Seismic Design of New R.C. Structures

Transcription

1 Seismic Design Philosophy Main Concepts Seismic Design of New R.C. Structures Prof. Stephanos E. Dritsos University of Patras, Greece. Energy dissipation Ductility Capacity design Learning from Earthquakes Pisa, March 2015 Energy Dissipation 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 ( u / y ): Ratio of the ultimate deformation at failure u to the yield deformation y. * 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. 3 4

2 In terms of displacements: Ductility Factors u = y u : ultimate deformation at failure y : yield deformation 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. In terms of rotations: (for members) θu θ = θ y θ u : ultimate rotation at failure θ y : yield rotation In terms of curvatures: (for members) ϕu ϕ = ϕ y φ u : ultimate curvature at failure φ y : yield curvature 5 Ductility and Behaviour Factor q Definition q= el. Flexible Structures T Tc : Rule of equal dispacement inel Ductility and Behaviour Factor q Stiff Structures T Tc q for T=0 q=1 for T=T c q=μ q 1max u 2 = = = 2max y2 μ 1 y2 u2 7 y u2 Rule of equal dissipating energy q el 1max = = = inel 2max (2 1) 1/ 2 Τ c T q= 1 ( 1) (Eurocode 8) T c Τ 8

3 Design spectrum for linear analysis The capacity of structural systems to resist seismic actions in the nonlinear 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 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 Importance Classes (Eurocode 8) 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: ku= (1 ao ) / 3 1 and 0,5 ao= Pr evailing wall aspect ratio =Σhwi / Σl 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))

4 Behaviour Factor (Eurocode 8) au/a1 in behaviour factor of buildings designed for ductility: due to system redundancy & overstrenght 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 Structural Regularity (Eurocode 8) Structural Regularity (Eurocode 8) For seismic design, building structures in all modern codes are separated in two categories: a) regular buildings b) nonregular 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 nonregular in elevation 15 16

5 Criteria for Regularity in Elevation (Eurocode 8) STRUCTURE OF EN19981:2004 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 How q is achieved? Material limitations for primary seismic elements 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..

6 Capacity Design Avoid weak column/strong beam frames 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 Capacity Design (Eurocode 8) column 1 beam 1 beam 2 column 2 Shear Capacity Design (Eurocode 8) Avoid Brittle failure M Column moment distribution E 1 M 1,d E M 2 = Μ x M Μ = l M 1,d or 2 M 2,d 2 M 2,d Exceptions: see EC (2) M Μ = = l 1, d 2, d max,c, l12 l12 clear max,c M = Μ 2, d 1, d l 12

7 Shear Capacity Design of Columns (Eurocode 8) Shear Capacity Design of Beams (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 ) M 1 M = 1 2 E CD gψq M 1,d M 2,d 1 2 Determination of M [M] or E M 1 M M M 1,d M 2,d 1 2 [M] 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 M [] Μ 2, d 1, d M max,b = l12 In DC H γ Rd =1.2 In DC M γ Rd =1.0 M max,b M = [] Μ 1, d 2, d l 12 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 In DC H γ Rd =1.3 In DC M γ Rd =1.1, 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) Local Ductility Conditions Relation between q and μ = q if T1 T c, = 1 ( q 1) Tc / T1 if T1< Tc ; Relation between μ and μ φ = 1 3( φ 1) Lpl / Ls (1 0.5 Lpl / Ls ); where L pl :plastic hinge length, L s : shear span 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 : φ 2 1 For T 1 T c φ= 2 1= 2q 1 Tc Tc For T 1 T c φ= 2 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: φ = 2qo 1 if T1 Tc Tc φ = 1 2( qo 1) if T1 < Tc T 1 Note: For Steel class B μ φ demand increases by 50%

8 Ductility Estimation for Beams Ductility Estimation for Beams Ductility increases when: ε cu ρ2 fc confinement ρ1 Compressive reinforcement neccessary While for tension reinforcement: the less the best Confined Concrete Model Ductility Estimation for Columns σc περισφιγμέν ο με FRP Fc Fs 2 Fc1 = N περισφιγμένο με χαλύβινα στοιχεία * fc v = N / bdf c φ = E φu 0.6 =1.2 s [ 1] ε cu f y v ( ρ1 k ρ 2 )( f y / f c ) φy fc 0,85fc f = β fc * c Ductility is reduced when axial load increases EC8 limits: vd > 0.65 for DCM and vd > 0.55 for DCH ε co ε * c u ε co 0 According to EC2 ε = β ε co * co 2 Adopting β 1 3, 7 p fc ε* ε cu p 0.5 a ωw fc ωw= Mechanical volumertic ratio of hoops When hoops are used 0.86 (Newman K. & Newnan J.B. 1971) β min 1 5 p p, fc fc ε cu* = p fc α=confinement effectiveness factor, Therefore β = min (1 2.5 aωw, aωw ) ε cu* = aωw a = as an

9 Detailing of primary beams for local ductility Detailing of primary beams for local ductility EN 19981:2004 (Ε) for DCM l cr = hw for DCH l cr =1.5hw For Tension Reinforcement For Comression Reinforcement ρ 2 = ρ 2req 0.5ρ Within ℓcr transverse reinforcement in critical regions of beams: dbw 6mm s More detailing rules for DCH Detailing of primary seismic columns for local ductility EN 19981:2004 (Ε) hw / 4 24 dbw 8 dbl ( DCM ) or 6 dbl ( DCH ) 225mm ( DCM ) or 175mm ( DCH ) Detailing of primary seismic columns for local ductility EN 19981:2004 (Ε) Everywhere 6 mm dbw 1 dbl,max 4 more restrictions for DCH critical regions c d Normilised Axial Load vd 0.65 for DCM vd 0.55 for DCH In critical regions s for DCM s For l cr / hc < 3.0 l cr = l cl for DCH s bo / 2 8 dbl,min 175 mm bo / 3 6 dbl,min 125 mm d bo = bc 2(c w ) 2 bi 200 mm for DCM ρtot = Astot bu min ρtot =1% max ρtot = 4% bi 150 mm for DCH At least 3 bars in every slide

10 Detailing of primary seismic columns for local ductility for DCM & DCH in critical region at column base EN 19981:2004 (Ε) BeamColumn Joints DCM ω 0.08 for DCM ω w 0.12 for DCH w Horizontal hoops as in critical region of columns At least one intermediate column bar at each joint slide DCH Specific rules in Types of Dissipative Walls Ductile Walls h w h cr h cr = max h cr h w l w / 6 2l w h for n 6 storeys s 2h for n 7 storeys s l w hs = clear storey height 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

11 No strong column/weak beam capacity design required in wall or wallequivallent dual systems (<50% of seismic base shear in walls) Design and Detailing of Ductile Walls For Shear Design in shear for from analysis, times:. 1.5 for DCM For DCH, Ed = ε ε 0.5 Ed strain distribution * = ε cu also l (0.15 l, 1.5 b ) c w c Confined boundary element of freeedge 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, etc max whereω ρ f f v= v yd, v / cd EN 19981:2004 (Ε) Detailing of Ductile Walls EN 19981:2004 (Ε) Detailing of Ductile Walls

12 Large Lightly Reinforced Walls Design and Detailing of Large Lightly Reinforced Walls 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 tiebeams is insufficient Impossible to form plastic hinge at the wall base. Wall will uplift & rock as a rigid body l max c 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 (b) Stirrups (EC (1)) In all storeysclosed stirrups d d 6 bl bw max( mm, 3 ) s min( 100mm, 8d ) w lw h storey/ 3 : d higher storeys: bl bl d bl 12mm 10mm No other particular regulations for LLRCW

13 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 PΔ. In more detail , , 5.7 Specific Provisions in EC8 for: LOCAL EFFECTS to masonry infills see 5.9 CONCRETE DIAPHRAGMS see 5.10 PRECAST CONCRETE STRUCTURES see 5.11 APPENDIX: Detailing & Dimensioning of seismic elements (Synopsis by M. Fardis) Thank you for your attention

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

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