Engineering Structures 33 (2011) 1859–1869

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Engineering Structures

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Experimental evaluation of the seismic performance of steel MRFs withcompressed elastomer dampers using large-scale real-time hybrid simulationTheodore L. Karavasilis a,∗, James M. Ricles b, Richard Sause b, Cheng Chen c

a Department of Engineering Science, University of Oxford, Oxford OX1-3PJ, UKb ATLSS Engineering Center, Department of Civil and Environmental Engineering, Lehigh University, Bethlehem, PA 18015, USAc School of Engineering, San Francisco State University, CA 94132, USA

a r t i c l e i n f o

Article history:Received 14 September 2010Received in revised form28 January 2011Accepted 30 January 2011Available online 29 March 2011

Keywords:Real-time hybrid simulationDamperElastomerSteel MRFPerformance-based seismic design

a b s t r a c t

Real-timehybrid simulation combines experimental testing and numerical simulation, and thus is a viableexperimental technique for evaluating the effectiveness of supplemental damping devices for seismichazard mitigation. This paper presents an experimental program based on the use of the real-time hybridsimulationmethod to verify the performance-based seismic design of a two story, four-bay steel momentresisting frame (MRF) equippedwith compressed elastomer dampers. The laboratory specimens, referredto as experimental substructures, are two individual compressed elastomer dampers with the remainderof the building modeled as an analytical substructure. The proposed experimental technique enablesan ensemble of ground motions to be applied to the building, resulting in various levels of damage,without the need to repair the experimental substructures, since the damage will be within the analyticalsubstructure. Statistical experimental response results incorporating the ground motion variability showthat a steelMRFwith compressed elastomer dampers can bedesigned to performbetter than conventionalsteel special moment resisting frames (SMRFs), even when the MRF with dampers is significantly lighterin weight than the conventional MRF.

© 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Passive damping systems can significantly enhance the seis-mic performance of buildings by reducing drift and inelastic de-formation demands on the primary lateral load resisting system,in addition to reducing the velocity and acceleration demandson non-structural components [1]. Among the different kinds ofpassive damping systems, solid viscoelastic dampers have beenextensively studied. These dampers generally consist of solidelastomeric pads bonded to steel plates. The elastomer pads ex-hibit both viscosity and elasticity and their mechanical proper-ties depend on loading frequency, deformation amplitude andtemperature.

Many researchers have performed individual viscoelasticdamper tests and developed models to predict damper behaviorunder earthquake loading. Tsai and Lee [2] and Kasai et al. [3]studied the effect of loading rate and temperature on viscoelasticmaterials and proposed fractional derivative models to predictdamper behavior. Lee [4] studied the behavior of elastomericdampers made of ultra high damping rubber and found from

∗ Corresponding author. Tel.: +44 (0)1865 2 73144; fax: +44 (0)1865 2 73010.E-mail address: theodore.karavasilis@eng.ox.ac.uk (T.L. Karavasilis).

0141-0296/$ – see front matter© 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2011.01.032

characterization tests the behavior of these dampers to be lesssensitive to frequency and ambient temperature compared toconventional viscoelastic dampers. Sause et al. [5] developed asequential asymptote formulation to model the cyclic behavior ofultra high damping rubber dampers.

Other studies have developed seismic design procedures forbuildings incorporating viscoelastic dampers and used nonlineardynamic history analysis to evaluate seismic performance anddamper designs. Fu and Kasai [6] presented a simplified theoryto design viscoelastic dampers for a given MRF. Their simplifieddesignmethod has been verified by performing nonlinear dynamichistory analysis for a ten-story steel MRF with dampers. Leeet al. [7] presented a simplified design procedure for buildingswith viscoelastic or high-damping elastomeric dampers. Thedesign procedure has been used recently to study the effect ofthe variation in steel moment resisting frame (MRF) propertiesand damper design criteria on the design of steel MRFswith elastomeric dampers [8]. The 2000 NEHRP Provisions [9]include equivalent lateral force and modal analysis procedures forbuildings with damping systems including viscoelastic dampers.The validity of the 2000 NEHRP procedures has been assessed byRamirez et al. [10].

Several experimental studies have been performed on steelframes with viscoelastic dampers. These studies include mainlyshaking table tests similar to those conducted by Chang and

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Lin [11] on a full-scale five-story frame, and recently by Kasaiet al. [12] on a full-scale five-story steel building.

Recent research studies haveproposednewkinds of viscoelasticdampers. Ibrahim et al. [13] proposed and analytically investigateda newvisco-plastic device that consists of a block of a high dampingrubber sandwiched between steel plates which are allowedto yield to provide additional energy dissipation. Karavasiliset al. [14] experimentally evaluated the hysteretic behavior ofa new innovative compressed elastomer damper developed bySweeney and Michael [15] and used the design procedure ofLee et al. [7] to design steel MRFs with compressed elastomerdampers. Nonlinear time history analyses confirmed the validity ofthe simplified design procedure and showed that steel MRFs withcompressed elastomer dampers can be designed to perform betterthan conventional steel special moment resisting frames (SMRFs),even when theMRF with dampers is significantly lighter in weightthan the conventional MRF.

Recent research has investigated the use of passive dampersto achieve harmonization of different performance levels betweenstructural and non-structural components. Pavlou and Constanti-nou [16] conducted a study of buildings with and without pas-sive dampers to investigate the response of secondary systemsand showed that significant benefits may be provided by viscousdamping systems in terms of reduced floor spectral accelerationsand floor absolute velocities. Vargas and Bruneau [17] studied theresponse of nonstructural components in buildings with metallicand viscous dampers acting in parallel and explained why in someinstances it is observed that adding viscous dampers to stronglyinelastic systems can result in increases in floor accelerations.Wanitkorkul and Filiatrault [18] studied the influence of passivedampers on structural and nonstructural fragilities of a steel build-ing. Their results indicate that viscous dampers reduce the seis-mic fragility of nonstructural components, while metallic damperscan be detrimental to the seismic fragility of acceleration sensitivenonstructural components.

To demonstrate the full potential of new types of dampers,damper designs and performance-based design procedures forstructural systems with dampers need to be experimentally vali-dated. The 2000NEHRP provisions [9] allow the design of buildingswith passive damping systems to experience controlled inelasticdeformations associated with typical design drifts limits, e.g., the2% drift limit [9]. Therefore, to experimentally validate damperdesigns and performance-based design procedures, inelastic re-sponse statistics incorporating groundmotion variability should beobtained. Full-scale testing [12] is a reliable but, at the same time,challenging experimental technique. In particular, conducting a se-ries of full-scale tests to obtain response statistics of structuralsystems under earthquake intensities which produce inelastic de-formations may be cost and time prohibitive since the damagedcomponents of the structural system need to be repaired or rebuiltafter each test.

Real-time hybrid simulation combines physical testing andnumerical simulation such that the dynamic performance of theentire structural system can be considered during the simulation[19–21]. When real-time hybrid simulation is used to evaluate theperformance of structures with rate-dependent damping devices,the damping devices can be treated as experimental substructuresand the remainder of the structural system modeled analytically.The added benefit of this experimental technique is that it allowsan unlimited number of ground motions to be applied to thestructure, resulting in various levels of damage, without the needto repair the experimental substructures, since the damage will bewithin the analytical substructure.

This paper presents an experimental program based on the useof real-time hybrid simulation to verify the performance-basedseismic design of a two-story, four-bay steel MRF equipped with

Fig. 1. Fabrication of compressed elastomer damper: (a) elastomeric materialwrapped around longitudinal bar; (b) elastomericmaterial and bar compressed intothe steel tube; (c) damper with additional transverse attachment bars in place and(d) installation to beam web [15].

compressed elastomer dampers. TheMRFwas designed using a re-duced base shear design force compared to a conventional SMRF,where the dampers are designed to control the drift of the struc-ture. The laboratory specimens, referred to as experimental sub-structures, are two individual compressed elastomer dampers. Theremainder of the building is modeled as an analytical substruc-ture. A series of real-time hybrid simulations are performed to ac-quire response statistics under the design basis earthquake (DBE)and the maximum considered earthquake (MCE). The DBE has anintensity that is two-thirds that of the MCE, where the MCE hasa 2% probability of exceedance in 50 years [9]. Real-time hybridsimulations are conducted using the Real-Time Integrated Con-trol System [22] of the Lehigh Network for Earthquake EngineeringSimulation (NEES) Real-time Multi-Directional Earthquake Simu-lation Facility (RTMD).

2. Compressed elastomer damper

The compressed elastomer structural dampers used in the studyare fabricated by bonding four pieces of an elastomer (butyl rubberblend) onto a longitudinal steel bar, as shown in Fig. 1(a). Thepieces of elastomer on this bar are then pre-compressed into a steeltube (Fig. 1(b)). Each prototype damper includes three tubeswhicharewelded together (Fig. 1(c)). To enable the damper to be attachedto the structure as shown in Fig. 1(d), transverse bars with boltholes are welded across the steel tubes and additional transverseattachment bars are welded across the narrow dimension of thelongitudinal bars (Fig. 1(c)).

The pre-compression of the elastomer into the tube improvesthe performance of the bond interface between the elastomerand the longitudinal bar. The interface between the elastomerand the steel tube is not mechanically bonded, which allows theelastomer to slip relative to the tube, producing frictionwhen largedeformations are imposed. The dampers are designed to slip beforethe elastomer tears or the bond to the longitudinal bar fails [15].There is no slip limitation of the damper as long as the steel tubesare long enough so that the elastomer remains in the tube duringthe earthquake response.

Characterization tests of the prototype damperwere conductedby Karavasilis et al. [14] at the RTMD facility [22]. The loadingprotocol for the characterization tests used ‘‘ramped’’ sinusoidaldisplacement histories with different amplitudes and differentfrequencies. The experimental results showed that the dampersexhibit elastomeric behavior under small deformation (less than

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Fig. 2. Damper hysteresis from characterization tests [14]: (a) before slip, and (b) after slip.

Fig. 3. Mechanical properties evaluated from characterization tests [14]: (a) equivalent stiffness, and (b) equivalent loss factor.

15mm) (Fig. 2(a)).When the deformation is larger than 15mm, slipof the elastomer compressed inside the steel tube occurs and thedampers exhibit a combined elastomeric and frictional behavior(Fig. 2(b)). The damper assembly was tested with two prototypedampers (i.e., a total of 6 tubes) acting in parallel, referred to hereinas a compressed elastomer damper.

The equivalent stiffness, Keq, and the loss factor, ηeq, of thecompressed elastomer damper were determined from the char-acterization test data. The Keq is the ratio of the maximum forceat maximum displacement to the maximum displacement, whilethe equivalent loss factor, ηeq, which represents the energy dis-sipation capacity, is defined as ηeq = ED/(2 · π · ES), where EDis the energy dissipated per cycle of sinusoidal loading and ES isthe maximum strain energy stored during a cycle of sinusoidalloading. ED can be determined by integrating the hysteresis loopsfrom the experimental data and ES can be calculated from themeasured maximum stress and strain data. The Keq and ηeq fromthe characterization tests are given in Fig. 3. Fig. 3(a) shows thatthe stiffness (Keq) decreases with increasing deformation, andslightly increases as the frequency increases for a given deforma-tion. The sensitivity of Keq to frequency diminishes as the deforma-tion increases. Fig. 3(b) shows that the energy dissipation (ηeq) isrelatively constant for small amplitudes of deformation (less than10 mm) and significantly increases after slip of the elastomer oc-curs at about 15 mm. There is a slight increase in ηeq as the fre-quency increases for a given deformation.

3. Steel MRF with compressed elastomer dampers

3.1. Prototype building

Fig. 4(a) shows the plan view of the 2-story, 6-bay by 6-bay prototype office building used for the study. The building isassumed to be located on a stiff soil site and has four identicalperimeter steel MRFs to resist lateral forces. Each MRF consists offour bays. The design study focuses on one typical perimeter MRF.This MRF is designed either as a conventional SMRF as defined inthe 2003 International Building Code [23], referred to herein as IBC

Fig. 4. Prototype building structure: (a) plan view, and (b) perimeter MRF withdampers and diagonal bracing.

2003, or as a MRF with compressed elastomer dampers using thesimplified design procedure (SDP) by Lee et al. [7]. In the latter case,dampers and diagonal braces are added to the two interior bays, asshown in Fig. 4(b).

The nominal yield stress of the steel members of the MRF is345 MPa. The gravity loads and load combinations considered inthe design are those described in IBC 2003. A smooth design re-sponse spectrum with parameters SDS = 1.0g, SD1 = 0.6g, T0 =

0.12 s and Ts = 0.6 s defined by IBC 2003 represents the DBE. Thevalues of SDS = 1.0g , and SD1 = 0.6g are based on the determinis-tic limits for the MCE ground motion in accordance with IBC 2003,where SS = 1.5g and S1 = 0.6g , along with Fa = 1.0 and Fv = 1.5are based on a stiff soil site. The program SAP2000 [24] is utilizedfor selecting the MRF member cross sections in accordance withthe AISC Seismic Provisions [25]. The same column cross-section isused in both stories of the MRF and different beam cross-sectionsare used for the two floors.

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Table 1Properties of MRF designs.

MRF Column section Beam sections Steel weight (kN) T1 (s) Story stiffness (kN/mm) θmax (%)

UD100V W14 × 211 1st story: W24 × 84 200 1.08 1st story: 66574 2.402nd story: W21 × 50 2nd story: 42018

UD50V W14 × 120 1st story: W24 × 55 124 1.48 1st story: 36007 3.232nd story: W18 × 40 2nd story: 23894

3.2. Design of perimeter MRF as a conventional SMRF withoutdampers

The perimeter MRF of Fig. 4(b) is initially designed as aconventional SMRF using the equivalent lateral force procedurefrom IBC 2003. This SMRF without dampers, referred to hereinas UD100V, satisfies the member strength criteria and the driftlimit of 2% of IBC 2003, where values of 8 and 5.5 are used forthe response modification factor, R, and the amplification factor,Cd, respectively.

To study whether MRFs with compressed elastomer damperscan be designed to have a reduced strength compared to aconventional SMRF (without dampers) and achieve a prescribedlevel of seismic performance, the perimeter MRF was redesignedwithout dampers to have a design base shear equal to 0.50V , whereV is the design base shear of UD100V. ThisMRF design is referred toas UD50V, and is significantly lighter than UD100V. A comparisonof weight is discussed later. UD50V is subsequently outfitted withcompressed elastomer dampers, where the SDP by Lee et al. [7] isused to design the dampers to limit the drift of the MRF to 1.65%.The SDP enables the design of the dampers to be integrated intothe system design by specifying performance objectives that thecombined MRF and damper system must achieve. Details of howthe SDP is utilized are discussed later.

Table 1 summarizes the properties for the two MRF designs(UD100 and UD50V). The table lists the column section, beamsections, steel weight, fundamental period of vibration, T1, andstory stiffness (used later to design the dampers for the UD50VMRF). The last column of Table 1 provides estimates (based onthe equal-displacement rule) of the expectedmaximum story drift,θmax, under the DBE earthquake. Under the assumption of theequal-displacement rule, the UD100V frame was found to exceedthe 2% story drift limit of IBC 2003, however, UD100V did satisfythe 2% story drift limit using the drift check procedure involvingthe use of Cd per IBC 2003.

3.3. Design of dampers for SMRF

The SDP idealizes the damper hysteresis loops as linear vis-coelastic ellipses and the damper design variables are the equiv-alent damper stiffness and the loss factor. The thickness and thearea of the elastomer assumed in the prototype MRF and in thehybrid simulations presented in this paper are 4 times larger thanthe thickness and the area of the elastomer of the dampers testedby Karavasilis et al. [14]. Such an elastomer thickness ensures thatthe dampers in the prototype MRF will remain undamaged (i.e.,no slip) under the DBE, while slip is expected under the MCE. Thisdesign strategy ensures no need to replace the dampers for seis-mic events lower than or equal to the DBE. For earthquakes largerthan the DBE (e.g., MCE), the dampers are treated as sacrificial ele-ments that should be replaced after the seismic event, if needed.The properties of the large-scale compressed elastomer damperdesignwere derived from the experimental data presented in Fig. 3as follows. With tref and Aref designated as the thickness and area,respectively, of the elastomer damper used in the characterizationtests, the properties (thickness t and area A) of the damper designsfor the prototypeMRF are expressed in terms of the ratios t/tref and

A/Aref. Given the stiffness, Keq(uref), and the loss factor, ηeq(uref), ofthe damper in the characterization tests, the stiffness and loss fac-tor of the damper designs are: Kd(ud) = (A/Aref) · (tref/t) ·Keq(uref)and η(ud) = ηeq(uref), where ud is the deformation imposed onthe damper in the MRF, and uref is the deformation of the damperin the characterization tests, related to ud through the expressionuref = ud · (tref/t). The expressions for Kd(ud) and η(ud) are derivedby transforming the characterization test results for the damperfrom force–deformation (Fref–uref) behavior to shear stress–shearstrain (τ–γ ) behavior using the tref and Aref dimensions (i.e., τ =

Fref/Aref and γ = uref/tref), and then by transforming the shearstress–shear strain (τ–γ ) behavior to force–deformation (Fd–ud)behavior of the damper designs using the t and A dimensions (i.e.,Fd = τA = Fref · A/Aref and ud = γ t = uref · t/tref).

The SDP developed by Lee et al. [7] is slightly modified hereinto account for the strong dependence of Kd(ud) and ηd(ud) of thecompressed elastomer dampers on deformation amplitude ud. Toachieve the target performance level (e.g., immediate occupancyunder the DBE), detailed design criteria, such as story drift limitsand limits on the internal forces of the members need to beestablished. For the study herein, a value of θmax = 1.65%under theDBE is specified as the target performance objective. The modifiedSDP is then used, as explained below:

(1) Select an appropriate α value (ratio of total brace stiffness perstory in the global direction to the MRF story stiffness). Thisratio should provide: (a) braces that are stiff enough so thatthe story drift produces damper deformation with minimalbrace deformation; (b) braces that do not buckle under themaximum forces transmitted by the dampers; and (c) only asmall increase in the steel weight of the structure.

(2) Select an appropriate β value (ratio of total damper stiffness perstory in the horizontal direction to the MRF story stiffness Ko).The β value should provide a reasonable required number ofdampers.

(3) Select an initial value of the damper loss factor, ηd. With theηd selected, the contribution of the dampers to the equivalentdamping ratio of the MRF with the dampers, ξeq, is estimatedbased on the lateral force energy method [26]. The dampingreduction factor, B, is then obtained [9] as a function of the totaldamping ratio, ξt , which equals the sum of ξeq and the inherentdamping ratio of the MRF building (assumed to be 2%).

(4) Response spectrum analysis. The elastic response spectrum isreduced by the B factor, and the story drifts and damperdeformation, ud, are calculated based on a response spectrumanalysis using the equal-displacement rule. In this analysis,dampers at each story are modeled with two linear springs(one spring at each interior bay) having a horizontal stiffnessequal to Ko · β/2. With ud known, the ηd(ud) = ηeq(uref) iscalculated from Fig. 3(b) using uref = ud · (tref/t). Iterations ofSteps 3 and 4 are performed until the value for ηd converges. Ifthe story drifts after convergence do not satisfy the establishedperformance criteria, Steps 2–4 are repeated, beginning byselecting a new value for β .

(5) Calculate required number of dampers. With the ud known, thedamper design stiffness Keq(uref) is determined from Fig. 3(a),and Kd(ud) = (A/Aref) · (tref/t) ·Keq(uref). The required numberof dampers, Nd, equals (Ko · β/Kd(ud)), rounded up to the

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Fig. 5. Real-time hybrid simulation: analytical and experimental substructures forming the complete structural system.

Table 2Design properties of UD50V MRF with dampers.

α Brace steelweight (kN)

β T1 (s) ηd ξt (%) B θmax (%) Nd

Story1st 2nd

10 17.2 1.0 1.04 0.60 15.00 1.35 1.65 8 5

nearest integer. If the number of dampers is too large, a revisedperformance criteria and/or MRF design should be consideredand Steps 1–5 are repeated.

Table 2 provides a summary of the damper design for theUD50VMRFwhere the performance criterion (as noted previously)is a design story drift of 1.65% under the DBE. It is observedthat the MRF with 8 compressed elastomer dampers in the firststory and 5 compressed elastomer dampers in the second storyexhibits a significantly better performance (θmax = 1.65%) thanthat of the conventional steel SMRF UD100V (θmax = 2.40%, seeTable 1), where the design prediction of θmax is based on the equal-displacement rule. Moreover, the UD50V MRF with dampers hasa steel weight equal to 124 kN (beams and columns) + 17.2 kN(braces) = 141.2 kN, while the steel weight of the conventionalsteel SMRF UD100V is 200 kN. Thus, the UD50VMRFwith dampershas a 30% reduction in steel weight compared to the conventionalsteel SMRF design, UD100V.

The damper imposes a limit on the peak damper forcetransmitted to the braces, the columns and foundations of thebuilding by exhibiting a plastic (friction) behavior at higher drifts.This is a clear advantage over a conventional viscoelastic damperwith uncontrolled peak damper force, since more economicaldesigns can be achieved and braces able to safely support thedampers without buckling under high seismic intensity levels canbe designed.

4. Real-time hybrid simulations

4.1. Real-time integrated control system architecture

The performance of a perimeter MRF with compressedelastomer dampers is experimentally evaluated by conducting

real-timehybrid simulations. The groundmotions only in the planeof the perimeter MRF were considered. The symmetry in the floorplan allowed only one perimeter MRF and the gravity framesand mass within the tributary area of the MRF to be considered.As illustrated in Fig. 5, the experimental substructures are twoindividual compressed elastomer damperswith the remaining partof the building (MRF, braces, and gravity frames (shown as a lean-on column in Fig. 5)) modeled as an analytical substructure.

Since the dampers at a story level are placed in parallel in theprototype MRF (Fig. 4(b)), they are subjected to the same velocityand displacement. Therefore, each of the damper setups in thelaboratory represents all of the dampers in one story. In a real-timehybrid simulation themeasured restoring force from a compressedelastomer damper is multiplied by the number of dampers in astory to obtain the total restoring force of all the dampers at thestory level in the MRF.

As discussed previously, the thickness and the area of theelastomer of the dampers that are used in UD50V MRF areconsidered to be 4 times larger than the thickness and the areaof the elastomer of the dampers in the experimental substructure.Consequently, in the real-time hybrid simulation the commanddisplacement of the dampers is scaled down by a factor of 4 andthe measured restoring force is amplified by a factor of 4.

A nonlinear finite element program [27] has been implementedinto the real-time integrated control system at the NEES RTMDFacility [22]. The architecture for the RTMD system is shown inFig. 6. A digital servo controller (Real-time Control Workstation)with a 1024Hz clock speed (sampling time δt = 1/1024 s) controlsthe motion of the servo-hydraulic actuators and is integratedwith the Real-time Target Workstation, Simulation Workstation,and Data Acquisition Mainframe using a shared common RAMnetwork (SCRAMNet). SCRAMNet has a communication rate ofabout 180 ns which enables the transfer of data among theintegratedworkstations in real-timewithminimal communicationdelay. The nonlinear finite element program has been developedin a manner that enables the analytical substructure modeling,servo-hydraulic control law, and actuator compensation scheme(discussed later) to be integrated into a single SIMULINK model onthe Simulation Workstation and then downloaded onto the TargetWorkstation using Mathworks xPC Target Software [28].

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Fig. 6. RTMD integrated control system architecture.

4.2. Analytical substructure modeling

The analytical substructure model of the MRF shown in Fig. 5has a total of 122 degrees of freedom and 71 elements. Inelasticbehavior is modeled by means of a bilinear hysteretic lumpedplasticity beam–column element with 3% hardening and anappropriate axial-moment yield surface [29]. In order to overcomethe shortcomings of the lumped plasticity modeling in predictingaccurately the plastic rotation in the members of the structure,each physical member (i.e., beams and columns) was modeledwith three beam–column elements in series, i.e., two elementswere used to model the two plastic hinge regions at each endof the member with a length equal to 5% of the member lengthand one element with a length equal to the remaining 90% ofthe member length. For the steel MRF under consideration, thismodeling approach was found to produce an inelastic responseclose to the response obtained with a rigorous analysis using fiberbeam–column elements [27]. Diaphragm action was assumed atevery floor in theMRF due to the presence of a composite floor slab.The lean-on column was used to model P–∆ effects on the MRFfrom gravity loads carried by the gravity columns of the buildingthat were in the tributary area of the perimeter MRF. The inherentdamping was modeled by constructing a Rayleigh damping matrixC based on a viscous damping ratio equal to 2% at the first andsecond modes of vibration.

4.3. Experimental substructure test setup

Fig. 7 shows the experimental setup for the real-time hybridsimulations, which consists of the experimental substructures(two compressed elastomer dampers) and two servo-hydraulicactuators with supports, roller bearings and reaction frames. Thetwo actuators (see Fig. 5) have a load capacity of 2300 kN and1700 kN with a maximum velocity of 840 mm/s. and 1140 mm/s,respectively, when three 1514 l/min three-stage servo-valves aremounted on each actuator. The 2300 and 1700 kN actuatorswere attached to the experimental substructures associated withthe first story damper and second story damper, respectively.The servo-controller for the actuator used in real-time hybridsimulations consisted of a digital PID controllerwith a proportionalgain of 20 and an integral time constant of 5.0 resulting in anintegral gain of 4.0, a differential gain of zero and a roll-offfrequency of 39.8 Hz.

4.4. Real-time integration of the equations of motion

For theMRFwith the dampers of Fig. 5, the temporal discretizedequations of motion at the i + 1th time step can be expressed as

M · xi+1 + C · xi+1 + rai+1 + rei+1 = Fi+1 (1)

Fig. 7. Compressed elastomer dampers: (a) closeup of damper, and (b) details oftest setup for each damper.

where xi+1 and xi+1 are the acceleration and velocity vectors of thestructure, respectively; rai+1 and rei+1 are the restoring force vectorsof the analytical and experimental substructures, respectively;M and C are the mass and damping matrices of the structure,respectively; and Fi+1 is the excitation force.

The CR unconditionally stable explicit integration algorithm[19,30] is used to solve Eq. (1) for the structural displacementvector xi+1. According to the CR algorithm, the variations ofthe displacement and velocity vectors of the structure over theintegration time step 1t are defined as

xi+1 = xi + 1t · α1 · xi (2a)

xi+1 = xi + 1t · xi + 1t2 · α2 · xi (2b)

where xi, xi and xi are the displacement, velocity and accelerationvectors of the structure at the ith time step, respectively; and α1and α2 are matrices of integration parameters defined as

α1 = α2 = 4 ·4 · M + 2 · 1t · (C + Ceq)

+ 1t2 · (K + Keq)−1

· M . (3)

In Eq. (3), K is the initial stiffness matrix of the structure whileKeq and Ceq are matrices that contain terms associated with theequivalent stiffness keq and the damping ceq, respectively, forthe compressed elastomer dampers. For a sinusoidal deformationloading history of cyclic frequency ω and deformation amplitudeud, keq and ceq are equal toKd(ud) andη(ud)·keq/ω, respectively [1].In the real-time hybrid simulations presented herein, ud and ωwere assumed equal to the expected damper deformation fromthe SDP and the first mode cyclic frequency of the building,respectively. Preliminary real-time hybrid simulations showedthat the response results where insensitive to small variations ofthe selected values of ud and ω. Chen and Ricles [31] showed thatit is necessary to include the damping and stiffness of the completestructure in Eq. (3) to ensure that the integration parameters resultin maintaining a stable solution. This will occur as long as the totalstiffness (K + Keq) in Eq. (3) is larger that that developed in thesystem during the hybrid simulation.

In a real-time hybrid simulation, Eqs. (2a) and (2b) are usedto obtain the velocity xi+1 and displacement xi+1 vectors at thei+1th time step. The displacement vector xi+1 is decomposed intothe analytical displacement vector xai+1 and the experimental (orcommand) displacement vector xei+1, which are imposed onto the

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analytical and experimental substructures, respectively, to obtainthe restoring force vectors rai+1 and rei+1. Strictly speaking, xei+1contains deformations, i.e., differences in the displacements of thenodes at the ends of the experimental substructures. The analyticalrestoring force vector rai+1 is obtained with a standard nonlinearstate-determination procedure for each beam–column element inthe analytical substructure [29], while the experimental restoringforce vector rei+1 is obtained from the feedback forces measuredusing load cells that are placed in each compressed elastomerdamper test setup. The equilibrium equation (1) is then employedto calculate the acceleration response vector xi+1 at the i+1th timestep, and the velocity xi+2 and displacement xi+2 vectors for thenext i+ 2th time step are then readily available from Eqs. (2a) and(2b). This process is repeated to obtain the response over thewholeduration of the earthquake ground motion.

The integration time step 1t used for the hybrid tests is amultiple of the servo-hydraulic controller sampling time δt of1/1024 s, and is equal to 10/1024 s. This size of the time step wasarrived at by performing a convergence study to ensure that thevalue for 1t was sufficiently small enough that the integrationalgorithm produced accurate results. A linear ramp generator isused to apply the command displacement vector xei+1 through thehydraulic actuators to the experimental substructures at the servo-controller sampling rate, i.e., at a time step δt of 1/1024 s. Theinterpolated command displacement vector is defined as

dc(j)i+1 =

jn

· (xei+1 − xei ) + xei . (4)

In Eq. (4), dc(j)i+1 is the command displacement vector at the

jth substep within the i + 1th time step; xei is the commanddisplacement vector at the ith time step; and j is the substep indexfor the interpolation within one single time step and ranges from1 to n, where n is the integer ratio of 1t/δt (i.e., equal to 10 for thetests presented herein).

As noted above, to proceed to the next (i + 2)th time stepthe restoring force vectors rai+1 and rei+1 at the end of the (i +

1)th time step must be obtained to calculate the displacementvector xi+2. The available time to perform the state determinationof the analytical substructure and form the rai+1 restoring forcevector is equal to the integration time step 1t . For the analyticalsubstructure of Fig. 5, rai+1 was obtained within the duration of 1twithout creating any time delay issues. However, if the measuredexperimental restoring force vector rei+1 is fed back at the end of thetime step after the actuators reach their corresponding commanddisplacement xei+1, a delay occurs while xi+2 is calculated and sentto the servo-controller, which reads the command displacementxei+2 one sampling time step δt later. To avoid this delay andensure a smooth and continuous movement of the actuators, theexperimental restoring force vector is extrapolated at the end ofthe (n − 1)th substep within each time step (e.g., the (i + 1)thtime step) to become available before the actuators reach theircommand displacement xei+1 [19], where for each experimentalsubstructure the restoring force contribution to rei+1 is:

rei+1 = rm(n−1)i+1 + keq · (xei+1 − dc(n−1)

i+1 ) + ceq · (xei+1 − xm(n−1)i+1 ). (5)

In Eq. (5) rm(n−1)i+1 is the measured restoring force of the

experimental substructure for the (n−1)th substep of the (i+1)thtime step, xei+1 and xm(n−1)

i+1 are the target relative velocity betweenthe nodes at the ends of the experimental substructure based onthe CR integration algorithm (Eq. (2a)) and the measured velocityin the damper for the (n − 1)th substep of the (i + 1)th time step,respectively. Also, as noted above, ceq and keq are the equivalentdamping and equivalent stiffness of the elastomeric damper ofthe experimental substructure, respectively. The velocity of theexperimental substructure is constant within the integration time

step 1t due to the linear ramp generator. Therefore, in theextrapolation procedure the last term in Eq. (5) is included tominimize the error in the velocity-dependent restoring force ofthe experimental substructure (elastomeric damper) at the endof the time step by correcting for the difference between thetarget velocity xei+1 and the velocity produced by the linear rampgenerator.

4.5. Actuator delay compensation

Due to inherent servo-hydraulic dynamics, the actuator has aninevitable time delay in response to the displacement command.This time delay is usually referred to as actuator delay and willresult in a desynchronization between the measured restoringforces from the experimental substructure(s) and the integrationalgorithm in a real-time hybrid simulation. Studies on the effectof actuator delay [32,31] show that actuator delay is equivalentto creating negative damping, which can destabilize a real-timehybrid simulation if not compensated properly.

To minimize the detrimental effect of actuator delay during thereal-time hybrid simulations, the adaptive inverse compensation(AIC) method developed by Chen and Ricles [33] was used tocompensate for actuator delay during the simulations. The AICmethod for a servo-hydraulic can be expressed using the followingdiscrete transfer function that relates the compensated commanddisplacement to the original command displacement for theactuator:

Gc(z) =(αes + 1α) · z − (αes + 1α − 1)

z. (6)

In Eq. (6), z is the complex variable in the discrete z-domain; αes isthe estimated actuator delay constant that is defined as the ratioof the duration for the servo-hydraulic to achieve the commanddisplacement to the hydraulic servo-controller sampling time δt;and 1α is an evolutionary variable with an initial value of zero.The AICmethod uses the initial estimated value for αes for actuatordelay compensation at the beginning of the hybrid simulation. Theevolutionary variable 1α is used to adjust the initial estimatedvalue forαes to achieve accurate actuator control during a real-timehybrid simulation. The adaptation of the evolutionary variable 1αis based on a tracking indicator TI [34]:

1α(t) = kp · TI(t) + ki ·∫ t

0TI(τ )dτ . (7)

In Eq. (7) kp and ki are proportional and integrative adaptivegains of the adaptive control law, respectively. The TI is based onthe enclosed area of the hysteresis in the synchronization subspaceplot shown in Fig. 8, where the actuator command displacementdc is plotted against the actuator measured displacement dm. Thecalculation of TI at each substep within a time step is formulatedas [34]

TI(j)i+1 = 0.5A(j)i+1 − TA(j)

i+1

. (8)

In Eq. (8), A(j)i+1 and TA(j)

i+1 are the accumulated enclosed andcomplementary enclosed areas at the jth substep of the rampgenerator at time step i + 1, respectively, and are calculated as

A(j)i+1 = A(j−1)

i+1 + dA(j)i+1

= A(j−1)i+1 + 0.5

dc(j)i+1 + dc(j−1)

i+1

dm(j)i+1 − dm(j−1)

i+1

(9a)

TA(j)i+1 = TA(j−1)

i+1 + dTA(j)i+1

= TA(j−1)i+1 + 0.5

dm(j)i+1 + dm(j−1)

i+1

dc(j)i+1 − dc(j−1)

i+1

. (9b)

The incremental values for the enclosed and complementaryenclosed areas, dA(j)

i+1 and dTA(j)i+1, respectively, are shown in Fig. 8

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Table 3Earthquake ground motions used in real-time hybrid simulations.

Earthquake Station Component Magnitude (Mw) Distance (km) PGA (g) Scale factorDBE MCE

Loma Prieta 1989 Hollister—S & P HSP090 6.93 27.67 0.18 1.99 2.99Manjil 1990 Abbar ABBAR–T 7.37 12.56 0.46 0.96 1.44Northridge 1994 N Hollywood—Cw CWC270 6.69 7.89 0.27 1.70 2.56ChiChi 1999 TCU105 TCU105-E 7.62 17.18 0.12 2.45 3.67ChiChi 1999 TCU049 TCU049-E 7.62 3.78 0.29 1.92 2.89

Fig. 8. Synchronization subspace with increment of enclosed area dA(j)i+1 and

complementary enclosed area dTA(j)i+1 utilized in the determination of the tracking

indicator TI .

for the jth substep of time step i + 1. At the beginning of thetest, the enclosed and complementary areas have initial values ofzero. The calculation of A and TA continues for every substep ofeach time step until the end of the real-time hybrid simulation.Chen and Ricles [33] showed that the use of the AIC methodfor real-time hybrid simulation of structures with experimentalsubstructures consisting of passive MR dampers resulted in goodactuator tracking and test results in comparison with numericalsimulation results for structural response.

For the real-time hybrid simulations a value of αes = 30 forthe estimate of the actuator delay constant along with the valuesfor the adaptive gains of kp = 0.4 and ki = 0.04 for both servo-hydraulic actuators were used. These values were established byChen by conducting parametric studies of the servo-hydraulicsystem at the RTMD [31].

5. Real-time hybrid simulation results

An ensemble of five earthquake ground motions recorded onstiff soil sites (without near-fault effects) are used in real-timehybrid simulation to evaluate the performance of the MRF withcompressed elastomer dampers. The ground motions were scaledto the DBE level using the scaling procedure of Somerville [35]. Theamplitudes of these DBE ground motions were further scaled by1.5 to represent MCE ground motions. Table 3 provides the scalefactors and information for the five ground motions, while Fig. 9shows their acceleration response spectra.

Time history results from real-time hybrid simulation arepresented for the HSP090 record from the Loma Prieta 1989 earth-quake scaled to the DBE and MCE intensities. A comparison be-tween the measured, dm, and command, dc , actuator displacementfor the two compressed elastomer dampers is presented in Fig. 10,where subspace synchronization plots of dc versus dm are plot-ted. Good agreement can be observed between dm and dc ; wherethe plots for each actuator show no noticeable deviation between

Fig. 9. Acceleration response spectra of the earthquake ground motions used inreal-time hybrid simulations.

themeasured and command actuator displacement. The rootmeansquare (RMS) error between dm and dc was evaluated as

RMS =

∑i

n∑j=1

dc(j)i − dm(j)

i

2

∑i

n∑j=1

(dc(j)i )2. (10)

The RMS values were found to be equal to 3.6e−4 and 3.7e−4 forthe actuators of the first story and second story damper under theDBE level, respectively. The corresponding RMS values for theMCElevelwere found to be equal to 2.5e−5 and 1.3e−4. The RMSvaluesand synchronization plots indicate that accurate actuator control isachieved during the real-time hybrid simulation. These values forthe RMS and the results shown in Fig. 10 are representative of theactuator control achieved in all of the hybrid simulations.

The hysteresis of the compressed elastomer dampers ispresented in Fig. 11. The dampers were able to undergo numerousseismic induced deformation cycles without degradation of theirhysteretic behavior. Under the DBE the dampers in both storiesexhibit an elastomeric behavior with fairly rounded peaks. (i.e.,Fig. 11(a) and (b)). Under the MCE the damper in the secondstory develops some minor slip (Fig. 11(c)), while the damper inthe first story experiences an elastomeric-frictional behavior withslip (Fig. 11(d)) that results in permanent deformation, althoughthe damper continues to develop energy dissipation. Experimentaldata such as that shown in Fig. 11(d) can be used to developand calibrate an analytical model for simulating the complexdamper hysteresis, enabling future numerical investigations of theuse of compressed elastomer dampers in enhancing the seismicperformance of buildings to be analytically investigated.

Fig. 12 shows the floor displacement time histories of theUD50V MRF with dampers. Also presented in Fig. 12 are thefloor displacement time histories of the conventional UD100VSMRF from numerical analysis. The real-time hybrid simulationsshow that the lighter UD50V MRF with dampers experiencessignificantly lower transient and permanent story drifts than thoseof the conventional UD100V SMRF. Under the DBE earthquake theUD50V MRF with dampers has negligible permanent story driftsince the dampers do not slip and have re-centering capability.Under the MCE the dampers act as sacrificial elements, which

T.L. Karavasilis et al. / Engineering Structures 33 (2011) 1859–1869 1867

Fig. 10. Actuator displacement subspace synchronization subspace plots, Loma Prieta 1989 HSP090 ground motion.

Fig. 11. Damper hysteresis from real-time hybrid simulation, Loma Prieta 1989 HSP090 ground motion.

develop permanent deformation due to slip, however as discussedpreviously, the dampers can be replaced after the earthquake.Some modest yielding occurs in the beams and at the groundlevel of the columns of the UD50V MRF with dampers. Aswill be discussed below, the plastic (and associated permanent)deformations in the MRF with dampers are small. If the damperswere replaced or re-centered after theMCE, the residual drift of theMRF with dampers under the MCE could be significantly reduced.

The added benefit of real-time hybrid simulation is that itallows an unlimited number of ground motions to be appliedto the structure and therefore, statistical experimental responseresults incorporating the ground motion variability can beobtained. In this paper, the seismic performance of the MRFwith dampers is quantified in terms of various damage indicesfor both structural and non-structural components, and includethe maximum story drift, θmax; maximum plastic hinge rotationfor beams, θpl.max_bm, and columns, θpl.max_col; peak floor absolutevelocity, vmax; peak floor absolute acceleration, amax; and the

floor acceleration response spectra, Sa,flr. vmax and amax are usefulfor quantifying the potential for damage of non-rigidly attachednon-structural components and for rigidly attached non-structuralcomponents, respectively, while Sa,flr is useful for quantifyingthe potential for damage to flexible attached equipment [36].Table 4 presents median experimental response values for theθmax, θpl.max_bm, θpl.max_col, vmax and amax of the UD50V MRF withdampers from the real-time hybrid simulations. Also presentedin Table 4 are the median values of the same response quantitiesof the conventional SMRF UD100V from the numerical analysis.Table 4 shows that the median θmax value of 1.35% and 1.40% forthe first and second stories, respectively, for UD50V MRF underthe DBE is lower than the anticipated θmax demand of 1.65% givenin Table 2, while the median value of 2.60% and 2.40% for thefirst and second stories, respectively, the median θmax for theUD100V SMRF is larger than the anticipated θmax demand of 2.4%given in Table 1. The UD50V MRF with dampers also shows asignificantly better performance than the conventional UD100V

1868 T.L. Karavasilis et al. / Engineering Structures 33 (2011) 1859–1869

Fig. 12. Floor displacement time histories from the real-time hybrid simulation, Loma Prieta 1989 HSP090 ground motion.

Table 4Median values of response parameters from real-time hybrid simulations.

Design θmax (%) θpl.max_bm (rad) θpl.max_col (rad) vmax (m/s) amax (m/s2)DBE MCE DBE MCE DBE MCE DBE MCE DBE MCE

UD100V conventional SMRF Story 1 2.60 2.90 0.008 0.014 0.010 0.015 0.78 1.00 5.32 6.60Story 2 2.40 2.60 0.000 0.003 0.000 0.000 1.11 1.28 5.66 6.36

UD50V MRF with dampers Story 1 1.35 2.50 0.002 0.006 0.002 0.010 0.61 0.90 4.18 5.70Story 2 1.40 1.80 0.000 0.000 0.000 0.000 0.77 1.10 5.16 6.50

SMRF in terms of the plastic hinge rotations. Decreases in themedian peak beam plastic hinge rotations in the UD50V MRFwith dampers are approximately 75% and 57% for the DBE andMCE, respectively, compared to UD100V SMRF. For the columns,the median peak plastic hinge rotations in the UD50V MRF withdampers are approximately 80% and 33% less than that in theUD100V SMRF for the DBE and MCE, respectively. The medianpeak floor velocities of the UD50V MRF with dampers are 22% and31% less at the first and second floors, respectively, than thoseof the UD100V SMRF for the DBE. For the MCE the median peakfloor velocities of the UD50V MRF with dampers are 10% and 14%less at the first and second floors, respectively, than those of theUD100V SMRF. The median peak floor accelerations of the UD50VMRF with dampers are 21% and 9% less at the first and secondfloors, respectively, than those of the UD100V SMRF for the DBE.Under the MCE, the UD50V MRF with dampers experiences a 14%reduction in the first floor median peak acceleration and a slightlyhigher second floor median peak acceleration than that of theUD100V SMRF.

Fig. 13 shows the median acceleration response spectra Sa,flrof UD50V MRF with dampers for the DBE and MCE levels. Alsopresented in Fig. 12 are Sa,flr of the conventional UD100V SMRFfrom numerical analysis. These spectra present the maximumpseudo-acceleration response of a 5% damped elastic single-degree-of-freedom system (SDOF) subjected to the motion (totalacceleration) of the 2nd floor of the frames. The spectra show thatthe UD50V MRF with dampers performs significantly better thanconventional UD100V SMRF. It is evident that the resonance at thefirst and secondmodes of vibration of UD50VMRFwith dampers is

Fig. 13. Median 2nd floor acceleration response spectra from the real-time hybridsimulation under DBE and MCE.

effectively damped (the period of vibration for the first and secondmodes are T1 = 1.04 s and T2 = 0.35 s, respectively). Only fora narrow period range (primarily in the period range between thefirst and secondmodes) does the conventional UD100VSMRF showa slightly better performance than the UD50V MRF with dampers.

6. Summary and conclusions

An experimental program based on the use of real-time hybridsimulation to verify the performance-based seismic design ofa steel perimeter MRF equipped with compressed elastomerdampers was presented. The experimental substructures for thesimulation consisted of two individual compressed elastomerdampers, with the remainder of the MRF and associated tributary

T.L. Karavasilis et al. / Engineering Structures 33 (2011) 1859–1869 1869

gravity columns and gravity loading of the building modeled asan analytical substructure. Real-time hybrid simulation allowedan ensemble of ground motions to be applied to the structureresulting in various levels of damage, without the need to repairthe test specimens, since the damage was within the analyticalsubstructure.

Statistical experimental response results incorporating theground motion variability showed that a steel MRF with com-pressed elastomer dampers can be designed to performbetter thanconventional steel SMRFs under the DBE and MCE, even when theMRF with dampers is significantly lighter in weight than the con-ventional SMRF. In particular, the steel MRF with dampers was de-signed with a practical number of dampers (eight dampers in thefirst story and five dampers in the second story) and with a 30%lower steel weight than that of the conventional steel MRF. Real-time hybrid simulations showed that the MRF with dampers ex-periences significantly lower peak story drifts, peak plastic hingerotations, lower peak absolute floor velocities and floor accelera-tions in addition to floor spectra accelerations, than those of theconventional steel SMRF.

Acknowledgements

This paper is based upon work supported by grants fromthe Pennsylvania Department of Community and EconomicDevelopment through the Pennsylvania Infrastructure TechnologyAlliance, and by theNational Science Foundation (NSF) underGrantNo. CMS-04002490 within the George E. Brown, Jr. Network forEarthquake Engineering Simulation Consortium Operation. Anyopinions, findings, and conclusions expressed in this paper arethose of the authors and do not necessarily reflect the views of thesponsors.

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