COINCIDENT VERTICAL RESPONSE ANALYSIS OF STRUCTURE AT MAXIMUM HORIZONTAL RESPONSE

Transcription

1 3 th Wold Confeence on Eathquake Engineeing Vancouve, B.C., Canada August -6, 4 Pape No. 433 COINCIDENT VERTICAL RESPONSE ANALYSIS OF STRUCTURE AT MAXIMUM HORIZONTAL RESPONSE Tomoyo TANIGUCHI, Mitsuu TAKESHITA SUMMARY A spectum-basis esponse analysis fo evaluating the vetical esponse with which coincides maximum hoizontal esponses of stuctues subected to hoizontal and vetical gound motions is developed. The atio of esponse coincidence, the vetical esponse to its absolute maximum at the maximum hoizontal esponse, is intoduced to expess the intensity and diection of the coincident vetical esponse. The atio foms a cetain pobabilistic distibution egadless of types of eathquake, soil, stuctue and lineaity/non-lineaity of stuctual estoing system popeties. The combination of the maximum expected value of the atio based on the allowable pobability of exceedance and the modal esponses enables to compute the maximum expected coincident vetical esponse at the instance of the maximum hoizontal esponse. INTRODUCTION To accomplish competent stuctues with minimizing seismic hazads, it is pudent to design fo the wost case, which takes into account the simultaneous esponse on each stuctual axis. Unlike numeical integation techniques, no method is available to calculate exact quantities of stuctual esponses at a specific time of inteest. The tanslational gound motion is usually esolved into thee components; two in the hoizontal plane and one in the vetical diection, and otational gound motions ae neglected. The peak esponse of stuctues due to each component of the gound motion is commonly evaluated by means of the esponse spectum method. Hee, the poblem aises if such a sepaate evaluation can appopiately povide a sevee esponse to be veified in designing the seismic esistance system of stuctues, although the simple combination of these sepaate evaluations gives suely the seveest case. Howeve, the senio autho pointed out the aeness of the esponse coincidence between maximum hoizontal and maximum vetical components viewing fom the pobability of occuence [,, 3]. Moeove, applying the seveest case fo Associate Pofesso, Depatment of Civil Engineeing., Tottoi Univesity, Tottoi, Japan. t_tomoyo@cv.tottoi-u.ac.p Enginee, Shimane Pefectual Govenment, Matsue, Shimane, Japan. takeshitamitsuu@pef.shimane.p

2 all stuctue needs caeful consideation, because the ecent knowledge shows that the stuctues should possess the easonable stength accoding to thei impotance. Howeve, the mao seismic design codes do not have any solution in tems of combination of stuctual esponses [4, 5, 6]. As the beginning of seies eseach and owing to the lage numbe of paametes involved in this poblem, the scope of this investigation is limited to the stuctues subected to the hoizontal and vetical gound motions. The ecent study of seismic damages implies impotance of consideation fo the vetical esponse and coesponding esponse analysis methods wee poposed [7, 8, 9]. The obective of this pape is to develop the analysis method fo evaluating the vetical esponse of stuctue, with which coincides the maximum hoizontal esponse of stuctue. The poposed method is based on the esponse spectum method with assistance of the pobability of esponse coincidence, which expesses the intensity and diection of the coincident vetical esponse, since the esponse spectum has no infomation about the time space such as when the hoizontal esponse eaches its maximum. This pape implicitly assumes that the citical esponse occus at the maximum hoizontal esponse of stuctues. COINCIDENT VERTICAL RESPONSE ACCELERATION ON SINGLE SPRING-MASS SYSTEM To find fundamental popeties of the vetical esponse of the stuctue at the instance of its maximum hoizontal esponse, the chaacteistics of esponse intensity and diection ae examined with a simple sping-mass system. This is because the popeties can be immediately applied to designing a simple stuctue and may be done in pediction of the vetical esponse of multi-stoy stuctues. Conside the single sping-mass system (SSM system), which possesses independent feedom in both hoizontal and vetical diections with % stuctual damping. The mass and sping ae specified to have pedefined natual peiod whose ange is set fom. to. second with.-second intevals in both diections, espectively. The hoizontal estoing system has thee types of sping popeties; linea, bilinea and slip type, which ae adopted accoding to the analysis pupose. This is because most inelastic stuctual behavio can be explained by the combination of these sping types []. The inelastic egion consideed is up to in the ductility facto, which may be enough accoding to ecent study on seismic damages []. In contast, the vetical estoing system maintains its lineaity despite the extent of hoizontal esponse. This study uses 4 acceleogams ecoded aound Japan that ae disseminated by National Infomation Cente fo Eathquakes and Disastes []. Accoding to the classification of soil types [6], 34 of 4 ae ecoded on the had soil (the natual peiod of the soil is less than. second); 9 of 4 ae on the soft soil (ove.6 second); and 4 of 4 ae on the medium soil (between. second and.6 second). This investigation compiles statistics on the atio, λ, of the coincident vetical esponse acceleation & z V + & y to the absolute maximum vetical esponse acceleation & z V + & y at the instance when the max hoizontal esponse acceleation eaches its absolute maximum acceleation & z H + & x. Hee, x and y ae max the hoizontal and vetical displacements of the SSM system, espectively. & z& H and & z& V ae the hoizontal and vetical gound acceleations, espectively (See Figue (a)). Fom the combination of the natual peiod of the SSM system, the numbe of expeiments fo a set of acceleogams is,. && zv + && y λ = at the instance of & z x max && z + && H + & () y V max

3 y x & z& V & z& H y x unit[mm] (a) Single sping-mass model (b) Multi-stoy stuctue model Model n m p q 5-stoy 5,, 5-stoy 5 6, 3 8, 3-stoy 3, 4 4, (c) Dimension of actual sections 5-stoy 5-stoy 3-stoy stoy section stoy section stoy section -3 55X55-3 7X7-8X X5 4-6X6 3-75X X X X X5 (d) Dimension of unealistic sections 5-stoy 5-stoy 3-stoy stoy section stoy section stoy section -5 6X6-5 65X65-3 7X7 FIGURE. ANALYTICAL MODELS AND THEIR STRUCTURAL DETAILS Fom this definition, λ is positive while the SSM system esponses upwad and λ is negative while the SSM system esponses downwad, and its ange is fom. to.. Figues (a) to (c) show the pobability density of λ along the specific ank of λ, while the hoizontal estoing system is the linea type. The pobability density λ is classified accoding to the soil type. Figues 3(a) to 3(c) show the pobability density of λ fo all ductility factos on each soil type, while the hoizontal estoing system is the bi-linea type. Figues 4(a) to 4(c) show the pobability density of λ fo all ductility factos on each soil type, while the hoizontal estoing system is the slip type. In computation of inelastic esponse, a set of ecoded acceleogams is amplified until the hoizontal esponse eaches the specific ductility. Fom these figues, the following emaks ae dawn.

4 ) The atio may be independent of the natual peiod of SSM system. ) The atio may be independent of the scale of eathquake. 3) The atio may be independent of the type of eathquake. 4) The atio may be independent of the type of soil. 5) The atio may be independent of the extent of inelastic esponse. 6) The atio may be independent of the sping type of estoing system. 7) The atio may have pobabilistic popeties egadless of paametes concened heein. (a) Had soil (b) Medium soil (c) Soft soil : Had soil, +: Medium soil, : Soft soil, -: appoximation FIGURE. PROBABILITY DENSITY OF λ (LINEAR TYPE) (a) Had soil (b) Medium soil (c) Soft soil : ductility facto=., +: ductility facto=3., : ductility facto=5., x: ductility facto=., : ductility facto=., -: appoximation FIGURE 3. PROBABILITY DENSITY OF λ (BI-LINEAR TYPE) (a) Had soil (b) Medium soil (c) Soft soil : ductility facto=., +: ductility facto=3., : ductility facto=5., x: ductility facto=., : ductility facto=., -: appoximation FIGURE 4. PROBABILITY DENSITY OF λ (SLIP TYPE) The pobability densities can be modeled by a beta distibution. Table shows the vaiance of each pobability density accoding to analytical conditions. Geneally, the vaiance becomes smalle when the natual peiod of soil and/o the ductility factos become lage. Howeve, since we can not find a paticula tend in them, we take the mean value.4 as thei epesentative value. In addition, the solid line on each figue is the beta distibution, which epesents the pobability densities of all case, whose

5 vaiance is.4 while the mean is zeo. Based on this pobabilistic investigation, the following emaks ae also yielded. ) The maximum vetical esponse acceleation may aely coincide with the maximum hoizontal esponse acceleation. ) Most of vetical esponse acceleations ae about zeo at the instance when the hoizontal esponse acceleation eaches its maximum acceleation. Theefoe, applying maximum hoizontal and vetical esponses in veification of the lateal stength of a simple stuctue independently o simultaneously may yield unde- o oveestimation of actual seismic event. The senio autho epoted the same emaks based on the linea analysis [,, 3]. TABLE VARIANCE OF λ Sping type Had soil Medium soil Soft soil Liniea type Bilinea type Slip type ductility ductility Moeove, since the atio of esponse coincidence maintains its pobabilistic popeties despite types of hoizontal estoing system, the poposed method can calculate the vetical esponse to be combined with the hoizontal esponse fo evaluating the ultimate lateal stength of the membe based on such as the enegy-consevation-ule. COINCIDENT AXIAL FORCES ON MULTI-STORY STRUCTURES Pactitiones need to know a pai of membe foces to veify the seismic esistance system of stuctues. In multi-stoy stuctues, the pactitione would like to know the column axial foce induced by the vetical gound motion, with which coincides the maximum column moment and coesponding axial foce induced by the hoizontal gound motion. The pevious investigatos pointed out the necessity of consideation of the coincident column axial foce fo stictly evaluating the seismic esistance system and its analysis method has been vigoously investigated [7, 8, 9]. This section pobabilistically investigates the atio, µ, of the coincident axial foce A to its maximum axial foce of column A when the moment of the column eaches its absolute maximum moment M. max max A µ = at the instance of max A max M ()

6 The suffix distinguishes the column of inteest. This investigation uses thee building models with diffeent stoies and spans and % stuctual damping illustated in Figue (b) and 4 acceleogams. The section of each column, which is followed actual building design, is also shown in Figue (c). Thei natual fequencies of the fist mode ae.53 second fo 5-stoy,.4 second fo 5-stoy and.9 second fo 3-stoy, espectively. To highlight effects of column stiffness on the pobability densities, thee buildings with the same configuations but unifom stiffness in height, that ae athe unealistic, ae also consideed (See Figue (d)). By the linea analyses with actual and unealistic sections, the pobability densities of the coincident axial foces at top, middle and base of the left column and its adacent column ae examined. In contast, using thee buildings with the actual section, the pobability densities of the coincident axial foces when the hoizontal estoing system of these buildings columns ae bi-linea and slip types ae investigated. The inelastic egion consideed is up to in the ductility facto. The numeical analyses ae caied out by the softwae TDAP III []. Figues 5 to 7 ae esults of linea analyses and Figues 8 to 3 ae esults of inelastic analyses. Hee, accoding to esults of the SSM system, the soil type does not significantly contibute on the distibution of pobability densities. Theefoe, the esults of the coincident axial foces ae pocessed iespective of soil types. Figues 5(a), 5(b) and 5(c) show the pobability density of µ obseved at top, middle and base column of five-stoy building, espectively. Figues 6(a) to 6(c) and 7(a) to 7(c) show those of fifteen-stoy and thity-stoy buildings, espectively. The legends on each figue identify the section used and the column of inteest. Employing the bi-linea type in the hoizontal estoing system, Figues 8(a), 8(b) and 8(c) show the pobability density of µ obseved at top, middle and base column of five-stoy building. Figues 9(a) to 9(c) and (a) to (c) show those of fifteen-stoy and thity-stoy buildings, while Figues (a) to 3(c) show those of slip type. The legends in each figue identify the ductility factos consideed. Fom these figues, the following emaks ae yielded. ) The atio may be independent of the building configuations. ) The atio may be independent of the column stiffness. 3) The atio may be independent of the location of column. 4) The atio may be independent of the scale of eathquake. 5) The atio may be independent of the type of eathquake. 6) The atio may be independent of the type of soil. 7) The atio may be independent of the extent of inelastic esponse. 8) The atio may be independent of the sping type of estoing system. 9) The atio may have pobabilistic popeties egadless of paametes concened heein : Actual section, x: Unealistic section, : Adacent column, -: appoximation FIGURE 5. PROBABILITY DENSITY OF µ (5-STORY, LINEAR TYPE)

7 : Actual section, x: Unealistic section, : Adacent column, -: appoximation FIGURE 6. PROBABILITY DENSITY OF µ (5-STORY, LINEAR TYPE) : Actual section, x: Unealistic section, : Adacent column, -: appoximation FIGURE 7. PROBABILITY DENSITY OF µ (3-STORY, LINEAR TYPE) : ductility facto=., +: ductility facto=3., : ductility facto=5., x: ductility facto=., : ductility facto=., -: appoximation FIGURE 8. PROBABILITY DENSITY OF µ (5-STORY, BI-LINEAR TYPE) : ductility facto=., +: ductility facto=3., : ductility facto=5., x: ductility facto=., : ductility facto=., -: appoximation FIGURE 9. PROBABILITY DENSITY OF µ (5-STORY, BI-LINEAR TYPE)

8 : ductility facto=., +: ductility facto=3., : ductility facto=5., x: ductility facto=., : ductility facto=., -: appoximation FIGURE. PROBABILITY DENSITY OF µ (3-STORY, BI-LINEAR TYPE) : ductility facto=., +: ductility facto=3., : ductility facto=5., x: ductility facto=., : ductility facto=., -: appoximation FIGURE. PROBABILITY DENSITY OF µ (5-STORY, SLIP TYPE) : ductility facto=., +: ductility facto=3., : ductility facto=5., x: ductility facto=., : ductility facto=., -: appoximation FIGURE. PROBABILITY DENSITY OF µ (5-STORY, SLIP TYPE) : ductility facto=., +: ductility facto=3., : ductility facto=5., x: ductility facto=., : ductility facto=., -: appoximation FIGURE 3. PROBABILITY DENSITY OF µ (3-STORY, SLIP TYPE)

9 The pobability density can be modeled by a beta distibution. Table (a) to (c) show the vaiance of pobability density accoding to the hoizontal estoing system types. As obseved on the SSM system, since we can not find a paticula tend in them, we take the mean value.47 as thei epesentative value. In addition, the solid line on each figue is the beta distibution, which epesents the pobability density of all cases, whose vaiance is.47 while the mean is zeo. Based on this pobabilistic investigation, the following emaks ae also yielded. ) The maximum axial foce may aely coincide with the maximum moment. ) Most of axial foces ae about zeo at the instance when the moment eaches its maximum. Theefoe, applying the maximum moment induced by hoizontal shaking and maximum axial foce induced by vetical shaking in veification of the lateal stength of stuctual membe independently o simultaneously may yield unde- o oveestimation of actual seismic event. Regading the multi-stoy stuctues, the emaks on the liteatue by the senio autho slightly diffe fom those on above [3]. These aise fom the shotage of analytical cases. TABLE (a) VARIANCE OF µ (LINEAR TYPE) 5-stoy 5-stoy 3-stoy Base Middle Top Base Middle Top Base Middle Top Actual section Unealistic section Adacent column TABLE (b) VARIANCE OF µ (BI-LINEAR TYPE) ductility facto 5-stoy 5-stoy 3-stoy Base Middle Top Base Middle Top Base Middle Top TABLE (c) VARIANCE OF µ (SLIP TYPE) ductility facto 5-stoy 5-stoy 3-stoy Base Middle Top Base Middle Top Base Middle Top It is woth to note that the pobability density of µ is almost the same as λ with the easonable accuacy despite analysis conditions consideed heein. It implies that the chaacteistics of the coincident axial foce on multi-stoy stuctues have inheited ones of the coincident vetical esponse acceleation

10 obseved on the SSM system. It suggests the possibility of the application of the supeposition of modal esponse fo estimating the coincident axial foces of abitay columns that ae induced by vetical gound motion. APPLICATION OF MODAL ANALYSIS TO COINCIDENT AXIAL FORCE ANALYSIS Since the same pobabilistic popeties appea in both the coincident vetical esponse acceleation of SSM system and the coincident axial foce of column of multi-stoy stuctues, the application of the modal analysis to pedict the coincident axial foce of the column is examined. This section examines the applicability of the modal analysis to the analysis of the coincident axial foce of multi-stoy stuctues at the instance of the maximum moment of the column. The modal analysis is known as computing a maximum axial foce at the th floo column ( A ) max of the n-stoy stuctue with assistance of esponse spectum. n n ( A ) = M s Vs V SVA ( V hv ) max β ω, φ = = (3) s Hee, M s = the concentated mass at s th floo, φ s = the modal vecto at s th floo in th mode, β = the paticipation facto in th mode, ω = the natual fequency of th mode, h = the damping coefficient of th mode, S A = the value of acceleation esponse specta in coesponding conditions. The suffix V shows quantities of inteest ae in a vetical diection. It is noted that the modal analysis holds no paticula advantage ove the numeical integation technique if an exact answe is desied. Thus it is desiable to use the modal analysis pocedue only to compute the maximum modal esponses athe than a complete time histoy of esponse, and supepose the modal maxima to obtain an uppe bound on the tue esponse. Moeove, the modal analysis does not deal with the time space and, hence, povides no answe to the questions such as when the esponse eaches its maximum. This implies that applying the modal analysis to the coincident axial foce analysis shall constitute without efeing any infomation fom the time space. On the contay, an assumption, which all hoizontal modes each thei maxima simultaneously, enables to combine the atio of the esponse coincidence with the modal analysis of multi-stoy stuctues. The vetical esponse acceleation of the th mode { S VA ( ω v, hv )} coin at the instance of the maximum hoizontal esponse acceleation of any mode can be calculated as; Hee, S (, h ) { SVA ( ω v hv )} = SVA ( ω v, hv ) λ coin, (4) VA ω v v is a value of the vetical esponse spectum, which gives a modal maximum and is egulatoy specified. λ is the atio of the coincident vetical esponse acceleation to the maximum vetical esponse acceleation in th vetical mode at the instance of the maximum hoizontal esponse acceleation of any mode. The detemination pocedue of λ is discussed late. The substitution of Eq. (4) into Eq. (3) gives a coincident axial foce at the th column ( A ) coin.

11 n n ( A ) = s Vs V { VA ( V V )} coin M β S ω, h φ = = (5) coin s Fom the pobabilistic popeties of λ descibed ealie, the atio is independent of types of eathquake, soil and stuctue, Eq. (5) can be ewitten as; n n ( A ) = M sφvs βv SVA ( ωv, hv ) coin λ = = (6) s The deivation of Eq. (6) also employs anothe assumption that setting the atio λ to each mode is invalid because the pobabilistic occuence of all modes shall be equally teated. The calculation of the ensemble aveage of Eq. (6) yields an expected coincident axial foce at the th column ( A. ) coin n n ( A ) = M sφvs βv SVA ( ωv, hv ) coin λ = = (7) s Hee, < > denotes the opeation of the ensemble aveage. Since the pobability density of λ can be appoximated as the beta distibution, the tem elated to λ gives the standad deviation of λ. Hee, p ( λ) is given as; = q λ λ p( λ) dλ = q + q + (8) + ( ) q ( λ + ) ( λ) ( q, ) q+ p λ =, λ (9) B Hee, q = =.9. Equation (8) means that the mean powe of λ is given by the oot-mean-squae value, which is the same oot of the modal analysis. It enables to combine the atio of esponse coincidence with the modal analysis. In addition, the theoy of exteme value distibution can be applied to this poblem, and the maximum expected value of the atio, λ, should be detemined by the pobability of passage of a theshold, denoted the allowable pobability of exceedance. Computing the coincident axial foce though this appoach means that the vetical esponse of stuctues is pobabilistically pedicted backed up by the pobability of occuence. The pactitiones implement the seismic design with ealistic esponses and the stuctual safety is explicitly secued unde a cetain pobable condition []. Viewing fom this sense, setting the allowable pobability of exceedance should be elated to the impotance of and/o the allowable damage of stuctues. Howeve, it is out of intent of the pape. Figue 4 shows the pobability of λ and its values coesponding to the allowable pobability of exceedance. Using linea stuctues with the ealistic column sections and setting the 5% allowable pobability of exceedance, the analytical accuacy of the poposed method is examined. The abscissa of Figue 5(a) to (c) shows the exact coincident axial foce of column of inteest computed by the numeical integation technique, while thei odinates show that computed by the poposed method. The numbe of appoximated axial foce, which exceeds exact axial foce, is within the numbe specified by the allowable

12 pobability of exceedance assumed. Theefoe, the poposed method can adequately calculate an uppe bound of the coincident axial foce of column of multi-stoy stuctues. Moeove, since the pobabilistic popeties of the atio of esponse coincidence ae the same despite popeties of hoizontal esponse, the vetical esponse to be combined with the hoizontal esponse fo evaluating the ultimate lateal stength of the membe based on the enegy-consevation-ule can be calculated by the poposed method. Pobability Allowable pobability of exceedance λ %.798 3%.696 5%.63 %.55 FIGURE 4 PROBABILITY OF λ AND ITS VALUES (a) Thitieth-stoy building Coincident axial foce by poposed method (MN).. top-had soil middle-had soil base-had soil top-medium soil middle-medium soil base-medium soil top-soft soil middle-soft soil base-soft soil.... Coincident axial foce by numeical integation (MN) (c) Fifth-stoy building (b) Fifteenth-stoy building Coincident axial foce by poposed method (MN) Coincident axial foce by numeical integation (MN) top-had soil middle-had soil base-had soil top-medium soil middle-medium soil base-medium soil top-soft soil middle-soft soil base-soft soil Coincident axial foce by poposed method (MN).. top-had soil middle-had soil base-had soil top-medium soil middle-medium soil base-medium soil top-soft soil middle-soft soil base-soft soil.... Coincident axial foce by numeical integation (MN) FIGURE 5 ANALYTICAL ACCURACY

13 CONCLUSION. Based on the esponse spectum with assistance of the pobability of esponse coincidence, the poposed method enables to compute the coincident vetical esponse of stuctue at the instance of maximum hoizontal esponse of stuctue.. The esponse coincidence is quantified as the atio, the vetical esponse to its absolute maximum at the maximum hoizontal esponse, which expesses the intensity and diection of the coincident vetical esponse. Its pobabilistic popeties ae investigated with the single sping-mass systems and multistoy stuctues. Despite types of eathquake, soil, stuctue and lineaity/ non-lineaity of stuctual esponse, the pobabilistic popeties of the atios of the single sping-mass systems and multi-stoy stuctues ae the same and fom a cetain beta distibution. 3. The combination of the modal esponses and the maximum expected value of the atio of esponse coincidence based on the allowable pobability of exceedance enables to calculate the maximum expected coincident vetical esponse. The poposed method is accuate, computationally simple and easy to implement in standad dynamic analysis. Howeve, the appopiate value of the allowable pobability of exceedance may be discussed view fom the stuctual impotance and/o the allowable damage of stuctues. 4. Since the atio maintains its pobabilistic popeties iespective of lineaity/non-lineaity of stuctual estoing system, the poposed method can compute the coincident vetical esponse to be combined with the hoizontal esponse fo evaluating the ultimate lateal stength by such as the enegyconsevation-ule. REFERENCES.. Taniguchi T, Muayama T, Mentani Y, Komoi H, Yoshihaa T. Slip veification method fo the flat-bottom cylindical shell tank duing eathquake. PVP, Seismic Engineeing, ASME, 999; 387: Taniguchi T., Muayama T., Mentani Y., Komoi H. and Yoshihaa T., Slip veification method fo the flat-bottom cylindical shell tank subected to hoizontal and vetical gound motion. Jounal of Stuctual Mechanics and Eathquake Engineeing, JSCE, ; 6(I-53): 95-5 (Japanese). 3. Taniguchi T. Vetical esponse of multi-stoy stuctues at the instance of maximum hoizontal esponse. PVP, Seismic Engineeing, ASME, ; 445-: Fo example, ANSI/ASCE 7-95, Minimum Design Loads fo Buildings and Othe Stuctues, Fo example, JEAG Technical Guidelines fo Aseismic Design of Nuclea Powe Plants, 987 (Japanese). 6. Fo example, Japan Road Association. Specifications fo Highway Bidges Pat V: Seismic Design, (Japanese). 7. Akiyama H, Yamada S. Response of multi-stoy fames subected to combined hoizontal and vetical gound motions. Jounal of Stuct. Const. Engng., AIJ, 99; 437: 5-57 (Japanese). 8. Uchida Y, Honbo A, Shintoku S. Effect of vetical gound motion on collapse behavio of buildings subected to eathquake excitations. Jounal of Stuct. Const. Engng., AIJ, ; 57: (Japanese). 9. Kusunoki K, Nakano R, Okada T. Effects of vetical gound motion on dynamic esponse of achitectual stuctue. Poceedings of Eathquake Engineeing, 997; 4: (Japanese).. Akiyama H. Eathquake-Resistant Limit-State Design fo Buildings (Japanese), Univesity of Tokyo Pess, 997. pp National Infomation Cente fo Eathquakes and Disastes, TDAP III ve... ARK Infomation Systems,.