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Seismic Resistant Design of Buildings according to Eurocode 8

Seismic Resistant Design of Buildings according to Eurocode 8. André PLUMIER Prof.Hon . University of Liege - Belgium Member of Eurocode 8 Drafting Committee. “ Eurocode 8” or “EN1998” EN1998-1: General rules seismic actions and rules for buildings EN1998-2: Bridges

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Seismic Resistant Design of Buildings according to Eurocode 8

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  1. Seismic Resistant Design of Buildings according to Eurocode 8 André PLUMIER Prof.Hon. University of Liege - Belgium Member of Eurocode 8 Drafting Committee

  2. “Eurocode 8” or “EN1998” • EN1998-1: General rules • seismic actions and rules for buildings • EN1998-2: Bridges • EN1998-3: Assessment and retrofitting of buildings • EN1998-4: Silos, tanks and pipelines • EN1998-5: Foundations, retaining structures • and geotechnical aspects • EN1998-6: Towers, masts and chimneys

  3. Content of EN 1998-1 1. General 2. Performance requirements and compliance criteria 3. Ground conditions and seismic action 4. Design of buildings - General rules - all materials 5. Specific rules - Concrete buildings 6. Specific rules - Steel buildings 7. Specific rules - Composite Steel-Concrete buildings 8. Specific rules - Timber buildings 9. Specific rules - Masonry buildings 10. Base isolation Annexes

  4. Eurocode 8 - The ideas behind the rules Manyuncertainties in seismic design… ►On seismichazard ● Poor data base : measures since1950 ●Major earthquakes rare events ●Knowledge of local geologyapproximate all recenteventsmakediscoverunknownfaults Northridge (1994), Kobe (1995), Kocaeli (1999) ► aftereachearthquake, seismicityrevised: Istanbulag 0,2g => 0,4g after Kocaeli (1999) ►On structures response dynamic non linear ►Ways to mitigateuncertainties ● more strength ● plastic deformationcapacity

  5. Mitigation of uncertainties An earthquake imposes a relative displacement Δrequired= SDe(T) between center of mass & basis Δ ≈ independent of type of response elastic or inelastic 2 possible design ● Elastic design ►resistances > action effects EC8 DCL= Ductility Class Low ● Dissipative or ductile design ►resistances  action effects computed under reduced action accounting for energy dissipation in cyclic plastic mechanisms ► capacity of deformation Δcapable > Δrequired EC8 DCM= Ductility Class MediumDCH = High Δ H H =Design base shear Δ Δrequired

  6. Accepting plastic deformations under earthquake? ●Reduce cost: design is for Fd << Fe Fd= Fe / q ← !!! ds = q. de ●Increase safety: ● Much energy dissipated permanently in plastic deformations EP loops ● Deformation capacity provided > required CONDITION: ductility of elements θmax > θy

  7. « Plastic hinge » in a steel structure Low plastic deformations Plastic failure Minor local buckling

  8. Conditions required for a very dissipative behaviour. ● Reliabledissipative zones Available plastic deformation capacity with constant resistance is limited Ex: θplastic class A  steel profile: θ ≈ 50 mrad ●Numerous dissipative zones To avoid excessive local deformation resulting from concentration in few points ●Alternatively few but bigdissipative zones (Ex:bottom of RC walls) ●Positions of plastic zones according to intended scheme Because not possible that all elements have everywhere adequate plastic capacity => Design refering to intended global plastic mechanism To avoid partial mechanism concept b  concept a For a same du : θconcept a= du/h(1 storey) θconcept b=du /h(4 storey) θconcept a=4 x θconcept b concept a concept b

  9. Design withreference to a global plastic mechanism Local plastic zones have a limited deformation capacity θult A global plastic mechanism allows a structure ultimate displacement Δu1 much greater than a local plastic mechanism Δu2 Dissipative structure Non dissipative structure θult x Hstruct= Δu1θult x Hstorey= Δu2 Δu1 >> Δu2

  10. Steps to achieve a global plastic mechanism in a standard design using an elastic analysis. ● Define the objective « global mecanism » standard or imagination => locations of dissipative zones are defined ● Run modal analysis or equivalent static Design spectrum reduced by q factor Only the elastic branch of the global behaviour is considered ● Give dimensions to dissipative zones Rd ≥ Ed ● Pay a price at locallevel for dissipative zoneslocal ductility criteria required local ductility μ q ●Pay a price at globallevel criteria for numerous dissipative zones ● « Capacity design » zones adjacent to dissipative ones = give them overstrength so that they remain elastic

  11. 1. Define the objective « global mechanism » Examples. Moment resisting framesplastic hinges in beams ULS not by plastic hinges in columns not by shear in beams&columns not in the connections Diagonal concentric bracings diagonals in plastic tension Excentric bracings Seismic link yielding in shear or bending

  12. 1. Define the objective « global mechanism » Examples. Shear walls = a single big plastic hinge Walls – MRF’s association plastic hinges in beams plastic hinges in columns OK if wall prevent soft storey

  13. 2.Pay a price at local levellocal ductility criteria With any material there are ●ductile ●non ductile phenomenoms Creating ductility => have ductile phenomenoms function first before any non ductile failure Condition: identify ductile &non ductile phenomenoms Reinforced concrete ● Steel εu,k > 50. 10-3 (class B) εy ≈ 500 / 200.000 = 2,5.10-3 Material ductility εs,max/ εy = μ ≈ 20 ● Concrete εcu2 = 3,5. 10-3 << 50. 10-3 Material ductility εcu2/ εy = μ = 2 => R.C. Ductility  => yield steel & do not crush concrete ● Only local ductile mechanism: bending with steel yielding first ● Many non ductile local mechanisms: shear, bond, bars buckling … to be avoided

  14. 2. Pay a price at local level Example: Criterion for local ductility in Reinforced Concrete Steel side Fcompression = Ftension If Rcompression > Rtension • Yield in tension in steel first • upper bound for ρ ρ = steel content • EC8 condition ρ max ρmax μφ q

  15. 2. Pay a price at local level Example: Criterion for local ductility in Reinforced Concrete Concrete side Confine concrete by stirrups to improve εcu2 to εcu2,c > 3,5.10-3 to increase ductility in bending Improve shear resistance => closed stirrups with 135° hooks and extensions of length 10dbw Incorrects Correct pour 4 barres longit. Not correct Correct for 4 longit bars <---Correct pour 8 barres longitudinales-----> Incorrect pour 8 barres Correct for 8 longit bars Not correct for 8 longit bars

  16. 2. Pay a price at local level identify local plastic mechanisms In steel structures => Tension Bolt in tension Shear Plastic deformations In narrow zone Bending Buckling DUCTILE Ovalization of holes Local buckling NON DUCTILE Friction Deformation of connectors

  17. 2. Pay a price at local level Plastic deformation capacity of steel elements in compression or bending • limitation of b/tf or c/tf => classes of sections of Eurocode 3 Ductility ClassBehaviour factor qCross Sectional Class DCH q > 4 class 1 DCM2 q  4 class 2 DCM 1,5 q  2 class 3 DCL q 1,5 class 1, 2, 3, 4

  18. 2. Pay a price at local level (continued) How to avoid reaching limits in components adjacent to dissipative ? ► « capacity design » of all components other than the dissipative ones =>overstrength of zones adjacent to the intended dissipative zone Ed ductile link FOther links K « fuse » « fragile » Design resistance RdF ≥ EdRdK ≥  RdF RdK related to RdFnot to action effectEd !!

  19. ► « Capacity design » Example: Beam in steel moment frame Dimensions to satisfy several criteria: Resistance 1,35 G + 1,5 Q Limit deflection Earthquakes Mpl,Rd ≥ MEd Checks of beam and connection close to plastic hinge Shear VEd,Mdue to Mpl,Rd,A and Mpl,Rd,BVEd can be >> VEd, analysis Bending 1,1 γov Mpl,Rdcan be >> Med, E Non seismic Seismic

  20. ► « Capacity design » Example: Shear walls RdMRd,wall Diagram of shear V a: from analysis b: design one V increased by 1,5 = simplified capacity design c: design one(superior modes) Diagram of bending Moments a: from analysis b: design one MRd≥ MEd Foundations EFd = EF,G+ Rd.EF,E EF,Gnon seismic action Rd overstrength coefficient (1,2 if q ≥ 3 ) . overstrengthRdi / Edi of plastic hinge at bottom of wall EF,E seismic action effect Ex. MFd = Rd.EF,E MEd = RdMRd,wall

  21. 3. Pay a priceat global level Criteria for numerous dissipative zones related to intended global plastic mechanism Example Criterion for numerous dissipative zones in Moment Resisting FramesHeriarchy of plastic hinges formation WBSC: WeakBeams-StrongColumns MRb resistance moments of beams= the fuses MRc resistance moments of columns « Weak Beams-Strong Columns » « Strong Beams-Weak Columns » Danger !

  22. 3. Pay a price at global level Example Concentric bracings ● Beams & columns => Gravity load G ● Diagonals => Earthquake force E ●Tension diagonales = plastic fusesNpl,RdNEd,E i= Npl,Rdi/Ned,E,i=> avoided achieved i “section overstrength” of diagonal i ●Beams & columns : should have overstrength thanks to capacity design NRd to satisfy: Ω = Ωi min Criteria for numerous dissipative zones => homogeneity of section overstrength i ‘s over building height: (max - min)/ min < 0,25

  23. Values of behaviour factor q? = Reflects energy dissipation potential of structural type 4 plastic hinges 1 plastic diagonal 0 plastic mechanism q=5 q=3 q=1,5 (min in EC8) DCH q = 5 à 6Moment resisting frames (steel, concrete composite) Eccentric bracings DCM q = 3 à 4Reinforced concrete shear walls X steel bracings DCL q = 1 à 2low dissipative structures qcode= estimatesgiving safety DCLstructures ● EC8: qmin = 1,5 => greater design forces and action effects ● classical checks Eurocodes 2, 3, 4 et 5 not Eurocode 8 ● « not recommended in moderate and high seismicity zones »

  24. Behaviourfactorsq in EC8 - Reinforcedconcrete structures Remarks: - A bonus to redundant structures by means of factor u/ 1 - Irregularity in elevationpenalised: q = qo/1,2 Notion of u/ 1

  25. Behaviourfactorsq in EC8 – Steel Structures

  26. Acceleration design spectrum Sd(T1)Fmax = M Sd(T1) function of : soil & site S dampingη capacity to dissipate energy in plastic deformations behaviour factor q Sd(T1) est fonction de la périodeT1 → q=1,5 q =4

  27. Some more insights into the EC8 General Rules for Buildings

  28. Conceptual Design • Beforecalculations: design architecture • Respectingprinciples of conceptual design • =>  loweradditionalcosts for resistance to earthquakes •  reduceproblems of analysis & resistancechecks • Basic principles of conceptual design of buildings • structural simplicity • uniformity, symmetry and redundancy • bi-directional resistance and stiffness • torsional resistance and stiffness • diaphragmatic behaviour at storey level • adequate foundation • Concept of primary and secondary seismic members • Principlesapply to buildings primary structure

  29. Conceptual Design Eurocode 8 definition Primary structure ● takes minimum 85% EQ action ●brings 85% of translational & torsional stiffness = backbone for resistance Secondary structure the rest => Freedom for architecture Looks irregular Looks regular But primary structure regular but primary structure irregular => it is not a wall structure an irregular moment frame structure => danger Secondary structure only request: ability to carry gravity loads follow the move => 2nd order effects (P-D effects) should be checked under gravity loads

  30. Conceptual Design Boumerdes, Algeria, 2003 The primary resisting structure of this building is a huge inside concrete core. The secondary structure are peripheral RC frames, which suffered little damage

  31. Conceptual DesignIdeal/Preferential Structural Configurations • Simple • Uniform, symmetrical, redundant • Resistance and stiffness in both directions • Torsional resistance and stiffness • Diaphragms at storey levels

  32. Conceptual DesignEffects of Irregularity in plan Eccentricity between Center of Mass CM Center of Stiffness CR

  33. Conceptual Design Solutions to minimize irregularity in plan. A - Deficient Situation B - Increase torsionalstifness C - Stiffness compensation D - Effective diaphragm

  34. Eurocode 8 criteria for regularity in plan of buildings • Compact outline in plan, enveloped by convex polygonal line • Re-entrant corners in plan don’t leave area up to convex polygonal envelope >5% of area inside outline. • In-plan stiffness of floors sufficiently large • Slenderness of building in plan  = Lmax/Lmin < 4 • Eccentricity limit: e0x ≤ 0,30 rx (to be checked in both directions) • e0x - structural eccentricity • rx - torsional radius” (square root of the ratio between the torsional stiffness and the lateral stiffness) • Torsional stiffness condition; rx. ≥ ls ls – radius of gyration of the floor mass

  35. Effects of irregularity in elevation Kobe 1994. Failure at the limit Composite steel-concrete and RC

  36. Effects of irregularity in elevation Primary structure (walls) interrupted in lower storeys

  37. Effects of irregularity in elevation Contribution of infills to the irregularity in elevation: short columns failing in shear

  38. Irregularity in elevation Eurocode 8 criteria for regularity in elevation in buildings with setbacks

  39. Redundancy of structural system • Provide large number of lateral-load resisting elements and alternative paths for earthquake resistance. • Avoid systems with few large walls per horizontal direction, especially in buildings long in plan:In-plane bending of long floor diaphragms in building with two strong walls at the 2 ends → intermediate columns overloaded, compared to results of design with rigid diaphragm Bonus to system redundancy: qo proportional to u/1 :

  40. Diaphragm action A – Effect of diaphragms B – Deformable vs rigid diaphragm (influencing the force distribution) C - Diaphragm strengthening D - Diaphragm chord interruption (deficient behaviour)

  41. Continuity of floor diaphragms • Smooth/continuous path of forces, from the masses to the foundation. • Cast-in-situ reinforced concrete 7cm thickness min ideal material for earthquake resistant construction, compared to prefabricated elements joined together at the site: the joints between such elements are points of discontinuity. • Floor diaphragms: strength to transfer inertia forces to the lateral-load-resisting system + adequately connected to it. • Large openings in floor slabs may disrupt continuity of force path => explicit analysis • Vertical elements of lateral-force resisting system connected together via floor diaphragms and beams: • at all horizontal levels where significant masses are concentrated • at foundation level

  42. Continuity of floor diaphragms Floors of precast concrete segments joined together and with structural frame via few-cm-thick lightly reinforced cast-in-situ topping, or waffle slabs with thin lightly reinforced top slab: Insufficient Collapse of buildings w/ precast concrete floors inadequately connected to the walls (Spitak, Armenia, 1988). Collapse of precast concrete industrial building, w/ floors poorly connected to lateral-load-resisting system (Athens, 1999)

  43. Structural Analysis • Modelling • Adequately represent the distribution of stiffness and mass (and resistance for nonlinearly analysis) • Consider rigid or flexible diaphragms (diaphragms may be taken as rigid if due to its deformation displacements do not vary more than 10%) • For regular buildings it is acceptable to use two separate plane models • In concrete, composite and in masonry buildings the stiffness of the load bearing elements should take into account the effect of cracking. Secant stiffness at yielding (unless more accurate information is available 50% of the gross stiffness may be taken) => EI = EI/2 ! • Consider the deformability of the foundation • Accidental torsion (eai = ±0,05 Li)

  44. Structural Analysis Analysis Methods • Linear Analysis  Lateral force method (limits of application: regularity in elevation T1 ≤ min(4TC; 2s)  Modal response spectrum analysis (reference method) Note: in Eurocode8, the analysis considers cracking of Reinforced concrete or masonry RC: EI = 0,5 EI Nonlinear Analysis  Non-linear static (pushover) analysis  Non-linear time-history analysis • When a 3D model is used, the design seismic action shall be applied along all relevant horizontal directions (with regard to the structural layout of the building) and their orthogonal horizontal directions

  45. Linear Analysis • Lateral Forces • Distribution of the forces • Accidental torsion effect: • Accidental torsion effect when using 2 plane models: • multiplication of the seismic internal forces in all elements by δ •  Symmetrical buildings: •  Other situations: • x – Distance of the element to the centre of mass • Le - Distance between the two outermost lateral load resisting elements

  46. Linear Analysis Modal Analysis • Sum of effective modal masses ≥ 90 % total mass • Consider all modes with effective mass greater than 5% • Special situations: Minimum number of modes: and • Combination of modal responses:  Independent modes satisfying: => Quadratic combination (SRSS)  Other cases: Complete Quadratic Combination CQC

  47. Nonlinear Analysis • Structural modelling • with mean values of the materials properties • Non-linear static “pushover” analysis • Lateral load F =  Fi • Capacity curve => δfailure • Target displacement δtarget from spectrum • OK if δfailure ≤ δtarget δfailure

  48. Nonlinear Analysis Nonlinear Dynamic Time-History Analysis Modelling of the behaviour of the members under cyclic loading • At least 3 accelerograms compatible with the design spectrum • Evaluation of the response in terms of displacement demand vs deformation capacity • Action effects Worst value, when using 3 to 6 accelerograms Mean value, when using 7 or more accelerograms • NationalAnnexmaylimitthe use of NL Analysis

  49. Combination of effects of seismic action components • Linear or nonlinear static (Pushover) analysis: Rigorous SRSS-combination of seismic action effects EX, EY, EZ of individual components X, Y, Z: E=±√(EX2+EY2+EZ2) Very convenient for modal response spectrum analysis (single analysis for all components X, Y, Z, combination of X, Y, Z simultaneous with that of modal contributions). Approximation: E=±max( │EX│+0,3│EY│+0,3│EZ│; │EY│+0,3│EX│+0,3│EZ│; │EZ│+0,3│EX│+0,3│EY│). In Pushover analysis vertical component Z is omitted. • Time-history nonlinear analysis: seismic action components X, Y, Z are applied concurrently

  50. Structural regularity and seismic analysis

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