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## Introduction to EN 1990 – Section 6

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**Workshop on Eurocodes: Training the trainers**Moscow - 09 December - 10 December, 2010 Introduction to EN 1990 – Section 6 TC250 Section 6: Verification by the partial factor method Annex B: Management of structural reliability for construction works Jean-Armand CalgaroChairman of CEN/TC250**Introduction to EN 1990 – Section 6**Section 6 - Verification by the partial factor method 6.4 Ultimate limit states 6.4.1 Verifications : General 6.4.2 Verifications of static equilibrium and resistance 6.4.3 Combination of actions 6.4.4 Partial factors for actions and combinations of actions 6.4.5 Partial factors for materials 6.5 Serviceability limit states 6.5.1 Verifications of serviceability 6.5.2 Performance criteria 6.5.3 Combination of actions 6.5.4 Partial factors for actions 6.5.5 Partial factors for materials 6.1 General 6.2 Limitations and simplifications6.3 Design values 6.3.1 Design values of actions 6.3.2 Design values of the effects of actions 6.3.3 Design values of material properties 6.3.4 Design values of geometrical data 6.3.5 Design resistance**Introduction to EN 1990 – Section 6**COMBINATIONS OF ACTIONS : PRINCIPLE Turkstra’sRule(1972) In the set of variable actions to beapplied to a construction works, one of these variable actions isselected and considered as the leading action and the other actions are accompanying actions; they are takenintoaccount in calculationswiththeircombination value. The set including permanent actions, the leading variable action and the variable accompanying actions form a combination of actions.**Introduction to EN 1990 – Section 6**ACTIONS Fi Fk,i Fd,i = f,iFk,i E(Fd,i ; ad) Action Design value of the action Effect of actions Characteristic value of the action Ed = SdE(Fd,i ; ad) Ed = E(F,iFk,i ; ad) F,i = f,i Sd Design value of action effect Design value of action effect (simplified expression)**Introduction to EN 1990 – Section 6**Key : adDesign value of geometrical data fPartial factor for actions, which takes account of the possibility of unfavourable deviations of the action values from the representative values SdPartial factor associated with the uncertainty of the action and/or action effect model is1,00 or 0, 1, or 2**Introduction to EN 1990 – Section 6**RESISTANCES Xi Xk,i Xd,i = (i/m,i)Xk,i R(Xd,i ; ad) Materialproperty Design value of the materialproperty Characteristic value of the materialproperty Structural resistance Rd = (1/Rd)R(Xd,i ; ad) Rd = R((i/M,i)Xk,i; ad) M,i = m,i Rd Design value of the structural resistance Design value of the structural resistance (simplified expression)**Introduction to EN 1990 – Section 6**• Key • ad Design value of geometrical data • m Partial factor for a material property • Rd Partial factor associated with the uncertainty of the • resistance model • Conversion factor taking account of : • volume and scale effects, • effects of temperature and moisture, • and any other appropriate factor.**Introduction to EN 1990 – Section 6**6.4 Ultimate limit states**Introduction to EN 1990 – Section 6**UltimateLimit-States EQU – STR – GEO**FAT**Introduction to EN 1990 – Section 6 EQU STR GEO**Introduction to EN 1990 – Section 6**6.4.2 Verifications of staticequilibrium and resistance Ultimatelimit states of staticequilibrium (EQU) : Ed,dstEd,stb Ultimatelimit states of resistance (STR/GEO) : Ed Rd 6.5 Serviceabilitylimit states Ed Cd Cd is the limiting design value of the relevant serviceability criterion. Ed is the design value of the effects of actions specified in the serviceability criterion, determined on the basis of the relevant combination.**Introduction to EN 1990 – Section 6**Ultimate limit states of STR/GEO - Fundamental combination for persistent and transient design situations Expression (6.10) Expressions (6.10a) and (6.10b) 0,85 £x£1,00**EN 1990 - ULS Verification (Persistent and Transient Design**Situations) Introduction to EN 1990 – Section 6 Ed ≤ Rd Applying Equation 6.10 from EN1990: Ed = E { Sj≥1gG,jGk,j “+” gpP “+” gQ,1Qk,1 “+” Si>1gQ,iψ0,iQk,i }**EN 1990 - ULS Verification (Persistent and Transient Design**Situation) Introduction to EN 1990 – Section 6 Design effect or design value of action effects Ed = E { Sj≥1gG,jGk,j “+” gpP “+” gQ,1Qk,1 “+” Si>1gQ,iψ0,iQk,i }**EN 1990 - ULS Verification (Persistent and Transient Design**Situation) Introduction to EN 1990 – Section 6 Design effect Ed = E { Sj≥1gG,jGk,j “+” gpP “+” gQ,1Qk,1 “+” Si>1gQ,iψ0,iQk,i } Effect of**EN 1990 - ULS Verification (Persistent and Transient Design**Situation) Introduction to EN 1990 – Section 6 Design effect Permanent actions Ed = E { Sj≥1gG,jGk,j “+” gpP “+” gQ,1Qk,1 “+” Si>1gQ,iψ0,iQk,i } Effect of**EN 1990 - ULS Verification (Persistent and Transient Design**Situation) Introduction to EN 1990 – Section 6 Design effect Permanent actions Ed = E { Sj≥1gG,jGk,j “+” gpP “+” gQ,1Qk,1 “+” Si>1gQ,iψ0,iQk,i } Effect of Combined with**EN 1990 - ULS Verification (Persistent and Transient Design**Situation) Introduction to EN 1990 – Section 6 Design effect Permanent actions Ed = E { Sj≥1gG,jGk,j “+” gpP “+” gQ,1Qk,1 “+” Si>1gQ,iψ0,iQk,i } Prestress Effect of Combined with**EN 1990 - ULS Verification (Persistent and Transient Design**Situation) Introduction to EN 1990 – Section 6 Leading variable action Design effect Permanent actions Ed = E { Sj≥1gG,jGk,j “+” gpP “+” gQ,1Qk,1 “+” Si>1gQ,iψ0,iQk,i } Prestress Effect of Combined with**EN 1990 - ULS Verification (Persistent and Transient Design**Situation) Introduction to EN 1990 – Section 6 Leading variable action Design effect Permanent actions Ed = E { Sj≥1gG,jGk,j “+” gpP “+” gQ,1Qk,1 “+” Si>1gQ,iψ0,iQk,i } Prestress Accompanying variable actions Effect of Combined with**Introduction to EN 1990 – Section 6**EN 1990: Table A1.1 - Recommended values of factors for buildings**Introduction to EN 1990 – Section 6**EN 1990: Table A1.1 - Recommended values of factors for road bridges**Introduction to EN 1990 – Section 6**Ultimate limit states of STR/GEO - Fundamental combination for persistent and transient design situations Expression (6.10) in EN 1990 Expressions (6.10a) and (6.10b) in EN 1990 0,85 £x£ 1,00**Introduction to EN 1990 – Section 6**Variation of the reliability index for one variable action for EN 1990**ULS EQU**TABLESA1.2(A) A1.2(B) A1.2(C) ULS STRwithout geotechnicalactions ULS STRwith geotechnical actionsULS GEO Introduction to EN 1990 – Section 6 APPROACH 1 APPROACH 2 APPROACH 3**Introduction to EN 1990 – Section 6**Safety in geotechnical design**Approach 1: Applying in separate calculations design values**from Table A1.2(C) and Table A1.2(B) to the geotechnical actions as well as the other actions on/from the structure. In common cases, the sizing of foundations is governed by Table A1.2(C) and the structural resistance is governed by Table A1.2(B) ; NOTE In some cases, application of these tables is more complex, see EN 1997. Approach 2 : Applying design values from Table A1.2(B) to the geotechnical actions as well as the other actions on/from the structure ; Approach 3 : Applying design values from Table A1.2(C) to the geotechnical actions and, simultaneously, applying partial factors from Table A1.2(B) to the other actions on/from the structure, NOTE The use of approaches 1, 2 or 3 is chosen in the National annex. Introduction to EN 1990 – Section 6**Introduction to EN 1990 – Section 6**Accidental design situations : expression 6.11b Seismic design situations : expression 6.12b**Introduction to EN 1990 – Section 6**EN 1990: Design values of actions for use in accidental and seismic combinations of actions for both buildings and bridges**Introduction to EN 1990 – Section 6**Serviceabilitylimit states It shall be verified that : Ed Cd (6.13) where : Cd is the limiting design value of the relevant serviceability criterion Ed is the design value of the effects of actions specified in the serviceability criterion, determined on the basis of the relevant combination**Introduction to EN 1990 – Section 6**• Serviceabilitylimit states : combinations of actions • For function and damage to structural and non-structural elements (e.g. partition wallsetc) the CharacteristicCombination (irreversible SLS)shouldbeused**Introduction to EN 1990 – Section 6**• Serviceabilitylimit states : combinations of actions • For comfort to user, use of machinery, avoidingponding of water etc. the FrequentCombination (reversible SLS) shouldbeused**Introduction to EN 1990 – Section 6**• Serviceabilitylimit states : combinations of actions • For appearance of the structure, the Quasi-permanent Combination (reversible SLS) shouldbeused**Introduction to EN 1990 – Section 6**Vertical deflections wcPrecamber in the unloaded structural member w1Initial part of the deflection under permanent loads of the relevant combination of actions according to expressions (6.14a) to (6.16b) w2 Long-term part of the deflection under permanent loads w3 Additional part of the deflection due to the variable actions of the relevant combination of actions according to expressions (6.14a) to (6.16b) wtot Total deflection as sum of w1 , w2 , w3 wmax Remaining total deflection taking into account the precamber**Introduction to EN 1990 – Section 6**Horizontal displacements**Introduction to EN 1990 – Section 6**Thank you for your attention