THE SEISMIC RESPONSE CHARACTERISTICS OF A NEW STRUCTURAL CONFIGURATION

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1 THE SEISMIC RESPONSE CHARACTERISTICS OF A NEW STRUCTURAL CONFIGURATION u a Zhag 1 iagu Qi ad Shel Cherry 3 1 Professor, Departmet of Civil Egieerig, Northwester Polytechical Uiversity, i a, Chia. PhD Studet, Departmet of Civil Egieerig, Northwester Polytechical Uiversity, i a, Chia 3 Professor, Departmet of Civil Egieerig, the Uiversity of British Columbia, Vacouver, Caada ABSTRACT : iaopig@wpu.edu.c I this paper a ew kid of structural cofiguratio, amed passive mega-sub cotrolled structure (PMSCS), is preseted, which is costructed by applyig the structural cotrol priciple ito structural cofiguratio itself, to form a ew structure with obvious respose self-cotrol ability. I the aalysis of PMSCS the equatios of motio of the seismically excited system are developed. The seismic respose cotrol effectiveess of the proposed PMSCS uder statioary ad ostatioary radom processes was evaluated by comparig its seismic respose with the respose of its covetioal (ucotrolled) mega-sub structure couterpart. A parametric study of the relative stiffess betwee the mega-frame ad substructure of the PMSCS is preseted ad discussed. The regio over which these structural characteristics yield the optimum seismic respose cotrol of the PMSCS is idetified ad serves as a very useful desig tool for practitioers. The results show that the proposed PMSCS offers a effective meas of cotrollig the seismic displacemet ad acceleratio respose of tall/super-tall mega-systems. KEYWORDS: Passive mega-sub cotrolled structure, seismic excitatio, structure respose, cotrollig effectiveess, relative stiffess 1. INTRODUCTION Oe of the maor egieerig challeges i the desig structures is to esure their structural itegrity uder extreme earthquake ad wid loads, ad their huma comfort uder ormal wid loads. Mega-sub structure (MSS) is a ew cofiguratio form of super tall buildig appeared recetly. The MSS cosists of two maor compoets: a mega-frame, which is the mai structural frame i the buildig, ad several substructures are rigidly coected to the mega-frame, each cotaiig may storeys that are used for commercial ad/or residetial purposes, as show i Fig.1. I this paper, a ew passive mega-sub cotrolled structure (PMSCS) cofiguratio is proposed based o covetioal MSS,as show i Fig.. I the desig of the PMSCS, the coectios betwee the mega-buildig ad the substructures were released, these sub structures are desiged as isolated sub structures, whose fuctio is similar to that of the covetioal tued mass damper system i priciple. It acts to covert the traditioal MSS ito a huge, self-cotrolled, passive mega-sub cotrolled structure that is capable of developig very high cotrol eergy to cotrol the resposes iduced i the PMSCS by these atural forces by the structure itself. The mass ratio betwee the sub ad mega structures is much higher (as high as 100%) tha that i the tued mass damper system (usually 1%). It is this feature that makes the proposed structure to cotrol the resposes much more effective. To overcome shortcomigs exhibited i

2 巨型框架 The 14 th earlier proposed mega-sub cotrolled structural cofiguratios by other scholars [Feg ad Mita 1995, Chai ad Feg 1997, La et al 00], additioal colums are itroduced at the top-level of some of the substructures serve to elimiate the shortcomigs associated with the excessively large-spa mega-beams. I additio, dampers (or amed as added dampers) are istalled betwee the mega-frame ad its substructures to prevets poudig betwee the mega-frame ad its substructures. I this paper, the dyamic behavior ad the respose cotrol effectiveess of this ew proposed PMSCS uder seismic excitatios is examied. A parametric study of the structural characteristics that ifluece the respose cotrol of this system is udertake ad leads to the defiitio of the structural parameter regio that should be satisfied to esure optimum seismic respose cotrol. mega-frame mega-frame sub-frame mega colum mega beam dampig device additioal colum sub-frame Figure 1 The covetioal mega-sub structure Figure The ew PMSCS cofiguratio. EQUATIONS OF MOTION OF PASSIVE MEGA-SUB CONTROLLED STRUTURE UNDER SEISMIC ECITATION adc s, z adc s, z adk s adk s-1-1 s= s-1 i z z adc 1, z adc1, z-1 Figure 3 The computig model of the ew PMSCS

3 I this proposed PMSCS, both the mega-frame ad its substructures are modeled as MDOF systems, as show i Fig.3, adc i,k is added dampig value ad adk i is additioal colums stiffess value. A PMSCS havig mega-storeys ad s substructures, each of which cosists of z storeys movig relative to the mega-frame, will have a total of N= + system uder seismic groud motios ca be expressed as: s Z degrees-of-freedom. The relative-respose equatios of motio for this M && + C & + K = -Γ&& x g (.1) T T T T T where, = [ x, x, x,..., x ] is the lateral deformatio vector of the system relative to its movig base, p 1 S with + variables, ad s z x p T = [ xp,1, xp,, L, xp, ], xi T = [ xi,1, xi,, L, xi, z ] (i=1,,, s ) are the lateral deformatio vectors of the mega-frame ad i th substructure, respectively. M, K, C ad Γ expresses the global mass matrix, stiffess matrix, dampig matrix ad mass vector of the system respectively [Zhag. A., Zhag J. ad et al 005], ad & x& g is the simulated seismic groud acceleratio at the base of the structure. I the preset study, i equatio. (.),& x& is modeled as a statioary radom process whe A(t)=1, or as a uiformly g modulated radom process, whose ostatioary properties offer a more reliable represetatio of the characteristics of real earthquake groud motios. & = A( t) ( t) (.) x g where (t) is the statioary radom processes with zero mea, ad A(t) is the modulatig fuctio that defies the ostatioary radom process. Through the umerical computig check, the equatio (.1) with the matrix C caot be decoupled, as the decouplig ecessary ad sufficiet coditio [T.K.Caughey ad M.E.J.O Kelly (1965)] is ot met. Hece, the complex modal aalytical theory must be employed [Fag. T(1995)]. The power spectral desity (PSD) of the displacemet vector S ad the acceleratio vector S ( ω ) ca be obtaied by deducig. For statioary radom seismic excitatio, && S T T = u H ( ω) G S H ( ω) u (.3) 4 S & = ω S (.4)

4 where u = u,u, L, ] is the right eigevector matrix, G is the coefficiet matrix, S (ω) is the PSD of [ 1 un the statioary acceleratio excitatio actig o the base of the structural system, here the Kaai-Taimi model is used, ad H ( ω ) ad H ( ω ) are, respectively, the i th modal frequecy fuctio ad th modal cougate i frequecy fuctio of -ω [Zhag et al 005].For ostatioary radom seismic excitatio, & x& g is chose as the uiformly modulated radom processes, ad Shiozhuka-Sato modulatig fuctio A(t) is adopted, such that S ( t, ) = u S ( t, ω) u T ω Z (.5) T T S & ( ω ) = up[ S ] P u (.6) & Z& iz & S Z i (, ω), (, ω) (, ω), t = g i I i t I t S (.7) ( t, ω) = g Z i, A( t) S + pi S Z ( t, ω) i, i, S & p + p g, I ( t, ω) S A( t) i i i + gi, I ( t, ω) S A( t) p (.8) where S (ω) is the PSD correspodig to (t) i expressio (.), p i is its i th eigevalue, g i, are the elemets of the coefficiet matrix G, ad Ii ( t, ω ) i equatio.(.7) ad (.8) ca be expressed as: p it ( pi 1 ) t ( pi + + ) t Ii( t, ω α ω α ω ) = e [ e 1] + [ e 1] ( pi + α1 + ω) ( pi + α + ω) (.9) where α 1, α are two expoetial parameters of A(t).Fially, the displacemet ad acceleratio mea square respose values for statioary ad ostatioary seismic excitatio are: = σ S dω (.10) = σ & S & dω (.11)

5 3. NUMERICAL EVALUATION OF THE SEISMIC RESPONSE PERFORMANCE OF AN EAMPLE PASSIVE MEGA-SUB CONTROLLED STRUCTURE To ivestigate the performace of the passive mega-sub cotrolled structure, with referece to the covetioal mega-sub frame used i Tokyo City Hall preseted i Fig. 4a, a steel passive mega-sub cotrolled frame is desiged, as show i Fig. 4b. The two buildigs have the same amout of total mass ad the same structural members as listed i the referece [Zhag. A., Zhag J. ad et al 005]. The structure is comprised of three mega-storeys ad three, 10-storey substructures. Here, the lateral coectios betwee the substructures ad the secod ad third storeys of the mega-frame have bee released. The seismic respose cotrol effectiveess of the proposed PMSCS was evaluated by comparig its seismic respose with the respose of its covetioal (ucotrolled) MSS couterpart, is a measure of the cotrol effectiveess of the proposed PMSCS. I order to further examie the cotrollig effectiveess of this passive mega-sub cotrolled frame with differet sub structural stiffess, the relative stiffess ratio RK betwee the mega frame ad the sub structure are respectively defied as followig: RK K = (3.1) K * sub * mega Where * K sub the shear stiffess of sub structure, ad K * mega the bedig stiffess of mega frame. (a) The covetioal steel MSS cofiguratio (b) The steel MSCS cofiguratio Figure 4 The two structural cofiguratios 3.1. Seismic Respose for PMSCS Fig. 5 shows the compariso of the PSDs for the displacemet ad acceleratio respose of the top mega-mass of the PMSCS ad the top mass of the covetioal MSS, whe the relative stiffess ratio RK=0.17, ad the seismic excitatio is ostatioary. It shows that the PSDs of displacemet ad acceleratio resposes at the top mass of the ew proposed PMSCS are much smaller tha the correspodig resposes of MSS. It clearly

6 explaied that the release of coectios betwee the mega-frames ad substructures make the PMSCS system act as a self-cotrolled structure is capable of developig very high cotrol eergy to cotrol the resposes. Displacemet respose PSD / cm s at the top mass of the covetioal MSS at the top mega-mass of the PMSCS Acceleratio respose PSD / cm /s 3 at the top mass of the covetioal MSS at the top mega-mass of the PMSCS frequecy / Hz (a) The compariso of the displacemet respose PSD frequecy / Hz (b) The compariso of the acceleratio respose PSD Figure 5 The compariso of the PSDs for the displacemet ad acceleratio respose of the top mega-mass of the PMSCS ad the top mass of the covetioal MSS, as RK=0.17, uder ostatioary seismic excitatio RMS resposes of the mega-frame of the PMSCS; elevatio of structure / m elevatio of structure / m RMS resposes of the secod ad third substructure of the PMSCS; RMS resposes of the secod ad third mega storey of the covetioal MSS (a) Displacemet RMS respose cm cm/s (b) Acceleratio RMS respose Figure 6 Distributios of the RMS resposes alog the structural secod ad third mega storey elevatio of the PMSCS ad the MSS, as RK=0.13, uder ostatioary seismic excitatio. Figs. 6 illustrate the displacemet ad acceleratio root mea square (RMS) respose distributios of each mass poit i the secod ad third mega-storey of both the PMSCS ad covetioal MSS. The figures illustrate that the displacemet RMS resposes ad acceleratio RMS resposes are sigificatly reduced i the cotrolled structure, with the exceptio of few substructural acceleratio RMS respose. It also shows that the resposes are icreased from the bottom up of structure, ad the maximum appeared at the top mass. So we ca ivestigate the cotrollig characteristic ad cotrollig effectiveess by the topmost respose of structure. Fig.7 further presets the RMS compariso of the displacemet ad acceleratio resposes at the top mass of the PMSCS ad MSS, we ca fid that: (i) The RMSs resposes of displacemet ad acceleratio at the top mega-mass ad sub-mass of PMSCS are both decreased obviously compared with those of the covetioal MSS, it also reveals the predomiace of PMSCS at cotrollig the structure resposes. (ii) The RMSs resposes of displacemet ad acceleratio at the top mega-mass are smaller tha those at the top sub-mass of PMSCS, especially the displacemet. Because the mega-frame is composed of mega beams ad mega colums, thereby has a strog capability of resistig lateral forces, so the displacemet of mega-frame is smaller.

7 Displacemet RMS respose/ cm Acceleratio RMS respose / cm/s At the top sub-mass of the PMSCS At the top mega-mass of the PMSCS At the top mass of the covetioal MSS Time / s (a) Displacemet RMS resposes Time / s (b) Acceleratio RMS resposes Figure 7 The compariso of RMS resposes of the two structures, as RK=0.17, uder ostatioary seismic excitatio. 3. Ifluece of Structural Stiffess Ratio o the Respose Ratio Displacemet RMS respose ratio Acceleratio RMS respose ratio At the top sub-mass/ o-statioary At the top sub-mass / statioary At the top mega-mass / o-statioary At the top mega-mass / statioary Relative stiffess RK Relative stiffess RK (a) The displacemet RMS respose ratio (b) The acceleratio RMS respose ratio Figure 8 The ifluece of the structural relative stiffess ratio RK o the RMS respose ratio RR I order to further ope out the respose cotrollig effectiveess of PMSCS, the respose ratio, RR, for the two structures is defied as: RR= the RMS respose of the PMSCS / the RMS respose of the covetioal MSS. Figure 8 presets the RMS respose ratio of displacemet ad acceleratio at the top mega-mass ad top sub-mass of PMSCS as the relative stiffess ratio RK=0~1. I this figure, the dotted lies ad dash-dot lies represet the RMS respose ratios of the top sub-mass ad the top mega-mass, uder the simulated ostatioary seismic excitatio. The dashed lies ad solid lies preset the RMS respose ratios at these same locatios, correspodig to the simulated statioary groud acceleratio. Figure 8 illustrates that: (1) Whe RK=0.1~0.3, the displacemet of mega-frame ad substructure is decreased evidetly, i this areas there exits a obvious cotrollig effectiveess for displacemet; the acceleratio is also decreased, but of substructure the cotrollig effectiveess is go to the bad comparatively whe RK=0.~0.3. () Whe RK 0.7, the cotrollig effectiveess of displacemet ad acceleratio resposes are all bad, so much as bigger tha covetioal MSS of substructural acceleratio. It idicates that there is take o defiite couplig domio effect betwee the cotrollig effectiveess ad the relative stiffess ratio of structure. (3) It ca be see that the cotrollig effectiveess of PMSCS is iflueced greatly by the relative stiffess ratio RK. For ostatioary radom seismic excitatio, whe RK=0.17, the displacemet respose ratio RR of mega-frame is 31% ad of substructure is 81%; the acceleratio respose ratio RR of mega-frame is 45% ad of

8 substructure is 48%.The resposes are all decreased to a great extet. So ratioal distributio of stiffess betwee mega-frame ad substructure should be cosidered i order to achievig the optimal cotrollig effectiveess whe desig the PMSCS. (4) Fig. 8 also illustrate that the RMS respose ratios calculated o the basis of the simulated statioary ad ostatioary seismic iputs are very early the same. This suggests that the statioary radom seismic simulatio process ca be used to approximate closed to the seismic respose cotrol effectiveess of the proposed PMSCS i practical egieerig desig, to reduce the computig time cosumedly. 4. CONCLUSION A ew structural cofiguratio of the practical passive mega-sub cotrolled frame is proposed for super tall buildigs, which employ the mega-sub structural cofiguratio to form a huge passive cotrollig structural system. The aalytical ad umerical studies udertake i this paper illustrate that the proposed passive mega-sub cotrolled system cofiguratio acts as a self-cotrolled structure that is capable of dissipatig large amouts of eergy iduced i the system by seismic groud motios. The displacemet ad acceleratio resposes of the proposed PMSCS are very much smaller tha those of the covetioal buildig MSS. The respose ratio, RR, of the displacemet respose at the top mega-mass ad top sub-mass i the example PMSCS ivestigated i this study were 31% ad 81%, respectively; the correspodig values for the acceleratio respose were 45 % ad 48 %. From these results it could be cocluded that this structural cofiguratio has a very strog ability i cotrollig displacemet ad acceleratio resposes. A proposed relative stiffess RK regio is first preseted which are usually used i practice desig, While RK is i some certai rage, such as 0.10~0.30, a remarkable cotrollig effectiveess ca be obtaied. However, as RK is greater tha 0.7, the cotrollig effectiveess is uacceptable. The optimum regio for the relative stiffess ratio, i which the passive mega-sub cotrolled structure resposes approximately reach their optimum (miimum) values, ca serve as a very useful tool for structural desigers. REFERENCES Chai. W. ad Feg. M. Q. (1997). Vibratio cotrol of super tall buildigs subected to wid loads. It J. No-liear Mechaic. 3:4, 657~668. Feg. M. Q. ad Mita. A. (1995). Vibratio cotrol of tall buildigs usig mega-sub cofiguratio. ASCE. Joural of Egieerig Mechaics. 11:10, 108~1087. La Z., Fag L. ad Wag. (00). Multifuctioal shock-absorptio system of RC megaframe structures. Idustrial Costructio. 3:, 1~4. Zhag u'a, Zhag Jiali, Wag Dog ad Jiag Jiesheg.(005). The Cotrollig Characteristics of Passive Mega-sub Cotrolled Frame Subected to Radom Wid Loads. Joural of Egieerig Mechaics. ASCE :10, Caughey, T.K ad O Kelly, M. E. J. (1965). Classical ormal modes i damped liear dyamic systems. Joural of Applied Mechaics ASME. 3, Fag.T. (1995). Egieerig radom vibratio. First editio, The Press of Natioal Defese Idustry, Beiig.