IMPLICATIONS OF YIELD PENETRATION ON THE REQUIREMENTS FOR CONFINEMENT OF R.C. WALL ELEMENTS

Transcription

1 IMPLICATIONS OF YIELD PENETRATION ON THE REQUIREMENTS FOR CONFINEMENT OF R.C. WALL ELEMENTS Sozana TASTANI 1 and Stavrola PANTAZOPOULOU 2 ABSTRACT Design of alls reqires that confinement for crvatre dctility in the critical (astic hinge) regions shold extend over a length in the compression zone of the cross section at the all base here strains in the ULS exceed the limit of Hoever performance of flexral alls in the recent earthqake in Chile (2010) indicates that the actal compression strains developed ere higher than estimated, being responsible for several of the reported failres by toe crshing. In this stdy, the method of estimating the confined region and magnitde of compression strains in slender alls are revisited in order to accont for the nely identified kinematic interaction ith the lmped rotations that occr at the all base de to penetration of bar yielding into the spporting anchorage. Design charts estimating the amont of yield penetration in terms of the reslting lmped rotation at the all base are sed to qantify the increased demands for compression strain in the critical section. The estimated strain increase exceeds over 30% of the base vale estimated from the existing design expressions, hich exains the freqently reported occrrence of toe crshing even in ell confined slender alls nder high drift demands. Exame cases are inclded in the presentation to illstrate the behavioral parametric trends and imications in seismic design of alls. INTRODUCTION The M8.8 Richter earthqake that occrred in Febrary of 2010 in Chile as marked by several all failres field observations identified several compression failres particlarly in slender alls (in high-rise bildings). This raised me anxiety in the engineering commnity, folloing the recent shift to disacement-based design of alls (in EC8-I and ACI318) here confinement reqirements are linked to the estimate of compressive strain demand at the all toe. Ths, sccess of this approach rides on the dependability of the compression strain estimate. Evidence from the Chile failres sggests that strains ell beyond the spalling / crshing limit of nconfined concrete developed dring this M8.8 Richer earthqake. Frther evidence reslting from comparin beteen analytical ith experimental vales of compressive strain in reinforced concrete shear alls bent in flexre have shon that there is a consistent tendency for nderestimation of deformations. Several experimental stdies point to a higher than estimated compressive strain in the compression zone (Hanneald et al., 2012, Wallace et al., 2012). This finding is consistent ith the observed compression crshing failres at the base corner of strctral alls mentioned in the preceding (Wallace and Moehle, 2012). Slender alls sally occr in taller strctres for hich T 1 >T C, and therefore EC8-I assmes that an pper limit to crvatre dctility demand μ φ, may be estimated from the behavior factor q throgh the relationship (eqal disacement rle): 1 Lectrer, Democrits University of Thrace, Xanthi - Greece, stastani@civil.dth.gr 2 Profesr, University of Cyprs, Nicosia-Cyprs, pantaz@cy.ac.cy 1

2 μ = 2q 1 (1) φ here, T 1 is the fndamental period of the bilding and T C the period at the pper limit of the constant acceleration region of the total acceleration design spectrm. The external most stressed part of the compression zone of the critical all section is reqired to be confined by a mechanical reinforcement ratio, a ω d that exceeds the limit: b a ωd 30 μφ ( ν d + ωv ) ε sy,d (2) b Parameters in Eq. (2) inclde, the mechanical ratio of vertical eb reinforcement, ω v =ρ v f yd,v /f cd, and the d sbscript identifies design material vales (these are taken eqal to the characteristic vales for the earthqake combination). Al, b is the thickness of the all section and b o the idth of the confined core in the bondary element of a all. The length of the all end that need be confined (confined bondary element) measred from the centroid of the otside stirrp is eqal to: c c = x ; ε cc, =. +. ε cc, l o ε 1 a ωd (3) here term ε c is the strain at compression spalling (taken for simicity eqal to ) and ε cc, the strain capacity of confined concrete. Ths, special transverse reinforcement is reqired over that part of the compression zone (i.e. l c ) here the compressive strains exceed the crshing strain of nconfined concrete, ε c = (EC8-I, Fig. 1a). Wall cross section N M (a) l (b) Δ Δ fl Δ sl b b d ε x,lim x l c Confined region h ε c = ε cc, s o /h cr ε (i) Strain distribtion de to flexre x,lim ε c Increased confined region ε c,φ ε c,sl (ii) Strain distribtion de to flexre & lot l c ε cc, L b s o h cr Tension bar slippage Concrete compression Bar bckling Figre 1. (a) Cross sectional definition of the confined bondary element by considering (i) only flexral response and (ii) flexral and lot response. (b) Cantilever model for deformation analysis of a shear all. According to Eq. (3) the check of the compressive strains along the compressive zone, x, is converted to a check for the depth of compression zone against a limiting vale, x,lim, asciated ith attainment of the ε c = The threshold vale of x,lim is defined by Eq. (4) here term θ is the local astic hinge rotation at the all base, defined as Δ /h ith Δ being the total peak disacement 2

3 S. Tastani and S. Pantazopolo 3 demand (Fig. 1b) for the all strctre, h is the all height (measred from the critical cross-section p to the point of inflection), and h cr is the astic hinge length (this is the length in the clear height of the all here yield penetration may occr and it is generally mch loer than the design length of critical region hich is sed for detailing). For slender alls, h cr is taken p to half the length of the all cross section, l (Wallace and Moehle 2012). Term Δ is estimated from the design earthqake (from spectral disacement, S d, as Δ = S d C d here S d is obtained from spectral acceleration S a, according ith, S d =S a T 2 /(4π 2 ), and C d is a coefficient arond 1.3 reqired to convert spectral disacement to disacement at the top of the all strctre). In design, the ltimate drift ratio demand is set eqal to the local astic hinge rotation at the all base, θ. The extreme fiber compressive strain ε cc,, at the critical cross section is obtained as: Δ θ = h ε φ = x cc, = φ h cr μφ ε = = x d x,lim sy ε x cc,,lim Combining Eqs. (2) and (3) regarding the strain ε cc, it reslts: ε cc, θ Δ x = x = 2 hcr h l hcr l = θ 600 θ ( a ) cr a ωd = x x = ωd hcr θ (4a) θ h = 0 1 (4b) Ths, from Eq. (4a) hen x >x,lim, confined bondary elements are reqired in the length l c =(x -x,lim ). The EC8-I reqires that l c =x -x,lim [0.15l, 1.5b ] in order for the all to provide the reqired deformation capacity. Al, Eq. (4b) relates the length of the compression zone x ith the attained astic hinge rotation and the confinement detailing of the critical cross section. Note here that l c =(h cr /θ ) (0.1aω d ) (l /θ ) (0.05aω d ), therefore, the rotational capacity of the all, θ is limited by the available amont of bondary confinement throgh the folloing: θ =(l /l c ) (0.05aω d ). KINEMATICS OF YIELD PENETRATION AND PULLOUT ROTATION Yield penetration is knon to destroy interfacial bar concrete bond alloing nhampered bar slippage. This affects the astic rotation capacity of the member by increasing the contribtion of bar lot. As a reslt secondary axial strains are enforced in the compression zone ithin the astic hinge region of strctral alls, hich may be critical in the disacement-based detailing procedres that link confinement of alls to compressive strains (EC8-I). The compressive strain in the compression zone of shear alls cold be increasingly affected by the lmped rotation at the critical cross section near the face of the spport de to lot of the tension reinforcement from its anchorage. In this case damage is concentrated at a single, large crack at the fondation - all interface (Fig. 2a), here the lmped rotation cold accont by as mch as 75% of the total member rotation (Fig. 2b, Wallace and Moehle, 2012). Becase the compression zone cannot penetrate into the spport as old be reqired by the end section rotation (assming the familiar cantilever model, Fig. 1b), it is forced to ndergo increased contraction strain in order to conterbalance the effects of rotation. A kinematic relationship has been proposed by Syntzirma et al. (2010) to accont for this compression strain increase, hich states that the compressive strain at the extreme fiber of the cross section, ε cc,, in the astic hinge region of a flexral member not only depends on the sectional crvatre φ and the depth of compression zone, x, bt al on the amont of reinforcement slip, s o, as follos: x s o o ε cc, = ε c, φ + ε c,sl = ε + = d x hcr d x ε + (5) hcr d x x s x 3

4 here, ε is the axial strain in the tension reinforcement at the critical section, d is the effective depth of the all cross-section (taken here as 0.8l here l is the section length) and x is the depth of the compression zone (see Fig. 1a). (When axial load v d is in the range of 0.1, term x is sally less than 0.5l, since, at balanced condition, here tension steel has yielded and the extreme compression strain of concrete is at its ltimate vale (0.0035): x =ε c /(ε c +ε sy ) d =0.0035/( ) 0.8l =0.47l.) (a) Concrete crshing Shear Force, (1 kip=4.45kn) Drift, Δ /h (b) (c) The large horizontal crack evinces bar lot Concrete crshing Bar bckling large horiz. crack Figre 2. (a) Shear all failre de to concrete crshing of the cross section compression zone and development of a single ide crack at the fondation-all interface (Karagiannis 2013). (b) Increased total drift as a reslt of the lmped rotation de to tension reinforcement lot from its anchorage (Wallace and Moehle 2012). (c) Bckling of bars de to excessive compression strain indced from tension bar lot from its anchorage. A schematic representation of Eq. (5) is shon in Fig. 1(a.ii) here the slip magnitde designated at the critical cross section (Fig. 1b) is divided by the critical astic hinge length h cr in order to be acconted for as an average axial strain increment in the cross-section (h cr is taken p to half the length of the all cross section). Note that in design, the astic hinge length h cr is taken as high as the sectional depth of shear alls in order to enforce greater amonts of detailing in the loer storey of all-bildings: in these cases the combined action of the relatively high axial load (in the order of v d =0.4) restrains / delays the tension reinforcement from yielding hereas the confining bondary elements allo the moment capacity to be increased as a reslt of the confinement provided to the compression concrete; throgh detailing the objective is to prevent the compression zone from blging ot as shon in Fig. 2(c). Hence, yielding penetrates pards along the all if the momentcrvatre response exhibits hardening, thereby effectively increasing the astic hinge length. Eqation (5) highlights a nely identified interaction beteen flexral action and lot behavior of the reinforcement: evidently, bar slip affects cross sectional eqilibrim throgh the effect it has on strain ε cc,. Given the cross sectional geometry and the material stress-strain las, the reslting moment crvatre (M-φ) relationship at the critical cross section is no longer niqe for a given axial load vale, bt it depends on the details and the state of stress in the reinforcement anchorage. Objective of the paper is to identify the practical imications of yield penetration on rotation capacity (i.e. Δ ) and the asciated confinement reqirements (i.e. x,lim ) of shear alls. EFFECTS ON COMPRESSION STRAIN DEMAND To identify the imication that slip of tension reinforcement has on the concrete compressive strain consider as an exame a all cross section having a idth b =200mm, height l =1000mm 4

5 S. Tastani and S. Pantazopolo 5 (d =0.8l =800mm), compression zone depth x =0.25l =250mm, astic hinge length h cr =0.5l and tension reinforcement strain beyond yielding, ε = The corresponding vale of ε cc, is if slip is ignored (i.e. s o =0 in Eq. 5), bt for as small a slip vale as s o =2mm the corresponding concrete strain ε cc, is increased to , hence the extreme fibers of the compression zone are at a state of delamination and crshing. The increase of compressive strain ε cc, in the astic hinge zone de to anchorage lot drives the concrete to enter faster in its stress strain ftening branch and if confinement is absent then the longitdinal reinforcement on the compression side is ssceptible to imminent bar bckling (Fig. 2c) hich is sally accompanied ith bar fractre on the tension side (Jiang et al. 2013). The slippage of the tension reinforcement is al acconted for in the total peak disacement Δ by considering that the latter is the sm of the flexral and the lot contribtions, Δ fl and Δ sl, as depicted in Fig. 1b. Ths, the increase of peak disacement de to slippage reslts in the redction of x,lim as per Eq. (4a) and to a commensrate increase of the reqired confined depth of the shear all as illstrated in Fig. 1a(ii). Eqation (5) nderlines the importance of dependably estimating bar slip, s o, as a prereqisite to accrately evalating the state of stress in the critical cross section of shear alls adjacent to monolithic connections. Note that hen the bar is strained beyond yielding, a large fraction of the slip measred in tests is oing to inelasticity spreading over the bar anchorage, knon as yield penetration. Calclation of slip in yielding anchorages is essential for accrate interpretation of the reported failres described in the preceding. These imications concern a nmber of different aspects: (a) The excessive amont of reinforcement slip from the yielded anchorage increases the flexibility of the member connection to its spport, here a large fraction of the rotation is oing to reinforcement lot from the anchorage rather than flexral crvatre over the member length. (b) The kinematics of rotation de to bar lot cases increased strains in the compression zone of the member, particlarly in the astic hinge zone h cr adjacent to the spport (Fig. 1b). Performance based detailing of certain strctral members is controlled by the amont of concrete compression strains (e.g. strctral alls, EC8-I and ACI318 Chapter 21). In these cases, the effects of yield penetration may cancel the design objective. (c) It is shon that yield penetration may limit the strain development capacity of longitdinal reinforcement, an isse that is particlarly important in existing constrction here either the available anchorage is limited, or, the strctral member has ndergone yielding dring previos seismic events thereby exhasting part of the dependable strain capacity of the anchorage of primary reinforcement. To address these isses the eqations for bond of yielding rebars (Tastani and Pantazopolo, 2013) are apied to exore the bar strain development capacity over yielded anchorages. BAR ANCHORAGE STRAIN DEVELOPMENT CAPACITY The ltion developed in this section evalates the strain development capacity of a bar ith an idealized bilinear stress-strain crve having a post-yielding hardening slope, E sh (no atea), anchored in concrete over a length L b (Fig. 3a); the assmed bond-slip crve has the characteristics depicted in Fig. 3(b). The imm slip, s o, that may be attained by an adeqately anchored straight bar at the critical cross section of the shear all is given by Eq. (6a). It comprises three contribtions (Tastani and Pantazopolo 2013), namely: (i) the slip of the anchorage end point at imminent anchorage failre, that is eqal to the slip at the end of the ascending branch of the local bond-slip la, s 1 (Fig. 3a & b), (ii) the slip oing to integration of the linearly varying bar strains - from zero at the anchorage end point, to the yield strain ε sy along the minimm bonded length, L b,min =D b /4(f sy /f b ) as 1/2ε sy L b,min (ths s 2 =s 1 +1/2ε sy L b,min ) and (iii) the slip de to yield penetration over the imm sstainable debonded length (MSDL), hich is estimated from: l r = (L b -L b,min ) as 1/2(ε sy +ε )l r. ( L L ) ε 1 1 = s1 + Lbε sy + b b,min (6a) 2 2 5

6 (a) s o ε s o (b) l r f b res f b f b L b ε sy s 2 L b,min f b f b res s s 1 s 1 s 2 s 3 Figre 3. (a) Attenations of inelastic bar strain capacity and the asciated bond stress and slip along the anchorage. (b) Simified elasto-perfectly astic ith a post-peak residal atea bond-slip la. Therefore, the definition of an MSDL is based on the postlate that prior to comete anchorage failre, the bar has become gradally debonded from concrete over the length l r, that the residal bonded length is jst adeqate to develop the bar force as reqired by eqilibrim, and that any frther increase in the bar strain at the critical section leads to lot failre. At that reference point of imminent anchorage failre, the lmped rotation at the base of the all may be estimated from: Δ h sl = d x The asciated tensile strain capacity of the reinforcement, i.e., the imm strain that may be developed by the anchorage, ε, and corresponding bar strain dctility, μ εs, are given by Eqs. (7): = ε sy + 4 ( L L ) b b,min res fb Db Esh ε ; Strain dctility: res ε Lb Lb,min fb μ ε s = = + 4 ε sy Db Esh ε sy (6b) 1 (7) Term f b res is the residal resistance of bond (see the degraded end of the bond-slip la in Fig. 3b), and D b is the bar diameter. Table 1. Bond strength vales for anchorage lot failre and ε ε sy (fib MC2010) f c (MPa) Good bond conditions: f b =2.5 f c (MPa) All other bond conditions: f b =1.25 f c (MPa) For S500 & D b 20mm: f bd =2 f bo = =2 n 1 n 2 n 3 n 4 (f c /20) Eqation (7) is investigated belo ith regards to the important parameters throgh a sensitivity stdy. Figre 4a ots the estimated strain dctility capacity μ εs =ε /ε sy of a straight anchored bar, hich can be spported by the normalized anchorage length L b /D b, for steel class S500, five different concrete types (f c =30MPa, 25MPa, 20MPa, 16MPa and 12MPa), to bond conditions (the characteristic bond strength f b as taken eqal to 2.5 f c and 1.25 f c for good and all other bond conditions respectively, vales taken from Table 1 in accordance ith fib MC2010) and to vales for the hardening modls of steel (1% and 5% of E s =200GPa). In Fig. 4a the loer the concrete qality, the thinner the line of the corresponding crve. Note that the method to develop sch diagrams has been presented elsehere (Tastani and Pantazopolo 2013). Similar diagrams to those of Fig. 4a are prodced by sing the design bond strength f bd (nominal vales are inclded in the forth line of Table 1 and are calclated as per the fib MC2010 throgh the expression f bd =2 f bo = =2 n 1 n 2 n 3 n 4 (f c /20) 0.5 ) 6

7 S. Tastani and S. Pantazopolo 7 24 Good bond cond. All other bond cond. 24 Good bond cond. All other bond cond. strain dctility, μ εs =ε /εsy f c = E sh =1%E s strain dctility, μ εs =ε /εsy f c = E sh =5%E s (a) strain dctility, μ εs =ε /εsy L b /D b 20 f c = E sh =1%E s E sh =5%E s (b) L b /D b ltimate slip, s o /Db 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 (c) L b /D b f c =12 30 E sh =5%E s Esh =1%E s strain dctility, μ εs =ε /ε sy Figre 4. (a) Anchorage strain dctility capacity verss the reqired anchorage length for steel category S500, to vales for hardening modls (E sh =1% and 5%E s ), five concrete strengths (f c =12, 16, 20, 25, 30MPa) and to bond conditions (see Table 1). When sing design bond strength f bd vales (4 th line of Table 1): (b) diagrams µ εs L b /D b and (c) charts of the ltimate slip as a fnction of strain dctility capacity. rather than the characteristic bond strength f b (Fig. 4b). Comparing corresponding crves of Figs. 4a,b (ith all other variables the same, i.e. E sh and f c ) it becomes clear that in design (Fig. 4b), conservatively, the reqired anchorage length is longer than that calclated by sing the characteristic bond strength (Fig. 4a) for the same target strain dctility. To illstrate the se of Fig. 4 and al the imications of Eq. (7) on design isses let s consider a bar at the all base ith yielding stress f sy =500MPa and a hardening modls E sh =5%E s, of diameter D b =20mm, ith design bond strength f bd =4MPa (f c =25MPa, Table 1) and s 1 =0.2mm anchored over a length L b =800mm (=40D b >L b,min =625mm). In Fig. 4b the grey crve denoted by f c =25MPa E sh =5%E s and the chosen anchorage length of L b /D b =40 reslt in a strain dctility capacity of the anchorage eqal to μ εs =ε /ε sy =3.5 (see the ble dashed line in Fig. 4b) and ths, the imm strain development capacity of the reinforcement is limited to: ε 0.009, hich is loer than the design ltimate strain of the reinforcement (ε d =0.02) and far less than the nominal rptre strain of the material (ε k =0.075 for class C, EC2 2004). The asciated slip calclated throgh Eq. (6) is s o 2mm (or 0.1D b - see the ble dashed line in Fig. 4c) hereas the lmped drift is in the order of 0.36% (d =800mm, and x =250mm). 7

8 Eqation (5) is sed tice ith the cross section data of the previos exame: once ithot and once ith de consideration of the slip magnitde. These to alternatives reslt in a imm confined strain demand of ε cc, (s=0)=0.004 and ε cc, (s=s o )=0.005 respectively that is an increase by 20% in the vale of peak compressive strain. For the same anchorage details, bt sing steel ith milder strain hardening (ths E sh =1%E s, see the black crves in Fig. 4b) the corresponding steel strain dctility magnitdes are μ εs =ε /ε sy =9.5 (see the red dashed line), and ths, the strain development capacity of the reinforcement is no, ε =0.024, ith s o 3.3mm (or 0.16D b - see the red dashed line in Fig. 4c) and the corresponding confined concrete strain demands eqal to ε cc, (s=0)=0.011, ε cc, (s=s o )= This highlights the significance that steel properties may have on the available deformation capacity of the anchorage. (Note that one cold approximate the reslts of the preceding analysis ithot the charts of Fig. 4, by only considering vales for f b, f b res, s 1 and E sh in Eqs. 6-7.) The reslt of the first exame, here E sh =5%E s, is interpreted as follos: Whereas the anchorage length sffices for the bar to develop its yielding strength hoever it imposes (a) limitations regarding the available bar strain development capacity and the flexral dctility of the strctral element, and (b) this finding has imications on the hierarchy of failre modes of the all cross section by seriosly increasing the imposed compressive strain demands in the confined region. DUCTILE ROTATION CAPACITY ASSOCIATED WITH THE ANCHORAGE DEFORMATION CAPACITY In design, the ltimate drift ratio demand is set eqal to the local astic hinge rotation at the all base, θ. Ths, it may be shon throgh the kinematics of the deformed member and the concrete mechanics that the term θ comprises flexral and lot (slip) components. Ths, Δ =Δ fl +Δ sl in Fig. 1b here, according ith Eq. 6b: Δ Δ Δ θ hcr + (8) d x fl sl = = + = φ h h h The cross sectional crvatre, φ, is analyzed considering the anchorage tensile strain capacity of the reinforcement ε (hich is a niqe magnitde), leading to Eq. (8a). Bt if φ is obtained by considering the increased concrete compressive strain throgh Eq. (5) then the ltimate drift is dobly affected by the bar slippage, as shon by Eq. (8b). Note that Eqs. (5) are apicable nder the reqirement that the anchorage is able to develop its strain capacity ε prior to the occrrence of other, competing modes of failre (e.g. bar bckling, shear failre, limiting flexral failre). θ ( ε ) = ε hcr + (8a) d x d x ε Eq.( ) cc, θ ( ε cc, ) = hcr + θ ( ε ) hcr + 2 (8b) x d x d x 5 ε cc, = d x To illstrate the impact of bond response (throgh the strain capacity ε and the asciated slip s o originating at the critical cross section here the all is connected ith the pedestal) on the attained ltimate drift ratio defined by Eq. (8b) the folloing parametric stdy is presented throgh the diagrams of Fig. 5. For to common cross section lengths (i.e. l =1000 and 3000mm) and for five levels of compression zone depths (i.e. x =0.1, 0.2, 0.3, 0.4 and 0.5 of l here the thinner the crve the loer the x vale in Fig. 5). Material properties ere, f c =25MPa and E sh =1%E s, ith a nominal design bond strength vale as listed in the 4 th line of Table 1 (Fig. 4b). The prodced diagrams correlate the ltimate drift ratio ith the strain dctility capacity of the anchorage and the mechanical confinement reinforcement ratio of the section, a ω d. The folloing points are dedced: (i) For a constant depth of compression zone after reinforcement yielding (e.g. here, x =0.4l ) the increase of the strain dctility capacity of the anchorage (for exame as a reslt of longer 8

9 S. Tastani and S. Pantazopolo 9 anchorage length) reslts in higher relative drift ratio. This is secred by increasing the confinement level (from a ω d = 0.3 to 0.4, see the pink dashed lines in Fig. 5a). (a) l =1000mm, f c =25MPa, E sh =1%E s x (b) l =3000mm, f c =25MPa, E sh =1%E s Figre 5. Design charts that correlate the ltimate drift of a all ith the strain dctility capacity of the anchorage and the confinement reinforcement ratio for all section heights (a) l =1000mm and (b) l =3000mm. (Note that the anchorage properties ere taken from Fig. 4b for steel S500 ith E sh =1%E s and concrete strength f c =25MPa.) (ii) For the same strain dctility capacity of the anchorage (e.g. here, μ εs =8, hich is independent to the all geometry, and it only depends on the anchorage detailing, i.e., for constant embedded length and good bond conditions), increasing the compression depth x from 0.1 to 0.4l reslts in a to higher demand of confinement reinforcement hich in trn improves the ltimate drift capacity of the all (see the red dashed lines in Fig. 5a). (iii) Comparing the diagrams of Fig. 5 (a) and (b) in order to establish the effect of cross section height l, for the same ltimate drift ratio (i.e. 2%, ble dot in Fig. 5) and a strain dctility capacity of the anchorage (μ εs =7) it is evident that the shorter element, for compression zone depth of x =0.2l, old reqire as confinement a transverse reinforcement ratio a ω d =0.1. To accomish these 9

10 reqirements ith the longer all element, the compression zone old have to extend over x =0.3l (see the ble dots in Fig. 5). PRACTICAL IMPLICATIONS OF YIELD PENETRATION A DESIGN EXAMPLE OF A SLENDER SHEAR WALL Consider a seven-storey all strctre or a total height of H=21m, here the expected distance to the point of moment reversal is h =2/3H=14m from the base (Fig. 6a). The all length is, l =3m, and all thickness is b =300mm (ths b o =250mm). The axial load ratio is v=0.1. Material properties for concrete and steel are, f c =25MPa, f sy =500MPa, respectively, ith ε sy =0.0025, E sh =1%E s. The all is reinforced in the end zones ith longitdinal bars having bars of diameter D b =16mm provided ith ame straight anchorage inside the footing (L b /D b =50). Setting the design behavior factor q eqal to 3.5, it follos from Eq. 1 that the reqired crvatre dctility at the critical section is μ φ =6. If the reinforcement ratio of vertical eb bars in the all is ρ v =0.002 (reslting in a mechanical reinforcement ratio of ω v =0.04) the loer reqired vale of the mechanical confining reinforcement ratio, a ω d, is eqal to (by imementing Eq. 2). In this case the strain of the extreme confined concrete fiber is ε cc, = (by imementing Eq. 3). For Type I elastic response spectrm (here a g =0.36g, ith g=9.81m/sec 2 ), for grond type B (ths S=1.2, T B =0.15sec, T C =0.5sec and T D =2sec) and period of an eqivalent linear single-degree-of-freedom system T=0.05 H 3/4 =0.49sec, the resltant elastic spectral acceleration demand is S a =a g S 2.5=0.36g ths S a =1.08g and the corresponding elastic disacement is S d =S a T 2 /(4π 2 )=0.065m; ths the top elastic disacement of the all is set to Δ el =1.3 S d =0.084m. By assming eqal energy abrption rle the resltant top astic disacement of the all is Δ =Δ el q/(2q-1) 0.5 =0.12m ths the astic rotation is θ =Δ /15m=0.57% (that is, loer than the minimm vale θ min =0.7% defined by ACI 318, Chapter 21). Considering as astic hinge length h cr =0.3l =900mm, imementation of Eq. (4) reslts in x =1190mm and x,lim =551mm, ths the bondary element length in each side of the section all is l c =x -x,lim 640mm (greater than the code limit of [0.15l,1.5b ]=450mm). The asciated tensile strain demand of the longitdinal bars is ε =ε cc, (d -x )/x =0.008 (it has been assmed that d =0.8l ). The imications of yield penetration on the above analysis are no examined by sing the charts of Fig. 6b. Considering the anchorage geometry and the given vales for the material strengths, for L b /D b =50 the strain dctility capacity of the anchorage is μ εs = ε /ε sy =14 ths ε =0.035 and s o /D b =0.4 ths s o =6.4mm. Hoever, to accont for the tensile strain demand of ε =0.008, hich corresponds to the compression strain ε cc, = (in this case μ εs =ε /ε sy =3), the effective anchorage is treated as being shorter (L b /D b =32, ble dashed line in the left diagram of Fig. 6b); in this case the attained slip is defined as s o 0.07D b =1.1mm. Based on the proposed model this amont of slip of the tension reinforcement imposes extra compression strain in the compressed zone of the section; imementing Eq. (5) the total compression strain is ε cc, = hereas the initial astic rotation θ =0.57% is increased throgh Eq. (8a) to the vale of 0.69% (the se of Eq. (8b) reslts in θ =0.76%). For θ =0.69% it is x,lim =455mm (it as 551mm), x =1141mm (it as 1190mm) hereas the bondary element length in each side of the section all is increased from 640mm to l c =x - x,lim 685mm. The compression strain increase by 16% nderscore the significance of confinement to avoid eb toe crshing a phenomenon often cited in post-earthqake reconnaissance reports as ell as in all experimental stdies. Clearly, acconting for the anchorage behavior in terms of attained slip at post-yield tensile strain demand, the bondary element geometry and confinement reqirements are redefined in order to provide the necessary resistance both to the lmped rotation de to lot and to the increased compression strain of the all cross section. A notable point that is al relevant is the observation that the design code ith the performance based reqirement for bondary element definition appears pre-occpied ith the strain magnitdes inside the confined part of the compression zone, thereby accepting that the cover ill be delaminated at the toe, for the performance level considered. Bt recent stdies sggest that additional measres sch as externally bonded FRP layers rapped locally arond the toe and anchored over the length of 10

11 S. Tastani and S. Pantazopolo 11 the bondary element ill preclde cover delamination thereby eliminating even this occrrence of damage (Fardis et al., 2013). l =3m (a) Δ el Δ Δ = Δ el q 2q 1 H=21m h=14m [M] S d l =3000mm b f c =25MPa (b) E sh =1%E s E sh =1%E s f c =25MPa s o =0.4D b =6.4mm s o =0.07D b Figre 6. a) Geometry of the exame all and b) the se of the anchorage detailing charts for the definition of its strain capacity and the asciated slip at the critical cross section of the all. CONCLUSIONS Pllot rotation at the base of alls ndergoing large lateral drifts de to yield penetration effectively increases the magnitde of compression strains and the extent over the all length here bondary element confinement shold be provided, the most critical being the ends here cover delamination is navoidable in the absence of pertinent external confinement. An algorithm as developed to evalate this effect. In deriving the nderlying mechanistic model it as assmed that compression zone contraction oing to lot rotation of tension steel affects the astic hinge length, hich, for the prposes of the analysis is taken eqal to half the all length; this assmption shold be frther stdied throgh correlation ith experimental data, ith particlar reference to the penetration of yielding into the region above the base. The effect stdied old be accentated significantly shold this strain amification be taken to occr over an even shorter astic hinge length. Althogh many other phenomena may be al responsible for the observed crshing failres in strctral alls dring recent earthqakes (Wallace and Moehle 2012, Wallace et al. 2012) sch as lateral bckling 11

12 de to ot of ane disacements and second order effects, the importance of flexre-slip interaction shold not be overlooked in light of the significant lot slip vales oing to yield-penetration, particlarly if shorter anchorages / lap-sices or less favorable bond conditions prevail in field exames. Note here that the effect stdied is al expected to overstrain longitdinal reinforcement in the compression zone of the all base cross section, leading to the symmetric bckling patterns that ere observed in field reconnaissance reports, sch as that depicted in Fig. 2(c). REFERENCES ACI 318 (2011) Bilding Code Reqirements for Strctral Concrete (ACI 318M-11) and Commentary. American Concrete Institte, Farmington Hills, U.S.A. ISBN Erocode 2 (EC2) (2004) BS EN : Design of concrete strctres General rles and rles for bildings. Eropean Committee for Standardization (CEN), Brssels. Erocode 8 (EC8-I) (2004) Design of strctres for earthqake resistance Part 1: General rles seismic actions and rles for bildings. Eropean Committee for Standardization (CEN), Brssels. Fardis Μ.Ν., Schetakis Α., Strepelias Ε. (2013) RC bildings retrofitted by converting frame bays into RC alls, Springer Bll Earthqake Engineering, 11: fib CEB-FIP (2010) fib Model Code Final draft, Volme 1. Blletin No. 65, International Federation for Strctral Concrete, Lasanne, Sitzerland. Hanneald P, Beyer K and Mihaylov B (2012) Performance based assessment of existing bridges ith all type piers and strctral deficiencies, presented in the ACI341 Session: Forming a Frameork for Performance based Seismic Design of Concrete Bridges, ACI Fall Convention, Toronto, Canada. Jiang H., Wang B., L X. (2013), Experimental stdy on damage behavior of reinforced concrete shear alls sbjected to cyclic loads, Jornal of Earthqake Engineering, Taylor and Francis, 17: Karagiannis Chr. (2013). Design, Response of Reinforced Concrete Strctres against earthqakes, Editor. Sofia A.E., ISBN , pp Syntzirma, D., Pantazopolo, S., and Aschheim, M. (2010). Load-history effects on deformation capacity of flexral members limited by bar bckling, ASCE Jornal of Strctral Engineering, 136(1):1 11. Tastani S.P. and Pantazopolo S.J. (2013). Yield penetration in seismically loaded anchorages: effects on member deformation capacity, Techno press Earthqake and Strctres, 5(5): Wallace JW and Moehle J (2012) Behavior and design of strctral alls Lesns from recent laboratory tests and earthqakes, Proceedings of the Int. Symposim on Engineering Lesns learned from the 2011 Great East Japan Earthqake, Tokyo, Japan, 1-4March, Wallace JW, Masne LM, Bonelli P, Dragovich J, Lagos R, Lüders C, and Moehle J (2012) Damage and imications for seismic design of RC strctral all bildings, Earthqake Spectra, 28(1):