1. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design [EN1990 – 02] Prof. Dr.-Ing. Jürgen Grünberg

2. Universität Hannover Twinning Latvia Basis of Structural Design Introduction of myself Name Date of birth Present position Key qualifications Contribution to Code Writing Jürgen Grünberg 18 May 1944 Professor of concrete structures and director of the Institute of Concrete Construction, University of Hannover Consulting engineer for structural design, testing and supervision in structural engineering, Hamburg Reliability analysis in structural engineering Material models for RC and UHPC structures Analysis of young concrete during the hydration process Fatigue design of concrete structures Structural design (e.g. towers, bridges, offshore structures) EN 1990 (in Germany: DIN 1055-100) EN 1991 (in Germany: DIN 1055-1 to 10) EN 1992 (in Germany: DIN 1045-1)

3. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Scope: Principles and requirements for  safety,  serviceability,  and durability. Direct application for buildings and civil engineering works  in conjunction with EN 1991 to 1999. Guidelines relating to safety, serviceabilty and durabilty  for designing structures out of the scope of EN 1991 to 1999,  to serve as reference document, e.g. for product codes. Basis of structural design [EN 1990 – 02] Application also for  the structural appraisal of existing construction,  in developing the design of repairs,  alterations or in assessing changes of use.

4. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Content: Annex B (informative) Management of structural reliability for construction works Annex C (informative) Basis for partial factor design and reliability analysis Basis of structural design [EN 1990 – 02] Annex D (informative) Design assisted by testing  EN 1992 to 1999 EN1990 – Main text Foreword 1 General 2 Requirements 3 Principles of limit state design 4 Basic variables 5 Structural analysis and design assisted by testing Principles and requirements Annex A1 (normative) Application for buildings  EN 1991-1 Annex A2 (not published) Application for bridges  EN 1991-2 Direct application 6 Verification by the partial factor method

5. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Topics: 1. Bases of safety concept (Principles and requirements; explanation of terms and definitions) 2.Combinations of actions (Verification by the partial factor method according to the different limit states and design situations) 3. Basis for partial factor design and reliability analysis (probabilistic analysis) Basis of structural design [EN 1990 – 02]

6. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1 Bases of safety concept To assure the structural safety the following measures are required: 1.Measures to avoid human errors (Assumptions and preconditions for structural design), 2. Measures to warrant a sufficient safety margin between action effect and structural resistance (Basic requirements for design and execution of structures), 3.Measures to prevent potential causes of failure and/or reduce their consequences (Limiting or avoiding of potential damage).

7. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1.1 Measures to avoid human errors (Assumptions and preconditions for structural design), Human errors are not covered by the safety margins defined in the design codes! 1.The choice of the structural system and the design of the structure is made by appropriately qualified and experienced personnel. 2.Execution is carried out by personnel having the appropriate skill and experience. 3.Adequate supervision and quality control is provided during execution of the work, i.e. in design offices, factories, plants, and on site 4.The construction materials and products are used as specified in EN 1990 or in ENs 1991 to 1999 or in the relevant execution standards or reference material or product specifications. 5.The structure will be adequately maintained. 6.The structure will be used in accordance with the design assumptions.

8. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1.2Basic requirements for structures The basic requirements for structures are established in the Interpretative Document „Mechanical Resistance and Stability" associated to the Construction Product Directive published by the European Community at 21-12-1988

9. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1.2Basic requirements for structures A structure shall be designed and executed in such a way that it will, during its intended life, with appropriate degrees of reliability and in an economical way :  sustain all actions and influences likely to occur during execution and use,  and remain fit for the use for which it is required. To reach a sufficient reliability, a structure shall be designed to have adequate:  structural resistance,  serviceability,  and durability. To assure structural resistance, the following events are not allowed to occur  collapse of the entire structure or of one structural element,  or large deformations exceeding the limits of failure. A structure shall not be damaged by events such as  explosion, impact, and the consequences of human errors, to an extent disproportionate to the original cause.

10. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1.3Limiting or avoiding of potential damage Furthermore, actions are possible which have not been considered in design, as they are resulting from insufficient knowledge and wrong activities of persons, e.g. the users of the structure who have not been informed about the loading limits from errors which were not detected although systematic inspections were performed, from the stochastic coincidence of extreme events, from exceeding the loading limits during the working life, from hazards which are caused by persons or nature (e.g. explosions), In spite of these two strategies – Measures to avoid human errors Measures to warrant a sufficient safety margin errors cannot be excluded completely ! There is a remaining risk.

11. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design To assure structural safety, the third strategy is to reduce the consequences of failure and, especially, to avoid injuring and even killing of people. Therefore, potential damage shall be avoided or limited by appropriate choice of one or more of the following : avoiding, eliminating or reducing the hazards to which the structure can be subjected; selecting a structural form which has low sensitivity to the hazards considered; selecting a structural form and design that can survive adequately the accidental removal of an individual member or a limited part of the structure, or the occurrence of acceptable localised damage; tying the structural members together. avoiding as far as possible structural systems that can collapse without warning; 1.3Limiting or avoiding of potential damage

12. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1.4Principles of limit state design Serviceability criterion (permissible stresses, crack widths, deformations) Design value of resistance (stabilising actions, material strengths, cross area resistances) Resistance Design value of action effects (stresses, crack widths, deformations) Design value of action effects (destabilising actions, internal forces) Action effects Rare or characteristic Frequent Quasi-permanent Persistent and transient Accidental Seismic Design situations Stress limitation Crack propagation Deformations Vibrations Loss of static equilibrium Failure by strength limitation Loss of stability Failure by fatigue Verification criteria Functioning of the structure Comfort of people Appearance of construction Safety of people Safety of the structure Requirements ServiceabilityUltimateLimit state

13. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1.5Representative values Characteristic values of actions ( F k ):  Action codes (EN 1991) Characteristic values of material properties ( X k ):  construction specific design codes (EN 1992 to EN 1999)  according material codes (EN 206 etc.) Characteristic values of actions The characteristic values of permanent actions G k generally are their mean values. The characteristic values of variable actions Q k generally are their 98 %-quantiles for the reference period of 1 year.

14. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Other representative values of variable actions … shall be defined as products of a characteristic value Q k and a combination factor  i (  1,0 ). 1.Combination value:Q rep,0 =  0  Q k The factors  0 are chosen such, that the failure probabilities for the action effect resulting from combination of actions and from a single action are adequate. 2.Frequent value:Q rep,1 =  1  Q k with a limited duration or frequency of being exceeded within the reference period. 3.Quasi-permanent value:Q rep,2 =  2  Q k determined as the value averaged on the reference period. In case of fatigue other representative values may be considered.

15. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Comparison of representative values of a variable action Q Design valueQ d =  Q  Q k Characteristic valueQ k Combination value  0  Q k Frequent value  1  Q k Quasi-permanent value  2  Q k t

16. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Characteristic values for material properties … generally are defined as quantiles of a statistical distribution, for instance: as 5 %-quantiles of material strength parameters, as mean values of structural stiffness parameters, as upper nominal values for determination of indirect actions. 1.5Representative values

17. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1.6Design values Design values of actions F rep represents either G k, Q k or Q rep. Design values of material properties or The conversion factor  takes into account volume and scale effects, effects of moisture and temperature, etc.

18. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Relations between individual partial factors Uncertainty of representative values of actions Model uncertainties Uncertainty of material properties Actions and action effects Structural resistances ff  Ed  Rd mm FF MM 1.6Design values

19. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Design values of geometrical data or Nominal values a nom Deviations  a ( e.g. in case of geometrical imperfections ) Design values of action effects The action effects (E) are the answers of the structure to the actions (F), depending on the geometrical data (a) and the material properties (X). General format: 1.6Design values

20. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Applying partial factors, the following formats can be derived: 1.General format: 2.Formats for combination of actions in non-linear analysis: 2.1.The action effect E d increases more than the leading action Q k,1 : 2.2.The action effect E d increases less than the leading action Q k,1 : 3.Format only to be used in linear-elastic structural analysis:

21. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design E Qd,1 Q1Q1 H Qd,1 >  Q,1  H Qk,1 (Arch structure) N Qd,1 =  Q,1  N Qk,1 (Suspension bridge) linear a) above proportionality b) below proportionality Q k,1 Q d,1 =  Q,1  Q k,1 N Qk,1 H Qk,1 1.6Design values Formats for combination of actions in non-linear analysis Predominant action effect E Qd,1 = E (Q k,1 ;  Q,1 ) in non-linear structural analysis

22. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Design values of resistances The resistances (R) depend on the geometrical data (a) and the material properties (X). General Format: 1.6Design values

23. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1.Format applying divided partial factors: 2.Format applying integrated partial factors: 3.Format applying on partial factor  R for structural resistance: Application: e.g. non-linear structural analysis of reinforced concrete structures Applying partial factors, the following formats can be derived:

24. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1.7Verification of limit states by the partial factor method It shall be verified that,  in all relevant design situations,  no relevant limit state is exceeded when the design values for actions or action effects and resistances are used in the design models. For the selected design situations and the relevant limit states the individual actions for the critical load cases should be combined using the  characteristic values or other representative values in combination with  partial factors (  F ;  M ) and other factors (e.g. combination factors  i ). However, actions that cannot occur simultaneously should not be considered together in combinations.

25. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1.7Verification of limit states Verification formats for Ultimate Limit states (ULS) The following ultimate limit states shall be verified as relevant: a)EQU: Loss of static equilibrium of the structure or any part of it considered as a rigid body b)STR: Internal failure or excessive deformation of the structure, one of its members or the foundation, where the strength of construction materials governs c)GEO: Failure or excessive deformation of the soil where the strengths of the soil or rock are significant in providing resistance d)FAT: Fatigue failure of the structure or structural elements (Note: For fatigue design see EN 1992 to EN 1999)

26. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1.7Verification of limit states Verification formats for Ultimate Limit states (ULS) Limit state of static equilibrium (EQU) (e.g. overturning, buoyancy, lifting off) Verification of a structure considered as a rigid body: E d,dst Design value of the effect of destabilising actions E d,stb Design value of the effect of stabilising action (= gravity resistance)

27. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Limit state of structural failure (STR) (rupture, excessive deformation) Verification of a structural cross area, member or joint: E d Design value of the effect of actions (internal forces, stresses) R d Design value of the structural resistance (bearing capacity) 1.7Verification of limit states Limit state of static equilibrium involving the resistance of anchoring structural members Furthermore, the limit state of structural failure has to be verified with respect to the anchoring structural member

28. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design E d Design value of the effects of actions (e.g. deformation, stress) C d Limiting design value of the effects of actions specified in the serviceability criterion (e.g. limiting values of deformations, stresses, etc.) 1.7Verification of limit states Verification formats for Serviceability Limit states (SLS)

29. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 2Combinations of actions 2.1Single actions for buildings A Ed Seismic actions AdAd Accidental actions Q k,  Q k,H 6. Indirect actions, caused by uneven settlements G k,H 4. Fluid pressure, permanent 5. Fluid pressure, variable G k,E 3. Earth pressure Q k,T 4. Thermal actions Q k,W 3. Wind loadsPkPk 2. Prestressing Q k,S 2. Snow and ice loads Q k,N 1. Imposed loads, life loadsGkGk 1. Self-weights Q ki Variable actionsG kj ; P k Permanent actions

30. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Generally, the self-weights of the structure and of the fixed equipment, as permanent loads, may be united to one common single action G k. In case of a limit state of static equilibrium, the permanent actions have to be subdivided into their unfavourable and their favourable parts (  G k,dst,j and G k,stb,j ). Generally, all the imposed loads and life loads within one building  coming from different categories of use appearing there  are assembled to one multi-component action Q N,k. 2.1Single actions for buildings

31. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 2.2Ultimate Limit States (ULS) Persistent and transient design situations (fundamental combinations) General format (special formats in non-linear structural analysis, see 1.6) Format used only in linear-elastic structural analysis Leading variable action effect:

32. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Alternatively for STR and GEO limit states, the less favourable of the following formats may be applied: Alternative format, general a) b) Alternative format, used only in linear-elastic structural analysis a) b)  j Reduction factor for unfavourable permanent actions G k,j (  j = 0,85 indicative)

33. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Accidental design situations General Format Format only used in linear-elastic structural analysis Leading variable action effect: 2.2Ultimate Limit States (ULS)

34. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Seismic design situations General Format Format only used in linear-elastic structural analysis: 2.2Ultimate Limit States (ULS)

35. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 2.3Serviceability Limit States (SLS) Formats for linear-elastic structural analysis (normal case) Rare (characteristic) combination normally used for irreversible limit states (e.g. remaining deformations): Leading variable action effect: ∙

36. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Frequent combination normally used for reversible limit states (e.g. corrosion attack on reinforcement in cracked concrete): Leading variable action effect: Quasi-permanent combination Normally used for long-term effects and the appearance of the structure (e.g. deformations of the structure): 2.3Serviceability Limit States (SLS)

37. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 2.4 Fatigue Limit State (FLS)  The level of the design values of actions – including the relevant numbers of load cycles – corresponds to the Serviceability Limit State (SLS).  The level of the design values of material resistances – depending on the numbers of load cycles – corresponds to the Ultimate Limit State (ULS).  For fatigue design, the combinations of actions depend on the kind of material and, therefore, are given in EN 1992 to EN 1999.

38. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 00,50,6Temperature (non-fire) in buildings 00,20,6Wind loads 00,20,5 Sites located at altitude H ≤ 1000 m above sea level 0,20,7 Sites located at altitude H > 1000 m above sea level Snow and ice loads 000 Category H:roofs 0,30,50,7 Category G:traffic areas,30 kN < v. weight  160 kN 0,60,7 Category F:traffic areas, vehicle weight  30 kN 0,80,91,0 Category E: storage areas 0,60,7 Category D: shopping areas 0,60,7 Category C:congregation areas 0,30,50,7 Category B:office areas 0,30,50,7 Category A: domestic, residential areas Imposed loads in buildings (see EN 1991-1-1) 22 11 00 Action 2.5  factors for buildings (recommended values)

39. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 1,00- AA accidental 1,001,30 QQ Variable, unfavourable 1,00 GG permanent C) Failure of the soil ground failure or loss of stability of a slope (GEO) 1,00- AA accidental 1,001,50 QQ variable, unfavourable 1,00  G,inf favourable 1,001,35  G,sup Permanent, unfavourable B) Failure of the structure, one of its members or of the foundation (STR) 1,00- AA accidental 1,001,50 QQ variable, unfavourable 0,95  G,inf small deviations 1,001,05  G,sup in case of 0,950,90  G,inf favourable 1,001,10  G,sup permanent, unfavourable A) Loss of static equilibrium (EQU) AP/T SituationSymbolActionsUltimate Limit State (ULS) 2.6 Partial factors  F applied to actions (recommended values)

40. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Differentiation of design values of permanent actions Loss of static equilibrium (EQU) The characteristic values of all the permanent actions are separated into two parts: all the parts acting unfavourably are multiplied by the factor  G,sup ; all the parts acting favourably are multiplied by the factor  G,inf. Failure of the structure, one of its members, or of the foundation (STR) All the characteristic values of one independent (single) permanent action G k are multiplied by one unique factor  G : by  G,sup, if the resulting effect of G k is unfavourable, by  G,inf, however, if the resulting effect of G k is favourable.

41. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Design of structural members (footings, piles, basement walls, …) (STR) Approach 1 Applying design values according to Limit State B (STR) as well as to Limit State C (GEO) – in two separate calculations – to the geotechnical actions as well as to the other actions on/from the structure. involving geotechnical actions and the resistance of the ground (GEO) Approach 2 Applying design values only according to Limit State B (STR) to the geotechnical actions as well as to the other actions on/from the structure. Approach 3 Applying design values according to Limit State C (GEO) to the geotechnical actions and, simultaneously, design values according to Limit State B (STR) to the other actions on/from the structure. The use of approaches, either 1 or 2 or 3, is chosen in the National Annex.

42. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Design of structural members (footings, piles, basement walls, …) (STR) involving geotechnical actions and the resistance of the ground (GEO) Advantage of Approach 2: The limit states STR and GEO are clearly separated. So the structural and geotechnical verifications can be performed independently.  Structural verification: Applying design values only according to Limit State B) Failure of the structure (STR) to the geotechnical actions as well as to the other actions on/from the structure.  Geotechnical verification: The limit state C) Failure of the soil (GEO) – e.g. ground failure or loss of stability of a slope – should be verified in accordance with EN 1997.

43. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 3Basis for partial factor design and reliability analysis 3.1Overview of reliability methods Historical methods Empirical methods First Order Reliability Method FORM (Level II) Full probabilistic methods (Level III) Semi-probablistic methods (Level I) Partial factor design Calibration Method a Method b Method c

44. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Most of the partial factors and  -factors established in the present Eurocodes are generated by calibration (c) of the partial factor method (Level  ) to the traditional procedures for verification (a). In both the Level  and Level  methods the measure of reliability should be identified with the survival probability P s : P s =  (  ) = (1 – P f ),  is the cumulative distribution function of the standardised Normal distribution  is the reliability index 3.1Overview of reliability methods where P f is the failure probability for the considered failure mode and within an appropriate reference period. P f =  (–  )

45. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Relation between  und P f If the calculated failure probability is higher than the target value  n : P f >  (–  n ), then the structure is considered unsafe! PfPf 10 -1 10 -2 10 -3 10 -4 10 -5 10 -6 10 -7  1,282,323,093,724,274,755,20 3.1Overview of reliability methods

46. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Target values of reliability index  for structural members 1,53,0 Serviceability (irreversible) 1,5 to 3,8 2) Fatigue 3,8 4,7 Ultimate (RC 2)  50 (n = 50 years) 1)  1 (1 year) Target reliability indexLimit state 2) Depends on degree of inspectability, reparability and damage tolerance 1) 3.1Overview of reliability methods

47. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Reliability differentiation in ultimate limit states (see Annex B)  50 (n = 50 years) 1)  1 (1 year) Target reliability indexReliability class (Consequences Class) 4,3 5,1 RC 3(CC 3) 3,8 4,7 RC 2(CC 2) 3,34,3RC 1(CC 1) 1) 3.1Overview of reliability methods Partial factors given in EN 1990 to 1999 are based on RC 2

48. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Definition of consequences classes (see Annex B) Consequences for loss of human life, or economic, social or environmental consequences Consequences Class Low: agricultural buildings, green houses CC 1 Medium: Residential and office buildings CC 2 High: Grandstands, public buildings, concert hallsCC 3 3.1Overview of reliability methods

49. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Quality assurance (see Annex B) 3.1Overview of reliability methods Reliability Class Consequences Class Design supervision level Inspection level RC 1 CC 1 Self-checkingSelf inspection RC 2 CC 2 Checking by different persons Specified inspection procedures RC 3CC 3 Third party checking Third party inspection

50. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 3.2R-E-Model R = structural resistance E = resulting action effect

51. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design r e f R,E (r,e) f R (r) f E (e) Distribution densities of R and E: 3.2R-E-Model

52. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design f R (r) f E (e) r e f R,E (r,e) If E and R are stochastically independent, then: f R,E (r,e) = f R (r) · f E (e) 3.2R-E-Model Distribution densities of R and E:

53. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design r e f R,E (r,e) f R (r) f E (e) mEmE mRmR EE RR Limit state function: Z = r – e = 0 Failure part: Z < 0 Failure probability: P f = ∫ Z<0 f R,E (r,e) · de ∙ dr = ∫ Z<0 f R (r) · f E (e) · de ∙ dr 3.2R-E-Model

54. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Distribution densities and limit state straight line (in the standardised space) Precondition: e and r are stochastically independent and standard normally distributed Survival part Failure part: P f = ∫ Z<0 f R ( ) · f E ( ) · d ∙ d Limit state straight line: Z = β – α R ∙ + α E ∙ Design point: y d  f (, ) = f R ( )  f E ( ) = const.

55. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Sensitivity factors Reliability index 3.2R-E-Model Design values (in the original space) βασmeandβασmr EEEdRRRd  Reliability parameters

56. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design 3.3Approach for calibration of design values Resulting action effect e d and structural resistance r d are separated. Survival part: Z > 0 Failure part: Z < 0 Design point: y d  min    max  Limit state straight line According sensibility factors  E and  R are assessed by fixed values with respect to the limit state expressed in standardized coordinates.

57. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design For limit state straight lines within the interval Therefore, the design values can be determined as follows: the sensibility factors are fixed by:  R = – 0,8 and  E = + 0,7 Then, the partial factors can be defined, each in relation to the according characteristic values:  E = e d / e k  R = r k / r d 3.3Approach for calibration of design values

58. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Partial factors for variable actions (Gumbel distributions) 3.3Approach for calibration of design values QQ V Q (V N ; V S ; V W )  S ;  W NN  E   50 = 0,7  3,8

59. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Sensibility factors  E1 and  E2 in case of two simultaneous actions (e 1, e 2 ) Survival part: Z > 0 Failure part: Z < 0 Design points: e d1 ; e d2  E   = 22,5  1,077  E   E1 = 0  E2 = 0  E1 =  E2 Limit state straight line for Limit state straight line for 3.3Approach for calibration of design values

60. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design In this case, the global sensibility factors  E und  R are multiplied by the accompanying sensitivity factors  Ei und  Ri. Design values on the safe side result, if  E1 =  R1 = 1,0 is used for the leading value, and  Ei =  Ri = 0,4 is used for the accompanying value Design values of accompanying basic variables: 3.3Approach for calibration of design values

61. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Combination of two actions (e 1, e 2 ) Design value of the leading action: Combination factor:  0 = e di / e d Design value of the accompanying action: where  ‘ is the reliability index referred to the basic time interval T 1 and N 1 is the number of basic time intervals during the design working life 3.3Approach for calibration of design values

62. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Design working life 3.3Approach for calibration of design values Indicative design working life (EN 1990, 2.3) 210-25Replaceable structural parts, e.g. gantry girders, bearings 315-30Agricultural and similar structures 450Building structures and other common structures 5100 Monumental building structures, bridges, and other civil engineering structures Design working life category Indicative design working life (years) Examples 110Temporary structures (1) 1) Structures or parts of structures that can be removed with a view to being re-used should not be considered as temporary.

63. Prof. Dr.-Ing. Jürgen Grünberg Universität Hannover Twinning Latvia Basis of Structural Design Combination factors  0,i for variable actions Q i 3.3Approach for calibration of design values  0,i VQVQ Design working life: T = 50  E = 0,7  50 = 3,8 N 1 = 1 N 1 = 10 N 1 = 200 N 1 = 600 N 1 = 1500 N 1 = 6000