CRITERIA AND METHODS FOR REDESIGN AND RETROFIT OF OLD STRUCTURES

Transcription

1 0NCEE Tenth U.S. Natonal Conference on Earthquake Engneerng Fronters of Earthquake Engneerng July -5, 0 Anchorage, Alaska CRITERIA AND METHODS FOR REDESIGN AND RETROFIT OF OLD STRUCTURES G. T. Thermou and S. J. Pantazopoulou ABSTRACT The potental of earthquake damage n structural systems may be dentfed from the pattern of localzaton of normalzed lateral drft ratos that are mplct n the fundamental translatonal mode of vbraton. Based on ths observaton a methodology has been developed, ntended for practcal desgn and proportonng of nterventons for sesmc upgradng of old substandard renforced concrete (R.C.) buldng structures. The procedures developed are ntended to mtgate the potental of excessve damage by elmnatng the tendency for drft localzaton. Ths s acheved by engneerng the translatonal mode-shape of the structure so as to optmze the dstrbuton of nterstorey drft near a target mean value pont-wse throughout the buldng (so as to mnmze member-to-member varablty n the value of drft demand wthn a floor or between successve floors n a structure). The method s a dsplacement-based scheme, developed n the form of a smple desgn tool that ams at smultaneous reducton of demand and enhancement of supply through controlled modfcaton of stffness along the heght of the buldng. Results from the proposed approach are summarzed n smple charts where demand s related to stffness. Commonly-used nterventon procedures consdered n ths paper are the addton of renforced concrete walls and addton of steel cross braces. Local modfcatons to enhance member deformaton capactes are also part of the detals of a complete retroft strategy. The paper ncludes a correlaton study through applcaton on a benchmark example from a shake table test whch s ncluded as a demonstratve example of applcaton of the retroft strategy n a practcal multstorey buldng case study. Lecturer, Dept. of Cvl Engneerng, Arstotle Unversty of Thessalonk, 5 Thessalonk, Greece, gthermou@cvl.auth.gr Professor, Dept. of Cvl & Envronmental Engneerng, Unversty of Cyprus, P.O. Box 057, 678 Ncosa, Cyprus, pantaz@ucy.ac.cy Thermou, G. T., and Pantazopoulou, S. J. Crtera and Methods for Redesgn and Retroft of Old Structures. Proceedngs of the 0 th Natonal Conference n Earthquake Engneerng, Earthquake Engneerng Research Insttute, Anchorage, AK, 0.

2 0NCEE Tenth U.S. Natonal Conference on Earthquake Engneerng Fronters of Earthquake Engneerng July -5, 0 Anchorage, Alaska Crtera And Methods For Redesgn and Retroft of Old Structures G. T. Thermou and S. J. Pantazopoulou ABSTRACT The potental of earthquake damage n structural systems may be dentfed from the pattern of localzaton of normalzed lateral drft ratos that are mplct n the fundamental translatonal mode of vbraton. Based on ths observaton a methodology has been developed, ntended for practcal desgn and proportonng of nterventons for sesmc upgradng of old substandard renforced concrete (R.C.) buldng structures. The procedures developed are ntended to mtgate the potental of excessve damage by elmnatng the tendency for drft localzaton. Ths s acheved by engneerng the translatonal mode-shape of the structure so as to optmze the dstrbuton of nterstorey drft near a target mean value pont-wse throughout the buldng (so as to mnmze member-to-member varablty n the value of drft demand wthn a floor or between successve floors n a structure). The method s a dsplacement-based scheme, developed n the form of a smple desgn tool that ams at smultaneous reducton of demand and enhancement of supply through controlled modfcaton of stffness along the heght of the buldng. Results from the proposed approach are summarzed n smple charts where demand s related to stffness. Commonly-used nterventon procedures consdered n ths paper are the addton of renforced concrete walls and addton of steel cross braces. Local modfcatons to enhance member deformaton capactes are also part of the detals of a complete retroft strategy. The paper ncludes a correlaton study through applcaton on a benchmark example from a shake table test whch s ncluded as a demonstratve example of applcaton of the retroft strategy n a practcal multstorey buldng case study. Introducton Prevous works have llustrated that mportant practcal crtera for assessng the sesmc adequacy of an exstng structure can be readly obtaned from the followng ndces: - The magntude of the fundamental perod of the structure and how much t devates from smple calbrated expressons such as those recommended by desgn codes, e.g. T desgn =0.n (sec) where n s the number of storeys n a frame structure or T EC8 =0.075H tot / (sec) where H tot s the overall buldng heght measured from ground level. Note that these values correspond to well-desgned buldngs, thus departure from these benchmark values to the upper end (.e. f T o >>T EC8 ) ndcate excessve flexblty that dctates the need for global nterventons for stffness ncrease. Lecturer, Dept. of Cvl Engneerng, Arstotle Unversty of Thessalonk, 5 Thessalonk, Greece, gthermou@cvl.auth.gr Professor, Dept. of Cvl & Envronmental Engneerng, Unversty of Cyprus, P.O. Box 057, 678 Ncosa, Cyprus, pantaz@ucy.ac.cy Thermou, G. T., and Pantazopoulou, S. J. Crtera and Methods for Redesgn and Retroft of Old Structures. Proceedngs of the 0 th Natonal Conference n Earthquake Engneerng, Earthquake Engneerng Research Insttute, Anchorage, AK, 0.

3 Storey Storey - The ndex of lateral sway of a structure, whch s defned as the rato of second order moments owng to P-Δ effects when a structure s dsplaced from the poston of stable equlbrum, over the frst order moments at a gven floor, owng to the estmated sesmc storey shear: =W /(V h ); s the elastc dsplacement obtaned from the cracked secton assumpton (here the nelastc storey dsplacement s taken equal to the elastc estmate based on the equal dsplacement rule, snce the types of structures lkely to have a sway problem are longer perod structures). The sway ndex must satsfy the lmt: <0. n all floors to elmnate the need for global nterventons (addton of stffness to the structure) durng retroft. - The area rato of vertcal elements n the crtcal floor of a structure: crtcal values for ths ndex n order to lmt the extent of damage are lnked to the number of storeys n the structure; the estmated value ncludes contrbutons from shear walls, nflls and all other types of components that contrbute to the lateral stffness of the structure []. Studes by the authors have llustrated that the mportant nformaton embedded n the above readly avalable crtera whch dentfy those buldngs wth an nherent lack of stffness that would, n a retroft desgn, requre global nterventons n order to remove ths defcency, may easly be traced n the shape of the fundamental mode of vbraton of the structure []. Consderng that the fundamental mode governs the response of a buldng to a random exctaton such as an earthquake, accountng for more than 75% of the lateral response (n most frame structures wth lumped masses and daphragm acton), mportant conclusons as to the lkelhood of damage localzaton are already avalable n the pattern of ths shape. For example, the relatve dsplacement of the floors, conveyed n the shape of the mode, s lnked to the dstrbuton of stffness heght-wse n the structure: unless sharp dscontnutes exst n the mass and stffness, the fundamental shape of lumped systems ncreases n lateral deflecton from the fxed base to the top whle producng a gradual reducton n deformaton of columns, consstently wth the gradual reducton of storey shears gong from the bottom up n the buldng Exstng Retroftted Exstng Stffnessx0^ (knm) Retroftted Fgure. Shape and stffness dstrbuton of the retroftted ICONS frame []. ICONS frame RC Jacketng In lght of the fact that any sharp dscontnutes or lack of stffness leads to localzaton that s evdent n the fundamental shape of vbraton, Thermou et al. [-] proposed that the retroft strategy ought to focus nto modfyng the fundamental vbraton mode shape to a favorable pattern that acheves the optmal dstrbuton of deformaton (and thus damage) throughout the structure (Fg. ). The stffness addtons requred to modfy the vbraton shape are determned easly through very smple calculatons the only pre-requste to defnng a complete retroft strategy s that a target shape of vbraton s chosen at the begnnng so as to acheve optmal dstrbuton of deformaton.

4 Targetng Towards a Vbraton Mode Shape A wdely held practce n performance-based earthquake engneerng s to quantfy sesmc demand, and therefore damage, n the ndvdual columns of a frame structure by the value of the nterstorey drft rato (IDD, or ). Ths parameter s defned as the relatve translaton between the ends of a column member dvded by the deformable length of the column t s related to damage because n the case of a column fxed at the ends and undergong lateral translaton, the value = /h (Fg. a) may be drectly obtaned through curvature ntegraton along the member, where curvature s a meanngful ndex of materal damage (stran n the cross secton over dstance to the neutral axs). However extendng ths concept to an arbtrary member of the laterally deformng structure does not generally produce accurate estmates of ether deformaton or damage: as llustrated n Fg. b, n order to quantfy deformaton, the rotaton of the member chord should be measured from the tangent to the member axs at the support; ths s actually the tangental nterstorey drft rato, t, rather than, where t may be obtaned from mnus the rgd body rotatons of the column ends ( owng to rotaton of the onts (e.g. rotatons resultng from deformatons occurrng n lower floors or the foundaton, see Fg. b). Δ Δ - Δ (+) th storey h θ θ / θ t th storey h (a) (b) θ - (-) th storey Fgure. (a) Frame structure under lateral sway; (b) Defnton of tangental nterstorey drft. Usng nstead of t s a common msconcepton n earthquake assessment; ths s the man reason behnd the generally accepted dea that nterstorey drfts,, should not necessarly be expected to follow the dstrbutons of storey shears, V. Actually, qute contrary to the t erratc - V relatonshp, the dstrbutons of match closely the pattern of storey shear demands. A stark example of ths behavor s the so-called flexural response shape (Fg. c) (e.g. wth a dstrbuton of lateral dsplacement, Φ =-cos(π/n) where the storey number, at z= h and n the total number of storeys n a multstory structure) whch would produce relatve nterstorey drft ratos =( - - )/h that ncrease from the base to the upper floors leadng erroneously to the expectaton of hgher damage n the upper floors whereas t s easy to show that the tangental drft of columns t = -(d/dz) - n ths case, follows the exact opposte pattern from, pontng to maxmum column deformaton demands and assocated shear forces at the lowest floors (detaled dervatons follow). The above dscusson s ntended to hghlght the relevance of the fundamental shape of vbraton of a structure n determnng the tendency for localzaton of damage n the event of a catastrophc earthquake, but also the crtera that ought to be used n selectng a target shape for the retroft strategy. As stated at the outset, the obectve through the selecton of the target shape s to acheve an optmum dstrbuton of deformaton throughout the structure. A number of smple dsplacement patterns may be used as benchmark for selectng a target shape for the fundamental vbraton shape n retrofttng an exstng, sesmcally defcent

5 Φ(z)=sn(πz/Htot) Φ(z)=-cos(π/Htot) structure. These optons are lsted n Fg. (a); (b); (c): (a) (b) (c) θ θ Fgure. Lateral dsplacement profles; (a) shear; (b) trangular; (c) flexural; (d) Flexural-type; (e) shear-type response floor rotatons. Shear type response: for the purposes of calculaton ths shape s approxmated by a trgonometrc functon, Φ(z )=sn(πz /H tot ) Φ =sn(π/n). Interstorey drft and tangental nterstorey drfts are obtaned from, chord rotaton slope of t tangent / : h sn n sn / : d dz cos n h n sn n sn n cos n h n h n Fg. plots the resultng dstrbutons for a 6 storey buldng usng h=m. Note that the tangental drft s more moderate n the lower floors above the frst storey of the structure where and concde as shown n Fg. e. Ths suggests that buldngs wth ths fundamental response shape have a natural tendency for localzaton of damage n the frst floor. As for the slope,, t determnes to a large extent the deformaton demands at beam ends: clearly n a shear type buldng larger beam rotaton demands and potental plastc hnge formaton are only expected n the lower floors. Flexural type response: the trgonometrc approxmaton for ths pattern was dscussed n the precedng (Fg. c, Φ(z )=-cos(πz /H tot ) Φ =-cos(π/n)) leadng to the followng expressons for and t : chord rotaton : h cos n cos n h d dz / / Φ(z)=z/Htot (d) sn n nh cos n cos n sn n h h (dφ/dz) z=z+ h t n As n the prevous case, the resultng dstrbutons are plotted for n= 6 n Fg.. Note that n the flexural buldng type, tangental drfts devate from relatve drfts, the dscrepancy ncreasng from top down. Beam rotatons n structures of ths type follow the dstrbuton of, thus, damage n beam plastc hnge regons s expected to be maxmum n the upper floors, whereas n the case of walls and columns, plastc hngng s expected at the base (=0, z=0), consstently wth the antcpated maxmum base shear value. Trangular Response Shape: A thrd alternatve whch separates the doman of flexural response from the shear response classfcaton s the trangular response shape: Φ(z )= z /H tot Φ =/n. Ths s a purely theoretcal condton that can never be actually acheved n practce; one (e) h (dφ/dz) z=z+h () ()

6 Storey number convenence of the trangular shape s that t represents the deal scenaro of constant nterstorey drft rato throughout the heght of the structure, thereby achevng equal moblzaton of all storeys n work through deformaton and thus the best possble case for even damage dstrbuton throughout the structure. The three benchmark shapes descrbed above represent acceptable target choces n a retroft scenaro. The closer towards a trangular or flexural shape, the greater the extent of the requred nterventon and thus the assocated cost. The shear type shape could serve as an acceptable compromse n lower cost retrofts, where a possble soft storey formaton may be reengneered towards ths opton for moderate mprovement. Fgure. Dstrbuton of nterstorey drft demand for the benchmark vbraton mode shapes of Fg., for a 6 storey buldng (h =m). Establshng a Retroft Desgn Strategy Engneered modfcaton of the fundamental mode of lateral vbraton s acheved through very smple calculatons when consderng the equatons of the egenvalue problem [5]: K M 0 M K where K and M are the stffness and mass matrces of the structure n the postcrackng elastc range of response (secant to yeldng). Multplyng both terms of Eq. () wth the flexblty matrx of the structure, F=K -, leads to: Drft rato,, t K M K K I F M () By selectng and prescrbng to both sdes of the equaton the target fundamental mode shape, and consderng that for lumped systems the mass matrx s usually dagonal (by settng the d.o.fs of the daphragm at the center of the storey mass) t s possble to solve for the terms of the flexblty matrx that satsfy the above. Note that the flexblty matrx n a mult-storey structure wth daphragms depends on the effectve storey stffnesses to lateral translaton, K, K, K, K n : ths problem was solved for the three benchmark cases (trangular, shear and flexural shapes) and results are gven here n tabular form (Table ) and n the charts of Fg. 5. The charts were derved consderng a storey heght, h = m and unt storey mass, m= ton; they can be used n order to defne for a target perod and chosen deflecton shape, the requred dstrbuton of stffness along the heght of the retroftted buldng. For example, for a 5-storey buldng and the selecton of trangular response shape a retroft scenaro could be as follows: From Fg. (a) t follows that the requred storey stffnesses should be at decreasng Drft rato, Shear shape Drft rato, Trang. shape Drft rato, Flex. shape Tang. drft, shear shape Tang. drft, trang. shape Tang. drft, flex. shape ()

7 towards the upper floors accordng wth the ratos: K =0.9K, K =0.80K, K =0.60K, K 5 =0.K where K the frst floor stffness. Takng the EC8-I [6] specfed value for the perod of a 5-storey buldng (0.57 sec) as the target value of the buldng s perod after retroft, the requred frst floor stffness s obtaned from Fg. 5(a) as: K /m=8. kn/m. Thus, through ths very smple approach, the requred stffnesses to acheve the desred pattern of drft dstrbuton and the structural perod n the retroft are completely defned. Therefore, essental steps n the retroft strategy are: Step : Select target value for the fundamental perod of the buldng (the acceptable range for selectng the target perod value n retrofttng a flexble buldng may be defned by the code prescrbed value as the most austere lower lmt, and the exstng perod of the structure, as the upper, more lenent lmt: 0.075H tot / T target T exstng ). Step : Select target shape for the fundamental mode of vbraton amng at mproved dstrbuton of column deformaton, from among the alternatves llustrated n Fg.. The smplest opton s to opt for the trangular response shape. Step : From the charts of Fg. 5, obtan the requred stffness value for the frst (crtcal) storey Step : From the charts of Fg. 6, obtan the requred stffness ratos for all floors (gven the number of floors n the structure); calculate the requred stffness values for all storeys. Step 5: Proceed wth detalng the retroft scheme so as to supply the requred storey stffness values. Ths topc s addressed n greater detal n the followng sectons. Practcal Implementaton n Retroft Desgn The procedure descrbed n the precedng secton enables estmaton of the requred storey stffnesses for a gven buldng (.e., wth known dstrbuton of mass) so as to acheve the specfed target perod and fundamental mode of vbraton characterstcs accordng wth the desgner s choce. Step 5 n the retroft strategy refers to detalng of the actual members of the buldng n order to acheve the prescrbed storey stffness values. At ths stage an mportant step f the selecton of the global nterventon method: ths, along wth the perod value and the shape of lateral vbraton are the three prmary decsons comprsng the retroft strategy. The range of possble nterventons ncludes but s not lmted to: (a) Strengthenng through R.C. acketng of selected columns n the buldng, (b) Addton of wall elements for lateral stffness, (c) Addton of masonry nflls n strategcally chosen locatons (not common n North Amerca), (d) Addton of steel X-Braces. Note that FRP acketng s only pertnent for local nterventons (.e. for enhancement of postyeldng ductlty of R.C. members through acketng/confnement however, as these measures have no effect on the strength and stffness of a column, (other than mtgatng premature collapse modes) they are consdered accompanyng measures and are not ncluded n the global strategy of the retroft. In order to practcally mplement the requred storey stffness K of the retroftted structure the stffness of those members that partcpate n the global nterventon scheme s expressed n terms of the technologcal detals of the retroft. For ths reason, the contrbutons of each of these technques / elements to the storey stffness, K, are lsted below for easy reference. Note that the requred storey stffness K of the retroftted structure that comprses l c RC acketed columns, l w walls and l mw masonry wall and l X spans of X-brace metallc pars s equal to: c w mw X mw X K K K K K (5) J w - Addton of R.C. walls: The addton of new RC walls or nfll walls (partal or full) n

8 K /m*0^ ( kn/m) strategcally-selected bays of the exstng frame s a common retroft method. The storey stffness owng to l w walls orented n the drecton of the earthquake, s expressed by: w A w w f E A c f w K K ρ wc, D ρwc, (6) h h l.50 h w,ave where E c s the elastc modulus of concrete, A f s the floor area, h s the storey heght, l w,ave s the average length of RC walls, and ρ wc, s the dmensonless area rato of RC walls at the -th storey. Table. Reference stffness ratos for the varous response shapes. Shape Stffness ratos, κ K K where =,, n n Trangular Φ n n Shear Φ π sn n Flexural Φ cos π n sn n π / n snπ / n snπ / n snπ / n snπ / n n cosπ / n cosπ / n cos π / n cosπ / n cos π / n n n (a) Trangular response shape (b) Shear response shape (c) Flexural response shape Number of 7.0 Number of Number of 7 storeys 9 storeys 5 storeys Perod, T (s) Perod, T (s) Perod, T (s) Fgure 5. Stffness to mass rato for the frst storey, K /m, vs perod for up to 8-storey frames. To obtan requred K values multply the ordnate wth the mass m (n tons). Floor stffness ratos, κ Trangular response shape Shear response shape Flexural response shape K /K K /K.65 K 8 /K K /K K 8 /K K /K (a) n-storey frame buldng (b) n-storey frame buldng (c) n-storey frame buldng Fgure 6. Floor stffness ratos k (=K :K ) for dfferent lateral deflecton shape patterns for - up to 8-storey frame buldngs. - Infll masonry walls: Addng nflls as a means of retrofttng moment resstng frames (MRF)

9 s a popular method n Southern Europe and t s encouraged by EC8-III [7]; n North Amerca ths retroft method s consdered controversal, as t s thought to be ncreasng the mass of the system wthout any effect on strength at large ductltes a counterargument s that by addng stffness n the range of elastc frame response, dsplacement demands are moderated, provded the wall s connected through ts thckness. Cauton should be exercsed should ths opton be pursued; the translatonal stffness of an nfll masonry wall deformng n ts plane s estmated wth reference to a dagonal strut used to dealze the nflls functon as a stffenng lnk [6, 7]. The stffness provded by the masonry wall s: mw A mw mw f 0.0 fbc f A mc f mw K K ρ mw mw mw, D ρmw, (7) h μ θ h y y where A f s the floor area, h s the storey heght, f bc and f mc s the compressve strength of the brcks and the mortar, respectvely, μ mw y s the drft ductlty of the masonry walls, θ mw y s the drft of masonry walls at yeld, and ρ mw, s the dmensonless area of masonry nfll walls at - th storey. - Renforced concrete acketng s the most common rehabltaton method for concrete buldngs n Southern Europe. The storey stffness contrbuton owng to a total of l c RC acketed columns s equal to: c J J Af hj,ave Af c K K Ec c, D c, h h (8) h where E c s the elastc modulus of concrete, h J,ave s the average heght of the RC acketed cross secton, and ρ c, s the column s area rato n the floor plan at -th storey. - Metallc Cross Braces: The stffness ncrease of a frame bay wth an encased par of metallc cross braces along ts dagonals may be estmated by consderng the state of deformaton n the braces when the bay dstorts due to lateral drft: If local bucklng falures have been elmnated through pertnent stffenng of the compresson braces, then both dagonal crossng components contrbute to the stffness accordng wth: EsAbr atan( h / L ); brace cos ; Fbrace D EsAbr cos ; Fbrace,x cos (9) D where D the length of the brace dagonals, L the clear span and h the clear heght, whereas the angle formng between the brace and the x-axs. Thus, X X X X EsAbr, K K cos (0) D The total stffness Κ of a typcal storey s estmated from: c w mw X J w mw X Af c wc K K K K K D c, D h mw mw Es Abr D N cos Illustratve example The ICONS frame (Fg. 8) was used as an example n applyng the proposed retroft desgn method. The frame s representatve of former constructon practces prevalng n Southern wc, brace X D brace Fgure 7: Estmaton of deformaton n metallc cross-braces ()

10 Europe n the 950 s and t was desgned for gravty loads only wthout specfc provsons for sesmc detalng and nelastc dsspaton mechansms. The confguraton of the frame and the cross-sectonal dmensons and detalng of the vertcal members are outlned n Fg. 8. All beams n the drecton of loadng were 50 mm wde by 500 mm deep, whereas transverse beams were 00 mm wde by 500 mm deep. The sold concrete slab thckness was 50 mm. Materals consdered n the desgn phase were, a low strength concrete havng a nomnal compressve strength of f ck =6 MPa and smooth longtudnal renforcng steel of class Fe Bk, wth nomnal yeld strength of f syk =5 MPa [8]. The fundamental natural perod of the orgnal frame was estmated by applyng Raylegh s method (usng secant-to-yeld floor stffnesses;.e. column equvalent E c I c values were obtaned from the rato of yeld moment to yeld curvature); the estmated value was, Τ o =0.79 sec (m=.7 ton, K o, =6 kn/m, Φ T =[.00, 0.77, 0., 0.0, 0.00] T, Fg. 6). The stffness at yeld of the frst storey columns were estmated as K o,a =68 kn/m, K o,b =99 kn/m, K o,c =790 kn/m, K o,d =09 kn/m. The retroft strategy s mplemented wth the followng steps: Step : The lower lmt for the target perod s: T mn =0.075 (.7) / =0.5 s. The target value selected s equal to T target =0.6 s (0.5<0.6 T o =0.79 s). Step : The trangular response shape s selected (Fg. b): Φ =/n Step : The requred stffness value for the frst (crtcal) storey may be obtaned from the chart of Fg. 5a. Thus, for a -storey buldng havng a storey heght m, the K /m=688. kn/m, whch corresponds to a T mn =0.8 s. In order to obtan the K /m value for the target perod T target =0.6 s, the K /m value obtaned from the chart s corrected by the factor ϐ=0.5 /0.60 =0.65. The target stffness value of the frst storey K = =905 kn. Hence, the stffness of the frst storey should be ncreased by 7% (=905/6). Interventon methods nclude RC acketng and placement of X-braces. Step : From the charts of Fg. 6, the requred stffness ratos for all floors are obtaned and the requred stffness value for each storey s calculated as follows: st storey K =905 kn, nd storey: K =k K = =9 kn, rd storey: K =k K = =8 kn, th storey: K =k K =0. 905=96 kn. Step 5: Detalng of the retroft scheme: Obectve s to lmt member to member varablty n the value of drft demand so as to avod vastly dfferent ductlty demands n the columns: - In the case of RC acketng, columns A, C and D are strengthened so that the total cross secton of the three columns s ncreased to A tot so that: E h h h c J,ave A tot kN / m; for E c =0GPa, h =.7m; assumng that sde acket of a mnmum dmenson of 00mm wll be placed on the weaker sectons, A, C and D, thereby ncreasng the secton dmenson n the drecton of acton to 0.m (from the avalable 0.m) t follows that h J,ave /h = /6.7, resultng n A tot =0.8m. The proposed acket scheme results n a column area of 0.m, whch s suffcently close to the targeted value of 0.8m. The same procedure s repeated n the upper floors; requred renforcement s estmated by settng the cracked value of the ndvdual column stffness E h h h c J,ave A equal to the stffness at yeldng of the retroftted column. - In the case of metallc braces, these elements are placed n pars, n the central span. Requred area of the brace cross secton s obtaned by establshng: E A D cos 9905kN / m s br ; wth D=5.6m, =atan(.7/5), E s =60GPa, t follows that the requred brace cross secton, A br =0.000m 0mm.

11 Φ Drecton of loadng A B C D CA-, CC- CB- 6Ø 00 Ø & 8Ø6 CC- 8Ø 00 Strrups Ø6/50 CD- 6Ø 00 CB- Ø & Ø Fgure 8. Confguraton and cross-sectonal detalng of exstng frame. Conclusons The paper presents a practcal methodology for settng the gudng obectves of sesmc retroft n substandard buldng structures leadng to the development of smple procedures for dmensonng and detalng the retroft scheme. Procedures developed are ntended to mtgate the potental of excessve damage by elmnatng the tendency for drft localzaton. Ths s acheved by engneerng the translatonal mode-shape of the structure so as to optmze the dstrbuton of nterstorey drft near a target mean value throughout the buldng. In practcal terms, the desgner must select the target value of the fundamental perod of vbraton of the structure, after retroft, and must also choose a desrable pattern of lateral drft durng vbraton. Wth these two crtcal decsons the retroft strategy s formulated n few steps wth the ad of pertnent charts that provde the deal dstrbuton of stffness n order for the buldng to acheve the target obectves. Stffness s then used to obtan requred member dmensons n order to lmt the varablty n deformaton lmts at the onset of yeldng between members wthn a sngle floor. Commonly-used nterventon procedures consdered n ths paper are, addton of renforced concrete ackets and steel cross braces. An example applcaton on a benchmark example from a shake table test s also ncluded n the presentaton for demonstraton of mplementaton of the procedures. References. Pardalopoulos SJ, Thermou GE, Pantazopoulou SJ (0). Screenng Crtera to Identfy Brttle R.C. Structural Falures n Earthquakes. Bulletn of Earthquake Engneerng 0; (): Thermou GE, Pantazopoulou SJ, Elnasha AS (007). Desgn methodology for sesmc upgradng of substandard RC structures. Journal of Earthquake Engneerng 007; (): Thermou GE, Pantazopoulou SJ (0). Assessment ndces for the sesmc vulnerablty of exstng R.C. buldngs. Journal of Earthquake Engneerng and Structural Dynamcs; 0(): 9-.. Thermou, G., S.J. Pantazopoulou, A. S. Elnasha, (0). Global nterventons for sesmc upgradng of substandard R.C. buldngs. ASCE J. of Structural Engneerng 0; 8(): Clough RW, Penzen J. Dynamcs of Structures. Mc Graw Hll: New York, Eurocode 8-I. Desgn of structures for earthquake resstance - Part : General rules, sesmc actons and rules for buldngs, EN :E, 00, European Commttee for Standardsaton CEN, Brussels. 7. Eurocode 8-III. Desgn of structures for earthquake resstance. Part : Assessment and retrofttng of buldngs, EN 998-:005(E), 005, European Commttee for Standardzaton (CEN), Brussels. 8. Pnto A, Verzelett G, Molna J, Varum H, Pnho R, Coehlo, E (00). Pseudo-dynamc tests on non-sesmc resstng RC frames (bare and selectve retroft frames). EUR Report 0EN, JRC, Ispra, Italy.