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Basis of Structural Design [EN1990 – 02] Prof. Dr.-Ing. Jürgen Grünberg

Basis of Structural Design [EN1990 – 02] Prof. Dr.-Ing. Jürgen Grünberg. Name Date of birth Present position Key qualifications Contribution to Code Writing. Jürgen Grünberg 18 May 1944

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Basis of Structural Design [EN1990 – 02] Prof. Dr.-Ing. Jürgen Grünberg

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

  2. 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) Introduction of myself

  3. Basis of structural design [EN 1990 – 02] • Principles and requirements for • safety, • serviceability, • and durability. Scope: • 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. • Application also for • the structural appraisal of existing construction, • in developing the design of repairs, • alterations or in assessing changes of use.

  4. 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 6 Verification by the partial factor method Direct application Annex A1 (normative)Application for buildings  EN 1991-1 Annex A2 (not published) Application for bridges  EN 1991-2 Basis of structural design [EN 1990 – 02] Content: Annex B (informative) Management of structural reliabilityfor construction works Annex C (informative) Basis for partial factor design and reliability analysis Annex D (informative) Design assisted by testing  EN 1992 to 1999

  5. Basis of structural design [EN 1990 – 02] 1. Bases of safety concept(Principles and requirements; explanation of terms and definitions) Topics: 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)

  6. To assure the structural safety the following measures are required: 1. Measures to avoid human errors (Assumptions and preconditions for structural design), 1 Bases of safety concept 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. The choice of the structural system and the design of the structure is made by appropriately qualified and experienced personnel. • Execution is carried out by personnel having the appropriate skill and experience. • Adequate supervision and quality control is provided during execution of the work, i.e. in design offices, factories, plants, and on site • 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. • The structure will be adequately maintained. • The structure will be used in accordance with the design assumptions. 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!

  8. 1.2 Basic 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. 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, • andremain fit for the use for which it is required. 1.2 Basic requirements for structures • 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, andthe consequences of human errors, • to an extent disproportionate to the original cause.

  10. Furthermore, actions are possible which have not been considered in design, as they are resulting • 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), • from insufficient knowledge and wrong activities of persons, e.g. the users of the structure who have not been informed about the loading limits In spite of these two strategies – • Measures to avoid human errors • Measures to warrant a sufficient safety margin errors cannot be excluded completely ! 1.3 Limiting or avoiding of potential damage There is a remaining risk.

  11. 1.3 Limiting or avoiding of potential damage 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; • avoiding as far as possible structural systems that can collapse without warning; • tying the structural members together.

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

  13. Characteristic values of actions ( Fk ):  Action codes (EN 1991) Characteristic values of material properties ( Xk ):  construction specific design codes (EN 1992 to EN 1999)  according material codes (EN 206 etc.) 1.5 Representative values Characteristic values of actions The characteristic values of permanent actions Gkgenerally are their mean values. The characteristic values of variable actions Qkgenerally are their 98 %-quantiles for the reference period of 1 year.

  14. Other representative values of variable actions … shall be defined as products of a characteristic value Qkand a combination factor i (  1,0 ). 1. Combination value: Qrep,0 = 0 Qk The factors 0are 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: Qrep,1 = 1 Qk with a limited duration or frequency of being exceeded within the reference period. 3. Quasi-permanent value: Qrep,2 = 2 Qk determined as the value averaged on the reference period. In case of fatigue other representative values may be considered.

  15. Comparison of representative values of a variable action Q Design value Qd = Q Qk Characteristic value Qk Combination value 0 Qk Frequent value 1 Qk Quasi-permanent value 2 Qk t

  16. 1.5 Representative values 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.

  17. Design values of actions Frep represents either Gk, Qk or Qrep. Design values of material properties or 1.6Design values The conversion factor  takes into account volume and scale effects,effects of moisture and temperature, etc.

  18. Uncertainty of representative values of actions f F Actions and action effects Ed Model uncertainties Structural resistances Rd M Uncertainty of material properties m 1.6Design values Relations between individual partial factors

  19. Design values of geometrical data or Nominal values anom 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. 1. General format: 2. Formats for combination of actions in non-linear analysis: 2.1. The action effect Edincreases more than the leading action Qk,1: 2.2. The action effect Edincreases less than the leading action Qk,1: 3. Format only to be used in linear-elastic structural analysis: Applying partial factors, the following formats can be derived:

  21. EQd,1 a) above proportionality HQd,1 > Q,1 HQk,1 (Arch structure) linear HQk,1 NQd,1 = Q,1 NQk,1 (Suspension bridge) b) below proportionality NQk,1 Q1 Qk,1 Qd,1 = Q,1 Qk,1 1.6Design values Formats for combination of actions in non-linear analysis Predominant action effect EQd,1 = E (Qk,1; Q,1) in non-linear structural analysis

  22. 1.6Design values Design values of resistances The resistances (R) depend on the geometrical data (a) and the material properties (X). General Format:

  23. 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. 1.7 Verification 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. 1.7 Verification of limit states Verification formats for Ultimate Limit states (ULS) The following ultimate limit states shall be verified as relevant: • EQU: Loss of static equilibrium of the structure or any part of itconsidered as a rigid body • STR: Internal failure or excessive deformation of the structure, one of its members or the foundation, where the strength of construction materials governs • GEO: Failure or excessive deformation of the soil where the strengths of the soil or rock are significant in providing resistance • FAT: Fatigue failure of the structure or structural elements(Note: For fatigue design see EN 1992 to EN 1999)

  26. 1.7 Verification 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: Ed,dstDesign value of the effect of destabilising actions Ed,stb Design value of the effect ofstabilisingaction (= gravity resistance)

  27. Limit state of structural failure (STR)(rupture, excessive deformation) • Verification of a structural cross area, member or joint: Ed Design value of the effect of actions (internal forces, stresses) Rd Design value of the structural resistance (bearing capacity) • 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 1.7 Verification of limit states

  28. 1.7 Verification of limit states Verification formats for Serviceability Limit states (SLS) EdDesign value of the effects of actions (e.g. deformation, stress) Cd Limiting design value of the effects of actions specified in the serviceability criterion (e.g. limiting values of deformations, stresses, etc.)

  29. 2 Combinations of actions 2.1 Single actions for buildings Permanent actions Gkj; Pk Variable actions Qki 1. Self-weights Gk 1. Imposed loads, life loads Qk,N 2. Snow and ice loads Qk,S 2. Prestressing Pk 3. Wind loads Qk,W 4. Thermal actions Qk,T 3. Earth pressure Gk,E 5. Fluid pressure, variable Qk,H 4. Fluid pressure, permanent Gk,H 6. Indirect actions, caused by uneven settlements Qk, Accidental actions Ad Seismic actions AEd

  30. 2.1 Single actions for buildings • Generally, the self-weights of the structure and of the fixed equipment, as permanent loads, may be united to one common single action Gk. • In case of a limit state of static equilibrium, the permanent actions have to be subdivided into their unfavourable and their favourable parts (Gk,dst,j and Gk,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 QN,k.

  31. General format (special formats in non-linear structural analysis, see 1.6) • Format used only in linear-elastic structural analysis Leading variable action effect: 2.2 Ultimate Limit States (ULS) Persistent and transient design situations (fundamental combinations)

  32. Alternative format, general a) b) • Alternative format, used only in linear-elastic structural analysis a) b) Alternatively for STR and GEO limit states, the less favourable of the following formats may be applied: j Reduction factor for unfavourable permanent actions Gk,j(j = 0,85 indicative)

  33. General Format • Format only used in linear-elastic structural analysis Leading variable action effect: 2.2 Ultimate Limit States (ULS) Accidental design situations

  34. 2.2 Ultimate Limit States (ULS) Seismic design situations • General Format • Format only used in linear-elastic structural analysis:

  35. 2.3 Serviceability 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. Quasi-permanent combination Normally used for long-term effects and the appearance of the structure (e.g. deformations of the structure): 2.3 Serviceability Limit States (SLS) Frequent combination normally used for reversible limit states(e.g. corrosion attack on reinforcement in cracked concrete): Leading variable action effect:

  37. 2.4 FatigueLimit 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. Action 0 1 2 Imposed loads in buildings (see EN 1991-1-1) Category A: domestic, residential areas 0,7 0,5 0,3 Category B: office areas 0,7 0,5 0,3 Category C: congregation areas 0,7 0,7 0,6 Category D: shopping areas 0,7 0,7 0,6 Category E: storage areas 1,0 0,9 0,8 Category F: traffic areas, vehicle weight  30 kN 0,7 0,7 0,6 Category G: traffic areas,30 kN < v. weight  160 kN 0,7 0,5 0,3 Category H: roofs 0 0 0 Snow and ice loads Sites located at altitude H > 1000 m above sea level 0,7 0,7 0,2 Sites located at altitude H ≤ 1000 m above sea level 0,5 0,2 0 Wind loads 0,6 0,2 0 Temperature (non-fire) in buildings 0,6 0,5 0 2.5  factors for buildings (recommended values)

  39. Ultimate Limit State (ULS) Actions Symbol Situation P/T A A) Loss of static equilibrium (EQU) permanent, unfavourable G,sup 1,10 1,00 favourable G,inf 0,90 0,95 in case of G,sup 1,05 1,00 small deviations G,inf 0,95 0,95 variable, unfavourable Q 1,50 1,00 accidental A - 1,00 B) Failure of the structure, one of its members or of the foundation (STR) Permanent, unfavourable G,sup 1,35 1,00 favourable G,inf 1,00 1,00 variable, unfavourable Q 1,50 1,00 accidental A - 1,00 C) Failure of the soil ground failure or loss of stability of a slope (GEO) permanent G 1,00 1,00 Variable, unfavourable Q 1,30 1,00 accidental A - 1,00 2.6 Partial factors F applied to actions (recommended values)

  40. 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 Gk are multiplied by one unique factor G: • by G,sup, if the resulting effect of Gk is unfavourable, • by G,inf, however, if the resulting effect of Gk is favourable. Differentiation of design values of permanent actions

  41. Approach 1 Approach 2 Approach 3 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. 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. 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. Design of structural members (footings, piles, basement walls, …) (STR) involving geotechnical actions and the resistance of the ground (GEO) The use of approaches, either 1 or 2 or 3, is chosen in the National Annex.

  42. 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. 3 Basis for partial factor design and reliability analysis 3.1 Overview of reliability methods First Order Reliability Method FORM (Level II) Full probabilistic methods (Level III) Historical methods Empirical methods Calibration Calibration Calibration Semi-probablistic methods(Level I) Method b Method c Partial factor design Method a

  44. 3.1 Overview of reliability methods 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 probabilityPs: Ps =   () = (1 – Pf), where Pf is the failure probability for the considered failure mode and within an appropriate reference period. Pf =  (– )  is the cumulative distribution function of the standardised Normal distribution is the reliability index

  45. 3.1 Overview of reliability methods Relation between  und Pf If the calculated failure probability is higher than the target value n: Pf >  (– n), then the structure is considered unsafe!

  46. 3.1 Overview of reliability methods Target values of reliability index  for structural members Limit state Target reliability index 1 (1 year) 50 (n = 50 years) 1) 4,7 3,8 Ultimate (RC 2) 1,5 to 3,8 2) Fatigue Serviceability (irreversible) 3,0 1,5 1) 2) Depends on degree of inspectability, reparability and damage tolerance

  47. RC 3 (CC 3) 5,1 4,3 RC 2 (CC 2) 4,7 3,8 RC 1 (CC 1) 4,3 3,3 3.1 Overview of reliability methods Reliability differentiation in ultimate limit states (see Annex B) Reliability class (Consequences Class) Target reliability index 1 (1 year) 50 (n = 50 years) 1) 1) Partial factors given in EN 1990 to 1999 are based on RC 2

  48. CC 1 Low: agricultural buildings, green houses CC 2 Medium: Residential and office buildings CC 3 High: Grandstands, public buildings, concert halls 3.1 Overview of reliability methods Definition of consequences classes (see Annex B) Consequences for loss of human life, or economic, social or environmental consequences Consequences Class

  49. CC 1 RC 1 Self-checking Self inspection Checking by different persons Specified inspection procedures CC 2 RC 2 Third party checking Third party inspection CC 3 RC 3 3.1 Overview of reliability methods Quality assurance (see Annex B) Design supervision level Inspection level Reliability Class Consequences Class

  50. 3.2 R-E-Model R = structural resistance E = resulting action effect

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