥ 27,5 N/mm² 1943 Definition of classes of concrete (B 120, B160, B225, B 300) mean value of compressive strength 1972  classification of concrete based on the quantile values of compressive strength distribution

11. Development in Rüdigers time Providing the quality of resistance Two concrete classes B I / B II subjected to compressive strength • quality controlling • qualifying examination • on site controlling (See Rackwitz: The Variation of the compressive strength of concrete cubes - Zur Streuung der Betondruckfestigkeit von Würfelproben; Beton 2, Februar 1971)

12. Development in the first half of 20th century Development in Rüdigers time How safe are structures? After the definition of the material properties: How can the structural safety be quantified? Diversification of structures in four classes of risk and corresponding allowable stresses (1937) global factor of safety n = 2,0 (buildings)n = 5,0 (railway bridges) Global safety factors (1972)nonlinear cross-section design  n = 1,75 (failure with indication)n = 2,1 (failure without indication)n = 1,0 (constraint)

13. Development in Rüdigers time Determination of action Beneath the statistical information of structural resistance, also a statistical model of loading is required:  Statistical information and stochastically determination of load concept Example of snow action per year in comparison with the maximum value of 21 years

14. Development in Rüdigers time Determination of action Determination of snow weight (roof) Example Traunstein (Height 618 m +NN) Snow action according DIN 1055-4 (1936) s0 = 0,75 kN/m² Characteristic value according government agency s = 1,50 kN/m² Snow action according DIN 1055-4 (2005) si = 2,56 kN/m² too small database  no realistic determination (Rackwitz) Proposal Rackwitz 1973: s = 1,90 kN/m² Snow action according DIN 1055-4 (1975) sk = 1,60 kN/m² Rackwitz, Müller: Some aspect of a realistic determination of snow action; Sicherheit von Betonbauten, Deutscher Beton-Verein; 1973 Map of area of snow (DIN 1055; 1976)

15. Development in Rüdigers time Combination of independent actions Problem of intermittency processes  Combination factors for every combination of action - according to DIN 1055-100 (2001) For example: Windy = 0,6 Snowy = 0,5 (< NN + 1000 m) y = 0,7 (> NN + 1000 m)

16. Development in Rüdigers time Model uncertainties e.g. geometric imperfections of members with eccentric axial forces Rackwitz, Maaß: Geometric imperfection of concrete structures, Beton- und Stahlbetonbau, Heft 1, 1980

17. Development in Rüdigers time Determination of structural safety Calculation of structural safety was possible by implementation of FORM / SORM (including the algorithm of Rackwitz / Fießler), first time.  Definition of the index of structural reliability

18. Content • Introduction • Development • Implementation of structural reliability in German standards • Designers questions to be solved • Conclusions

19. Structural reliability in German standards Fundamental idea of GruSiBau (1981) • Structural Safety to be independent of construction types • Derivation of elements of structural safety,based on: • statistical information(materials, geometry, loads) • the target reliability index • rules for design and construction • different limit states(ULS, SLS) • Additional elements of structural safety • qualification of engineers, responsibilities • ensure quality • controlling • maintenance

20. Structural reliability in German standards CEB-FIP Model-Code 1990 • Method of partial coefficients is adopted (numerical values of partial coefficients, introduced in each theoretical model of calculation) • Description of generalized behavior models (bond stress-slip relationship, tension stiffening, pullout, rotation capacity, etc.; each model correspond to a set of g) • Structural analysis, verification of limit states (ULS, SLS), durability aspects • Uncertainties depending on their source (different partial factors)  Basic reference document for the development of Eurocode 2

21. Structural reliability in German standards Comparison of previous / new concrete and action codes Previous Standard DIN 1045 (1988) DIN 1055 (1971 - 1986) New Standard DIN 1045-1 (2001) DIN 1055-100 (2001) Global safety concept S Ei ≤ R / g Semi-probabilistic concept S (gF,i Ei) ≤ S (Rk / gR,i) Structural analysis linear Structural analysis linear / non-linear • Constraint (shrinkage, differential settlement, thermal effect, etc.) • Red. Modulus of elasticity  red E • Red. Reliability  red E / g • Constraint (shrinkage, differential settlement, thermal effect, etc.) • Red. Modulus of elasticity  red E Durability enhanced requirements, detailing rules (e. g. concrete cover)

22. Content • Introduction • Development • Implementation of structural reliability in German standards • Designers questions to be solved • Conclusions

23. Designers questions to be solved Determination of internal forces Since 1972 • Nonlinear cross-section design • Internal forces based on the theory of elasticity • Internal forces based on the theory of elasticity with limited redistribution Since 2001 - complex structural analysis • linear-elastic analysis • linear-elastic analysis with limited redistribution • plastic analysis • nonlinear analysis Discrepancy Nonlinear structural analysis– different structural safety compared to linear structural analysis?(Rackwitz: Zum Sicherheitskonzept bei nichtlinearen Berechnungen – ein altes Thema, DAfStb-Kolloquium 2000)

24. Designers questions to be solved Combination of two independent actions (snow and wind) Problem similar to define load assumption of a single action Wind and snow;Station Munich-Riem; 1985-2005 y0 Combination factor for combined action wind and snow (Studies TU Munich, 2006) y = 0,4 Combination factorsaccording to DIN 1055-100 (2001) Wind y = 0,6 Snow y = 0,5 (< NN + 1000 m) y = 0,7 (> NN + 1000 m) wind; station Munich-Riem; 1985-2005 snow; station Munich-Riem; 1985-2005 Is it possible to solve this problem on the database of today? Study TU Munich (2006)

25. Designers questions to be solved Design resistance of foundations (a) Load bearing capacity of soil DIN 1054: • favorable dead load • characteristical value  Required size of foundation Combination factor should be neglected!

26. Designers questions to be solved Design resistance of foundations (b) State of equilibrium DIN 1055-100: • favorable dead load • design value  Required size of foundation

27. Designers questions to be solved Design resistance of foundations (c) Design of concrete foundation DIN 1045-1: • favorable dead load • design value  static equilibrium in theultimate limit state

28. Designers questions to be solved Redundancy of building structures • Serial system • Parallel system (Daniels-system) Reliability depending on failure mode (brittle or ductile) Can be use this in practice?

29. Designers questions to be solved Redundancy of building structures External pre-stressing system • inspection • maintenance

30. Designers questions to be solved Demands for the future Is it possible to calculate the gross / human error? Structural design in the past: Approach of static calculation today: Errors generally easier detectable!  Errors hardly detectable! (Nomogram of Mörsch, 1907) Administration (building)

31. Content • Introduction • Development • Implementation of structural reliability in German standards • Designers questions to be solved • Conclusions

32. 3.5 3.5 Independent components 3 3 exact 2.5 2.5 0 0 2 2 Full costs of failure Costs of renewal 1.5 1.5 Kosten/C costs/C after failure 1 1 Costs of reparation 0.5 0.5 0 0 0.5 0.5 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 := := aa aa Erneuerungsintervall Interval of renewal a a Conclusions What is the quantity of the probability of failure? Is it now possible to describe the conceptional idea of safety for building structures? Is it possible to define by a rational approach? At the point of view of an engineer: Structural safety should be defined by mathematical formulation!  index of structural safety b numerical value - calibrated by longtime experience (pedestrian bridge North Carolina 2000; built in 1995; Corrosion of tendons)

33. Thank you for your attention! Thank you for your cooperation !