Seismic Design of New R.C. Structures

Transcription

1 Seismic Design of New R.C. Structures Prof. Stephanos E. Dritsos University of Patras, Greece. Pisa, March 2015

2 Seismic Design Philosophy Main Concepts Energy dissipation Ductility Capacity design Learning from Earthquakes

3 Energy Dissipation 3

4 Ductility and Ductility Factors Ductility is the ability of the system to undergo plastic deformation. The structural system deforms before collapse without a substantial loss of strength but with a significant energy dissipation. The system can be designed with smaller restoring forces, exploiting its ability to undergo plastic deformation. Ductility factor (δ u /δ y ): Ratio of the ultimate deformation at failure δ u to the yield deformation δ y. * δ u is defined for design purposes as the deformation for which the material or the structural element loses a predefined percentage of its maximum strength. 4

5 In terms of displacements: Ductility Factors µ δ = δ δ u y δ u : ultimate deformation at failure δ y : yield deformation In terms of rotations: (for members) µ θ = θ θ u y θ u : ultimate rotation at failure θ y : yield rotation In terms of curvatures: (for members) µ ϕ = ϕ ϕ u y φ u : ultimate curvature at failure φ y : yield curvature 5

6 Behaviour q Factor The q factor corresponds to the reduction in the level of seismic forces due to nonlinear behaviour as compared with the expected elastic force levels.

7 Ductility and Behaviour Factor q V Definition q = el. V Flexible Structures T Tc : Rule of equal dispacement inel q V 1max u2 = = = V δ δ 2max y2 µ δ δ y2 δ u2 δ 7

8 Ductility and Behaviour Factor q Stiff Structures T Tc q for T=0 q=1 for T=T c q=μ δ μ δ 1 δ y δ u2 Rule of equal dissipating energy q V el 1max = = = µ δ V inel V V 2max (2 1) 1/2 δ q Τ c T = 1 + ( δ 1) T µ (Eurocode 8) c Τ 8

9 Design spectrum for linear analysis The capacity of structural systems to resist seismic actions in the non-linear range permits their design for resistance to seismic forces smaller than those corresponding to a linear elastic response. The energy dissipation capacity of the structure is taken into account mainly through the ductile behavior of its elements by performing a linear analysis based on a reduced response spectrum, called design spectrum. This reduction is accomplished by introducing the behavior factor q. 9

10 Design spectrum for linear analysis (Eurocode 8) For the horizontal components of the seismic action the design spectrum, S d (T), shall be defined by the following expressions: a g is the design ground acceleration on type A ground (a g = γ I.a gr ); γ I =importance factor T B is the lower limit of the period of the constant spectral acceleration branch; T C is the upper limit of the period of the constant spectral acceleration branch; T D is the value defining the beginning of the constant displacement response range of the spectrum; S is the soil factor S d (T) is the design spectrum; q is the behaviour factor; β is the lower bound factor for the horizontal design spectrum, recommended β=0,2 10

11 Importance Classes (Eurocode 8) 11

12 Behaviour Factor (Eurocode 8) The upper limit value of the behavior factor q, introduced to account for energy dissipation capacity, shall be derived for each design direction as follows: q = q o k w 1,5 Where q o is the basic value of the behavior factor, dependent on the type of the structural system and on its regularity in elevation; k w is the factor reflecting the prevailing failure mode in structural systems with walls: k = (1 + a ) / 3 1 and 0, 5 a = Pr evailing wall aspect ratio =Σh / Σ u o o wi wi Low Ductility Class (DCL): Seismic design for low ductility, following EC2 without any additional requirements other than those of 5.3.2, is recomended only for low seismicity cases (see 3.2.1(4)). 12

13 Behaviour Factor (Eurocode 8) A behaviour factor q of up to 1,5 may be used in deriving the seismic actions, regardless of the structural system and the regularity in elevation. Medium (DCM) and High Ductility Class (DCH): For buildings which are not regular in elevation, the value of qo should be reduced by 20% 13

14 a u /a 1 in behaviour factor of buildings designed for ductility: due to system redundancy & overstrenght

15 Structural Regularity (Eurocode 8) For seismic design, building structures in all modern codes are separated in two categories: a) regular buildings b) non-regular buildings This distinction has implications for the following aspects of the seismic design: the structural model, which can be either a simplified planar model or a spatial model ; the method of analysis, which can be either a simplified response spectrum analysis (lateral force procedure) or a modal one; the value of the behavior factor q, which shall be decreased for buildings non-regular in elevation 15

16 Structural Regularity (Eurocode 8) 16

17 Criteria for Regularity in Elevation (Eurocode 8) All lateral load resisting systems, such as cores, structural walls, or frames, shall run without interruption from their foundations to the top of the building or, if setbacks at different heights are present, to the top of the relevant zone of the building. Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually, without abrupt changes, from the base to the top of a particular building. When setbacks are present, special additional provisions apply. 17

18 STRUCTURE OF EN1998-1:2004

19 How q is achieved? Specific requirements in detailing (e.g. confining actions by well anchored stirrups) Avoid brittle failures Avoid soft storey mechanism Avoid short columns Provide seismic joints to protect from earthquake induced pounding from adjacent structures..

20 Material limitations for primary seismic elements

21 Capacity Design Avoid weak column/strong beam frames

22 Capacity Design Provide strong column/weak beam frames or wall equivalent dual frames, with beam sway mechanisms, trying to involve plastic hinging at all beam ends

23 Capacity Design (Eurocode 8) column 1 beam 1 beam 2 column 2 Exceptions: see EC (2)

24 Shear Capacity Design (Eurocode 8) Avoid Brittle failure M M 2 V Column moment distribution = Μ V x M Μ = M 1,d +E 1 -E M 1,d or M 2,d M 2,d V M +Μ = = + 1, d 2, d max,c, clear V max,c = M +Μ + 2, d 1, d 12

25 Shear Capacity Design of Columns (Eurocode 8) + M 1,d Similarly - M 1,d γ Rd M Rc,1 +, when ΣΜ Rb > ΣΜ Rc, weak columns γ Rd M Rc,1 + (ΣΜ Rd,b \ ΣΜ Rd,c ), when ΣΜ Rb < ΣΜ Rc, weak beams: (moment developed in the column when beams fail) γ Rd M Rc,1 -, when ΣΜ Rb < ΣΜ Rc γ Rd M Rc,1 - (ΣΜ Rd,b \ ΣΜ Rd,c ) Also similarly for M 2,d+, M - 2,d ΣΜ Rb, ΣΜ Rc for the corresponding direction of seismic action (+E or -E) In DC H γ Rd =1.3 In DC M γ Rd =1.1

26 Shear Capacity Design of Beams (Eurocode 8) M M 2 = V CD V g+ψq M V M M 2 +E - + M 1,d M 2,d Determination of V M -E + - M 1,d M 2,d [M] or + - [M] + [V] - [V] V M max,b = M +Μ + 2, d 1, d In DC H γ Rd =1.2 In DC M γ Rd = V M max,b = M +Μ + 1, d 2, d 12

27 Shear Capacity Design of Beams (Eurocode 8) + M 1,d Similarly - M 1,d γ Rd M Rb,1 +, when ΣΜ Rb < ΣΜ Rc, weak beams γ Rd M Rb,1 + (ΣΜ Rd,c \ ΣΜ Rd,b ), when ΣΜ Rb > ΣΜ Rc, weak columns: (moment developed in the column when beams fail) γ Rd M Rb,1 -, when ΣΜ Rb < ΣΜ Rc γ Rd M Rb,1- (ΣΜ Rd,c \ ΣΜ Rd,b ) Also similarly for M 2,d+, M - 2,d ΣΜ Rb, ΣΜ Rc for the corresponding direction of seismic action (+E or -E) In DC H γ Rd =1.3 In DC M γ Rd =1.1

28 Local Ductility Conditions Relation between q and μ δ δ = q if T1 T c, = 1 + ( q 1) T / T if T < T ; µ µ δ c 1 1 Relation between μ δ and μ φ = 1+ 3( 1) L / L (1 0.5 L / L ); µ µ where L pl :plastic hinge length, L s : shear span δ φ pl s pl s Relation of L pl & L s for typical RC beams, columns & walls * ( considering : εcu = aωw ) Lpl 0.3Ls and for safety factor 2 : Lpl 0.15 Ls Then : µ φ 2µ δ 1 For T 1 T c µ φ = 2µ δ 1= 2q 1 Tc Tc For T 1 T c µ φ = 2µ δ 1 = 2[1 + ( q 1) ] 1 = 1+ 2( q 1) T1 T1 In EC8 q o is used instead of q concervatively to include irregular buildings (q<q o ) Therefore: µ φ µ φ = 2qo 1if T1 Tc Tc = 1+ 2( qo 1) if T1 < T T 1 c Note: For Steel class B μ φ demand increases by 50% c

29 Ductility Estimation for Beams

30 Ductility Estimation for Beams Ductility increases when: ε cu fc confinement ρ2 ρ1 Compressive reinforcement neccessary While for tension reinforcement: the less the best

31 Ductility Estimation for Columns F + F F = N c s2 c1 v = N / bdfc φu Es 0.6 µ φ = = 1.2 [ 1] ε φ f v+ ( ρ kρ )( f / f ) y y 1 2 y c cu Ductility is reduced when axial load increases EC8 limits: v > 0.65 for DCM and v > 0.55 for DCH d d

32 Confined Concrete Model σ c περισφιγμένο με FRP f c * περισφιγμένο με χαλύβδινα στοιχεία f c 0,85f c According to EC2 f = β f ε = β ε * * 2 c c co co Adopting 1 3, 7 p β + fc (Newman K. & Newnan J.B. 1971) 0 ε co ε ε* c u co 0.86 p β min 1+ 5, fc ε * cu = p f c p fc ε* c u ε When hoops are used p 0.5aωw fc ω w = Mechanical volumertic ratio of hoops α=confinement effectiveness factor, a= aa s n Therefore β = min ( aωw, aωw) * ε = aω cu w

33 Detailing of primary beams for local ductility EN :2004 (Ε) For Tension Reinforcement req ρ2 = ρ ρ For Comression Reinforcement More detailing rules for DCH

34 Detailing of primary beams for local ductility for DCM for DCH cr cr = h w =1.5h w Within l cr transverse reinforcement in critical regions of beams: d bw s 6mm h w /4 d ( DCM ) or 6 dbl ( DCH ) 225mm ( DCM ) or 175 mm ( DCH ) 24 bw 8d bl

35 Detailing of primary seismic columns for local ductility EN :2004 (Ε) d bw Everywhere 6mm 1 d,max 4 bl more restrictions for DCH critical regions In critical regions s For / h < 3.0 = cr c cr cl for DCM s for DCH s b o /2 d 175mm 8 bl,min b o /3 6 d bl,min 125mm

36 Detailing of primary seismic columns for local ductility EN :2004 (Ε) c d Normilised Axial Load v v d d for DCM for DCH d b = 2( + w o bc c ) 2 b 200 mm for DCM i b i 150mm for DCH ρ tot A bu = stot ρ tot ρ tot min = 1% max = 4% At least 3 bars in every slide

37 Detailing of primary seismic columns for local ductility for DCM & DCH in critical region at column base EN :2004 (Ε) ω 0.08 for DCM ω w 0.12 for DCH w

38 Beam-Column Joints DCM - Horizontal hoops as in critical region of columns - At least one intermediate column bar at each joint slide DCH Specific rules in

39 Types of Dissipative Walls

40 Ductile Walls w h cr = max h w /6 h w h cr h cr 2 w h for n 6 storeys s 2h for n 7storeys s l w hs = clear storey height µ φ after q = q M / M o o Ed Rd M / M at the base Ed Rd Normilised axial load for DCM v > 0.40 and for DCH v > 0.35 d d

41 No strong column/weak beam capacity design required in wall or wallequivallent dual systems (<50% of seismic base shear in walls) For Shear Design in shear for V from analysis, times:. 1.5 for DCM For DCH, V Ed = ε V ε 0.5 Ed

42 Design and Detailing of Ductile Walls strain distribution * = ε cu also (0.15, 1.5 b ) c w c Confined boundary element of free-edge wall end: Longitudinal reinforcement ρ tot 0.5% Same restrictions as in columns e.g. ω 0.08 ( DCM ) ω wd 0.12 ( DCH ) wd S, max etc where ω f f v = ρv yd, v / cd

43 EN :2004 (Ε) Detailing of Ductile Walls

44 EN :2004 (Ε) Detailing of Ductile Walls

45 Large Lightly Reinforced Walls

46 Design and Detailing of Large Lightly Reinforced Walls

47 Design and Detailing of Large Lightly Reinforced Walls Large l w Foundation Problem Large moment at the base and very low normalized axial force Usual way of footing with tie-beams is insufficient Impossible to form plastic hinge at the wall base. Wall will uplift & rock as a rigid body

48 c max Large Lightly Reinforced Walls Boundary elements b w 3b w σ cm /f cd σ cm = mean value of concrete compressive stress Longitudinal Reinforcement of Boundary Elements (a) Diameter of vertical bars (EC (2)) lower storeys when higher storeys: (b) Stirrups (EC (1)) In all storeys-closed stirrups d d 6 bl bw max( mm, 3 ) s min( 100mm, 8d ) w h : w storey / 3 bl d bl d bl 12mm 10mm No other particular regulations for LLRCW

49 Secondary Seismic Members A limited number of structural members may be designated as secondary seismic members. The strength and stiffness of these elements against seismic actions shall be neglected. The total contribution to lateral stiffness of all secondary seismic members should not exceed 15% of that of all primary seismic members. Such elements shall be designed and detailed to maintain their capacity to support the gravity loads present in the seismic design situation, when subjected to the maximum deformations under the seismic design situation. Maximum deformations shall account for P-Δ. In more detail , , 5.7

50 Specific Provisions in EC8 for: LOCAL EFFECTS to masonry infills see 5.9 CONCRETE DIAPHRAGMS see 5.10 PRECAST CONCRETE STRUCTURES see 5.11

51 Thank you for your attention

52 APPENDIX: Detailing & Dimensioning of seismic elements (Synopsis by M. Fardis)

53 APPENDIX: Detailing & Dimensioning of seismic elements (Synopsis by M. Fardis)

54 APPENDIX: Detailing & Dimensioning of seismic elements (Synopsis by M. Fardis)

55 APPENDIX: Detailing & Dimensioning of seismic elements (Synopsis by M. Fardis)

56 APPENDIX: Detailing & Dimensioning of seismic elements (Synopsis by M. Fardis)

57 APPENDIX: Detailing & Dimensioning of seismic elements (Synopsis by M. Fardis)

58 APPENDIX: Detailing & Dimensioning of seismic elements (Synopsis by M. Fardis)