Effect of torsional resistance by transverse frames on seismic drift demand of torsionally-unbalanced building structures

Transcription

1 Effect of torsioal resistace by trasverse frames o seismic drift demad of torsioally-ubalaced buildig structures *Kyug Ra Hwag ), Abegaz Ruth Ali ) ad Ha Seo Lee 3) ), ),3) School of Civil, Evirometal, ad Architectural Egieerig, Korea Uiversity, Seoul, 084, Korea ) dh849@korea.ac.kr ABSTRACT I this study, theismic drift demad of torsioally-ubalaced RC frame structures i low-seismicity regios is estimated accoutig for torsioal resistace by trasverse frames perpedicular to the directio of groud motio by usig the acceleratio-displacemet respospectrum diagram ad the plaar aalysis approach proposed by Lam et al. (06). The ratio of the maximum edge drift to the cetral drift (Δ max /Δ o ) of two torsioally-ubalaced structures with two differet pla aspect ratios are preseted by icreasig the torsioal irregularity for thtructural respose to acceleratio, velocity, ad displacemet cotrolled excitatios. The torsioal resistace by the trasverse frame is expected to reduce the ratio of max / 0. The ratios of max / 0 accoutig for the torsioal resistace by the logitudial ad trasverse frames are 80~90% of those cosiderig the torsioal resistace by the logitudial frame oly. The liear time history aalyses were also coducted usig the MDOF system to verify the drift demads obtaied from the plaar aalysis approach usig the SDOF structure. The max / 0 ratios for the MDOF system are larger tha those for SDOF system, ad the ratio icreases up to approximately 5% with the icreasig the umber of thtory from five to te due to their havig differet vertical modal distributios.. INTRODUCTION Past earthquake evets demostrated that the level of damage ad collapse to the buildig was closely related to the drift demad. Particularly, the drift demad at a certai part of a asymmetric-pla (torsioally-ubalaced, TU) structure havig a torsioal irregularity ca bigificatly larger tha those required by symmetric-pla (torsioally-balaced, TB) structures. ) Research Assistat Professor ) Graduate Studet 3) Professor

2 I curret buildig desig codes (ASCE 7-0 ad KBC 06), torsioal irregularity is defied to exist where the maximum story drift, Δ, at the ed of the structure is more tha. times the average of thtory drifts, Δ 0, at the two eds of thtructure. At this poit, a accidetal torsio, T a, is icluded to accout for ucertaities i the actual locatio of the ceters of mass ad stiffess, the rotatioal compoet of groud motios, ad other ucertaities ot explicitly cosidered. For the TU structures assiged to theismic desig category D, the modal spectrum aalysis or seismic respose history aalysis should be carried out by applyig the amplified T a, eve though the height of thtructure is less tha 0m or six stories. It seems to be complicated for the low-rise buildig structures i low-to-moderateismicity regios. The use of the accidetal torsio, T a, is also questioable for the cotrol of deformatio ad damage. (Lee ad Hwag 05) Lam et al. (06) suggested a simplified method for assessig seismic drifts of low-rise TU buildig structures i lower seismicity regios usig the acceleratiodisplacemet respospectrum (ADRS) diagram. This approach is valid oly for assessmet of liear elastic behavior but ca represet the desig demad for lower seismicity regios. However, the cotributio of the trasverse frame perpedicular to the directio of excitatio to torsioal resistace was igored. I this study, theismic drift demad of TU structures i low-seismicity regios is estimated accoutig for torsioal resistace by trasverse frames (-directio) perpedicular to the directio of groud motio (-directio) by usig thimplified method proposed by Lam et al. (06). These results are obtaied uder the assumptio of thigle-degree-of-freedom (SDOF) systems. Thus, the drift demads are verified by the compariso of the results of modal time history aalyses of multidegree-of-freedom (MDOF) framtructures.. ASSESSMENT OF SEISMIC DRIFT DEMANDS OF SDOF TU STRUCTURES. Simplified method cosiderig the effect of trasverse frames Displacemet demads are of key iterest i thizig ad detailig of structural elemets for earthquake resistace. The drift demad for the TB buildig structure assumed to be SDOF structure is simply predicted ad verified usig the ADRS diagram overlaid o capacity diagrams as show i Fig.. However, the dyamic behaviors of the torsioally-ubalaced buildig ievitably lead to o-uiform displacemet demads of the lateral resistig plaes of thystem. To predict the displacemet demads for the torsioally-ubalaced buildig structure, Lam et al. (06) suggested a simplified method for assessig seismic drift demads of the SDOF torsioally-ubalaced structure. The maximum drift demad at the ceter was obtaied from the ADRS diagram, ad the critical ratio of displacemets at the edge to that of the ceter i thtructural pla, Δ/Δ 0, was estimated by adaptig a plaar aalysis approach. It was established with the modal resposes for the torsioal modes coupled with the traslatio. I this study, the method is expaded to the geeral case icludig the cotributios of trasverse frames, which is perpedicular to the directio of excitatio, to torsioal resistace as show i Fig..

3 K / K / RSA (g) RSA (g) RSA max RSV max RSD max KBC 06 (site class: S C ) T 0 T T Period, T (sec) T Demad diagram Capacity curves (π/t) T KBC 06 (site class: S C ) RSD (cm) (a) Acceleratio respospectrum (b) ADRS Fig. Desig respospectrum i KBC 06 (06) Before thimplified method is itroduced, the SDOF structural model is assumed to be rectagular i pla with width B ad with the ceter of stiffess (CS) offset from the ceter of the buildig by the eccetricity ( ) as show i Fig.. The torsioal stiffess parameters, b x, b y, ad b, defied i Fig. ad Eq. () are used to represet the torsioal stiffess properties of the model. The higher the b value, the higher the torsioal stiffess of the lateral supportig elemets i relatio to their collective traslatioal stiffess (Lam et al. 06). Equivalet stiffess K / b x b x +B CS CM b y -B K / -B = B +B = B b y xi yi yi xi i i kxid yi k yid xi K i K i y ad b x K K kxi kyi i i K K K k d k d b Fig. Defiitio of torsioal rigidity parameter, b x ad b y a K K b K K ab b / ad / y x (),,y () aesy a 0 x x r r 0 0 r 0 esx 0 y 0 0 y 0 r r 0 0 r 0 aesy e ae sx sy e ab sx y b x ( ) r r r r r (3) esy ( a a ) x / sy ( ) r re a y / r ( ) esx / r (4) ( ( B/ r)) yb, ( t) U ( t) (5) 3

4 Thimplified equatios give by Lam et al. (06) to calculate the frequecy ratio, λ, ad the ormalized torsioal rotatio, θ are derived by assumig oly the effect of the logitudial frames. However, thimplified equatios i Eqs. () to () are derived by cosiderig the effect of both logitudial ad trasverse frames (Fig. ). The relatioship of atural frequecies betwee the TB ad TU structures is give i Eq. (). The TU structure always has two or three coupled traslatioal ad torsioal modes. The example model i Fig. has the two coupled modes due to the asymmetric pla i the directio. Usig the relatioship of atural frequecies (Eq. ()), the equatio of motio for the SDOF pla asymmetric structure is give by Eq. (), which is ormalized by the mass radius of gyratio, r, to geeralize the lateral ad torsioal stiffess. Thtiffess matrix is determied by thtatic eccetricity, /r, ad the parameters a ad b/r i Eq. (). The ormalized displacemet vector is also derived i Eq. (4). Based o these defiitios, the time history of modal displacemet at the edge +B ad -B ca be derived from Eq. (5), which is composed of the ormalized torsioal rotatio ad displacemet time history of the SDOF system, U Ω (t). All parameters used i Eqs. () to (5) are defied i the last sectio. More details o the procedure are give i Lam et al. (06). The maximum drift demads of the asymmetric structure are preseted regardig the ratio of displacemet at the edge to ceter, Δ/Δ 0, expressed as fuctios of the frequecy ratio, λ, ad the ormalized torsioal rotatio, θ, for acceleratio, velocity, ad displacemet cotrolled coditios as give i Eqs. (6) to (8). The maximum drift i Eqs. (6) to (8) is obtaied from the combiatio of the modal displacemets defied i Eq. (5) by usig thquare root of thum of thquares (SRSS) method. The maximum value of time history displacemet, U Ω (max), ca be determied by the respospectral displacemet (RSD) i the ADRS diagram (Fig. (b)) depedig o where the atural period (T) ad dampig ratio (ζ) are the acceleratio, velocity, ad displacemet cotrolled rages. ( ( B/ r)) 0 RSD( T, ) i acceleratio cotrolled coditio T RSD(T, ) RSA RSA, ad U (max) RSD(T, ) max max y ( ( B/ r)) 0 RSD( T, ) i velocity cotrolled coditio T RSD(T, ) RSVmax RSVmax, ad U (max) RSD(T, ) ( ( B/ r)) 0 RSD( T, ) max y i displacemet cotrolled coditio RSD(T, ) RSD, ad U (max) RSD(T, ) (6) (7) (8) 4

5 RSA (g) Frame Frame Frame Frame Frame Frame Torsioally balaced structure Frame Torsioally ubalaced structure Coupled mode Δ θ +B Δ λ -B Δ -B Frame θ Frame Coupled mode λ Δ +B Δ 0 = CM=CS Frame λ CS CM Frame λ CS CM Frame. Estimate the Δ 0 from ADRS Estimate the desig demad, RSD, usig ADRS diagram i accordace with thtructural respose to acceleratio, velocity, ad displacemet cotrolled excitatios RSA max T= 0.5s RSV max T = s KBC 06 (S C ) RSD max 0. T =.5s RSD (cm) T RSD RSAmax for costat accel. RSD -B RSVmax RSD RSD max +B T for costat vel. for costat disp. For example, T = 0.5s RSD=.7cm T =.0s RSD=5.8cm T =.5s RSD=RSD max =.5cm Assumptios: This approach is valid oly for assessmet of liear elastic behavior, but ca represet the desig demad reasoably for a low-to-moderateismicity regio.. Defitatic eccetricity ad torsioal stiffess for Eq. (3) The λ ad λ are determied by thtatic eccetricity ( ) ad the torsioal stiffess (K θθ ). e sy -B Traslatioal mode Mode Mode frequecy, ω y Ω = = λ ω y Ω = = λ ω y k d xi yi yi xi i i ad esx K K xi yi yi xi y x i i kxid yi k yid xi K i K i by ad bx K K kxi k yi i i Assumptios: ) The distaces from CM to each frame are fixed. ) No static eccetricity by the -directioal frames (y = 0; ad b y = costat) 3) The value of K is costat. 4) a = K /K K ( ab b ) K b K ; ad b K / K. Icreasig x from 0 to 50% of B with a costat value of K θθ a. Adustig the lateral stiffess of stiff ad flexible frames i the -dir. with the costat K. (: the umber of all frames, q: the umber of stiff frames) K K ky, stiff a ; ad ky, flex K qa (preseted i Fig. 4) q b. The equatios of x ad b x ca be expressed as the liear fuctio of a. As the x icreases, the b x also icreases. c. To be kept the costat value of b related with K θθ, the ratio a should decrease. k d K K K k d k d b K b K k d Torsioal resistace by trasverse frames y x q yi xi q i esx dxi dxi a dxi K i q iq q iq +B kyidxi q i q x dxi dxi xi K i q iq q iq b a d K b K ( ab y bx ) K costat costat Icreases with icreasig x 3. Derive the frequecy ratio λ ad ormalized deformatio θ usig Eq. (3) 4. Calculate Δ/Δ 0 at thtiff ad flexible edges usig Eq. (6) to (8) -B +B Assessmet of maximum displacemet at thtiff ad flexible edges, RSD Δ/Δ 0 If the x varies from 0 to 50% of B by icreasig a with costat b/r, the b x value icreases but the ratio a decreases. If the b/r varies from.5 to.67 with costat x, the b x value is costat but the ratio a icreases. Fig. 3 Procedure for assessmet of maximum drift (Hwag et al. 06) 5

6 H eff =0m H eff =0m H eff =74m B/ B/ 3 B B. Seismic drift demads with differet degrees of torsioal irregularity Thimplified method for assessig seismic drifts is applied to two example sigle-story TU structures with differet pla aspect ratios, Pla types I ad II, i Figs. 4(a) ad (b), respectively, which have a asymmetric pla i the directio. The ratio of Δ/Δ 0 at thtiff ad flexible edges for the acceleratio, velocity, ad displacemet cotrolled coditios is calculated by icreasig the value of with varied values of torsioal stiffess, b/r =.5 to.68. Eve if the value of icreases, the total torsioal stiffess is kept costat with decreasig the torsioal cotributio by the - directioal frames expressed as the ratio a. The higher values of b/r tha.47 i Pla Type I ad.37 i Pla Type II are obtaied from the ratio a beig larger tha. The maximum displacemet demads, Δ 0, of TB buildig structures at periods, T = 0.5,.0, ad.5s, obtaied from the ADRS diagram (Fig. 3) by thtructural respose to acceleratio, velocity ad displacemet cotrolled excitatios are preseted i Fig. 5. A height correspodig to each period is derived from the equatio of approximate period i KBC 06. The maximum displacemet ratios of Δ/Δ 0 at the flexible edges of the SDOF structure with Pla Types I ad II for the acceleratio, velocity, ad displacemet cotrolled coditios (Eqs. (6) to (8)) are preseted i Figs. 6 ad 7. I the acceleratio (Figs. 6(a) ad 7(a)) ad velocity (Figs. 6(b) ad 7(b)) cotrolled coditios, the ratio of Δ/Δ 0 icreases as the value of icreases. The curves of Δ/Δ 0 for the displacemet-cotrolled coditio i Fig. 6(c) ad 6(c) are ot thame treds of those for the acceleratio ad velocity cotrolled coditios. I the displacemet cotrolled coditios, the ratio of Δ/Δ 0 is withi the upper limit of.3 ad.48 i the Pla Type I ad II, respectively, regardless of the torsioal stiffess despite the much larger value of /B. 3 d y d y3 d y3 d y B B Type I d x d x3 3 No. of frames, = 3 No. of stiff frames, q = k y,stiff = k y ; k y,flex = k y = k y3 (a) Pla Type I (pla aspect ratio = ) B Type II d x d x d x4 dx B No. of frames, = 5 No. of stiff frames, q = k y,stiff = k y = k y ; k y,flex = k y3 = k y4 = k y5 (b) Pla Type II (pla aspect ratio = ) Fig. 4 Exampltructures with pla types I ad II Approximate period i KBC 06 T a =N/0 (N: o. of story ) T a = 0.073h 3/4 for RC momet frame Acceleratio cotrolled 0 = 7 mm 0 /H eff = 0.7% M T a = 0.5s (5-story) Velocity cotrolled 0 = 58 mm 0 /H eff = 0.9% M T a =.0s (0-story) Displacemet cotrolled 0 = 5 mm 0 /H eff = % M T a =.5s (37-story) H eff = /3H (H: height of buildig) Story height = 3m Fig. 5 Estimatio of maximum displacemet i TB buildig 6

7 Edge displacemet ratio (Δ/Δ 0 ) Edge displacemet ratio (Δ/Δ 0 ) Edge displacemet ratio (Δ/Δ 0 ) Edge displacemet ratio (Δ/Δ 0 ) Edge displacemet ratio (Δ/Δ 0 ) Edge displacemet ratio (Δ/Δ 0 ) costat b/r values.5.36 (.84) θ flex. Δ (.39) stiff Δ.4.47 Δ 0. B Flexible edge Eccetricity ratio, /B (%) (a) Acceleratio cotrolled coditios 3 Flexible edge. costat b/r values.4.5 (.3) (.60) stiff Δ.5 Δ 0 B Eccetricity ratio, /B (%) θ flex. Δ (a) Acceleratio cotrolled coditios costat b/r values (.55) (.34) stiff Δ. θ Δ 0 Flexible edge Eccetricity ratio, /B (%) (b) Velocity cotrolled coditios B flex. Δ costat b/r values (.5).5 stiff Δ (.83).5. Flexible edge Eccetricity ratio, /B (%) (b) Velocity cotrolled coditios B θ Δ 0 flex. Δ costat b/r values stiff Δ Flexible edge Eccetricity ratio, /B (%) θ B Δ 0 flex. Δ (c) Displacemet cotrolled coditios Fig. 6 Flexible-edge displacemet ratio of Pla Type I costat b/r values stiff Δ Flexible edge Eccetricity ratio, /B (%) B θ Δ 0 flex. Δ (c) Displacemet cotrolled coditios Fig. 7 Flexible-edge displacemet ratio of Pla Type II 7

8 3. VERIFICATION OF DRIFT DEMAND B COMPARISON WITH ELASTIC TIME HISTOR ANALSES OF MDOF STRUCTURES 3. Aalytical modelig of MDOF example buildig structures The drift demads i Figs. 6 ad 7 are obtaied uder the assumptio of the SDOF systems. I this chapter, therefore, the drift demads are verified by the compariso of the results of modal time history aalyses of MDOF framtructures. The exampltructures are ordiary TU RC framtructures with Pla types I (two by two bays) ad II (two by four bays), show i Figs. 4(a) ad (b), respectively. Each pla type has two umbers of stories, five ad te, which are related to the acceleratio ad velocity cotrolled coditios, respectively, i Fig. 5. Thtory height of structures is 3m, ad the width of each bay was 5m. The desig cocrettregth, f c, is MPa. For all cases, the lateral stiffess is determied by the vertical elemets (colums) oly. Thize of colums is give i Table for each pla type with x /B =0% ad 5%, respectively. Theismic weight icludes the dead load as give i Table. The periods for the TB ad TU structures are also give i Table. I the case of TU, there are two coupled modes betwee the -directioal traslatio ad torsio, ad the periods, T, (where is represetig the coupled modes) were calculated usig T =π/λ ω y (Eq. ()) i Table. The -directioal traslatioal mode is ot dealt i this study, so the two coupled modes are called the first ad secod modes for coveiece. Liear modal time history aalyses were performed for the eight example structures. The ie iput groud motios (Table 3) werelected from PEER NGA Database (0) to represet the desig earthquake (DE) i Korea as show i Fig. 8. The dampig ratio was assumed to be 5%. A rigid floor diaphragm with all theismic mass (Table ) was lumped at the ceter of mass of each floor. Colum size * (uit: mm) Table. Summary of the colum properties Pla type I (B=0m) Pla type II (B=0m) x /B =0% x /B =5% x /B =0% x /B =5% Stiff side 550x x870 70x x960 flexiblide 590x x50 780x60 700x490 Pla type I II x /B 0% 5% 0% 5% Coditio Table. Mass ad period for TB ad TU structures Seismic weight (kn) TB structure Traslatioal mode, T y (sec) TU structure Coupled mode Coupled mode T, (sec) T, (sec) 5-story* 4, story* 9, story 4, story 9, story 9, story 9, story 9, story 8, * 5-story ad 0-story structures are related to the acceleratio ad velocity cotrolled coditios. 8

9 Acceleratio, S a (g) Acceleratio, S a (g) Acceleratio, S a (g) Acceleratio, S a (g) Table 3. Summary of iput groud motios* (PEER 03) Earthquake Name ear Statio Name Mag. HypD PGA PGV PGD (Mw) (km) (g) (cm/s) (cm) M Ker Couty 95 Taft Licol School M Loma Prieta 989 Aderso Dam (Dowstream) M3 Northridge LA - Cypress Ave M4 Chi-Chi, Taiwa TCU M5 L'Aquila, Italy 009 GRAN SASSO (Assergi) M6 Chuetsu-oki 007 Tokamachi Matsuoyama M7 Ker Couty 008 Miase uzawa M8 Loma Prieta 99 Morogo Valley Fire Statio M9 Northridge-0 00 SPFS * Thoil class for all groud motios is C. 0.8 M M M3 M4 M5 M6 M7 M8 M9 Ave. DE directio 0.8 M M M3 M4 M5 M6 M7 M8 M9 Ave. DE directio Period, T (sec) (a) Acceleratio respospectrum M M M3 M4 M5 M6 M7 M8 M9 Ave. DE directio Period, T (sec) 0.8 M M M3 M4 M5 M6 M7 M8 M9 Ave. DE directio Displacemet (cm) Displacemet (cm) (b) ADRS Fig. 8 Respospectra of the iput groud motios 3. Seismic drift demads of MDOF buildig structures Table 4 presets the values of max ad 0 ad the ratio of max / 0 from the time history aalyses usig ie differet groud motios. All the max occurred at the flexible edge. The values of max ad 0 are take at thame istat time. For the SDOF system, the value of 0 i Eqs. (6) ad (7) is equal to the RSD value correspodig to the period, T y, i the ADRS (Fig. (b)). The RSD values for the period of the 5-story structures are about 5mm, ad those of the 0-story structures are about 40mm. For the MDOF system, the max ad 0 i Table 4 are ot the roof drift but the iterstory drift, so the values of displacemet for the SDOF ad MDOF systems caot be compared at thame level. 9

10 I Table 4, the ratio of max / 0 is quite differet due to the differece of iput groud motios. I the case of the 5-story PI-0, the miimum ratio of max / 0 was.33 uder M4, ad the maximum ratio of max / 0 was.86 uder M5. So, the mea values of max ad 0 ad the mea ratio of max / 0 were calculated to miimize the effect of iput motios. All ratios exceed the desig limit value,., i ASCE 7-0 ad KBC 06. The ratio of max / 0 icreases as the umber of stories ad the value of x icrease at thame pla type. Table 4. Maximum edge drift ratio max / 0 obtaied from elastic time history aalysis PI-0: Pla type I with x /B = 0% coditio M M M3 M4 M5 M6 M7 M8 M9 Mea Δ max 5-story* (mm) 0-story* story (mm) 0-story max / 0 5-story story PI-5: Pla type I with x /B = 5% coditio M M M3 M4 M5 M6 M7 M8 M9 Mea Δ max 5-story (mm) 0-story story (mm) 0-story max / 0 5-story story PII-0: Pla type II with x /B = 0% coditio M M M3 M4 M5 M6 M7 M8 M9 Mea Δ max 5-story (mm) 0-story story (mm) 0-story max / 0 5-story story PII-5: Pla type II with x /B = 5% coditio M M M3 M4 M5 M6 M7 M8 M9 Mea Δ max 5-story (mm) 0-story story (mm) 0-story max / 0 5-story story * 5-story ad 0-story structures are related to the acceleratio ad velocity cotrolled coditios. 3.3 Compariso of seismic drift demads Table 5 presets the ratio of max / 0 for three differet cases. The first case is SDOF systems by cosiderig oly the effect of the logitudial (-dir.) frame. The secod case is the SDOF systems by cosiderig the effect of logitudial (-dir.) ad trasverse (-dir.) frames. The third case also cosiders the effect of logitudial ad trasverse frames, but it is MDOF systems. The value of b/r for all cases is.5. I the 0

11 Story Story first case, the ratio of max / 0 at b/r =.5 was ot give, so the ratios were obtaied by a liear iterpolatio betwee b/r =. ad.3. Effect of trasverse frames (Case versus Case ) The lateral resistace of trasverse frame is expected to reduce the ratio of max / 0. However, the pla aspect ratio also affects the ratio of max / 0. Whe the pla aspect ratio icreases from to i Case with icreasig the ratio of a (=K /K ), the ratios of max / 0 icrease. The ratios of max / 0 for Case -Pla type I armaller tha those for Case regardless of the height of thtructure, while the ratios of max / 0 for Case -Pla type II arimilar or larger tha those for Case. Compariso betwee SDOF ad MDOF (Case versus Case 3) The ratios of max / 0 for the MDOF system are larger tha those for SDOF system except the case of PI-5. The ratios of max / 0 i Case i the VC rage (0-story) armaller tha those i the AC rage (5-story), while the ratios of max / 0 i Case 3 icrease as the umber of story icreases. This differece is due to their havig differet vertical modal distributios i the first two coupled modes as show i Fig. 9. Table 5. Compariso of seismic drift demads max / 0 Pla a DOF Case e typx /B b/r b x /r AC* VC* (K /K ) (5-story) (0-story) Logitudial frames oly 0% Case -.5 (Lam et al., 06) 5% Both logitudial ad 0% SDOF I trasverse frames 5% Case.5 (Fig. 6(a) ad (b), 7 (a) 0% II ad (b)) 5% % I Both logitudial ad 5% MDOF Case 3.5 trasverse frames 0% II 5% * 5-story ad 0-story structures are related with the acceleratio ad velocity cotrolled coditios (AC ad VC) SDOF-st SDOF-d MDOF-st MDOF-d 0. Normalized modal disp SDOF-st SDOF-d MDOF-st MDOF-d 0. Normalized modal disp. (a) Acceleratio cotrolled coditio (5-story) (b) Velocity cotrolled coditio (0-story) Fig. 9 Vertical modhapes i the first two coupled modes

12 4. CONCLUSIONS Theismic drift demad of the torsioally-ubalaced structures i lowseismicity regios is estimated accoutig for torsioal resistace by trasverse frames is estimated i this paper. The followigs are mai features of this paper: () The maximum edge displacemet ratios, max / 0, at the flexible edges of two torsioally ubalaced structures with a differet pla aspect ratio, ad, are preseted by icreasig thtatic eccetricities, x /B, up to 50% by the structural respose to acceleratio, velocity, ad displacemet cotrolled excitatios. I the acceleratio ad velocity cotrolled coditios, the max / 0 ratio at the flexible edge liearly icreases as the value of icreases, which exceeds.0 at = 5% i the acceleratio cotrolled coditio. I the displacemet cotrolled coditio, however, the max / 0 ratio is less tha the upper limit of.3 ad.5 for the pla aspect ratio ad, respectively, regardless of the value of torsioal stiffess. () The torsioal resistace by the trasverse frame is expected to reduce the ratio of max / 0. For the pla aspect ratio, the ratios of max / 0 accoutig for the torsioal resistace by the logitudial ad trasverse frames are 80~90% of those accoutig for the torsioal resistace by the logitudial frame oly. However, the pla aspect ratio (geometric property) also affects the ratio of max / 0. As the pla aspect ratio icreases from to with icreasig the torsioal resistace of trasverse frame, the ratios of max / 0 icrease over those accoutig for the torsioal resistace by the logitudial frame oly. (3) The drift demads obtaied from the plaar aalysis approach usig the SDOF structure were verified by performig liear time history aalyses usig the MDOF system. Nie iput groud motios werelected correspodig to the desig earthquake i Korea. The mea ratio of max / 0 for the MDOF system are larger tha those for SDOF system, ad the ratio icreases up to approximately 5% with the icreasig the umber of stories from five to te. The differece is due to their havig differet vertical modal distributios i the first two coupled modes. ACKNOWLEDGMENTS The research preseted herei was supported by the Natioal Research Foudatio of Korea (NRF-06RCB06653 ad NRF-07RDAB ) ad the Korea Uiversity Grat. The authors are grateful for thesupports. REFERENCES America Society of Civil Egieers (00), Miimum desig loads for buildigs ad other structures, ASCE/SEI 7-0, Resto, Virgiia, US.

13 Architectural istitute of Korea (AIK) (06), Korea Buildig Code. KBC 06, Seoul, Korea. (I Korea) Hwag, K.R., Lee, H.S. ad Ali, A.R. (06), Assessmet of seismic drift i torsioallyubalaced buildigs accoutig for torsioal resistace by trasverse frames, The 8th SEEBUS, d December, 06, Taia, Taiwa. Lam, N.T., Wilso, J.L. ad Lumatara, E., (06), Simplified elastic desig checks for torsioally balaced ad ubalaced low-medium rise buildigs i lower seismicity regios, Earthquakes ad Structures, (5), pp Lee, H.S. ad Hwag, K.R. (05), Torsio desig implicatios from shake-table resposes of a RC low-rise buildig model havig irregularities at the groud story, Earthquake Egieerig & Structural Dyamics, 44, PEER (0), Pacific Earthquake Egieerig Research (PEER) NGA Database, Available from: [accessed o Jue 07]. 3