Seismic Design, Assessment & Retroitting o Concrete Buildings Table 5.1: EC8 rules or detailing and dimensioning o primary beams (secondary beams: as in DCL) DC H DCM DCL critical region length 1.5h w h w Longitudinal bars (L): ρ min, tension side 0.5 ctm / yk 0.6 ctm / yk, 0.13% (0) ρ max, critical regions (1) ρ +0.0018 cd /(µ φε sy,d yd ) (1) 0.04 A s,min, top & bottom Φ14 (308mm ) A s,min, topspan A s,topsupports /4 A s,min, critical regions bottom () 0.5A s,top A s,min, supports bottom A s,bottomspan /4 (0) d bl /h c bar crossing interior joint (3) d bl /h c bar anchored at exterior joint (3) 6.5(1 + 0.8ν d ) ctm ρ' (1 + 0.75 ) yd ρ max 6.5(1 + 0.8ν ctm d ) yd 7.5(1 + 0.8νd ) ctm ρ' (1 + 0.5 ) yd ρmax ctm 7.5(1 + 0.8ν d ) yd Transverse bars (w): (i) outside critical regions spacing s w 0.75d ρ w 0.08 ( ck (MPa)/ yk (MPa) (0) (ii) in critical regions: d bw 6mm spacing s w V Ed, seismic (4) 6d bl, h w, 4d bw, 175mm 8d bl, 4 M Rb (4) 1. ± Vo, g+ ψ q V Rd,max seismic (5) V Rd,max =0.3(1 ck (MPa)/50)b wo z cd (5), V Rd,s, outside critical regions (5) h, 4d bw, 5mm w 4 M Rb (4) ± Vo, g+ ψ q l cl rom analysis or design seismic action plus gravity As in EC: V Rd,max =0.3(1 ck (MPa)/50)b wo z cd sinδ As in EC: V Rd,s =b w zρ w ywd cotδ (5), V Rd,s, critical regions (5) V Rd,s =b w zρ w ywd (δ=45 o ) As in EC: V Rd,s =b w zρ w ywd cotδ, (6) I ζ V Emin /V Emax <0.5: inclined bars at angle ±α to beam axis, with crosssection A s /direction I V Emax /(+ζ) ctd b w d>1: A s =0.5V Emax / yd sinα & stirrups or 0.5V Emax (0) NDP (Nationally Determined Parameter) according to Eurocode. The Table gives the value recommended in Eurocode. (1) µφ is the value o the curvature ductility actor that corresponds to the basic value, q o, o the behaviour actor used in the design (Eqs. (5.)) () The minimum area o bottom steel, A s,min, is in addition to any compression steel that may be needed or the veriication o the end section or the ULS in bending under the (absolutely) maximum negative (hogging) moment rom the analysis or the design seismic action plus concurrent gravity, M Ed. (3) h c is the column depth in the direction o the bar, ν d = N Ed /A c cd is the column axial load ratio, or the algebraically minimum value o the axial load due to the design seismic action plus concurrent gravity (compression: positive). (4) At a member end where the moment capacities around the joint satisy: M Rb > M Rc, M Rb is replaced in the calculation o the design shear orce, V Ed, by M Rb ( M Rc / M Rb ) (5) z is the internal lever arm, taken equal to 0.9d or to the distance between the tension and the compression reinorcement, dd 1. (6) V Emax, V E,min are the algebraically maximum and minimum values o V Ed resulting rom the ± sign; V Emax is the absolutely largest o the two values, and is taken positive in the calculation o ζ; the sign o V Emin is determined according to whether it is the same as that o V Emax or not. (5),
Seismic Design, Assessment & Retroitting o Concrete Buildings Table 5.: EC8 rules or detailing and dimensioning o primary columns (secondary columns as in DCL) DCH DCM DCL h v /0 i θ=pδ/vh>0.1 (1) Crosssection sides, h c, b c 0.5m i 0.5m θ=pδ/vh>0.1 (1) critical region length (1) 1.5h c, 1.5b c, 0.6m, l c /5 h c, b c, 0.45m, l c /6 h c, b c Longitudinal bars (L): ρ min 1% 0.1N d /A c yd, 0.% (0) ρ max 4% 4% (0) d bl 8mm bars per side 3 Spacing between restrained bars 150mm 00mm distance o unrestrained bar rom nearest restrained 150mm Transverse bars (w): Outside critical regions: d bw 6mm, d bl /4 spacing s w 0d bl, h c, b c, 400mm at lap splices, i d bl >14mm: s w 1d bl, 0.6h c, 0.6b c, 40mm Within critical regions: () d bw (3) 6mm, 0.4( yd / ywd ) 1/ d bl 6mm, d bl /4 s w (3),(4) 6d bl, b o /3, 15mm 8d bl, b o /, 175mm ω wd (5) 0.08 αω wd (4),(5),(6),(7) 30µ * φ ν d ε sy,d b c /b o 0.035 In critical region at column base: ω wd 0.1 0.08 αω wd (4),(5),(6),(8),(9) 30µ φν d ε sy,d b c /b o 0.035 Capacity design check at beamcolumn 1.3 M Rb M Rc joints: (10) No moment in transverse direction o column Veriication or M x M y N: Truly biaxial, or uniaxial with (M z /0.7, N), (M y /0.7, N) Axial load ratio ν d =N Ed /A c cd 0.55 0.65 V Ed seismic (11) ends ends M Rc (11) M rom analysis or Rc (11) 1.3 1.1 design seismic action plus gravity (1), (13) V Rd,max seismic As in EC: V Rd,max =0.3(1 ck (MPa)/50)b wo z cd sinδ, V Rd,s seismic (1), (13), (14) As in EC: V Rd,s =b w zρ w ywd cotδ+n Ed (hx)/l (13) cl, 1 cotδ.5 (0) Note (0) o Table 5.1 applies. (1) h v is the distance o the inlection point to the column end urther away, or bending within a plane parallel to the side o interest; l c is the column clear length. () For DCM: Ι a value o q not greater than is used or the design, the transverse reinorcement in critical regions o columns with axial load ratio ν d not greater than 0. may just ollow the rules applying to DCL columns. (3) For DCH: In the two lower storeys o the building, the requirements on d bw, s w apply over a distance rom the end section not less than 1.5 times the critical region length. (4) Index c denotes the ull concrete section and index o the conined core to the centreline o the perimeter hoop; b o is the smaller side o this core. (5) ω wd is the ratio o the volume o conining hoops to that o the conined core to the centreline o the perimeter hoop, times yd / cd. (6) α is the coninement eectiveness actor, computed as α = α s α n ; where: α s = (1s/b o )(1s/h o ) or hoops and α s = (1s/b o ) or spirals; α n = 1 or circular hoops and α n =1{b o /((n h 1)h o )+h o /((n b 1)b o )}/3 or rectangular hoops with n b legs parallel to the side o the core with length b o and n h legs parallel to the one with length h o. (7) For DCH: at column ends protected rom plastic hinging through the capacity design check at beamcolumn
Seismic Design, Assessment & Retroitting o Concrete Buildings joints, µφ* is the value o the curvature ductility actor that corresponds to /3 o the basic value, q o, o the behaviour actor used in the design (see Eqs. (5.)); at the ends o columns where plastic hinging is not prevented because o the exemptions listed in Note (10) below, µφ* is taken equal to µφ deined in Note (1) o Table 5.1 (see also Note (9) below); ε sy,d = yd /Ε s. (8) Note (1) o Table 5.1 applies. (9) For DCH: The requirement applies also in the critical regions at the ends o columns where plastic hinging is not prevented, because o the exemptions in Note (10) below. (10) The capacity design check does not need to be ulilled at beamcolumn joints: (a) o the top loor, (b) o the ground storey in twostorey buildings with axial load ratio ν d not greater than 0.3 in all columns, (c) i shear walls resist at least 50% o the base shear parallel to the plane o the rame (wall buildings or wallequivalent dual buildings), and (d) in oneoutoour columns o plane rames with columns o similar size. (11) At a member end where the moment capacities around the joint satisy: M Rb < M Rc, M Rc is replaced by M Rc ( M Rb / M Rc ). (1) z is the internal lever arm, taken equal to 0.9d or to the distance between the tension and the compression reinorcement, dd 1. (13) The axial load, N Ed, and its normalized value, ν d, are taken with their most unavourable values or the shear veriication under the design seismic action plus concurrent gravity (considering both the demand, V Ed, and the capacity, V Rd ). (14) x is the neutral axis depth at the end section in the ULS o bending with axial load.
Seismic Design, Assessment & Retroitting o Concrete Buildings Table 5.3: EC8 rules or the detailing and dimensioning o ductile walls DCH DCM DCL Web thickness, b wo max(150mm, h storey /0) max(l critical region length, h w, H w /6) (1) cr min(l w, h storey ) i wall 6 storeys min(l w, h storey ) i wall > 6 storeys Boundary elements: a) in critical region: length l c rom edge 0.15l w, 1.5b w, length over which ε c > 0.0035 thickness b w over l c 0.m; h st /15 i l c max(b w, l w /5), h st /10 i l c >max(b w, l w /5) vertical reinorcement: ρ min over A c =l c b w 0.5% 0.% (0) ρ max over A c 4% (0) conining hoops (w) () : d bw 6mm, 0.4( yd / ywd ) 1/ d bl 6mm, in the part o the spacing s w (3) 6d bl, b o /3, 15mm 8d bl, b o /, 175mm section where ρ L >%: ω wd () 0.1 0.08 as over the rest o the αω wd (3),(4) 30µ φ(ν d +ω ν)ε sy,d b w /b o 0.035 wall (case b, below) b) over the rest o the wall height: In parts o the section where ε c >0.%: ρ v,min = 0.5%; elsewhere 0.% In parts o the section where ρ L >%: distance o unrestrained bar in compression zone rom nearest restrained bar 150mm; hoops with d bw max(6mm, d bl /4) & spacing s w min(1d bl, 0.6b wo, 40mm) (0) up to a distance o 4b w above or below loor beams or slabs, or s w min(0d bl, b wo, 400mm) (0) beyond that distance Web: vertical bars (v): ρ v,min Wherever in the section ε c >0.%: 0.5%; elsewhere 0.% 0.% (0) ρ v,max 4% d bν 8mm d bv b wo /8 spacing s v min(5d bv, 50mm) min(3b wo, 400mm) horizontal bars: ρ hmin 0.% max(0.1%, 0.5ρ v ) (0) d bh 8mm d bh b wo /8 spacing s h min(5d bh, 50mm) 400mm axial load ratio ν d = N Ed /A c cd 0.35 0.4 I H w /l w, design moments rom linear envelope o rom analysis or Design moments M Ed : maximum moments M Ed rom analysis or the seismic design seismic action design situation, shited up by the tension shit a l & gravity Design shear orce V Ed = shear orce V Ed rom the analysis or the design seismic action, times actor ε: Design shear orce in walls o dual systems with H w /l w >, or z between H w /3 i H w /l w (5) : ε=1.m Rdo /M Edo q i H w /l w > (5), (6) : ε = M Rdo S q e 1. + M 0.1 Edo Se q 1 ( TC ) ( T ) 0.75z 1 1.5z H V ( ) = + (0) 1.5 w Ed z εved εved Hw 4 Hw 3 ε=1.5 ε=1.0 rom analysis or design seismic action & gravity
Seismic Design, Assessment & Retroitting o Concrete Buildings and H w : (7) V Rd,max outside critical region As in EC: V Rd,max =0.3(1 ck (MPa)/50)b wo (0.8l w ) cd sinδ, with V Rd,max in critical region 40% o EC value As in EC V Rd,s in critical region; web reinorcement ratios: ρ h, ρ ν (i) i α s =M Ed /V Ed l w : ρ ν=ρ v,min, ρ h rom V Rd,s : As in EC: V V Rd,s =b wo (0.8l w )ρ h Rd,s =b wo (0.8l w )ρ h ywd cotδ, ywd (ii) i α s <: ρ h rom V Rd,s : (8) V Rd,s =V Rd,c +b wo α s (0.75l w )ρ h yhd As in EC: V Rd,s =b wo (0.8l w )ρ h ywd cotδ, ρ v rom: (9) ρ ν yvd ρ h yhd N Ed /(0.8l w b wo ) Resistance to sliding shear: V via bars with total area A Rd,s =A si yd cosα+ si A at angle ±α to the horizontal sv min(0.5 yd, 1.3 ( yd cd ))+ (10) 0.3(1 ck (MPa)/50)b wo x cd ρ v,min at construction joints (9),(11) 0.005, 1.3 yd ctd + 1.5 N A cd Ed c yd (0) Note (0) o Tables 5.1 and 5. applies. (1) l w is the long side o the rectangular wall section or rectangular part thereo; H w is the total height o the wall; h storey is the storey height. () For DC M: I, under the maximum axial orce in the wall rom the analysis or the design seismic action plus concurrent gravity the wall axial load ratio ν d = N Ed /A c cd satisies ν d 0.15, the DCL rules may be applied or the conining reinorcement o boundary elements; these DCL rules apply also i this value o the wall axial load ratio is ν d 0. but the value o q used in the design o the building is not greater than 85% o the qvalue allowed when the DC M conining reinorcement is used in boundary elements. (3) Notes (4), (5), (6) o Table 5. apply or the conined core o boundary elements. (4) µφ is the value o the curvature ductility actor that corresponds through Eqs. (5.) to the product o the basic value q o o the behaviour actor times the value o the ratio M Edo /M Rdo at the base o the wall (see Note (5)); ε sy,d = yd /Ε s, ων d is the mechanical ratio o the vertical web reinorcement. (5) M Edo is the moment at the wall base rom the analysis or the design seismic action plus concurrent gravity; M Rdo is the design value o the lexural capacity at the wall base or the axial orce N Ed rom the same analysis (design seismic action plus concurrent gravity). (6) S e (T 1 ) is the value o the elastic spectral acceleration at the period o the undamental mode in the horizontal direction (closest to that) o the wall shear orce multiplied by ε; S e (T c ) is the spectral acceleration at the corner period T C o the elastic spectrum. (7) A dual structural system is one in which walls resist between 35 and 65% o the seismic base shear in the direction o the wall shear orce considered; z is distance rom the base o the wall. (8) For b w and d in m, cd in MPa, ρ L denoting the tensile reinorcement ratio, N Εd in kn, V Rd,c (in kn) is given by: N 0. Ed VRd c ( ρ ) 0. = max 10 100 1/ 3, 35 1+ 1/ 6 ck ck + bwd d 1 + d 1/ 3, 1 0. 15 Ac N Ed is positive or compression; its minimum value rom the analysis or the design seismic action plus concurrent gravity is used; i the minimum value is negative (tension), V Rd,c =0. (9) N Ed is positive or compression; its minimum value rom the analysis or the design seismic action plus concurrent gravity is used. (10) A sv is the total area o web vertical bars and o any additional vertical bars placed in boundary elements against shear sliding; x is the depth o the compression zone. (11) ctd = ctk,0.05 /γ c is the design value o the (5%ractile) tensile strength o concrete.