EN 1992 : 2003 Eurocode 2: Design of concrete structures

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1 Technical Chamber of Greece Structural Eurocodes meeting Development and basic aspects of EN 1992 and EN 1998 Prof. A.J. Kappos Dept. of Civil Engineering Aristotle University of Thessaloniki Athens, 11 October 26 EN 1992 : 23 Eurocode 2: Design of concrete structures 1

2 GENERAL STRUCTURE OF EUROCODE 2 EN EN EN EN GENERAL RULES AND RULES FOR BUILDINGS FIRE DESIGN DESIGN ON CONCRETE BRIDGES SILOS AND TANKS Content of EN General 2. Basis of design 2.1 Requirements 2.2 Principles of limit state design 2.3 Basic variables 2.4 Verification by the partial factor method 2.5 Design assisted by testing 2.6 Supplementary requirements for foundations 2.7 Requirements for fastenings 3. Materials 3.1 Concrete 3.2 Reinforcing steel 3.3 Prestressing steel 3.4 Prestressing devices 4. Durability and cover to reinforcement 4.1 General 4.2 Environmental conditions 4.3 Requirements for durability 4.4 Methods of verification 2

3 EN : Content (cont d) 5. Structural analysis 5.1 General 5.2 Geometric imperfections 5.3 Idealisation of the structure 5.4 Linear elastic analysis 5.5 Linear analysis with limited redistribution 5.6 Plastic analysis 5.7 Non-linear analysis 5.8 Second order effects with axial load 5.9 Lateral instability of slender beams 5.1 Prestressed members and structures 5.11 Analysis for some particular structural members 6. Ultimate limit states (ULS) 6.1 Bending with or without axial force 6.2 Shear 6.3 Torsion 6.4 Punching 6.5 Design with strut and tie models EN : Content (cont d) 6.6 Anchorages and laps 6.7 Partially loaded areas 6.8 Fatigue 7. Serviceability limit states (SLS) 7.1 General 7.2 Stress limitation 7.3 Crack control 7.4 Deflection control 8 Detailing of reinforcement and prestressing tendons - General 8.1 General 8.2 Spacing of bars 8.3 Permissible mandrel diameters for bent bars 8.4 Anchorage of longitudinal reinforcement 8.5 Anchorage of links and shear reinforcement 8.6 Anchorage by welded bars 8.7 Laps and mechanical couplers 8.8 Additional rules for large diameter bars 8.9 Bundled bars 8.1 Prestressing tendons 3

4 EN : Content (cont d) 9. Detailing of members and particular rules 9.1 General 9.2 Beams 9.3 Solid slabs 9.4 Flat slabs 9.5 Columns 9.6 Walls 9.7 Deep beams 9.8 Foundations 9.9 Regions with discontinuity in geometry or action 9.1 Tying systems 1. Additional rules for precast concrete elements and structures 1.1 General 1.2 Basis of design, fundamental requirements 1.3 Materials 1.5 Structural analysis 1.9 Particular rules for design and detailing EN : Content (cont d) 11. Lightweight aggregated concrete structures 11.1 General 11.2 Basis of design 11.3 Materials 11.4 Durability and cover to reinforcement 11.5 Structural analysis 11.6 Ultimate limit states 11.7 Serviceability limit states 11.8 Detailing of reinforcement - General 11.9 Detailing of members and particular rules 11.1 Additional rules for precast concrete elements and structures res Plain and lightly reinforced concrete structures 12. Plain and lightly reinforced concrete structures 12.1 General 12.2 Basis of design 12.3 Materials 12.5 Structural analysis: ultimate Limit states 12.6 Ultimate limit states 12.7 Serviceability limit states 12.9 Detailing of members and particular rules 4

5 EN : Content (cont d) Annexes A (Informative) Modification of partial factors for materials B (Informative) Creep and shrinkage strain C (Normative) Reinforcement properties D (Informative) Detailed calculation method for prestressing steel relaxation losses E (Informative) Indicative Strength Classes for durability F (Informative) Reinforcement expressions for in-plane stress conditions G (Informative) Soil structure interaction H (Informative) Global second order effects in structures I (Informative) Analysis of flat slabs and shear walls J (Informative) Examples of regions with discontinuity in geometry or action EN : 1: General Overview Comparative studies show that the overall economy of construction of designs to EC2 are largely similar to those currently designed using actual national design standards There is little practical difference in results of design for bending The style of the Eurocodes and the way they are implemented are appreciably different, and there are some significant changes in aspects of the design process. There are associated changes arising through related Eurocodes and product standards. These make a suite of documents,, including: EN26 Concrete: Performance, Production, Placing and Compliance Criteria, and EN1367 Execution of Concrete Structures 5

6 FUNDAMENTAL REQUIREMENTS SAFETY (STRUCTURAL RESISTANCE) SERVICEABILITY DURABILITY ECONOMY - Design working life - Inspection and maintenance levels AESTHETICS Verification of safety and serviceabilty by the partial factor method for : ULTIMATE LIMIT STATES ULS SERVICEABILITY LIMIT STATES SLS Basis of design partial safety factors Action Comment Symbol Value Shrinkage Prestress Fatigue loads Materials Concrete Steel (reinforcement) Steel (prestressing) Favourable effect ULS with external prestressing Unfavourable local effects Comment Persistent and transient design situations Accidental design situation Persistent and transient design situations Accidental design situation Persistent and transient design situations Accidental design situation γ SH γ P,fav γ P,unfav γ P,unfav γ F,fat Symbol γ C γ S γ S 1. 1, 1,3 1,2 1, Value , , 6

7 Structural Analysis Linear elastic analysis (ULS-SLS) SLS) Linear analysis with limited redistribution (ULS) Plastic analysis (ULS) Non-linear analysis (ULS-SLS) SLS) Design value of prestressing forces P m,t P d = γ P Pm P, t γ = 1 mean value at time t. Ultimate Limit States : bending with or without axial force Assumptions Plane sections remain plane Tensile strength of concrete ignored No relative slip between concrete and steel Possible strain distributions in cross-sections sections 7

8 Possible strain distributions in the Ultimate Limit State A s2 (1- εc2/εcu2)h or (1- εc3/εcu3)h B h d Ap A Δεp εp() C As1 εs, ε p ε ud εy εc2 (ε c3 ) εcu2 (ε ) cu3 εc A - Reinforcing steel tension strain limit B - Concrete compression strain limit C - Concrete pure compression strain limit V Rd,c V Rd,s Ultimate limit state Shear,c Design shear resistance of the member without shear reinforcement V Rd,max Design value of the shear force which can be sustained by the yielding shear reinforcement Design value of the maximum shear force which can be sustained by the member limited by crushing of the compression struts General verification procedure : V Ed 1) V Ed V Rd,c V Rd 2) V Ed V Rd,s and V Ed V Rd Rd,max 8

9 Truss Model & Notation for Shear Reinforced Members Ultimate limit state Shear (contnd) V Rd,c = [(,18/γ c )k(1 ρ l f ck ) 1/3 +,15 σ cp ] b w d k = 1 + (2/d) 1/2 d effective depth of the cross-section section in mm ρ l = A sl / b d <,2 A w sl area of the tensile reinforcement, b w smallest width of the cross- section in the tensile area σ cp = N Ed / A c (> compression) Min. value V Rd,c = (, 35k 3/2 3/2.f 1/2 ck 1/2 +,15σ cp ) b w d 9

10 Ultimate limit state Shear (contnd) Inf. of and V Rd,max V Rd,s = (A( sw /s) z f ywd cotθ ywd cot,max = b w z ν f cd /(cotθ + tanθ ) ν =,6 [ 1-1 f ck / 25 ] 1 < cot θ < 2,5 or 45 > θ > 22 In case of a compression axial force : α cw cw V Rd,max Increased resistance 1 1,25,25 > α c w > 1 where < σ cm <,6f cd Reduced resistance α cw < 1 where σ cm >,6 f cd Shear between web and flanges of T-sectionsT 1, cotθ f 2, (compression flange) 1, cotθ f 1,25 (tension flange) Shear at the interface between concrete cast at different times C and µ are factors which depend on the roughness of the interface 1

11 Ultimate limit state verifications TORSION A - Centre-line B - Outer edge of effective cross- section, circumference u, C - Cover PUNCHING A - Basic control section B - Basic control area A cont C - Basic control perimeter u 1 D Loaded area A load C A tef zi TEd tef/2 B B D θ 2d θ A d h 2d θ = arctan (1/2) = 26,6 c r cont C Design with strut and tie models For zones where a non-linear strain distribution exists Verification of struts (concrete) struts without transverse tension struts with transverse tension (compressed and cracked zones) bef a F bef a F Verification of ties : D B D b F h = b H b F z = h/2 h = H/2 B Continuity region D Discontinuity region bef = b bef =,5H +,65a; a h 11

12 Examples of strut and tie models: for half joints ( 1 precast concrete elements & structures) for a corbel (Annex J- regions with discontinuities) Serviceability limit state Functioning of the structure in normal use Comfort of people Appearance The verification rules are deemed to ensure: the appropriate serviceability level the durability for the design working life 12

13 Serviceability criteria E d C d The verifications relate to: stress limitation limitation of crack width limitation of deformations limitation of vibrations Actions and material properties are taken into account with their representative values (partial factors equal to 1, unless otherwise specified) EN : 24 Eurocode 8 : Design of structures for earthquake resistance 13

14 Contents of EN : 24 Eurocode 8: Design of structures for earthquake resistance FOREWORD 1 GENERAL 1.1 SCOPE 1.2 NORMATIVE REFERENCES 1.3 ASSUMPTIONS 1.4 DISTINCTION BETWEEN PRINCIPLES AND APPLICATION RULES 1.5 TERMS AND DEFINITIONS 1.6 SYMBOLS 1.7 S.I. UNITS 2 PERFORMANCE REQUIREMENTS AND COMPLIANCE CRITERIA 2.1 FUNDAMENTAL REQUIREMENTS 2.2 COMPLIANCE CRITERIA 3 GROUND CONDITIONS AND SEISMIC ACTION 3.1 GROUND CONDITIONS 3.2 SEISMIC ACTION 4 DESIGN OF BUILDINGS 4.1 GENERAL 4.2 CHARACTERISTICS OF EARTHQUAKE RESISTANT BUILDINGS 4.3 STRUCTURAL ANALYSIS 4.4 SAFETY VERIFICATIONS 5 SPECIFIC RULES FOR CONCRETE BUILDINGS 5.1 GENERAL 5.2 DESIGN CONCEPTS 5.3 DESIGN TO EN DESIGN FOR DCM 5.5 DESIGN FOR DCH 5.6 PROVISIONS FOR ANCHORAGES AND SPLICES 5.7 DESIGN AND DETAILING OF SECONDARY SEISMIC ELEMENTS 5.8 CONCRETE FOUNDATION ELEMENTS 5.9 LOCAL EFFECTS DUE TO MASONRY OR CONCRETE INFILLS 5.1 PROVISIONS FOR CONCRETE DIAPHRAGMS 5.11 PRECAST CONCRETE STRUCTURES 14

15 6 SPECIFIC RULES FOR STEEL BUILDINGS 6.1 GENERAL 6.2 MATERIALS 6.3 STRUCTURAL TYPES AND BEHAVIOUR FACTORS6.4 STRUCTURAL ANALYSIS 6.5 DESIGN CRITERIA AND DETAILING RULES FOR DISSIPATIVE STRUCTURAL BEHAVIOUR COMMON TO ALL STRUCTURAL TYPES 6.6 DESIGN AND DETAILING RULES FOR MOMENT RESISTING FRAMES 6.7 DESIGN AND DETAILING RULES FOR FRAMES WITH CONCENTRIC BRACINGS 6.8 DESIGN AND DETAILING RULES FOR FRAMES WITH ECCENTRIC BRACINGS 6.9 DESIGN RULES FOR INVERTED PENDULUM STRUCTURES 6.1 DESIGN RULES FOR STEEL STRUCTURES WITH CONCRETE CORES OR CONCRETE WALLS AND FOR MOMENT RESISTING FRAMES COMBINED WITH CONCENTRIC BRACINGS OR INFILLS 6.11 CONTROL OF DESIGN AND CONSTRUCTION 7 SPECIFIC RULES FOR COMPOSITE STEEL CONCRETE BUILDINGS 7.1 GENERAL 7.2 MATERIALS 7.3 STRUCTURAL TYPES AND BEHAVIOUR FACTORS 7.4 STRUCTURAL ANALYSIS 7.5 DESIGN CRITERIA AND DETAILING RULES FOR DISSIPATIVE STRUCTURAL BEHAVIOUR COMMON TO ALL STRUCTURAL TYPES 7.6 RULES FOR MEMBERS 7.7 DESIGN AND DETAILING RULES FOR MOMENT FRAMES 7.8 DESIGN AND DETAILING RULES FOR COMPOSITE CONCENTRICALLY BRACED FRAMES 7.9 DESIGN AND DETAILING RULES FOR COMPOSITE ECCENTRICALLY BRACED FRAMES 7.1 DESIGN AND DETAILING RULES FOR STRUCTURAL SYSTEMS MADE OF REINFORCED CONCRETE SHEAR WALLS COMPOSITE WITH STRUCTURAL STEEL ELEMENTS 7.11 DESIGN AND DETAILING RULES FOR COMPOSITE STEEL PLATE SHEAR WALLS 7.12 CONTROL OF DESIGN AND CONSTRUCTION 15

16 8 SPECIFIC RULES FOR TIMBER BUILDINGS 8.1 GENERAL 8.2 MATERIALS AND PROPERTIES OF DISSIPATIVE ZONES 8.3 DUCTILITY CLASSES AND BEHAVIOUR FACTORS 8.4 STRUCTURAL ANALYSIS 8.5 DETAILING RULES 8.6 SAFETY VERIFICATIONS 8.7 CONTROL OF DESIGN AND CONSTRUCTION 9 SPECIFIC RULES FOR MASONRY BUILDINGS 9.1 SCOPE 9.2 MATERIALS AND BONDING PATTERNS 9.3 TYPES OF CONSTRUCTION AND BEHAVIOUR FACTORS 9.4 STRUCTURAL ANALYSIS 9.5 DESIGN CRITERIA AND CONSTRUCTION RULES 9.6 SAFETY VERIFICATION 9.7 RULES FOR SIMPLE MASONRY BUILDINGS 1 BASE ISOLATION 1.1 SCOPE 1.2 DEFINITIONS 1.3 FUNDAMENTAL REQUIREMENTS 1.4 COMPLIANCE CRITERIA 1.5 GENERAL DESIGN PROVISIONS 1.6 SEISMIC ACTION 1.7 BEHAVIOUR FACTOR 1.8 PROPERTIES OF THE ISOLATION SYSTEM 1.9 STRUCTURAL ANALYSIS 1.1 SAFETY VERIFICATIONS AT ULTIMATE LIMIT STATE ANNEX A (INFORMATIVE) ELASTIC DISPLACEMENT RESPONSE SPECTRUM ANNEX B (INFORMATIVE) DETERMINATION OF THE TARGET DISPLACEMENT FOR NONLINEAR STATIC (PUSHOVER) ANALYSIS ANNEX C (NORMATIVE) DESIGN OF THE SLAB OF STEEL-CONCRETE COMPOSITE BEAMS AT BEAM-COLUMN JOINTS IN MOMENT RESISTING FRAMES 16

17 EUROCODE 8 (SEISMIC DESIGN): SPECIFIC RULES FOR CONCRETE BUILDINGS Ductility classes New ductility classes (DC) (changes dictated by national comments supported by a number of background studies) DC H ( old Μ, increased q, CD for V Sd in beams,...) DC Μ ( old L, increasedq,cd forv Sd in beams,...) DC L (EC2, no brittle steel Α, q 1.5) Basic value of behaviour factor (q ) STRUCTURAL TYPE DCH DCM Frame system, dual system, coupled wall system 4,5α u /α 1 3,α u /α 1 Wall system 4,α u /α 1 3, Core system 3, 2, Inverted pendulum system 2, 1,5 17

18 Overstrength α 1 : seismic action at first yield (anywhere) α u : seismic action at development of overall structural instability (collapse mechanism) Obtained from pushover analysis (α u /α 1 1.5), or defaults: Frames (or frame-equivalent dual): α u /α 1 =1.3 (1.1 for one-storey, 1.2 for one-bay frames) Wall (or wall-equivalent dual): Wall systems with only two uncoupled walls per horizontal direction: α u /α 1 =1. Other uncoupled wall systems: α u /α 1 =1.1 Wall -equivalent dual, or coupled wall systems: α u /α 1 =1.2 Final behaviour factor q=q o. k w 1,5 New structural systems Large lightly reinforced wall system: comprises at least two walls with horizontal dimension not less than 4m and 2h w /3, which collectively support at least 2% of the total gravity load above in the seismic design situation has a fundamental period T 1, for assumed fixity at the base against rotation, less or equal to.5sec If a structural system does not qualify as a system of large lightly reinforced walls, then all its walls should be designed and detailed as ductile walls Frame, dual or wall systems without a minimum torsional rigidity (e o <.3r) should be classified as torsionally flexible (core) systems 18

19 Design criteria Local resistance condition: E d R d Capacity design rule: E d from equilibrium conditions, assuming plastic hinges with their possible overstrengths formed in adjacent areas to avoid brittle or undesirable failure mechanisms Local ductility condition: high plastic rotational capacities in potential plastic hinge regions sufficient curvature ductility (post-failure 85%-moment resistance level) in all critical regions of primary elements μ φ =2q o -1 if T 1 T C μ φ =1+2(q o -1)T C /T 1 if T 1 <T C (based on μ φ =2μ δ -1 and μ δ =q if T 1 T C, μ δ =1+(q-1)T C /T 1 if T 1 <T C ) Note that q<q o for irregular structures (no reduction in μ φ,req!) Structural redundancy: high degree of redundancy accompanied by redistribution capacity (otherwise lower q-factor) Secondary seismic members and resistances: resistances or stabilising effects not explicitly taken into account (e.g. membrane reactions of slabs mobilised by upwards deflections of structural walls) non-structural elements (esp. masonry infills!) Specific additional measures (to reduce uncertainty): minimize geometric errors (min dimensions, max b/h etc.) minimize ductility uncertainties (min μ φ, minρ l, ν max ) 19

20 Safety verifications For ULS verifications, partial safety factors for materials γ c and γ s shall account for strength degradation due to the cyclic deformations γ c =1.5 and γ s =1.15 (as in EC2) can be taken (convenient for practice!) assuming that due to local ductility provisions the ratio between the residual strength after degradation and the initial one is roughly equal to the ratio between the γ M -values for accidental and fundamental load combinations if strength degradation is appropriately accounted in the evaluation of the material properties, the γ M -values adopted for the accidental design situation may be used Design to Eurocode 2 (EN1992-1) 1) Recommended only for low seismicity areas In primary elements, reinforcing steel of class B or C (table C.1 EN1992-1) shall be used Behaviour factor up to q=1.5 may be used in deriving the seismic actions, regardless of the structural system and of regularity in elevation 2

21 Properties of reinforcement (EC2 Annex C) Note: The values for the fatigue stress range with an upper limit of β f yk and for the minimum relative rib area for use in a Country may be found in its National Annex. The recommended values are given in Table C.2N. The value of β for use in a Country may be found in its National Annex. The recommended value is,6. Design for DC M: M Geometrical constraints and materials Material requirements use of concrete <C16 not allowed in primary elements use of concrete >C5 (HSC) for DC M is not covered only ribbed bars are allowed as longitudinal reinforcing steel in critical regions of primary elements in primary elements, reinforcing steel of class B or C (table C.1 EN1992-1) shall be used welded wire meshes of steel B or C are allowed (should be ribbed if used as longitudinal reinforcement) 21

22 Geometrical constraints BEAMS eccentricity of beam axis < b c /4 width b w min { b c + h w ; 2b c } COLUMNS unless θ.1, in primary columns b.1l o (l o : distance from end to point of contraflexure) DUCTILE WALLS web thickness b wo max{15mm, h s /2} (h s : clear storey height) additional requirements for confined boundary elements LARGE LIGHTLY REINFORCED WALLS web thickness b wo max{15mm, h s /2} Design for DC M: M Design action effects Moments and axial forces from analysis, except in primary ductile walls; redistribution of M permitted Shear forces from capacity design (shears V max,i,v min,i calculated for end moments M i,d ) Beams (γ Rd =1.) M i, d = γ Rd M Rb, i M min(1, M Rc Rb ) 22

23 Columns M i, d = γ Rd (γ Rd =1.1) M Rc, i M min(1, M to account for overstrength due to strain-hardening and confinement Rb Rc ) Ductile walls: Redistribution between primary walls, up to 3% Redistribution between coupling beams, up to 2% Design bending moment diagram (slender walls): b a a M Ed M Ed M' Ed a l wall systems a l M' Ed dual systems a = from analysis b = design envelope a = tension shift l 23

24 Design shear force diagram (dual systems with slender walls): V wall,top>v wall,base/2 design envelope c a=from analysis b=magnified c=design envelope b a 2 3 h w (b) 1 3 h w V wall,base Special provisions for large lightly reinforced walls: to ensure that flexural yielding precedes attainment of ULS in shear, shear force V Ed from analysis is increased V Ed ' q +1 = VEd 2 additional dynamic axial forces developed due to uplifting shall be taken into account in the ULS verification (M, N) may be taken as 5% of the axial force in the wall due to the gravity loads (g+ψ 2 q) if q 2, these dynamic axial forces may be neglected 24

25 Beams Design for DC M: M ULS verifications and detailing bending and shear resistances are computed according to EN part of topreinforcement in T- beams (& Γ-beams) may be placed outside the web, within effective flange width b eff a 2h f 2h f h f 4h f 4h f b d 2h f 2h f h f h f c h f Detailing of DCM beams for local ductility critical regions: <5mm h w s l cr l cr within l cr, μ φ, req is provided through: additional ρ ½ρ at bottom of supports tension reinforcement within l cr, hoops with: d bw 6mm and spacing ρ ρ max ρ s = min{h w /4; 24d bw ; 225mm; 8d bl },18 f = ρ' + μ ε f ρ min φ sy, d f =,5 f ctm yk.18? cd yd 25

26 Columns bending and shear resistances are computed according to EN simplified biaxial bending check with.7m Rd,uniax in primary columns normalised axial force ν d.65 Detailing of DCM columns for local ductility long. reinforcement ratio 1% ρ l 4% at least one intermediate bar (between corner bars) critical (end) regions: l max{ h ; l / 6; 45mm} cr = if l cl /h c <3 (short column), the entire height l cl =l cr within l cr, μ φ, req (e.g. =2q o -1) is provided if μ φ, req involves ε cu.35 confinement required! c cl confinement reinforcement within l cr (DC M) α. ω wd 3. bc μ φ νd εsy, d, 35 b o b i ω wd volume of confining hoops = volume of concretecore f f yd cd s h o h c b o b c confinement effectiveness factor α=α n α s for rectangular cross sections: α n n 2 i = 1 b / 6b h o o α s = ( 1 s / 2bo )( 1 s / 2ho ) min ω wd =.8 for circular cross sections with spiral reinforcement: α n α = 1 = ( 1 s / 2 ) s D o b c 26

27 to prevent early local buckling of longitudinal bars within l cr : s = min{b o /2; 175mm; 8d bl } distance between supported bars s max 2 mm transverse reinforcement within l cr at the base of primary columns may be determined as specified in EN1992-1, provided that ν d.2 and q 2. Beam-column joints horizontal confinement reinforcement in joints of primary beams with columns shall not be less than that provided within l cr of columns if beams with b w b c frame into all four sides of the joint, spacing of horizontal confinement reinforcement in the joint may be increased to twice that required above, but s 15 mm at least one intermediate (between column corner bars) vertical bar shall be provided at each side of a joint of primary beams and columns 27

28 Ductile walls bending and shear resistances computed according to EN in primary walls, normalised axial force ν d.4 vertical web reinforcement shall be included in calculation of flexural resistance of wall sections flexural resistance of composite sections (L, T, U, I or similar) based on effective flange width, min of: actual flange width ½ distance to adjacent web of the wall 25% of total height of wall above the level considered Detailing of DCM walls for local ductility height of critical region h cr above the base h cr = max w, [ l H / 6] w but h 2 lw hs 2 h required μ φ as in columns, but using q o multiplied by M Ed /M Rd at base of wall (e.g. μ φ =2q o M Ed /M Rd -1), to be provided by confinement of boundary elements for walls with rectangular section wd cr for n 6 storeys for n 7 storeys f αω 3μ ρ ( ) b c yd v d sy d where, φ ν + ων ε,, 35 ω v = v bo f cd for barbelled walls, N and ω v refer to h c b c f cd if x u l c, otherwise analysis with confined concrete model needed s 28

29 confinement of boundary elements should extend vertically: over h cr horizontally: over l c (assuming ε cu2 =.35) not good practice minl c {,15 l w or 1,5.b w } no confined boundary element is required over wall flanges with thickness h f >h s /15 and width b f > h s /5 in boundary elements: minρ l =.5% (=½ minρ l,col ) thickness b w 2, also: above h cr EC2 applies, but if ε c >.2, minρ l =.5% ω w in boundary elements may conform to EC2 only, if: axial load ν d.15 axial load ν d.2 and q reduced by 15% 29

30 Large lightly reinforced walls bending resistances computed according to EN when V Ed V Rd,c =[C Rd,c k(1ρ l f ck ) 1/3 +.15σ cp ]b wd ρ w,min in the web is not required sliding shear check is done according to EN1992-1, but anchorage length of clamping bars increased by 5% hoop and cross-tie vertical spacing min{1mm, 8d bl ) vertical bars engaged by hoop or cross-tie with d 6mm, within boundary elements with l c min{b w 3b w σ cm /f cd }, (σ cm : mean value of concrete stress in compression zone) horiz. + vert. ties according to EN provided along all intersections of walls around openings in the wall at all floor levels Design for DC H generally similar to DCM, but more stringent detailing more detailed verification of beam-column joints if VEd > VE = ( 2 + ζ ) fctd bw d max, cross-inclined reinforcement required to resist shear in beams explicit calculation of joint resistance V jhd ν d ηfcd 1 b η j h c 2 V jhd Ash f ywd b j h jc fctd b j h jw fctd + ν d fcd explicit calculation of sliding shear resistance of walls V = V + V + V V Rd, S dd dd 1,3 ΣA = min,25 f id sj fd fcd f ΣA yd sj yd V fd V id = ΣA f cosϕ si μ f = min,5ν f yd [( ΣA f + N ) ξ + M / z] cd sj ξ yd l w b wo Sd Ed 3

31 Provisions for anchorages and splices hoops should be closed stirrups with 135 hooks and 1d bw long extensions Anchorage of reinforcement Columns anchorage length l bd of column bars in critical regions based on A s,req /A s,prov = 1 first 5d bl of column bar within a joint not included in l bd if N Ed is tensile in a column, l bd increased by 5% Beams the part of beam bars bent in joints for anchorage should be placed inside the corresponding column hoops to prevent bond failure limit d bl passing through joints interior beam-column joints d h bl c 7,5 f γ f Rd ctm yd 1+,8 νd 1+.75k ρ' / ρ D max exterior beam-column joints DC H DC M k D 1 2/3 γ Rd d h bl c 7,5 fctm 8 γ f Rd yd ( 1+, ν ) d if limit on d bl difficult to satisfy, use special measures top or bottom bars passing through interior joints, shall terminate at distance l cr from the face of the joint 31

32 Additional measures for anchorage in exterior beam-column joints a) exterior stubs l b h c > 5d bl for DCH h c b) plates welded to end of bars anchor plate c) transverse bars inside the bend > 1 d bl d bw>.6dbl hoops around column bars d bl Splicing of reinforcement lap-splicing by welding not allowed within the l cr splicing by mechanical couplers allowed in columns and walls, if covered by appropriate (cyclic) testing spacing of transverse reinforcement in the lap zone: s = min{b/4; 1mm} required area of transverse reinforcement A st within the lap zone Ast = s ( dbl / 5)( f yl, d /f ywd ) area of one leg of transverse reinforcement 32

33 Design and detailing of secondary seismic elements designed/detailed to maintain bearing capacity, when subjected to max deformations under seismic actions does not apply to non-seismic members (e.g. slab ribs) max deformations calculated from analysis, in which the contribution of secondary elements to lateral stiffness is neglected and primary elements are modelled with their cracked flexural and shear stiffness verification: M d M Rd and V d V Rd where M d, V d calculated from above max deformations and cracked flexural and shear stiffness of secondary elements Local effects due to masonry or concrete infills the entire length of columns in infilled ground floors considered as critical length and confined accordingly if h inf <l cl,col, l cr =l cl plus special measures: design shear calculated from CD based on l cl and γ Rd M Rc corresponding ties placed within l cl +h c if free length < 1.5h c, diagonal reinforcement needed if masonry infill on one side of column only, l cr =l cl length l c of column over which the diagonal strut force of the infill is applied, should be verified in shear for min of horiz. component of strut force and CD shear 33

34 Seismic performance of multistorey R/C buildings designed to the pren EN : Trial application of the new provisions to four typical multistorey buildings, 6-storey and 1-storey with reinforced concrete (R/C) frame system with dual (frame+wall) system Similar buildings previously designed (Kappos / Athanassiadou, EEE, 1997) for old ductility classes H and M comparisons between the old and new designs in terms of cost of materials and of seismic performance Codes: EC2, EC8 (pren) Materials: C2/25 S4 Design PGA: α g =.25 Code spectrum Type 1(Μ s >5.5) Effective Stiffness: EI eff =.5EI g Design of 6-storey 6 buildings 34

35 Behaviour factors q q=1.5, for DC L q= k w q o, for DC M and H - frame system / DC M : q=3.9 - dual system / DC M : q=3.6 - frame system / DC H : q= dual system / DC H : q=5.4 Very similar q-factors for both systems! detailing of frame system / DC L Εξωτερική στήριξη δοκού 1ου-2ου ορόφου Εσωτερική στήριξη δοκού 1ου-2ου ορόφου εσωτερικό υποστύλωμα 1ου - 2ου ορόφου 2Φ22 3Φ2 εξωτερικό υποστύλωμα 1ου - 2ου ορόφου 2Φ16 2Φ18 4Φ16 2Φ14 Φ6/17 4Φ14 Φ6/11 4Φ16 2Φ22 3Φ2 Φ8/155 2Φ18 2Φ16 Φ8/19 2Φ1 4Φ16 2Φ1 3Φ14 3Φ16 εσωτερικό υποστύλωμα 3ου ορόφου 4Φ2 2Φ18 Εξωτερική στήριξη δοκού 3ου-4ου ορόφου 4Φ16 Εσωτερική στήριξη δοκού 3ου-4ου ορόφου 4Φ16 4Φ2 2Φ18 Φ8/15 εξωτερικό υποστύλωμα 3ου - 4ου ορόφου 3Φ18 2Φ14 Φ6/165 4Φ14 Φ6/115 2Φ14 εσωτερικό υποστύλωμα 4ου ορόφου 4Φ2 2Φ18 3Φ18 Φ8/21 2Φ14 2Φ16 2Φ16 2Φ14 4Φ2 Εξωτερική στήριξη δοκού 5ου-6ου ορόφου Εσωτερική στήριξη δοκού 5ου-6ου ορόφου 2Φ18 Φ8/215 εξωτερικό υποστύλωμα 5ου - 6ου ορόφου 2Φ16 1Φ14 4Φ16 1Φ16 2Φ18 Φ6/21 Φ6/195 2Φ18 εσωτερικό υποστύλωμα 1Φ16 5ου - 6ου ορόφου Φ8/18 4Φ2 2Φ14 3Φ14 4Φ2 Φ8/215 35

36 detailing of frame system / DC M εξωτερική στήριξη δοκού 1ου - 2ου ορόφου 3Φ16 εσωτερική στήριξη δοκού 1ου - 2ου ορόφου 2Φ163Φ14 εσωτερικό υποστύλωμα 1ου - 2ου ορόφου 4Φ18 εξωτερικό υποστύλωμα 1ου - 2ου ορόφου 1Φ16 2Φ18 Φ6/11 Φ6/11 4Φ18 2Φ18 1Φ16 2Φ14 3Φ14 Φ8/12 Φ8/1 εξωτερική στήριξη δοκού 3ου - 4ου ορόφου 3Φ16 εσωτερική στήριξη δοκού 3ου - 4ου ορόφου 2Φ16 2Φ14 εσωτερικό υποστύλωμα 3ου - 4ου ορόφου 4Φ18 εξωτερικό υποστύλωμα 3ου - 4ου ορόφου 1Φ16 2Φ18 Φ6/11 2Φ14 Φ6/11 3Φ14 4Φ18 Φ6/12 2Φ18 1Φ16 Φ6/1 εξωτερική στήριξη δοκού 5ου - 6ου ορόφου εσωτερική στήριξη δοκού 5ου - 6ου ορόφου εσωτερικό υποστύλωμα 5ου - 6ου ορόφου εξωτερικό υποστύλωμα 5ου - 6ου ορόφου 3Φ14 2Φ16 2Φ14 1Φ18 2Φ2 3Φ14 Φ6/11 Φ6/11 2Φ2 1Φ18 Φ6/14 3Φ14 Φ6/11 2Φ14 3Φ14 detailing of frame system / DC H Εξωτερική στήριξη δοκού 1ου-2ου ορόφου Εσωτερική στήριξη δοκού 1ου-2ου ορόφου Πόδας εσωτερικού υποστυλώματος 1ου ορόφου Πόδας εξωτερικού υποστυλώματος 1ου ορόφου 2Φ14 2Φ12 4Φ14 4Φ2 2Φ2 1Φ18 4Φ2 2Φ2 1Φ18 Φ6/7 Φ6/8 Φ8/1 Φ8/9 2Φ14 2Φ14 Κεφαλή εσωτερικού υποστυλώματος 1ου- 2ου ορόφου Κεφαλή εξωτερικού υποστυλώματος 1ου- 2ου ορόφου Εξωτερική στήριξη δοκού 3ου-4ου ορόφου 3Φ14 Εσωτερική στήριξη δοκού 3ου-4ου ορόφου 4Φ14 4Φ2 4Φ2 2Φ2 1Φ18 2Φ2 1Φ18 Φ8/12 Φ8/15 Φ6/8 Φ6/8 Εσωτερικό υποστύλωμα 3ου - 4ου ορόφου 4Φ18 Εξωτερικό υποστύλωμα 3ου - 4ου ορόφου 2Φ18 1Φ16 2Φ14 Εξωτερική στήριξη δοκού 5ου-6ου ορόφου 4Φ12 2Φ14 Εσωτερική στήριξη δοκού 5ου-6ου ορόφου 6Φ12 4Φ18 Φ8/15 2Φ18 1Φ16 Φ8/9 Φ6/7 Φ6/7 Εσωτερικό υποστύλωμα 5ου - 6ου ορόφου 2Φ2 1Φ18 Εξωτερικό υποστύλωμα 5ου - 6ου ορόφου 3Φ14 2Φ2 3Φ12 3Φ12 1Φ18 Φ8/15 3Φ14 Φ6/75 36

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