TAKING INTO ACCOUNT THE STRUCTURE SELF-VARIABLE STIFFNESS FOR ESTIMATION OF EXISTING BUILDINGS SEISMIC RESISTANCE

Transcription

1 13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 2004 Paper No TAKING INTO ACCOUNT THE STRUCTURE SELF-VARIABLE STIFFNESS FOR ESTIMATION OF EXISTING BUILDINGS SEISMIC RESISTANCE Jacob BLOCH 1, Moshe DANIELI 2, Iakov ISKHAKOV 3, Yur RIBAKOV 4 SUMMARY One of the typcal structural system of dwellng-houses s the frame buldng wth masonary walls. Sometmes,the calculaton of such exstng buldngs on the bass of modern sesmc codes showes that ther sesmc resstance does not provde under earthquakes adequate to gven regon. One of reasons for that s the nsuffcent consderaton of self-varable stffness of the buldng under the sesmc exstaton. The expermental and theoretcal nvestgatons show that under strong earthquakes the RC structural system ndependently changes hs stffness for adaptaton to the gven earthquake. In ths case, the sesmc forces decrease sgnfcantly (possbly two tmes), and the buldng can be take nto consderaton as structure wth suffcent sesmc resstance. We taked nto account ths fact for gettng the common estmaton of the exstng buldngs. The estmaton method ncludes also the sol characterstcs of the regon, archtectural and structural peculartes, qualty of the constructon and materals, and common stage of the buldng. If we get the negatve resulte,.e. the sesmc resstance of the buldng does not provde, t s necessary to use by addtonal braces wth passve or actve controlled stffness. In ths paper, the estmaton model s gven for calculaton of the sesmc resstance of the exstng buldng n Israel wth consderatng ts self-varable stffness durng earthquake exctaton. INTRODUCTION One of the problems n developng the earthquake resstance theory s estmaton of exstng buldngs state n sesmc regons. Exstng approaches are manly based on the buldng s earthquake resstance qualtatve estmaton. For more accurate estmaton, a quanttatve evaluaton should be done. It can be done n a smlar way to that descrbed by Sekhnashvl [1], Danelashvl [2,3] etc.. Accordng to the suggested method, the sesmc resstance of an exstng buldng s estmated Head of Dep. of cvl engneerng, Dr., The College of Judea and Samara,Israel.Emal:blochj@zahav.net.l 2 Senor lecturer, Dr., The College of Judea and Samara,Israel.Emal:madanel@reseaarch.yosh.ac.l 3 Senor lecturer, Dr., The College of Judea and Samara,Israel.Emal:yzhak@ycarel. yosh.ac.l 4 Lecturer, Dr., The College of Judea and Samara,Israel.Emal:rbakov@ yosh.ac.l

2 .Takng nto account the real non-lnear stress-stran stage of the structure durng an earthquake, allows a reevaluaton of the sesmc resstance. Iskhakov [4] has shown, that RC fully braced frame changes ts stffness and adapts ts propertes n order to provde an optmal sesmc response. The frame regulates ts behavor, attenuatng the sesmc response through autonomous dsengagement of ts concrete braces n tenson. The advantage of concrete physcal non-lnearty n compresson s also taken nto account. The system has several levels of sesmc regulaton and a sutable one s selected for optmal response to agven earthquake. The above factors sgnfcantly reduce the sesmc forces and dynamc dsplacements, and create an optmal scheme of the structure Iskhakov[4]. The bracng system adopts the optmal state of the RC structure. As a result energy dsspaton s ncreased and the sesmc forces are reduced accordngly. It yelds a hgher sesmc resstance estmaton of the structure. If, however, the estmated sesmc resstance s stll not enough for a gven sesmc regon, then an artfcal varable stffness system Kobory [5] or other energy dsspaton systems based on actve or sem-actve control Rbakov [6] should be used. EVALUATION METHOD FOR A BUILDING S EARTHQUAKE RESISTANCE The estmated earthquake resstance level E er = R er S er. (1) where R er s the requred level, and S er s the estmated earthquake resstance shortage. Another concept of the proposed method s the relatve earthquake resstance, K re. It s assumed to be an expert estmaton of the devaton between a desgn soluton for the exstng buldng condton and that, requred by the sesmc desgn codes. Accordng to Eq. (1), t s requred to calculate the value of S er, snce the value R er was prevously set, accordng to the relevant sesmc desgn code. The value of S er s determned accordng to the value of the Relatve Earthquake Resstance Coeffcent K re. The functonal dependence between S er and K re s descrbed n further detals below. The Relatve Earthquake Resstance of a buldng and the correspondng coeffcent K re are expressed as a fracton of a unt, accordng to the requred earthquake resstance level: accordng to the characterstcs and concepts of the sesmc desgn codes and recommendatons, that are vald durng the expert estmaton; as regards certan man factors (about 25), that are dentfed as mportant to determne the earthquake resstance of a buldng; settng the weght of each chosen factor, based on the estmated conformty of tested buldngs to the vald sesmc desgn codes; settng the degree of wear and damage of a certan weght factor and ther nfluence on the earthquake resstance of the sad factor. The fnal nfluence of each factor s determned based on the quanttatve estmaton of the earthquake resstance of each factor that equals the product of the three stated parameters. A set of factors, whch are used for calculatng the Relatve Earthquake Resstance Coeffcent K re, s determned by the man formalzed concepts of the sesmc desgn regulatons, recommendatons and codes. These factors are ncluded n specal questonnares (an example for a completed questonnare on a concrete buldng n Jerusalem s presented below). Three parameters are used to descrbe each factor. The frst, q, estmates the weght of ths factor to form the overall earthquake resstance of a buldng. It s expressed n fractons of a unt. The value 1 means that the factor has a vtal mportance for the earthquake resstance of the buldng. Conversely, the value 0 means that ths factor s not mportant. The second parameter, s, estmates the degree of devaton of the factor from the requrements accordng to the man concepts of the sesmc desgn recommendaton as set by the codes and regulatons. The value 1 for the second parameter means that all the desgn requrements and recommendatons are completely met. The value 0 means that the condton of the factor s totally wrong. The value of the second parameter s also expressed n a unt fracton. For exstng buldngs and engneerng structures, the wear and damage coeffcent d s also consdered for estmatng the factor. Of course, the coeffcent d s estmated only for wear- and damage-related coeffcents. For other factors, we assume that d equals 1 for smplcty purposes and accordng to the formalzed approach. The numercal values for all factors are provded accordng

3 to the expert estmaton. The product of coeffcents q, s and d leads to the relatve coeffcent of decreasng the earthquake resstance by ths factor. The total of the relatve earthquake resstance coeffcents for the entre buldng, accordng Danel [3], s estmated as follows : K re = q s d / q. (2) The factors taken nto consderaton may be conventonally dvded nto two groups. The frst group ncludes general factors for varous structural systems. It outlnes the most general concepts of the sesmc desgn codes and provsons. The second group conssts of varous factors for varous types of structural systems (frames, precast concrete large panels, load-carryng concrete and masonry walls, etc.). Correspondngly, two questonnares are flled out for each type of buldng. The frst estmates the nfluence of the general suggeston for the earthquake resstant constructon on the buldng s earthquake resstance and the second estmates the nfluence of the legal requrements on the buldng s earthquake resstance of the tested type. For exstng and partly damaged buldngs, the wear and damage coeffcents may be estmated accordng to specal data. Numercal values of the estmated shortage of earthquake resstance Ser are approxmated accordng to the followng formulas: or S er =0.008(1-K re )+0.921(1-K re ) (1-K re ) (1-K re ) 4 (3) 1 S er = ln ; K re 0.75 (3a) Ths dependence corresponds to the ncrease n the value of the shortage of earthquake resstance by 0.1, as the relatve earthquake resstance factor decreases twce ths rate. Eq. (3) and (3.a), should be used when K re > These values of S er cover the range of the coeffcent s horzontal ground acceleratons Z 0.3. The functonal expresson s presented n Fg. 1. Based on the dagram of Fg. 1 t can be assumed that the slope of the graph for the value of K re that tends to K re = 1, s smaller than the left zone of the graph. It may be used to explan the followng pont: n case that K re = 0.9, small dfferences n the expert estmatons wll have smaller nfluence on the value of S er than n the case of smaller values of K re. Durng the determnaton of factors S er and E er there s a certan lack and uncertanty of nput data and the earthquake resstance estmaton s characterzed n a conventonal way. Therefore, the estmated value of E er requres a correcton whle consderng the exact condton and propertes of a tested buldng. The value of E er s to be analyzed n relaton to two adjacent values of Z (Z 0, Z 0 ) accordng to Israel Standards (IS ), n order to meet the followng condton: Z 0 E er Z 0. Then, the value of E er must be approxmated as equal to Z 0 or Z 0 (towards the nearest value). If 0.06 E er < 0.075, t s assumed that E er = Accordng to the mentoned above, for Z > 0.1, t s requred that the earthquake resstance level wll be for K re = 0.810; S er = and for Z 0.1 for K re = =0.875; S er = DETERMINING THE EARTHQUAKE RESISTANCE LEVEL FOR AN EXISTING RESIDENTIAL BUILDING IN JERUSALEM The proposed method s appled to a real resdental buldng n Jerusalem (Z = 0.1) and correspondngly R er = 0.1. Fgures 2, 3 and 4 present typcal drawngs of a floor, elevaton and overall vew, respectvely, of the tested buldng. The Relatve Earthquake Resstance Coeffcent Kre was estmated based on the desgn data and the results of the nspecton at the buldng ste. Then, two specal questonnares were flled out (see Table for detals). The Relatve Earthquake Resstance Coeffcent Kre was fnally estmated, accordng to the data shown n the Table 1.. The value of the related sesmc safety factor of the buldng was calculated accordng to Eq. (2) : K re

4 K re = q s d + + ( 1) (2) q ( 1) (2) q s d q = = = The ndex n the round brackets (near the sum sgn) corresponds to the table number as shown above. Correspondngly, the value of the estmated shortage of earthquake resstance Ser, as approxmated accordng to Eq. (3) and dagram (Fg. 1), s S er = The estmated earthquake resstance level of Ser Kre Fg. 1. The K re - S er relaton. a buldng E er, accordng to ts defnton and Eq. (1) equals the dfference between the values of R er and S er : E er = R er - S er = = The calculated value of the estmated earthquake resstance level Eer s to be compared wth two adjacent values of the ground s desgn horzontal acceleraton Z. The values of Z (for E er = ) are Z 0 = 0.10 and Z 0 = Therefore, accordng to the value of the estmated earthquake resstance level E er = > = The fnal value of the estmated earthquake resstance 2 level for the tested resdental buldng wll be E er = 0.1. Ths value corresponds to the ground s desgn horzontal acceleraton for the regon Z = 0.1. The obtaned values of the shortage of earthquake resstance Ser and the estmated earthquake resstance level E er are the expert quanttatve characterstcs of the earthquake resstance for the tested buldng. Accordng to the descrbed method, the tested buldng meets the requred earthquake resstance level E er = Z. Sometmes, there s a sgnfcant estmated shortage of earthquake resstance or that the estmated earthquake resstance level s less than requred. In such cases, the mult-factor estmaton approach (see Table 1) as descrbed above, may be used for takng a decson on the mprovement of the desgn solutons. In addton, usng ths method of quanttatve expert estmaton for the earthquake resstance of a buldng may be helpful n order to take a correct desgn decson and to choose optmal structural schemes of a buldng for a new desgn. Moreover, the method may be used for testng exstng partly damaged buldngs and for desgnng ther strengthenng. If the estmaton shows that the buldng does not correspond to the sesmc resstance requred for a certan sesmc zone, non-lnear stress-stran behavor of structural elements and contrbuton of varable stffness should be taken nto account. For example a multstory braced frame s studed.

5 Fg. 2. Schematc structural typcal desgns of a floor (unt: cm). 1. level ; 2. level (unt: m).

6 Fg. 3. A schematc elevaton vew A A of a buldng n the transverse drecton (unt: m) Fg. 4. The buldng s overall vew

7 ## Table 1. A mult-factor estmaton of the relatve earthquake resstance for Calculatng K re for a test of a resdental buldng n Jerusalem. The name of the factor that affects the earthquake resstance The conformty of a factor to the regulatons and recommendatons of the codes and general prncples of sesmc constructon The factor s Import ance q The value of factor s Wear and damag e coeffc ent d General factors for varous structural systems q I xs x x d Sol condtons The mportance factor of a buldng Structural characterstcs (regularty; symmetry; unform dstrbuton of shear walls and masses; general dmensons) Structural scheme of a buldng Integrty homogenous propertes structures and of Unfavorable condtons for a sesmc buldng that s located on a sloped area. The slope angle s more than 20 degrees. Sol type: rock. Resdental buldng (number of flats 8). Non-regular buldng, nonsymmetrcal desgn (partal symmetrcal for the frst 2 floors only n the traverse drecton). Number of floors dffers for dfferent zones n the desgn (from 2 to 6), non-unform dstrbuton of masses and rgdtes. Dmensons n a desgn 12,9x18,0 m, heght of a buldng 9,0-18,0 m. For vertcal loads a system of mult-span flat beams and columns, shear walls. For horzontal loads shear walls. All load-carryng structures (beams, columns, shear walls) are desgned as monolth structures, the same concrete class (desgn strength 30 MPa) s assumed for all structures Structural expanson jonts due to sesmc condtons Expanson jonts are absent

8 The backgrounds A seres of structural analyss was for a structural done (modal analyss) accordng to desgn (IS ): the coeffcent of the ground s predcted horzontal acceleraton Z=0.1; the torson modes of vbratons were also 7 taken nto consderaton. The earthquake resstance of a buldng by analyss was assumed as provded, after addng some new shear walls and ncreasng the column renforcement (fnal stage of analyss). Zones of starcases Starcases are located nonsymmetrcally 8 n buldng s drawng. The starcases are separated from other structures. 9 Floor slabs Concrete slabs (sold and bdrectonal rbbed floor slabs) Parttons The materal of parttons: lght 10 concrete hollow blocks unted by sand-cement mortar. The parttons are not connected wth slabs and columns by steel lnks or bars Protrudng elements (enclosure elements, balcones) Renforced concrete framework and rbbed slabs flled wth lghtweght concrete blocks. Balcony slabs sold renforced concrete. Foundatons Ple foundatons. Contnuous renforced concrete beams n both drectons connectng the ples. Addtonal elements retanng walls The qualty of constructon and materals Cantlever type renforced concrete retanng walls are used to decrease the nfluence of a slope at a buldng ste on the earthquake resstance of the buldng. The constructon qualty s good. The real strength of concrete was estmated by a dedcated standard hammer about 40 MPa, to compare wth the desgn strength 30 MPa. Total 1) ( ) 11. ( 8

9 2. Typcal factors for renforced concrete buldngs The connectons Specal strengthenng of jonts between the bearng by addtonal meshes, spral elements of a system type lnks and sloped 1 (between columns and renforcement bars was not beams, between mplemented beams and shear walls, columns and walls) Strengthenng of column and beam zones n the jont regons The presence of rgd walls (shear walls, daphragms, coupled shear walls) Fllng of external walls; connectng the walls to structural elements The connectons of stone claddng to a masonry wall The resstance of structural elements to plastc deformatons Decreased strrups spacng n columns and beams was used n the jont regons. Separate and coupled shear walls are present. Shear walls are located non-symmetrcally and non-unformly by the drawng and by the buldng s heght. Fllng of lght hollow concrete blocks between renforced concrete elements was used. Renforced concrete border beams and josts, accordng to (IS ) were used. The connectons between the fllngs and load-carryng elements were provded by longtudnal concrete nserts n the fllng. The rgdty of fllngs was not taken nto consderaton n the structural analyss. Stone claddng was connected to the masonry walls wth steel connecton bars and cement mortar. The necessary condtons for the development of plastc deformatons are present. Cross-sectons of the renforced concrete elements are properly desgned, the amount of steel for a crosssectonal renforcement s not too large. Total ( 2) ) 4. ( 4

10 DESIGN SCHEME The structure s a monolthc RC sx-story two-bays frame wth flat-slab floors Iskhakov [4]. Its dmensons are m, the spacng of the column s 6 m n ether drectons, story heght s 3 m. Each story has dagonal braces n both bays. The cross secton dmensons of the elements are as follows: columns m; braces m; floors m. The braces are renforced n ther mddle part aganst the bendng moment due to the dead load and nclude the constructve renforcement only n ther man part up to 0.5 m from the jonts. The constructve renforcement s able to get the tensle force n the crack. The actng forces consst of the ead load and statc lve load, plus the horzontal sesmc forces concentrated at the floor levels. It was assumed that the dead and the lve loads per unt floor are 0.52 and 0.26 t/m 2 respectvely. A total frame load s 3.12 and 1.56 t/m. It has been shown Iskhakov [4] that ts vbraton perod s 0.638s. The horzontal sesmc forces n the frame at the floor levels are as follows: 2.19t (frst story); 4.38 t; 6.57 t; 8.75 t; t; t (sxth story). The braces are structural elements of the frame, desgned aganst axal tenson and compresson forces and arranged symmetrcally n the two spans under control drect. Ther bearng capacty s 96 ton n compresson and 7.2 ton n tenson. Under tensle forces a brace cracks, and n the absence of renforcement would yeld unlateral dsengagement. However, n practce falure does not occur, because the stress rapdly allterates n sgn and the brace s constructvely renforced. Upon reversal of the vbraton sgn, the cracks close and the brace s re-engaged n compresson. When a new vbraton cycle begns, the brace does not more wthstand tenson and works unlaterally n compresson only (at the modulus value of the precedng cycle). The latter decreases from cycle to cycle, but so long as the compressve force exceed 96t, the brace adjusts to the gven earthquake and retans the fnal modules value. Up to ths stage the energy dsspaton occurs. If, however, the above force level s exceeded, the brace dsengages rreversbly and the vbraton perod of the structure ncreases. The braces thus have two dsengagement levels - n tenson and n compresson, representng dstnct (jump-type) levels of dsspaton of the system energy, as well as numerous supplementary levels assocated wth the changng values of the stress-stran modulus. THE SELF VARIABLE STIFFNESS (SVS) MECHANISM Unlateral (n tenson only) or complete (n compresson as well) dsengagement of the braces yelds substantal reducton of the system stffness. On the one hand t weakens the sesmc forces, and on the other - lengthens the vbraton perod, thereby mantan the structure out of resonance. A partcular role s played n ths process by the vertcal statc loadng. When a brace s dsengaged n tenson and asymmetry s created, the structure acqured a horzontal components n ts deflectons, opposte to ts dsplacements under the sesmc forces. Snce, however, the latter are themselves functon of the structure mass and the lve load, ncrease of the sesmc forces makes for a correspondng ncrease n the counter-effect of the statc loadng. All the above factors unlateral or complete dsengagement, reducton of the stress-stran modulus, the counter-effect just mentoned - substantal reducton (over 50%) of the sesmc forces and dynamc dsplacements, and create an optmal scheme for the structure wth respect to the earthquake n queston. In vew of the ndvdual character of the scheme, however, t cannot be prescrbed n advance. A total of seven schemes were analyzed, numbered from 1 (full bracng) through 7 (unbraced frame) (Fg. 5), whle scheme 4 represents a frame wth unlateral dsengagement. For each scheme, the followng data were sought: the perods of the frst three modes of vbraton; the brace forces; the horzontal dsplacements of the system (total and separate for each loadng); the story drfts; the normal forces n the columns and the bendng moments n the floors. Also analyzed was the effect of a Loma Preta type earthquake over a 10s nterval, wth maxmum acceleraton ampltude 1.874m/s 2 and 2.384m/s 2 n the x and y drectons respectvely - n terms of the base shears and brace normal

11 forces. The analyss was carred out for two cases of modulus (constant and varable) and the two load combnatons (F g F q + F D and F D ; F g and F q beng the dead ( statc 1 ) and lve ( statc 2 ) loads and F D the sesmc load). Each of the seven schemes beng a partcular response, the adaptaton process of the structure. In scheme 5 through 7 dsengagement n compresson took place, ndcatng that the forces n these braces reached the 96 ton level. DYNAMIC ANALYSIS OF THE SVS SYSTEM The structural response to real earthquakes was obtaned usng the ETABS [7] software. The vbraton perods for all modes are seen to ncrease regularly wth the seral number of the scheme, and so do the maxmal horzontal dsplacement drft ratos, whereas the stress-stran modulus of the braces n compresson decrease. When the brace force n the gven scheme s zero, ths means that n the precedng scheme t has exceeded the 7.2 ton lmt, and brace s now unlaterally dsengaged n tenson but stll engaged n compresson. Fg. 6 shows the tme hstores of the base shears for the schemes 1,4 and 7 (E c const). The analyss shows Iskhakov[4], that scheme 4 (Fg. 5) s the threshold case, after whch the shear deformatons are largely stablzed and the bendng ones (those of the lower stores) ncrease. Note that the optmal effect of the statc loadng s manfested for stores 2, 4 and 6 n the schemes wth the same numbers,.e. optmzaton s a process n tself. The mutual dsplacement of consecutve stores (.e. the shear n the columns) ncreases steeply after scheme 4. The same apples to the bendng deformatons wthn each story, jadng by the varaton pattern of the drft ratos themselves. The horzontal dsplacements of the frame also ncrease steeply after scheme 4. In scheme 4 the counteractve effect of the statc loadng reaches maxmum. The scheme also represents the threshold for the frst vbraton mode even though already before t the vbratons are almost relatve to scheme 1. All the makes for substructure weakenng of the sesmc forces. As a consequence, the next brace may reman engaged, ndcatng that the structure has adapted to the gven earthquake and ts state s the correspondng scheme s optmal. Ths s the essence of the SVS system. Fg. 5. Frame schemes (4 - optmal scheme).

12 Fg. 6. Base shears tme hstores: (a) scheme 1; (b) scheme 4; (c) scheme 7 Fg. 7. The prncpal scheme of an actve frcton damper. 1-nternal element; 2-external element; 3-pressure devce ACTIVE CONTROLLED STRUCTURE WITH VARIABLE STIFFNESS Actve varable stffness systems (AVSS), descrbed by Kobor[5], Rbakov[6], etc. are amed to reduce the response of structures to earthquakes by actve control of the structure s stffness. Hence, these systems can be used n the cases, when the structures own potental ncludng nonlnear strength-stran relatonshp does not provde proper sesmc resstance. The AVSS have the advantage that the control forces at every structural level can be changed wthn a wde range due to an actve or sem-actve devces mplemented at each story. The control forces n the devces are actvely controlled accordng to an optmal control algorthm. Rbakov[6] have analysed a frcton damped seven story structure. The prncpal scheme of the damper s shown n Fgure 7. It conssts of an nternal element (1) connected to the rgd floor daphragm, two external elements (2) connected to an nverted V-shaped brace, and to a pressure devce (3). The frcton force produced n the contact surface between the nternal and external elements depends on the pressure. By changng the pressure at every tme step, the frcton forces n the devces at each level can be regulated accordng to the requrements of the optmal soluton. Rbakov[6] have demonstrated a sgnfcant mprovement n 2

13 structural response compared to those of a passve controlled and an uncontrolled structures dscussed above (Iskhakov[4]). Under the earthquake hstores that were examned the passve controlled structure had a peak dsplacement reducton of up to 50% compared to the uncontrolled one. For the actve controlled structure a peak dsplacement reducton of up to 75% (compared to the uncontrolled structure) was acheved. CONCLUSIONS Ths paper descrbes the method of Multfactor Quanttatve Estmaton of the earthquake resstance of exstng buldngs. About 25 man factors, assumed to be sgnfcant, are taken nto consderaton. The weght parameter that stands for the mportance degree s taken nto account n the total sesmc safety of each factor. The mult-factor estmaton s used for a correct decson durng the retrofttng n order to choose more optmal structural schemes of a buldng for a new desgn. An example for a quanttatve estmaton of a real resdental buldng earthquake resstance s presented. For buldngs, that accordng to the above method do not satsfy the sesmc resstance requrements, a self varable stffness system s proposed to be used. The basc propertes of concrete regulatng the structural sesmc response and adoptng ts optmal state wth maxmum energy dsspaton. Ths fenomena leads a reducton of the sesmc forces about twce. The system has several modes of sesmc adaptaton (n terms of materal, structure and loadng) whch t apples for adaptng tself to the gven earthquake. Actve control sgnfcantly mproves the behavor of buldngs durng earthquakes. A reducton of the sesmc forces n buldngs wth such systems s about 75% compared to uncontrolled ones. The above descrbed methods for protecton of structures from earthquakes enable to reduce the sesmc forces more than twce, adaptng the structure to a regon wth hgher sesmc actvty. REFERENCES 1.Sekhnashvl E.A., Danelasvl M.A.,and Zhorzholadze T.A Instructon for Investgatng the Techncal Condtons and Sesmc Stablty of Cvl and Publc Buldngs n Georga, Mnstry of Archtecture and Buldng, Academy of Scences of Georga, Tbls 1992, 140. (n Georgan). 2.Danelasvl M.A. and Tchatchava T. N. A Method for Quanttatve Estmaton of the Earthquake Resstance of Buldngs, Earthquake Engneerng,1,1999.Moscow,pp (n Russan). 3.Danel (Danelashvl) M..,.Bloch J, Aronchk A. (2002 ). An Expert System of Safety Evaluaton n Sesmc Regons. In: 7 th US Natonal Conference on Earthquake Engneerng (7NCEE), Urban Earthquake Rsk, July 21-25, 2002.Boston, Massachusetts, USA.Vol. III, pp (n Englsh) 4Iskhakov I. Study of Self Varable Stffness System optmal Sesmc Response wth Concrete Braces, Proceedngs of the Internatonal Symposum on Earthquake Engneerng, Montenegro, 2000, pp Kobor, T, Kamagata, S. Dynamc Intellgent Buldngs Actve Sesmc Response Control, Intell. Structures 2, Montorng and Control, Elsever Appled Scence, New York,1992. pp Rbakov, Y. and Gluck, J. Actve Controlled Frcton Damped MDOF Structure wth Varable Stffness, Eghts Canadan Conference on Earthquake Engneerng, Vancouver. Canadfa,1999. pp ETABS, The Three- Dmensonal Analyss of Buldng Systems, User Manual, Computers & Structures Inc., Berkeley, Calforna, U.S.A., 1990.