Scientia Iranica� Vol� ��� Nos� ���� pp ����

c� Sharif University of Technology� April ���

Design Method and Feasibility Study

of Fully Actively Controlled Frames

A� Joghataie� and M�M� Asbmarz�

In this paper� results of a preliminary study on the feasibility of using an Active Tendon Control�ATC� mechanism for frame structures subject to earthquakes is presented� So far� the ATCmechanism has mainly been considered as a means for installation on structures to mitigatetheir response under severe loading� In this study� it is desired to evaluate the possibility of usingthe ATC mechanism to serve as the main means for the stability of frames against earthquakes�Hence� a methodology is presented for the integrated design of frames with ATC mechanisms�which is tested numerically� A number of �ve�� ten�� �fteen� and twenty�story steel frames areused for this purpose� To this end� �rst� each of the frames is designed in accordance with theUniform Building Code of Practice �UBC�� Then� the same structure is re�designed for its deadload only� but equipped with a number of ATC mechanisms that help the structure withstandearthquake loading� so that its overall behavior is similar to the UBC frame� This results in areduction of the cross�sectional dimensions and weight of the columns at the expense of providingthe required hydraulic actuator�s�� the sensory system� the controller chip�s� and the prestressedtendons� The ATC frame so designed is� then� considered to be equivalent or comparable to theUBC frame� Furthermore� the behavior of the ATC and UBC designs are compared�

INTRODUCTION

The attention of researchers in the area of activecontrol of structures� has been attracted mainly to�wards proposing new structural control algorithmsand mechanisms� including their assessment throughnumerical simulation� The interested reader mayrefer to Leipholz ��� and Soong ��� for more detailsabout classical and optimal control and� also� Joghataieand Ghaboussi ���� Ribakov et al� ��� Joghataie andVahidi ��� Bani�Hani and Ghaboussi ��� and the pro�ceedings of the Third World Conference on StructuralControl ��WCSC � �� ���� for a few examples of themore recently proposed active control methods andmechanisms� Some researchers have tried to provide amore realistic understanding of the idea of active struc�tural control through experimenting with reduced scalemodels of frame structures ������ �� Some attemptshave been made by a number of companies in Japan toinstall some sorts of hybrid and active mass damperson the top of several buildings there� as reported

�� Corresponding Author� Department of Civil Engineering�Sharif University of Technology� Tehran� I�R� Iran�

�� Department of Civil Engineering� Sharif University ofTechnology� Tehran� I�R� Iran�

in Spencer and Sain ����� However� little attentionhas been paid to the methodology of engineeringdesign� technology and the required hardware for theimplementation of active control mechanisms to realstructural systems and its related economics� Althoughit may seem too early to comment on these issues� aswe are still far from routinely constructing actively con�trolled structures� the provision of information in thisregard is essential in bringing the idea closer to realityby opening new discussions and viewpoints about howto try to make these ideas more practical� This studyis hoped to serve as another step towards this goal� Tothis end� through numerical simulations� a number offrames of di�erent heights were designed according tothe Uniform Building Code �UBC� ����� ����� Then�the same frames were designed for their dead loadsonly� However� they were equipped with one or severalactive tendon control �ATC� mechanisms to withstandearthquake� The methodology for designing ATCframes is detailed in the paper�

The instantaneous optimal control algorithm pro�posed by Yang et al� ����� was used for the derivationof control rules� Reduction in the weight of thematerial used� on the one hand� versus the requiredactuator�s� capacity�s� � tendon length� on the otherhand� is reported as the criteria for assessing the

Feasibility Study of Fully Actively Controlled Frames �

bene�t and cost of the active control strategy usedhere�

In the following sections� �rstly� a brief about theinstantaneous optimal control algorithm is presented�Secondly� the methodology of integrated design ofATC frames is provided� Results of the UBC andATC designs of a number of �ve�� ten�� �fteen� andtwenty�story frame structures are reported in detailand� �nally� some preliminary conclusions are drawnon the economics of the active tendon control strategy�compared to the conventional code�based design of theframes�

INSTANTANEOUS OPTIMAL CONTROLMETHOD

Amongst the many proposed control methods� theclosed�loop instantaneous optimal control is one of thesimplest� whilst one of the most suitable� for studiessuch as this� A thorough explanation of the method canbe obtained from Yang et al� ���� and Soong ���� Theprocedure for obtaining the control rule is explained asfollows� The equation of motion of a structure is�

Mx���t� �Cx��t� �Kx�t� � Du�t� �Ex��g �t�� ���

where t is time� ��� is derivative of �� with respect totime� M�C�K and D are the mass� damping� sti�nessand control location matrices� E is the earthquakelocation vector and x�t��x��g �t� and u�t� are the relativedisplacement vectors of the structure� with respect tothe ground� the ground acceleration and the controlforce� respectively� Next� an objective cost function isde�ned as�

J�t� � zT �t�Qz�t� � uT �t�Ru�t�� ���

where J�t� and z�t� are the cost function and statevectors� respectively� and Q and R are some weightingmatrices� which are positive semi�de�nite and de�nite�respectively� The state equation of the system can beexpressed as�

z��t� � Az�t� �Bu�t� �Hx��g �t�� ���

where A�D and H are found from M�C�K and D asfollows�

A �

� I

�M��K �M��C

��

B �

�

M��D

�� H �

�

M��E

�� ��

where I represents the unit matrix� By the optimiza�tion of J�t�� the control rule is obtained as�

u�t� � ���t���R��BTQz�t�� ��

where �t is the sampling period� i�e� the time intervalused for the updating of the control force� In this study�both Q and R matrices are considered diagonal as�

Q � Unit matrix � �I�� R � r�I�� ���

where r is the only parameter representing the cost�bene�t relation of the control job� Also� �t � � �seconds has been used in this research�

Feed�Back� Delay andStructure�Actuator�Tendons Interaction

As a �rst study on the subject of the integrated designof ATC frames� it was decided to assume the mostoptimistic conditions for the ATC system� This ismainly because it was desired to see the probable ad�vantages of the ATC design of frames as compared withthe conventional designs� Considering e�ects such asoutput feedback� time delay and lag and degradations�due to structure�actuator�tendon interaction� couldmake the results and� hence� the judgment about thepotential of the integrated design� more complicated atthis stage� On the other hand� it is expected that inthe near future� with more advancement in sensor andactuator manufacturing technology� the above issueswill be of much less signi�cance�

Hence� full state feedback was assumed availableto be used in the control algorithm where the statecould be obtained by integrating the acceleration mea�surements by accelerometers�

No time delay or lag was considered in the controlloop and� also� structure�actuator�tendon interactionwas not considered of signi�cance� It was assumedthat the actuators were capable of applying the force�dictated by the controller� on the structure� with greatprecision�

UBC DESIGN OF A FIVE�STORY FRAME

The �ve�story steel frame� shown in Figure �� wasdesigned in accordance with the UBC� where the deadloads on the �oors of the frame� the properties of itscolumns� the second moment of inertia �denoted by Ias determined to take the base shear according to theUBC� and the natural period of the frame �T � ����sec�� are also reported in the �gure� A small modaldamping ratio of �� was considered for all of themodes� Considering both economics and constructionconstraints� it was assumed desirable to use the samecross�section for the columns of the �rst three storieswhile changing them for the fourth and �fth �oors� asshown in the �gure� After its designing� the frame wassubjected to the El Centro ��� � S E� earthquake�with a Peak Ground Acceleration of �PGA� � ��� g�where g � the gravitational acceleration� The peak

� A� Joghataie and M�M� Asbmarz

Figure �� The �ve�story frame designed based on UBC�

inter�story drift and stress in this case have been foundto be ��� cm and �� MPA� respectively� This peakstress is obviously larger than the normal allowablestress of steel� which is about � MPA� This isbecause� in the UBC design� use is made of materialnon�linearity� Since� in this study� it was desired todesign an ATC frame equivalent to the UBC design�

it was assumed that when both of the frames hadthe same response under the assumption of materiallinearity� they could be considered equivalent� Again�this seemed a suitable assumption for the present studywhere a linear control algorithm was used to design theATC frames� It is possible to use non�linear controllers�such as neuro or fuzzy controllers� which are able tohandle non�linear control problems well �Joghataie andGhaboussi ���� Bani�Hani and Ghaboussi ����� However�the literature on the subject is still limited and suchcontrollers have been designed only for small frames ofup to � stories� The subject of non�linear control oflarger frames is an issue that could not be consideredin this paper�

Hence� the above peak inter�story drift and stressvalues ���� cm� �� MPA� were� then� also used forthe design of an ATC system for the frame�

ATC DESIGN OF THE FIVE�STORYFRAME

It was decided to control the frame by using onlyone actuator� which could apply a control force onone of the �oors� through prestressed tendons� Theframe in Figure �a� called here the uncontrolled frame�is di�erent from that shown in Figure �� which wasdesigned according to the UBC� since it has nowbeen designed for its dead load only� Hence� thecolumns are lighter and have smaller lateral sti�ness

Figure �� The �ve�story frame designed for its dead load only �a� Without ATC� �b� With ATC where the actuator is onthe ground and connected to the �rst oor� �c� With ATC where the actuator is on the ground and connected to the topoor� �d� With ATC where actuator is on the fourth oor and connected to the top oor�

Feasibility Study of Fully Actively Controlled Frames �

in this case� as represented in Figure �a� Also� thenatural vibration period of this frame is T � �����sec�� which is larger than that of the UBC designedframe� which is T � ���� sec� Figures �b to �drepresent � di�erent alternatives for the placementof the actuator and tendons on the uncontrolledframe�

The methodology and criteria used for the designof an ATC frame� with an equivalent performance toits UBC designed counterpart� is explained here�

Methodology of Integrated ATC Design ofFrames

The El Centro earthquake was assumed appropriateas the design earthquake for the ATC frames of thisstudy� However� in general� design earthquakes shouldbe selected depending on the seismicity of the region�soil properties� etc� For each of the � alternatives shownin Figures �b to �d� the actuator capacity was selectedso that the ATC frames could satisfy the following safedesign criteria�

Safe Design Criteria� Using the El Centro �� S E earthquake as the design earthquake� neither thepeak inter�story drift nor the peak internal stress inan ATC designed frame should exceed the peak inter�story drift and the peak internal stress in its UBQdesigned counterpart� as the allowable maximum driftand stress� respectively�

In all of the cases of Figures �b to �d� as well asin the rest of the study� shear frame models were usedand the e�ect of the vertical component of the controlforce was considered in the determination of the columnstresses�

In case �b� of Figure �� the actuator is installedon the ground and the tendons are connected to the�rst �oor� For case �c�� the actuator is again on theground but connected to the top of the frame and��nally� for case �d�� the actuator is on the fourth �oorand is connected to the top of the frame� Figure � isa graphical representation of the e�ect of r� the onlyinstantaneous optimal control parameter� as explainedbefore� on the peak inter�story drift and peak stressand required actuator capacity� which were obtainedfor each of the cases in Figures �b to �d� scaled bydividing to ��� cm� �� MPA and KN� respectively�Hence� the safe design criteria is satis�ed only whenthe inter�story drift and stress ratios for a given r areless than� or equal to� �� For each of these cases� an rvalue was found so that the criteria of a good control� asstated above� was satis�ed with the minimum possibleactuator capacity� This resulted in r � ����v� ��

and r � ����v� �� for cases �b� and �c� of Figure ��respectively� while� as can be concluded from Figure �c�an appropriate r value could not be found for the caseof Figure �d� In cases �b� and �c� of Figure �� the peak

Figure �� E�ect of r on the maximum drift stress andactuator capacity for each of the frames of Figures �bto �d when subjected to the El Centro earthquake�

inter�story drift is equal to ��� cm� which is equal tothe peak obtained in the dynamic analysis of the UBCdesigned frame subjected to the El Centro earthquake�With this drift� which controlled the design of theATC system� the peak stress was found to be ���MPA in both cases� which is less than �� MPA stressfound for the UBC design� The appropriate actuatorcapacity for each of the cases is� F � � KN forcase �b� and F � � KN for case �c� of Figure �� Asexpected� case �c� of Figure � is the optimum amongthe � alternatives for the placement of the actuator�Hence� it was selected as the basis for the rest of thestudy�

Testing the UBC and ATC Frames for OtherEarthquakes

To provide a better understanding of the performanceof the UBC and the ATC designed frames� theirresponse to di�erent test earthquakes was monitored�Since the El Centro earthquake� with PGA � ��� g�was used as the design earthquake� other earthquakeswith di�erent spectral displacements but with� ap�proximately� the same PGA� were used in testing�To this end� the Park�eld earthquake ������ S�E�with PGA � ��� g and � �������� � times thePacoima Dam earthquake ������ S��E� with PGA �� �������� ������ g � ��� g were selected� Also�the response of the frames to a number of sinusoidalground accelerations of di�erent periods in the rangeof ����� seconds� all with an amplitude of ��� g�were studied� Finally� to examine the reserved capacityof the frames� they were subjected to the severe

A� Joghataie and M�M� Asbmarz

earthquake of the unreduced Pacoima Dam with PGA� ���� g� Results are explained here�

Response to the Park�eld and �������� ��Pacoima Dam Earthquakes

Figure represents the time history of the responseof the frames to the Park�eld earthquake� which isapproximately of the same intensity as that of the ElCentro earthquake� but with a signi�cantly di�erentspectral displacement� The dotted� the dashed andthe solid lines in Figure represent the peak inter�story drift and stress of the UBC designed frame� theuncontrolled frame designed for its dead load only andthe ATC designed frame� respectively� As can be seen�the active controller has been capable of reducing theresponse of the uncontrolled structure considerably�bringing it closer to that of the UBC� The peak inter�story drift and stress were ���� cm and ��� MPA forthe UBC frame and ��� cm and �� MPA for theATC frame� all well below the maximum allowable driftand stress� according to the safe design criteria statedbefore� For this earthquake� the uncontrolled framehas also performed satisfactorily� according to the safedesign criteria for the allowable drift and stress� thoughmarginally� It can be seen that for the ATC designedframe� the peak drift and stress are reduced to about� � of those of the uncontrolled frame�

The response to � �������� � the Pacoima Dam

Figure �� Test and comparison between the uncontrolledUBC designed and ATC designed �ve�story frames whensubjected to the Park�eld earthquake�

earthquake is ����� cm� ��� MPA� and ���� cm��� MPA� for the UBC and ATC designed frames�respectively� all well below the allowable values of���� cm� �� MPA�� Again� as in the case of thePark�eld earthquake� the UBC designed frame hasperformed slightly better from a safety viewpoint�However� the peak acceleration is ��� cm�s� for theUBC and �� cm�s� for the ATC frames� which meansthat considerably more serviceability is associated withthe ATC frame under this earthquake�

Response to the Unreduced Pacoima DamEarthquake

Response to the Pacoima Dam earthquake� which isabout � times that of the El Centro earthquake� isin favor of the UBC designed frame� In this case�the response is ��� cm� �� MPA� for the UBC and����� cm� � �� MPA� for the ATC frames� Regardingthe allowable drift and stress ���� cm� �� MPA�� bothframes have violated the safety criteria� however� theUBC frame has performed better�

Response to Sinusoidal Ground Accelerations

Both frames were subjected to sinusoidal ground accel�erations of di�erent vibration periods� between ����� seconds� with ��� g amplitude� which is the same asthe PGA of the El Centro earthquake� Results shownin Figures a and b are the peak inter�story drift andacceleration� which� in both cases are plotted againstthe period of vibration of the ground� As can be seen�both frames su�er from resonance in the vicinity oftheir natural vibration periods� which are ���� secondsfor the UBC frame and ���� seconds for the ATCframe� The shape and peak of the curves for bothframes are considerably similar� though shifted withrespect to each other� As expected� it is the spectraldisplacement of an earthquake that has determined theresponse of the frames� Figure c shows the spectraldisplacement of the Pacoima Dam� El Centro andPark�eld earthquakes� Focusing on the Pacoima Damearthquake� it is obvious that the ATC frame is muchmore susceptible to this earthquake than the UBCframe� due to the larger spectral displacement at itsnatural vibration period� Also� in Figures a and b�the response of the uncontrolled frame is representedto show how successful the ATC mechanism has beenin its duty� reducing the response of the uncontrolledframe to about � � at the resonance�

Bene�t and Cost of Using the ATC Mechanism

The bene�t of using the ATC over the UBC design hasbeen in the saving of about ��� KN of steel used forthe columns� at the expense of providing an actuator

Feasibility Study of Fully Actively Controlled Frames

Figure �� �a� Maximum drift of the uncontrolled theUBC designed and the ATC designed �ve�story framessubjected to sinusoidal noises of di�erent periods but withthe same intensity of ���� g� �b� Same as �a� but forMaximum Stress� �c� Spectral displacement of the ElCentro Park�eld and Pacoima Dam earthquakes�

of � KN capacity� plus a cable of approximately � m�plus the required sensory system� including the sensorsand the transducers� plus the information processingsystem� which could be a simple chip� Obviously� forthe time being� the cost associated with the ATC designis much larger than its bene�t�

UBC AND ATC DESIGNS OF TEN��FIFTEEN� AND TWENTY�STORYFRAMES

It was desired to study the relationship between theframe height and the actuator capacity for ATC de�signed frames� Hence� �rstly� � frames of moderateheights of ten� �fteen and twenty stories were designed�according to the UBC� Figure � contains informationabout the UBC designed frames� where the sti�nessof the columns and the natural period of vibration ofeach frame are also included in this �gure� For the

sake of construction ease� it was decided to change thecross�section of the columns at the third� �fth �oorand every �ve �oors consecutively� For example� thecolumn sections were changed at the levels of �� � � and � �oors for the twenty�story frame� This resultedin �� and di�erent cross�sections for the columns ofthe ten�� �fteen� and twenty�story frames� respectively�The response in these cases� including the values of thepeak inter�story drift and peak stress were �� cm��� MPA�� ����� cm� �� MPA� and ����� cm� MPA� for the ten�� �fteen� and twenty�story frames�respectively�

Then� the same frames were redesigned as ATCframes� Again� as for the �ve�story frame of the previ�ous section� the columns of each frame were designedto carry its dead load only� Then� ATC mechanismswere added to the frame for its strengthening againstearthquakes� The safe design criteria for the peak�inter�story drift and stress in ATC frames� which wasexplained in the previous sections� was used here also�Again� the El Centro �� earthquake was taken as thedesign earthquake�

It was decided that the actuators should beinstalled every �ve �oors� i�e� on the ground� the th�oor� the � th �oor and so on� This resulted in ��� and actuators for the ten�� �fteen� and twenty�story frames� respectively� This decision was based onpersonal judgement� which seemed satisfactory at thisstage of the work� The authors plan to work on theproblem of optimal placement of control mechanismsin future studies�

It was then assumed that the actuators couldapply any required force� speci�ed by the controller�without any upper limit on their capacities and� then�the peak value of the control force� applied by each ofthe actuators during the design earthquake� was takenas its capacity� However� a minimum capacity wasspeci�ed for the actuators� This minimum actuatorcapacity� denoted by ACmin� was taken as�

ACmin � AC�W�W� ���

where AC� is the actuator capacity found for thecontrol of the �ve�story frame of the previous section� KN� W� is the weight of the ATC designed �ve�story frame � �oors � �� KN�m� � m � � KN and W is the weight �KN� of the frame abovethe �oor where the actuator was located� The reasonbehind this selection of the minimum capacity wasthat it was assumed� in an ideal situation� that eachactuator would control the �oors which were locatedabove it� Although more complicated conditions onthe minimum capacity could be set forth� this seemeda simple and logical condition� Figure � containsinformation about the capacities of the actuators also�As can be seen� for a speci�c frame� a combination of

� A� Joghataie and M�M� Asbmarz

Figure �� Schematics of the ATC designed frames of di�erent heights�

actuators of di�erent capacities has been found to beappropriate� For the ten�� �fteen� and twenty�storyframes� the same as for the �ve�story frame� the peakinter�story drift has controlled the design� resultingin the following peak response� �� cm� MPA������� cm� � MPA� and ����� cm� �� MPA� for the� � � and twenty�story frames� respectively� recallingthat the peak inter�story drift for the ten�� �fteen� andtwenty�story UBC frames has been �� ���� and ����cm� respectively� Also� it is noteworthy that comparedto the values reported above for the UBC designed

frames� the maximum stress in the ATC frames isconsiderably smaller�

RESPONSE TO OTHER EARTHQUAKES

The ten�� �fteen� and twenty�story frames� designedusing the UBC and the integrated ATC methods�were then subjected to earthquakes other than thedesign earthquake� To this end� each of the � frames�consisting of � UBC and � ATC designs� were subjectedto the same Park�eld and � �������� �� Pacoima

Feasibility Study of Fully Actively Controlled Frames �

Dam earthquakes� In all of these cases� both the UBCand the ATC designed frames performed pretty similarto each other� The designs were successful� Figures �aand �b are for these two earthquakes� In both �gures�the horizontal and vertical axes represent the numberof �oors and the peak inter�story drifts of the �ve�ten�� �fteen� and twenty�story frames divided by theallowable drift� which is ��� cm� respectively� Also� forbetter representation� the points have been connectedby smooth curves� It may roughly be concluded fromthese �gures that the performance of an ATC frameis better than its UBC equivalent when the number ofstories is more than � �

Reserved Capacity of the UBC and ATCFrames During Severe Earthquakes

Next� for studying UBC and ATC reserved capacities�all their designed frames were subjected to the� severe�unreduced Pacoima Dam earthquake� when all of themviolated the safe design criteria�

The peak inter�story drift of the frames� normal�ized to the allowable drift of ��� cm� is shown inFigure �c� Again� the performance of the ATC frameimproved� as the number of stories increased�

Figure �� Bene�t to Cost Ratio �BCR� as a function offrame height for the ATC designed frames�

ECONOMICS OF ATC AND UBC DESIGNS

The main goal of this study has been to provide apreliminary qualitative assessment of the cost versusbene�ts associated with the use of the ATC mecha�nism to control frame structures of moderate height�compared with the UBC based designs� Since thetechnology of the ATC is not yet su�ciently developedto �t the structural needs� it is not possible to providean exact estimate of the cost required for its use in thecontrol of frames against earthquake loading� However�as one of the results of this study� the reduction in thetotal column weight of the ATC designed frames� asthe main bene�t of using the ATC mechanism� on theone hand� and the required actuators capacity� plus theapproximate tendon length� as a measure of its cost�on the other hand� are reported in Table �� The �rstcolumn represents the number of stories of the frame�while the second and third columns show the bene�tand cost of using the ATC mechanism� Also� if thevalue of the saved weight divided by the total capacityof the actuators� as represented in the fourth column�is considered as a logical measure of the Bene�t to CostRatio �BCR� for the ATC design� it can be seen that itis approximately constant for frames of di�erent heightsof up to � �oors� Generalization of this result to tallerframes requires more study of the subject� noting thatwind loading is often more decisive than earthquakeloading for tall frames� Figure � represents BCR as afunction of the number of stories graphically�

SUMMARY AND CONCLUSIONS

The economics associated with a fully active tendoncontrolled frame �ATC frame� design of up to twentystories was studied in this paper� As a �rst step� amethodology for the design of the ATC frames waspresented� so that they could behave similar to theirUBC designed counterparts and� hence� could becomeconsidered as their equivalent� To this end� �rst� a

Figure � Comparing the performance of the UBC andATC frames of di�erent heights based on their response totwo test earthquakes of Park�eld and Pacoima Dam withtheir maximum drifts observed during the occurrence ofthe earthquakes normalized by their division to theallowable drift �a� Park�eld �b� Pacoima Dam�

� A� Joghataie and M�M� Asbmarz

Table �� Bene�t and cost of using ATC mechanism in the design of ATC frame equivalent to their UBC designedcounterparts for �ve� ten� �fteen� and twenty�story frames�

Number of

Stories of

the Frame

Weight �KN� Saved

in the Columns

Capacity of the Actuator�s�

� Tendon Length

Weight Saved�

Total Actuator

Capacities

��� ��KN���m� �����

� ��� ��� ��KN�� �m� ����

� ��� �� ��� �����KN�� �m� �����

� ���� �� ��� ���������KN�� �m� �� �

safe design criterion for ATC frames was proposed�The criterion states that under the e�ect of a speci�eddesign earthquake� for example� the El Centro �� S E earthquake� neither the peak inter�story drift northe peak stress in an ATC designed frame should exceedthe peak inter�story drift and stress in its UBC designedcounterpart� respectively�

Then� through numerical studies and using theinstantaneous optimal control algorithm� a number of�ve� ten�� �fteen� and twenty�story ATC frames weredesigned� according to the safe design criteria� A min�imum actuator capacity was speci�ed as a constrainton the selection of the required actuators�

It was observed that the designed ATC framesexhibited a similar performance to their UBC designedcounterparts� not only under the design earthquake�here the El Centro earthquake� but also� for two othertest earthquakes of di�erent spectral density but ofsimilar peak ground acceleration to that of the designearthquake� These two test earthquakes were thePark�eld ������ and the reduced Pacoima Dam �������

Also� to study the reserved capacity of the UBCand ATC frames to withstand severe earthquakes� theunreduced Pacoima Dam earthquake� with a PGAof about � times that of the El Centro earthquake�was applied to the frames� Both the UBC and ATCframes violated their allowable drift and stress limits�However� the performance of the ATC design wasbetter for taller frames�

The ratio of bene�t to cost �BCR� of an ATCdesign was de�ned as the ratio of the weight savedin the material divided by the total capacity of theactuators� It was found that BCR was approximatelyconstant for all of the frames in this study� i�e�� framesof up to twenty�stories high� Generalization of thisresult to taller frames requires more research�

Also� although it was found that it is not eco�nomical to consider ATC design of frames as a suitablesubstitute for the conventional UBC design for the timebeing� the authors do hope and believe that studies likethis could provide more information to look at activecontrol of structures from a practical viewpoint� to try

to �nd ways to make its technology cheaper and bringit closer to real world applications�

ACKNOWLEDGMENT

This research has been partially supported by theNational Research Council of Iran� Grant number �� The �rst author would like to acknowledgethis support� Furthermore� the cooperation of theCivil Engineering Department of Sharif University ofTechnology� Tehran� I�R� Iran� during this research� isgreatly appreciated�

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�� Leipholz H�H�E� and Abdel�Rohman M� Control ofStructures Martinus Nijho� Publishers �������

�� Soong T�T� Active Structural Control� Theory andPractice Longman Scienti�c and Technical ���� ��

�� Joghataie A� and Ghaboussi J� �Neural networks andfuzzy logic in structural control� Proceedings of theFirst World Conf� on Struct� Control ��� Aug� LACA USA pp WP������ �Aug� ������

�� Ribakov Y� and Gluck J� �Active control of MDOFstructures with supplemental electrorehological uiddampers� Earthquake Engineering and Structural Dy�namics � pp ������� �������

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