Energy-based Design of Steel Structures According to the Predefined Interstory Drift Ratio 1

Transcription

1 Dgest 01, December 01, Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato 1 Onur ERTER* Özgür BOZDAĞ** ustafa DÜZGÜ*** ABSTRACT The methods whch take lace n current buldng codes and used n sesmc desgn of structures are generally lnear elastc. Inelastc behavor of the structures under the effect of earthquake s consdered ndrectly n sesmc desgn codes. Recent studes enable nelastc behavor of structures to be taken nto account roerly n the structural desgn. In ths study, a calculaton method orented towards the desgn of new structures whch fulfll the redefned nterstory drft rato accordng to the usage functon of the structures was offered by consderng the nelastc behavor of the structural members and by usng the energy balance of the structures. Interstory drft ratos when the steel structure dslacements reach the target dslacements were comared wth the ntal nterstory drft ratos and the results were nterreted. Keywords: Inelastc behavor, energy-based desgn, target dslacement, erformance based desgn. 1. ITRODUCTIO Structures generally behave nelastc under excessve sesmc loadng. When earthquake loads whch exceed the workng load lmts aroach the lateral load caacty of the structures, stresses roduced n structural members exceed elastc lmts and dslacements n structural elements become too large. Therefore, yeld mechansms of structures have a great mortance n nonlnear structural behavor. Earthquake-resstant structures are desgned by usng dslacement-based and energy-based methods n addton to force-based methods. In the force-based desgn methods, t s amed that the caacty of structural members to be hgher than the nternal forces of the members under external loads. The reventon of excessve dslacement of the structures and structural elements under sesmc loads s targeted as a desgn crteron n the dslacementbased desgn methods. However, n the energy-based earthquake-resstant desgn methods elastc and nelastc sesmc energy dssatons wthn the structures are amed to be more than the earthquake nut energy. * Dokuz Eylül Unversty, İzmr, Turkey - onur.merter@deu.edu.tr ** Dokuz Eylül Unversty, İzmr, Turkey - ozgur.bozdag@deu.edu.tr *** Dokuz Eylül Unversty, İzmr, Turkey - mustafa.duzgun@deu.edu.tr Publshed n Teknk Derg Vol. 3, o. 1 January 01, :

2 Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato There are many studes n lterature about the energy-based sesmc desgn of structures. The alcaton of energy-based sesmc analyss rocedures n earthquake-resstant structural desgn was frst roosed by Housner [1]. In the study, t was shown that the velocty sectra of earthquakes tend to be stable over the wde erod range and also the earthquake nut energy to mult-degree-of-freedom systems was exressed. any other studes were also erformed to determne the earthquake nut energy and alcaton of nut energy n earthquake-resstant structural desgn and evaluaton [, 3, 4]. Uang and Bertero [] offered new comutaton methodology to obtan the earthquake nut energy to the structures and they also formulated the energy-balance equaton for sngle-degree-offreedom systems. Akyama [5] defned the elastc energy dssaton n structures assumng that the structures are treated as sngle-degree-of-freedom systems. An energy-based methodology for earthquake-resstant desgn of structures was also used n Surahman s study [6]. In the methodology wthn the study, energy dssatons n structures and energy dssaton caactes of the structural members were emhaszed. In Leelatavwat s study [7] a new method whch can be used n structural desgn was resented by wrtng energy balance equatons for a reselected yeld mechansm. The energy-based method was used n the desgn of steel structures by ncludng nterstory drft rato concet. The develoment of energy balance concet for mult-degree-of-freedom systems and the alcaton of energy balance n the evaluaton of structures under sesmc load effects were dscussed n Leelatavwat and Goel s studes [8, 9, 10]. Energy concet n earthquake-resstant structural desgn and erformance-based desgn of mult-story moment resstng frames by usng the energy-based aroxmatons were researched n Shen and Akbaş s studes [11, 1, 13]. In Lee and Goel s study [14], structural desgn was erformed by usng the energy concets and base shear force was obtaned by usng an energy-based desgn method as used n Leelatavwat s study [7]. any studes n lterature are about steel structures. In the study of Km and Cho [15], the energy-based desgn of mult-story braced steel frames was erformed and results were valdated wth nonlnear tme hstory analyses. Performance-based structural desgn s a tye of desgn whch exects fulfllment of the requred crtera for the structure. In the energy-based and erformance-based methodology wthn ths study, arrangement of the method develoed by Leelatavwat [7] s made to comly wth the Turksh Sesmc Desgn Code. Interstory drft rato s chosen as a erformance-based desgn crteron and t s taken from ATC-13 [16] reort wthn the study. Structures are desgned accordng to the target nterstory drft rato whch s selected n lne wth the usage functon of the structures. The energy-based base shear force that acts on the structure s determned and the structural system s desgned. Beams are assumed to have the same dmensons throughout the desgn rocess. After the end of the desgn, nonlnear statc ush-over analyses are erformed and ushover curves of the structures are obtaned. Interstory drft ratos of all stores n the structures whch are ushed u to the target dslacements are obtaned by usng the seventh chater of the Turksh Sesmc Desgn Code, 007 [17]. Interstory drft results obtaned from nonlnear analyses are comared wth the drfts whch are reselected at the begnnng of the energy-based desgn and the results are nterreted. 1574

3 Onur ERTER, Özgür BOZDAĞ, ustafa DÜZGÜ. EERGY-BASED DESIG ETHOD FOR ULTI-STORY STEEL STRUCTURES In the energy-based methodolgy whch s for desgn of new structures, t s assumed that some orton of sesmc nut energy are dssated by the elastc behavor and the remanng sgnfcant orton of sesmc nut energy are dssated by the nelastc behavor of the structures. Housner researched the velocty sectra of some major earthquakes n the world such as El Centro (1934, 1940), Olyma (1940) and Taft (195) ground motons and he showed that sectra are tend to be stable over a wde erod range [1]. In the energy-based desgn methodology wthn ths study, Equaton (1) whch was defned by Housner [1] s used to calculate the sesmc nut energy to the mult-degree-offreedom structural systems. 1 EI t SV (1) In Eq. (1); E : s the total nut energy to the structure wth the earthquake, I t : s the total mass of the system and S V : s the elastc sectral velocty. The total nut energy equaton that was defned by Housner wth Eq. (1) can be rearranged by substtutng the requred exressons as: Wga T E I () 8 where W : s the total weght of the structure, g : s the acceleraton of gravty, T : s the natural vbraton erod of the frst mode and a : s the coeffcent of the elastc sectral acceleraton (dmensonless acceleraton). a can be determned from both secal desgn acceleraton sectrum whch s created by usng dfferent ground moton records and standard elastc desgn acceleraton sectrum that s defned n the Turksh Sesmc Desgn Code [17]. In the desgn methodology wthn the study, the Turksh Sesmc Desgn Code [17] s consdered and the coeffcent of elastc sectral acceleraton s calculated accordng to the Turksh Sesmc Desgn Code. The total energy nut that was defned by Housner wth Eq. (1) can be rewrtten as n Eq. (3) assumng that the energy s dssated by elastc and nelastc behavor. E I E E (3) e In Eq. (3); E e : s the elastc energy and E : s the lastc energy of the system. In the study, t s acceted that the lastc energy s dssated n lastc hnge regons. Elastc and lastc energes of the system are gven n Fgure 1. Fgure 1 reresents the deal elastolastc behavor of the structural system. 1575

4 Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato Fgure 1. Elastc and lastc energy concets from Dslacement-Lateral Force grah (deal elasto-lastc behavor) In Fgure 1; a : s the yeld dslacement and m :s the maxmum dslacement. Akyama [] defned the elastc energy term wth Equaton (4) assumng that the structural system can be reduced nto a sngle-degree-of-freedom system. E e 1 T V g W t t ( ) (4) In Eq. (4), V t : s the base shear force. After total and elastc energes are exressed, lastc energy E can be obtaned by subtractng Eq. (4) from the Eq. () as: E WT g [ a 8 Vt ( ) W ] (5) After the lastc energy s obtaned from Eq. (5), t can be rewrtten by usng classcal work-energy rncle as n Eq. (6). In the structure, the yeld mechansm s acceted as can be seen from Fgure. The frame structure s assumed to undergo a lastc rotaton from the base and the lastc energy equaton s rewrtten for the yeld mechansm (6). The total lastc energy n the collase lmt state of the structure can be calculated by Eq. (6) for the reselected yeld mechansm. E ( n ) (6) b 1 j1 cj 1576

5 Onur ERTER, Özgür BOZDAĞ, ustafa DÜZGÜ Fgure. Yeld mechansm of a two-story and two-san frame structure, lastc moment of structural members, external desgn loads In Eq. (6) and Fgure ; b : s the lastc moment of the beams n th story and cj : s the base lastc moment of the columns. : s the total number of stores, n : s the number of beams n a story and : s the total number of columns n ground floor. In Fgure ; : s the lastc dslacement of the roof story and h : s the heght of the th story. Acceted yeld mechansm n the desgn can be seen from Fgure. In the yeld mechansm t s assumed that lastc hnges occur n the beam edges and column bases. onlnear deformatons are assumed to be n these lastc hnge regons and the other sectons are acceted as lnear-elastc. Eq. (7) s obtaned by equatng the nternal work n lastc hnge regons wth the external work done by the desgn forces of the system. n F h F h (7) b cj 1 j1 1 In Eq. (7); F : s the equvalent statc sesmc force n the Turksh Sesmc Desgn Code [17], (Equaton 8). 1577

6 Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato F wh ( Vt F ) (8) w h j1 j j In Eq. (8); F : s the addtonal sesmc force that acts on the roof ( th ) story. w and w j : are the weghts of the stores and j; h and h j : are the heghts of the stores and j from the base. F s calculated by usng the equaton n the Turksh Sesmc Desgn Code [17], (Eq. 9): F 0, 0075 (9) V t where : s the total number of stores from the base. Plastc energy ( E ) equaton can be rewrtten by substtutng Eq. (7) nto Eq. (6) as: E ( F h F h ) (10) 1 Eq. (10) can be arranged by substtutng Eq. (8) for the F force and Eq. (9) for the F force and then energy-based base shear force V t can be obtaned by equatng (10) wth Eq. (5). V t can be obtaned from dfferent lastc energy equaltes as [7,18,19]: Eq. V t W 4 a (11) where : s a dmensonless arameter that s based on the terms such as yeld mechansm, natural vbraton erod for the frst mode, story heghts, story number and story weghts. The coeffcent s calculated by usng Eq. (1), [19]. d e f (1) d, e and f coeffcents n the equaton (Eq. (1)) are gven n Eqs. (13), (14) and (15), resectvely [19]. 1578

7 Onur ERTER, Özgür BOZDAĞ, ustafa DÜZGÜ d ( 1 1 w h w h 8 ) T g (13) e ( 1 1 wh 0,06 ) T g w h (14) f 0,06 h (15) T g In Eqs. (13), (14) and (15); : s the reselected lastc rotaton value. The total reselected rotaton ( T ) can be exressed by the sum of elastc yeld rotaton ( y ) and lastc rotaton ( ), (Eq. (16)). = T y (16) In ths study, y whch s used ndrectly n the energy-based desgn methodology s taken as 1% consderng the acceted value n the lterature [18]. Interstory drft ratos wll be the same n the lmt collase state of the structure. Because of ths, nterstory drft ratos can be used as a desgn crteron n determnaton of T. Table 1 from ATC-13 reort s resented to defne the structural damage [16]. Table 1. Performance levels accordng to nterstory drft ratos [ATC-13 (1985)] Performance Level Damage State Interstory Drft Rato (%) I one <0. II Slght 0.<<0.5 III Lght 0.5<<0.7 IV oderate 0.7<<1.5 V Heavy 1.5<<.5 VI ajor.5<<5 VII Destroyed >5 The total rotaton ( T ), whch s used n structural desgn, can be determned from Table 1 accordng to damage state. 1579

8 Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato 3. DETERIATIO OF STRUCTURAL EBERS Beam and column members are chosen accordng to lastc desgn rules after determnng the total base shear force wthn the study. The yeld mechansm of the structure s acceted as shown n Fgure. Plastc hnges are assumed to form n the beam edges and column bases as ndcated n revous chaters. Plastc regons n the structural members are modeled wth lastc hnges by usng lumed lastcty aroach. Strong column weak beam behavor, whch exsts n the Turksh Sesmc Desgn Code, s also controlled n the desgn wthn the study. b moment n Eq. (7), whch s obtaned by equatng the nternal work on the lastc hnges to the external work by the desgn loads vares based on lateral rgdty and shear force of the story. Therefore, lastc moment of the beams n th story can be descrbed by Eq. (17) as the rato of the reference moment. b (17) br In Eq. (17); b : s the lastc moment of the beams n th story, : s the shear strength factor for the beam and Eq. (17) nto Eq. (7); br : s the reference lastc moment of the beamsubsttutng 1 F h F h 1 n (18) br j1 cj s obtaned. The shear strength factor for the beam can be generally exressed by Eq. (19), [7]. V ) b ( (19) V In Eq. (19); V : s the shear force of the story and V : s the shear force of the roof story ( th ) level. b s the numercal factor and descrbed by Lee and Goel [14] as: 0,5 0, b T (0) The numercal factor b n Eq. (0) was wdely nvestgated by several researchers. In ths study, Eq. (0) defned by Lee and Goel s used for the b factor deendng uon the frst natural erod of vbraton (T ). : The shear strength factor whch s exressed by Eq. (19) s shown schematcally n Fgure 3. The lastc moment values ( b ), whch are obtaned by usng factor, are wrtten n story levels n Fgure 3. The lastc moment values for all beams n a story ( ) can be calculated after determnng reference lastc b 1580

9 Onur ERTER, Özgür BOZDAĞ, ustafa DÜZGÜ moment ( br ) wth Eq. (18) and shear strength factor ( ) wth Eq. (19). Beams n a story are chosen accordng to the lastc moments ( b ) whch are calculated by usng Eq. (17). Column desgn s erformed after the desgn of beam. cj, the lastc moment of column bases, can be estmated by usng several aroaches based on the shear force n a story. In the study uto ethod s used for determnaton of column lastc moments. In the beams, stran hardenng effect s consdered and strength ncrease s assumed. Therefore, lastc moments of beams are multled by a coeffcent whch s called the strength ncrease factor wthn the study. The ncreased lastc moment ( ) s used n the column b desgn nstead of beam lastc moment ( b ). Assumng the strength ncrease rato to be aroxmately equal to 5%, s taken as 1.05 wthn ths study. s taken 1 because; n the roof story level lastc hnges do not affect the behavor of the mechansm. In the study, column axal loads and bendng moments are obtaned n the lmt collase (yeld) state. Steel column sectons whch are under the effect of combned bendng and axal loads are chosen by usng the yeld surfaces [0] of the sectons. Alcaton stes of the desgn methodology can be seen from Fgure 4 (flow chart). Fgure 3. arameters and lastc moments for the beam desgn 1581

10 Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato Selecton of nterstory drft ratos accordng to the usage functon of the structure [ATC-13 (1985)] The end of the desgn wth chosen sectons YES Pre-desgn of structural members Calculaton of desgn base shear force for re-desgned structure Vt 4a ( ) W Determnaton of beam reference lastc moment br [Eq. (18)] usng : Shear strength factor and cj : Plastc moment of columns at the base O Are the structural steel sectons the same as n the re-desgn of structural members? Determnaton of steel column sectons accordng to the calculated axal loads and bendng moments Obtanng of column bendng moment grahs by usng the b lastc moments Determnaton of beam lastc moments b [Eq. (17)] usng the reference lastc moment Calculaton of the ncreased lastc moment: b Selecton of steel rofle sectons for the beams accordng to the Euroean Standard Profles Determnaton of column axal loads n the yeld mechansm Fgure 4. Flow chart of the energy-based structural desgn methodology 158

11 Onur ERTER, Özgür BOZDAĞ, ustafa DÜZGÜ 4. CASE STUDY, 5 and 8-story steel frames are desgned accordng to the dfferent reselected nterstory drft ratos usng the energy-based methodology wthn the study. In the desgn; 1.5%, % and 3.5% nterstory drft ratos are chosen from the ATC-13 reort to reresent the moderate, heavy and major damage states (Table 1). In the alcaton of the desgn methodology, steel rofles whch have the yeld strength of 40 Pa and modulus of elastcty of Pa are used. Steel structures are desgned by usng the Euroean Standard Profles. HEB rofles are used for the columns and IPE rofles are used for the beam sectons. Regular steel frames wth unform mass and stffness along the buldngs are used n the alcaton of the desgn methodology. All story heghts are 3 meters and all beam sans are 6 meters. Dstrbuted load on the beams s taken as 30 k/m and the weghts of the frames are gnored. Structures are assumed to be n the frst degree earthquake zone and sol tye Z4 s assumed. Buldng mortance factor s taken as I=1.0 for the usage functon of the structures [17]. Base shear forces actng on the steel frame structures are calculated ntally n the desgn. Parameters and V t /W ratos for the 1.5%, % and 3.5% of T are gven n Table, 3 and 4 for the, 5 and 8-story steel frame structures n the lmt state. Fnal beam and column sectons are shown n Fgures 5, 6 and 7. Story umber Table. Desgn arameters of the -story frames T (sec.) a y V t /W Story umber Table 3. Desgn arameters of the 5-story frames T (sec.) a y V t /W Story umber Table 4. Desgn arameters of the 8-story frames T (sec.) a y V t /W

12 Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato Fgure 5. Energy-based desgn of -story frames accordng to the nterstory drft ratos of 1.5%, % and 3.5% Fgure 6. Energy-based desgn of 5-story frames accordng to the nterstory drft ratos of 1.5%, % and 3.5% 1584

13 Onur ERTER, Özgür BOZDAĞ, ustafa DÜZGÜ Fgure 7. Energy-based desgn of 8-story frames accordng to the nterstory drft ratos of 1.5%, % and 3.5% 1585

14 Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato 5. EVALUATIO OF EERGY-BASED DESIG In ths chater,, 5 and 8-story steel frames whch are desgned by usng the method exlaned n revous chaters are controlled by erformng nonlnear statc analyses to see f the frames satsfy the target nterstory drft ratos or not. SAP000, a structural analyss rogram, s used n the analyses. Secton moment-rotaton relatons are defned as deal elasto-lastc and second-order effects are neglected n the nonlnear analyses. Grahs whch are obtaned by convertng ushover curves to modal caacty curves [1] for the, 5 and 8-story frame structures desgned accordng to the nterstory drft ratos of 1.5%, % and 3.5% can be seen from Fgures 8, 9 and 10. Dslacement demands of the frames obtaned by usng the method n the Turksh Sesmc Desgn Code are shown n the same fgures. Because the nterstory drft ratos are used n the desgn methodology as desgn crtera, when nterstory drft ratos are reached the dslacement demands are comared wth the nterstory drft ratos whch are reselected n the desgn. Interstory drft ratos obtaned from nonlnear statc analyses and target nterstory drft ratos n the desgn are gven n Fgure 11, 1 and 13. It can be seen from the results that the nterstory drft ratos are exceeded n -story frames. In 5 and 8-story frames, the target nterstory drft ratos are not exceeded and reman smaller than the reselected target drft ratos. Fgure 8. odal caacty grahs of -story frames (Interstory drft ratos:1.5%, % and 3.5%) 1586

15 Onur ERTER, Özgür BOZDAĞ, ustafa DÜZGÜ Fgure 9. odal caacty grahs of 5-story frames (Interstory drft ratos:1.5%, % and 3.5%) Fgure 10. odal caacty grahs of 8-story frames (Interstory drft ratos:1.5%, % and 3.5%) 1587

16 Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato Fgure 11. Interstory drft ratos of -story frames desgned wth the energy-based method Fgure 1. Interstory drft ratos of 5-story frames desgned wth the energy-based method 1588

17 Onur ERTER, Özgür BOZDAĞ, ustafa DÜZGÜ Fgure 13. Interstory drft ratos of 8-story frames desgned wth the energy-based method 6. COCLUSIOS Energy-based desgn methodology accordng to the redefned nterstory drft rato s resented wthn the study., 5 and 8-story steel frame structures are chosen to nvestgate the alcablty of the methodology. onlnear statc analyses are erformed to check the target nterstory drft ratos reselected n the desgn to see whether the target drft ratos are exceeded or not. A comuter software that conssts of roer calculaton algorthms s needed because the desgn methodology s an teratve methodology. crosoft Excel rogram s used to reduce the tme-consumng comutaton rocesses and hence the desgn results are obtaned n a shorter erod of tme. The flow chart exlanng the methodology s seen n Fgure 4. Inelastc behavor of the structures s consdered wthn the desgn methodology. The desgn s erformed by usng the energy concet dfferng from the force-based and dslacement-based desgns. Energy concet s suorted wth the yeld mechansm and nterstory drft rato concets and so the energy-based methodology s develoed. It s seen from the nonlnear analyses that target dslacements of the -story steel frames are exceeded n all story levels for the nterstory drft ratos of 1.5% and %. The nterstory drft rato values whch are obtaned from nonlnear analyses reman less than the targeted drft ratos n the desgn of -story frames accordng to the drft ratos of 3.5%. In the desgn of 5-story frames, target nterstory drft ratos are not exceeded n all story levels and t can be seen from the nonlnear analyses that nterstory drft ratos are close to the targeted drft ratos n the desgns. Target nterstory drft ratos are not exceeded n 8-story frames, 1589

18 Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato too, and drft ratos obtaned from nonlnear analyses reman less than the targeted values. It can be observed from the study that the energy-based desgn methodology gves better results for medum heght frame structures. Further research should be done to obtan better results from the energy-based exstng desgn methodology. The calculaton rocedure s develoed for the frst-mode domnated structures. Frst mode shae of the structure s used n the desgn. It s necessary to study the desgn methods that consder hgher modes of the structures. The desgn methodology can be develoed by evaluatng arameters such as san number, nterval length and story heght. Elastc rotaton of the structure s acceted as 1% n ths study. It wll be very useful to develo the acceted elastc rotaton accordng to the heght and the other roertes of the structure. Symbols : Coeffcent of the elastc sectral acceleraton a b d e E e : umercal factor used n the calculaton of shear strength factor for the beam : Coeffcent whch s based on several structural roertes and used n the calculaton of coeffcent : Coeffcent whch s based on several structural roertes and used n the calculaton of coeffcent : Elastc energy of the system E I E f F g h h : Sesmc nut energy of the system : Plastc energy of the system whch s assumed to be dssated n lastc hnge regons : Coeffcent whch s based on several structural roertes and used n the calculaton of coeffcent : Equvalent earthquake force whch acts on the th story : The acceleraton of gravty : The heght of the th story : The heght of the th story : Total column number on the ground floor : Plastc moment of the column b : Plastc moment of the beams n the th story level 1590

19 Onur ERTER, Özgür BOZDAĞ, ustafa DÜZGÜ br : Reference lastc moment of the beams cj : Plastc moment of the column at the base level on j axs t n s dt S V T V V t V w W a m : Total mass of the mult-degree-of-freedom system : Beam number n a story : Total story number from the base : Plastc axal load of the column : Sectral target dslacement : Elastc sectral velocty : atural vbraton erod of the frst mode : Shear force of the th story : Energy-based base shear force : Shear force of the roof story : The total weght of the th story : The total weght of the structure : Dmensonless arameter whch s used n the calculaton of energy-based base shear force : Shear strength factor for the beam : Yeld dslacement : axmum dslacement : Plastc dslacement : Interstory drft rato n the ATC-13 reort F : Addtonal earthquake load whch acts on the roof level of the structure T y : Preselected lastc rotaton : Preselected total rotaton : Elastc yeld rotaton : Strength ncrease factor for the beams 1591

20 Energy-based Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato Acknowledgements Frst author thanks to Dokuz Eylul Unversty: The Graduate School of atural and Aled Scences for ther suort. References [1] Housner, G. W., Lmt Desgn of Structures to Resst Earthquakes, Proceedngs of the 1st World Conference on Earthquake Engneerng, Earthquake Engneerng Research Insttute, Oakland, Calforna, 5, 1-13, [] Uang, C.-., Bertero, V. V., Evaluaton of Sesmc Energy n Structures, Earthquake Engneerng and Structural Dynamcs, 19, 1, 77-90, [3] Khashaee, P., ohraz, B., Sadek, F., Lew, H. S. and Gross, J. L., Dstrbuton of Earthquake Inut Energy n Structures, atonal Insttute of Standards and Technology Interagency Reort, ISTIR 6903, Gathersburg, D, Unted States of Amerca, 003. [4] Aok, H. and Ikeda, K., Hysteress odel of Low-rse Steel-frame Buldng and Its Sesmc Performance, Steel Structures, 6, , 006. [5] Akyama, H., Earthquake-Resstant Lmt-State Desgn for Buldngs, Unversty of Tokyo Press, Tokyo, [6] Surahman, A., Earthquake-Resstant Structural Desgn Through Energy Demand and Caacty, Earthquake Engneerng and Structural Dynamcs, 36, , 007. [7] Leelatavwat, S., Drft and Yeld echansm Based Sesmc Desgn and Ugradng of Steel oment Frames, Ph.D. Thess, Unversty of chgan, [8] Leelatavwat, S., Saewon, W. and Goel, S. C., Alcaton of Energy Balance Concet n Sesmc Evaluaton of Structures, Journal of Structural Engneerng, 135,, , 009. [9] Goel, S. C., Lao, W-C. and Leelatavwat, S., An Energy Sectrum ethod for Sesmc Evaluaton of Structures, Conference on Imrovng the Sesmc Performance of Exstng Buldngs and Other Structures, Aled Technology Councl and the Structural Engneerng Insttute of ASCE, San Francsco, CA, 009. [10] Leelatavwat, S., Saewon, W. and Goel, S. C., An Energy Based ethod for Sesmc Evaluaton of Structures, 14th World Conference on Earthquake Engneerng: Innovaton Practce Safety, Bejng, Chna, 008. [11] Akbaş, B. and Shen, J., Energy Aroach n Performance-Based Sesmc Desgn of Steel oment Resstng Frames for Basc Safety Objectve, The Structural Desgn of Tall Buldngs, 10, , 001. [1] Akbaş, B., Energy-Based Earthquake Resstant Desgn of Steel oment Resstng Frames, Ph.D. Dssertaton, Graduate College of Illons Insttute of Technology,

21 Onur ERTER, Özgür BOZDAĞ, ustafa DÜZGÜ [13] Akbaş, B. and Shen, J., Earthquake-Resstant Desgn and Energy Concets, Techncal Journal, Turksh Chamber of Cvl Engneers, 14,, , 003 (n Turksh). [14] Lee, S-S. and Goel, S. C., Performance Based Desgn of Steel oment Frames Usng Target Drft and Yeld echansm, Research Reort, UCEE 01-17, The Unversty of chgan, Deartment of Cvl and Envronmental Engneerng, 001. [15] Km, J. and Cho, H., Energy-Based Sesmc Desgn of Structures wth Bucklng- Restraned Braces, Steel and Comoste Structures, 4, 6, , 004. [16] ATC-13, Earthquake Damage Evaluaton Data for Calforna, Aled Technology Councl, ATC-13 Reort, Redwood Cty, Calforna, [17] Turksh Earthquake Code, TEC, Secfcaton for Buldngs to be Bult n Earthquake Regons, nstry of Publc Works and Settlement, Government of the Reublc of Turkey, 007 (n Turksh). [18] Leelatavwat, S., Goel, S. C. and Stojadnovc, B., Energy-based Sesmc Desgn of Structures usng Yeld echansm and Target Drft, Journal of Structural Engneerng, 18, 8, , 00. [19] erter, O., Energy-based Performance Analyss of Structures, Dokuz Eylül Unversty, The Graduate School of atural and Aled Scences, İzmr, 008 (n Turksh). [0] Özer, E., Lecture otes: onlnear Analyss of Structural Systems, htt:// 008 (n Turksh). [1] Federal Emergency anagement Agency, FEA 440 Imrovement of onlnear Statc Sesmc Analyss Procedures, Washngton D.C.,