CODES OF ASSESSMENT OF BUILDINGS: A COMPARATIVE STUDY ABSTRACT

Transcription

1 CODES OF ASSESSMENT OF BUILDINGS: A COMPARATIVE STUDY S. G. Chassioti 1, D. V. Syntzirma 2 and S. J. Pantazopoulou 3 ABSTRACT In displaement based design, the so-alled aeptane riteria ride on the ability to assess with onfidene the deformation apaity of the individual members of a struture. Codes of assessment of existing strutures (Euroode 8-(Part III) and FEMA 356 and 44) provide a relatively omplex proedure for evaluation of deformation apaity; however, ontrary to strength estimations, deformation apaity estimates demonstrate a signifiant degree of dispersion with respet either experimental databases or analytial models, partiularly when used to evaluate lightly reinfored members representative of older onstrution praties in North Ameria and Europe up to the 8 s. In this paper a benhmark test is introdued and proposed to be used for evaluation and omparison of deformation omponents estimated with either mehanial models or Code expressions. The paper summarizes the first priniples underlying the mehanial problem of deformation apaity alulation, the basi Code Models established in the US and European assessment pratie, and omparatively evaluates the performane of these three alternatives with referene to the proposed Benhmark test, in order to illustrate the parameters responsible for the satter and unertainty in the evaluated results. Introdution This paper ritially reviews the available methods of assessment of deformation apaity of reinfored onrete (R.C.) prismati members, with partiular emphasis on Code expressions reommended for use in displaement-based assessment of existing strutures. Of partiular onern are lightly reinfored prismati onrete members typially found in substandard onstrution built prior to the introdution of modern seismi detailing. Suh members are suseptible to premature modes of failure prior to the realization of the full deformation apaity whih would be normally estimated based on lassial mehanis of flexural response. As the deformation apaity estimates obtained using the Codes of Assessment against test data generally illustrate a poor preditive apaity, a omparative study is onduted in this paper onsidering the estimated deformation apaities obtained from a model developed from first priniples (Syntzirma and Pantazopoulou 26), with the estimates obtained from 1 Civil Engineer, Dept. of Civil Engineering, Demokritus Univ. Thrae, Greee, stamhas@ivil.duth.gr 2 PhD, M.S., Civil Engineer, Dept. of Civil Engineering, Demokritus Univ.of Thrae, Greee, dsyntz@ivil.duth.gr 3 Professor, Dept. of Civil Engineering, Demokritus Univ. of Thrae, Vas. Sofias 12A, Xanthi 671, Greee, , pantaz@ivil.duth.gr

2 reommended seismi ode proedures. A series of olumn-elements are examined; these represent various pratial problems of old onstrution with substandard details, typially enountered in assessment pratie and termed non-onforming as per FEMA 356 (2). The olletion of example ases onsidered, are proposed in this paper as a benhmark test for omparative evaluation of alternative methods and definitions of deformation apaity for seismi assessment and design. Definition and modelling of deformation mehanisms in R.C. members The behaviour of R.C. frame members under ombined axial load, yli shear and flexure, suh as ourring during earthquakes, is usually interpreted with the antilever model depited in Fig. 1a, whih represents the shear span (i.e. half the length) of the member. Deformations of the antilever are owing to flexure, shear ation, and pullout slip of the reinforement from the support. These response mehanisms are onsidered to at in series, therefore their effets are additive as refleted by the mehanial analogue used in alulations of deformation apaity (Fig. 1b): here the member itself develops elasti urvature over its length, ontributing to the total drift, whereas all other effets (inelasti rotation over the plasti hinge region, shear deformation and pullout slip) are modelled through pertinent springs, eah ontributing to the tip displaement of the antilever (and therefore to drift) separately. These mehanisms were originally assumed to at independently of eah other, and therefore, the total deformation obtained for any given load ombination was approximated by the summation of the individual ontributions of the partiipating mehanisms; resistane urves were established for eah mehanism from first priniples (Fig. 2). The shear fore sustained by eah mehanism and the orresponding deformation or drift of the antilever (drift is the hord rotation of the member with respet its original orientation), follow the relationship: V=V fl =M/L s =V sh =V sl ; = fl+ sh+ sl (1) The same onept has been extended to deformation apaity (a measure of total deformation that the member may undergo without signifiant irreversible loss of strength; by international onvention lateral drift or deformation apaity are values assoiated with a 2% loss of strength beyond the peak point.) The result of Eq. 1 has been tested against hundreds of tests ontained in a number of databases, inluding R.C. members with modern detailing as well as members with substandard details representative of old design praties (Inel 22, Panagiotakos 21, Syntzirma 22). The suess of the approah is limited to estimations of realisti values for well detailed members, whih generally demonstrate quite high deformation apaity partiularly when their axial load ratio is less than.4. Values beome irrelevant when this onept is applied to members experiening premature modes of failure, suh as often enountered with old-type frame members. Clearly, if the strength of one of the springs in the assembly of Fig. 1b is overome at some value of deformation, then this event terminates the response urve of the member, well before the development of the estimated nominal deformation apaity of the other springs. For this reason, the approah underlined by Eq. 1 has been retained of late, only to desribe behavior up to the onset of yielding, i.e. θ y =θ y fl +θ y sl +θ y sh. For response beyond yielding, opinions diverge as to how to estimate deformation apaity. Thus, the revised ASCE-41 doument (Elwood 27) evaluates diretly the total inelasti drift apaity, θ u, through empirial rules, the result being a single ompound value that aounts for the various effets and design parameters through pertinent binary rules: here, the total rotation

3 apaity is θ u =θ y +θ pl. Similar is the approah drafted for the next round of EC8-III (25), whih provides diret estimates for the total inelasti rotation apaity θ u through alibrated expressions in terms of the relevant design variables. A summary of the essential elements of both approahes for alulation of drift or rotation apaity is outlined in the Appendix of this paper. V tanθ=l s /d d L s M=V L s shear strain inelasti flexural deformation slip Figure 1. Cantilever model and moment distribution, Mehanisms of behaviour modelled through pertinent springs D u D flex D sl D sh V q u D sh D sl q slip l p Figure 2. Contribution of the various response mehanisms to the total drift D fl D Reognizing the fundamental relevane of the model depited in Fig. 1b the authors attempted to improve on the orrelation of Eq. 1 with the test data, by modifying the expression: ontributions of the individual ontributing mehanisms were saled to the onset of ourrene of any type of premature failure (Syntzirma 26). The framework was referred to as Capaity - Based Prioritizing (CBP) of failure modes. Cantilever strength values assoiated with failure of eah individual response mehanism of resistane in the spring-series of Fig. 1, namely Flexural (V u,fl ), Shear (V u,sh ), Anhorage/Lap Splie (V u,sl ), or Compression Bar Stability (V u,bukl ) are onsidered in establishing the hierarhy of member failure, with the lower strength spring ontrolling the mode of damage and possibly, failure of the member. Thus, V fail is defined by, V = min{ V, V, V, V } (2) fail u, fl ush, u, sl ubukl, and it is then used to estimate the weight w u in the amended expression for deformation apaity: θy = w y θy, fl + θysh, + θ ysl, ; θu = θy, fl + w u θ p, fl + θpsh, + θ psl, (3) Subsripts y and u orrespond to yield and ultimate states; θ and are the drift and displaement of the element. Fators w y, w u represent strength ratios for strength-ontrolled mehanisms of

4 behaviour or deformation ratios for strain-ontrolled mehanisms of behaviour. For example, if V u,sh =V fail <(V u,fl ; V u,sl ), then w y =V fail /V u,fl <1 and θ u =θ y, whereas if w y =1, then, w u =(µ fail -1)/(µ fl -1), where µ fail is the displaement dutility orresponding to the point when the redued values of either of the nominal strengths of the shear and slip mehanisms, V u,sh or V u,sl beome equal to the flexural strength V u,fl (Fig. 2), and µ fl is the theoretial available dutility of the member when onsidering full flexural ation. (Here referene is being made to the value of nominal strength terms whih are onsidered to deay with inreasing imposed dutility, µ. Even when flexural yielding is possible for µ=1, the relative hierarhy of the strength terms may be reversed for larger µ values, sine they deay at different rates. In the above a simplifiation has been made, whereby all plasti displaement omponents have been assumed to inrease proportionally with dutility; a summary of the essential omponents of this approah is outlined in the Appendix.) Parametri study A omparative study of the estimates obtained from the CBP proedure outlined above and from the two referene assessment standards (ASCE-41, EC8-III) is onduted on a series of olumn-elements representative of field assessment examples; most ases have reinforing details aording with former detailing praties (i.e. sparse stirrups, with inadequate anhorage or lap-splie of long. reinforement et.) The olletion of ases onsidered is depited in Fig. 3, and has been designed to systematially test the performane of analytial methods for deformation apaity estimation with respet to all those design variables that ould prematurely ause member failure and should therefore be expliitly aounted for in the evaluation study. Thus, olumn represents the basi ase study having a 35mm 4 mm ross setion; two ases of longitudinal reinforement are onsidered, namely either 8, 18mm diameter bars (4 bars on eah side of the ross setion) or 4, 18 mm diameter bars (2 bars on eah side of the ross setion); transverse reinforement omprises retangular stirrups with 8mm diameter at a spaing of either 1 or 2 mm; stirrups are anhored either with 135 or with 9 hooks. Another variable is the normalized axial load v (=the applied axial load divided by the olumn ross setion A g and the onrete strength f ), taken here either equal to v=.1 or equal to v=.35. Referene material properties are, onrete strength f =2MPa, S5 steel for longitudinal reinforement (f y =5MPa), whereas transverse reinforement omprises S22 (f y =22MPa). Column in Fig. 3 has been derived from by introduing a short lap-splie (=15D b ) of longitudinal reinforement at the base; ase () derives from but has a short length (=15D b ) of embedment of primary reinforement; ase is idential to but due to half-height masonry infills, it is expeted to funtion as a aptive olumn; has a 7mm deep ross setion (i.e. a lower aspet ratio than ); similarly, ase (f) with a onstrution hinge at the base has twie the aspet ratio of. Sine all possible ombinations of detailing harateristis seen in ase are also onsidered in ases -(f), a very large number of possible situations are evaluated with the three models onsidered; results are presented in Figs. 4-9, in the form of barharts. Eah group of bars in the typial hart orresponds to the estimated rotation apaity for the respetive olumn, obtained with the alternative models (blue for the CBP mehanial model, purple for the ASCE-41 Model, and beige for the EC8-III model), for eah ase study onsidered. For easy referene the following system of ase identifiation is used in the remainder of this presentation: the first numeral in the I.D. ode represents the aspet ratio, i.e., the shear span to the height of the ross setion ratio, L s /h. Next C, A, S or H for: adequately anhored ontinuous reinforement (C), poorly anhored (A), or lap-splied (S) longitudinal reinforement at the base of the olumn above the footing, or a hinge-type (H) primary

5 reinforement arrangement. Letter L or M identifies ases with a light (ν=.1) or moderate (ν=.35) axial load ratio; this is followed by the number of longitudinal bars (integer 4 or 8). Last the ode gives the spaing and anhorage detail of transverse stirrups. For example, the identifiation ode 3.75CL8/2-135 refers to a type olumn with a light axial load, a 4mm high ross setion, 8 longitudinal bars (D b =18 mm), retangular stirrups spaed at 2mm and anhored with 135 hooks. b h (in mm) () (f) Φ8/2 or 1.5 m 3. m Φ8/1 l b =15D b l b =15D b 3.75C 3.75S 3.75A 1.88C 2.14C 7.5H Figure 3. Benhmark problems used in the omparative parametri study Eah of the figures summarizing the results ontains 16 bar groups in the horizontal axis: the first eight orrespond to the low axial load ratio (v=.1), whereas the other eight orrespond to the moderate axial load ratio (v=.35). In eah of the eight ases within the two subgroups, ases are organized in the horizontal axis with the sequene shown in Fig. 4b. Comparative plots give the terms of Eq. (2) namely V u,fl, V u,sh, V u,sl and the deformation apaity indies θ y and θ pl. Note that all models onsistently estimate a signifiant redution in the response terms assoiated with the moderate axial load ratio (seond group of eight ases onsidered, as opposed to the first group). Owing to the utoff region in the ASCE-41 and EC8-III whih is used for flexural ases with low axial load ratio, the substantial deformation apaity of olumn 7.5H for the ase of 4Φ18 longitudinal reinforement and with spaing of stirrups 1mm with 9 hooks as alulated from the mehanisti approah presents an exessive value as ompared to the ode reommended values. In many ases the approahes onverge, partiularly when the governing mode of failure is flexural. Deviations our in ases where the prevailing mode is related to some form of anhorage or lap splie failure, either diret, or after sustained flexural yielding and subsequent yield penetration; deviations are also notieable in expressions estimating the shear strength. These are the axes where further alibration and refinement of deformation apaity models is needed, to ahieve improved estimates from the ode expressions, onsistent with the mehanisti models and the available experimental trends. CONCLUSIONS A Benhmark test is proposed for parametri evaluation of the sensitivities of mehanisti and ode-based models used in alulating the deformation apaity of substandard reinfored onrete members (i.e., lightly reinfored members representative of older praties). It is worth noting that simplifiation of the proess by elimination of riteria onerning some

6 less understood modes of failure suh as yield penetration after flexural yielding, debonding of the over due to reversal of onrete over strains et. is not always on the side of safety, an ourrene that may be easily identified from systemati use of the Benhmark evaluation. 3 3 V sh (kn) () 1 L8/2-135 L4/2-135 L8/1-135 L4/1-135 L8/2-9 L4/2-9 L8/1-9 L4/1-9 M8/2-135 M4/2-135 M8/1-135 M4/1-135 M8/2-9 M4/2-9 M8/1-9 M4/ Figure 4. Parametri analysis for speimen 3.75C V sh (kn) () L8/2-135 L4/2-135 L8/1-135 L4/1-135 L8/2-9 L4/2-9 L8/1-9 L4/1-9 M8/2-135 M4/2-135 M8/1-135 M4/1-135 M8/2-9 M4/2-9 M8/1-9 M4/ Figure 5. Parametri analysis for speimen 3.75S

7 V sh (kn) () L8/2-135 L4/2-135 L8/1-135 L4/1-135 L8/2-9 L4/2-9 L8/1-9 L4/1-9 M8/2-135 M4/2-135 M8/1-135 M4/1-135 M8/2-9 M4/2-9 M8/1-9 M4/ Figure 6. Parametri analysis for speimen 3.75A V sh (kn) () L8/2-135 L4/2-135 L8/1-135 L4/1-135 L8/2-9 L4/2-9 L8/1-9 L4/1-9 M8/2-135 M4/2-135 M8/1-135 M4/1-135 M8/2-9 M4/2-9 M8/1-9 M4/ Figure 7. Parametri analysis for speimen 1.88C

8 75 75 V sh (kn) () L8/2-135 L4/2-135 L8/1-135 L4/1-135 L8/2-9 L4/2-9 L8/1-9 L4/1-9 M8/2-135 M4/2-135 M8/1-135 M4/1-135 M8/2-9 M4/2-9 M8/1-9 M4/ Figure 8. Parametri analysis for speimen 2.14C V sh () L8/2-135 L4/2-135 L8/1-135 L4/1-135 L8/2-9 L4/2-9 L8/1-9 L4/1-9 M8/2-135 M4/2-135 M8/1-135 M4/1-135 M8/2-9 M4/2-9 M8/1-9 M4/ Figure 9. Parametri analysis for speimen 7.5H

9 Appendix ASCE/SEI-41 For onrete: ε o =.2 and ε u =.5; for steel ε su =.5; f u =1.25f y Conforming elements: s d/3 and V s.75v n.5 f N Shear strength: V = k( µ ) 1+.8Ag Ls / d.5ag f Asw fyhd Vs = k( µ ) ; if s d/2.5 Vs; if s d Vs = s for µ 2 k = 1.; for 2< µ 6 k =.1µ + 1.2; for µ > 6 k =.6 2/3 B= 2 for Db N.6 Ldavail, L 1.25f d y Longitudinal Reinf.: fs= 1.25ζfy ; = ; B= 1.66 for Db N.7 L d Db B f o B= 5.4 for 9 hooks k(µ ) V flex / V n.6 & A sw /b w s>.2%; s/d<.5 F.F. F. F. S. F. 1 F. F. S. F. S. F. >1 S. F. S. F. z 1..2 DCR=2 s/d<1/3 s/d >1/3 EC8-III For onrete: ε o =.2; ε u =.35; ε * u =.35+k eff ρ sw f yh /f but if 9 hoops k eff = and for steel ε su =.75; f u =1.15f y Ls Shear strength: Vshear = k( µ )(.16 max(.5;1 ρtot)(1.16min(5; ) f.8 Ag) + h d d' + min { N;.55Af } tan a+ k( µ ) Asw fyh s for µ 5 k =.5µ +1. ; for µ >5 k=.75 Drift omponents: θ Variable a v = if V fl <V, otherwise a v =1. If V fl >V shear then θ y is redued by multiplying by V sh /V fl. θ y ( ) 1 Ls + az v h ε y Df b y = r + + y Ls z 6 f θ y, fl θ ysh, θ ysl, max(.1, ω ) = = = max(.1, ω) pl v.2 um.14 n1, pl n2, pl n3 n4 n5 where n1, pl.25 ; n2, pl f.3

10 θ v max(.1, ω ) Ls =.16 n n n n n where n =.3 ; n = f ; n = ; max(.1, ω) h um 1, t 2, t , t 2, t 3 a ρsw fyh / f 1ρ 4 = 25 ; n5 = 1.25 d n Additional oeffiients: for old-formed steel n 6 =.5; for smooth bars: n b,t =.575, n b,pl =.375; for strutures with brittle details: n old =.825, n 4 =1; for lapped regions: double value of ω in n 2 ; whereas in ase of defiient splies (ribbed bars): n L =L d,avail /L d,min where: L D d,min b fy = and B= keff, L ρ B f For lapped reinforement the strain ε y and the stress f y are obtained by multiplying with L d,avail /L d,min : L davail, fy D fs = fy ; Ld,min = L d,min 3.3 f b C.B.P. model For onrete: ε o =.2 and ε u =.5; for steel ε su =.5; f u =1.25f y ; ε u,max =ε y L anh /L b,min Shear strength: N f y ' d N if ( s1 s2) ( ).5 1 ; otherwise ' ρ ρ V = k ' µ f + A ' g V = A Ls.5 f g f f A g V Lap-splie strength: f s =f steel + f on ; f steel =1.4A st f yh L b /(s n b A b ) f u ; f on =(2.5D b +2d st +2) f t L b /A b Referenes Elwood K., Matamoros A., Wallae J., Lehman D., Heintz J., Mithell A., Moore M., Valley M., Lowes L., Comartin C., Moehle J., (27). Update to Conrete Provisions, Earthquake Spetra, 23(3), FEMA 356, (2). Prestandard and ommentary for the Seismi rehabilitation of buildings sw f f yh s = k( µ ) Ast fst, i; nst= d/ s (int. part) but if hoops 9 fst, i = fyst, Lbi, /.7Lb nst for µ 2 k = 1.; for 2< µ 6 k =.1µ + 1.2; for µ > 6 k =.6 Euroode 8, (25). Design of strutures for earthquake resistane Part 3: Assessment and retrofitting of buildings, European Committee for Standardisation Inel M. and Ashheim M., (22). Displaement Based Strategies for the Performane Based Seismi Design of 'Short' Bridges Considering Embankment Flexibility, CD release, MAE Center, Univ. Illinois at Urbana-Champaign Panagiotakos T., and Fardis M. N., (21). Deformation of R.C. Members at Yielding and Ultimate, ACI Strutural Journal, 98(2), Syntzirma D. V. and Pantazopoulou S. J., (22), Performane Based Seismi Evaluation of R.C. Building Members, CD-ROM Proeedings, Paper Referene 816, 12 th European Conf. on Earthq. Engineering, 9 13 Sept., London U.K. Syntzirma D. V., Pantazopoulou S. J. (26), Deformation Capaity of R.C. Members with Brittle Details under Cyli Loads, ACI Speial Publiation 236, 1-22