Evaluation Of Displacement-Based Analysis And Design .
View metadata, citation and similar papers at core.ac.ukbrought to you byCOREprovided by University of Queensland eSpaceEvaluation of Displacement-Based Analysis and DesignMethods for Steel Frames with Passive Energy DissipatorsbyM.S. Williams1 and F. Albermani2Civil Engineering Research Bulletin No. 24University of QueenslandDepartment of Civil EngineeringHawken Engineering BuildingBrisbane, Queensland 4072AustraliaISBN 186 499 75401Visiting from: University of Oxford, Department of Engineering Science, Parks Road, Oxford OX1 3PJ, UK.Email: martin.williams@eng.ox.ac.uk2Email: f.albermani@uq.edu.au
AbstractThis report investigates the use of displacement-based, or pushover methods of analysis in thedesign of frames incorporating passive dissipative devices. An extensive analysis and designstudy of 3-, 6- and 10-storey frames, both undamped moment-resisting frames (MRFs) andretrofitted with hysteretic and frictional dissipators has been performed. Frames weremodelled using the finite element program Sap2000 and were analysed using both non-linearstatic pushover analysis and non-linear time history analysis. The principal aims were toassess the degree of improvement in performance achieved through use of the devices, and thesuitability of various displacement-based analysis methods for estimating the seismicresponse of frames fitted with dissipative devices.It was found that both dissipative systems led to substantial improvements in frameperformance, in terms of plastic hinge formation (reduced to virtually zero) and deformation(reduced by a factor of more than 2). Base shears remained similar to those for the undampedMRFs.Pushover analyses were found to be a useful design tool for the unretrofitted frames, givinggood estimates of the overall displacement demands, base shears and plastic hinge formation.However, the various pushover approaches proved less successful at estimating theperformance of the dissipative frames, where they appeared to underestimate the beneficialeffects of energy dissipation.Of the various pushover methods assessed, the FEMA 356 approach appears to offer the mostaccurate and realistic estimate of seismic performance, with the exception of the inter-storeydrift distribution.For the 6- and 10-storey frames (both ductile MRFs and dissipative frames), pushovermethods using fixed, single load patterns gave rather poor estimates of the distribution ofinter-storey drift with height. Far better drift estimates were obtained using the modalpushover method, in which pushover results obtained using force distributions based on thefirst three modes are combined by the SRSS method.Bulletin no. 24-2-December 2003
AcknowledgementsThe work described in this report was conducted while the first author was an academicvisitor at the University of Queensland, between July and December 2003. We are grateful tothe Head of the Civil Engineering Department, Associate Professor Peter Dux, and the Deanof the Engineering, Physical Sciences and Architecture Faculty, Professor Michael Kenniger,for their help and support in arranging this visit. The generous financial support provided bythe UK’s Royal Academy of Engineering under the grant “Dissipative devices in seismicdesign” is also gratefully acknowledged.Some of the framed structures used in the evaluations were based on designs created by theundergraduate thesis group of Daniel Chambers, Debbie Macmillan and Daniel Moore. Theirhard work is warmly acknowledged.Bulletin no. 24-3-December 2003
ContentsAbstract . 2Acknowledgements . 3Contents. 41.Introduction . 52.Selection of Dissipator Types . 53.Design Parameters. 83.13.24.Building Designs . 94.14.25.Modelling of the Structure . 15Modelling of the Dissipators . 15Pushover Analysis Methods . 16Simple Design Methods for Frames with Dissipators. 23Time History Analysis . 24Results . 246.16.26.36.46.56.67.Moment resisting frames. 9Dissipative frames . 13Analysis and Design Methods. 155.15.25.35.45.56.Response spectrum. 8Generation of spectrum-compatible accelerograms . 9Natural Period . 24Target Displacements. 25Base Shear . 28Plastic Hinge Formation. 30Inter-StoreyDrifts . 30Link Deformations . 41Conclusions . 41References . 43Appendix A. Spectrum-Compatible Time Histories . A1Bulletin no. 24-4-December 2003
1.IntroductionPassive dissipative devices have the potential to provide significant improvements to theseismic performance of structures without the need for the sophisticated technology and costassociated with active control systems. In recent year numerous different dissipative systemshave been proposed and some structures have been built or retrofitted with such devices. Mostdevices dissipate energy through one of three mechanisms – hysteresis, friction or viscousdamping. In all cases their behaviour is, of course, highly non-linear.At the same time, approximate displacement-based methods of seismic design, based on theuse of non-linear static pushover analysis, have undergone a rapid increase in popularity andare starting to find their way into design guides and codes of practice. Several differentapproaches exist, based on different levels of simplification, and no consensus has yetemerged as to the most convenient or reliable method.This report brings together these two important topics by assessing the suitability of pushovermethods for the analysis and design of frames incorporating passive dissipative devices. Aseries of analyses of steel framed structures, with and without the addition of passivedissipative devices, have been performed using the program Sap2000 (CSI, 2002). Theprincipal aims are to assess (a) the degree of improvement in performance achieved throughuse of the devices, and (b) the suitability of various displacement-based analysis methods forestimating the seismic response of frames fitted with dissipative devices.Dissipator properties are briefly discussed in Chapter 2. Chapters 3 and 4 then present thedesign criteria adopted and he building designs chosen for the study. Chapter 5 describes thedifferent analysis approaches used and Chapter 6 presents comparisons between the variousmethods.2.Selection of Dissipator TypesA very wide range of passive dissipative devices exists or has been proposed. Substantialreviews have been published by Constantinou et al (1998) and Soong and Spencer (2002).The major categories of device are: Hysteretic devices based on metallic yielding – examples include the ADAS (AddedDamping And Stiffness) device (Aiken and Kelly, 1992) and the knee element (AristazabalOchoa, 1986; Williams et al., 2002). A companion report to this one (Williams andAlbermani, 2003) describes tests on a simple yielding shear panel device, based on anunpublished proposal by Dorka. Obviously these elements are elastic up to yield and thengenerally display a typical steel hysteresis loop, often with significant strain hardening, suchas that shown in Figure 2.1 for a knee element. Frictional systems such as the well-known Pall damper (Pall and Marsh, 1982), whichcomprises a series of clamped plates surfaced with brake lining material. These are generallytaken to be rigid up to their slip load, then to slip at constant load. Figure 2.2 shows the resultsof experiments on a similar device achieved by Wu at al (2003). However, Wu et al. have alsoshown that, due to geometric non-linearities in the devices, brace forces may increasesignificantly after slip.Bulletin no. 24-5-December 2003
Solid visco-elastic dampers (e.g. Xu and Zhang, 2001), in which materials such as acryliccopolymers are bonded between steel plates and dissipate energy through shear deformationas the plates move. These materials have no activation level and exhibit elliptical hysteresisloops, Figure 2.3. Fluid viscous dampers, which generally comprise non-linear stiffness and dampingcomponents. For example, the French company Jarret Devices quote the following governingequations for their dampers:F Fd Fe(2.1)αFd c sgn( x&) x&Fe k 2 x (2.2)(k1 k 2 ) x kx 1 1F0 (2.3)R 1/ R 6005030025Force (kN)Force (kN)where c is a damping coefficient with units of kN(s/mm)α, the exponent α takes a valuebetween 0.1 and 0.2, k1 and k2 are the initial and post-yield stiffnesses, F0 is the pre-load andthe exponent R is usually taken as 5. Figure 2.4 shows plots of the resulting hysteresis loopsfor two different values of pre-load: with a large pre-load the bilinear stiffness is clearlyevident, while with a very small pre-load the second term in Equation (2.3) becomesnegligible and only the post-yield stiffness is evident. In each plot hysteresis curves are shownfor several different rates of sinusoidal loading – it can be seen that, because of the low valueof α, the response is not particularly on (mm)Figure 2.1Hysteresis of 152 152 30UC knee elementBulletin no. 24-6--20-10010Displacement (mm)Figure 2.2Hysteresis of Pall-type friction elementDecember 200320
ForceDisplacement100100505010mm at 1HzForce (kN)Force (kN)Figure 2.3 Hysteresis of solid visco-elastic damper (after Xu and Zhang, 2001)0-5020mm at 1Hz10mm at 2Hz020mm at 2Hz10mm at 4Hz-5020mm at 4Hz-100-100-60-3003060-60-30030Displacement (mm)Displacement (mm)(a)(b)60Figure 2.4 Hysteresis of Jarret fluid viscous damper: (a) with high preload, (b) with negligible preloadInitially it was intended to include three different types of dissipator in the study: hysteretic,frictional and fluid viscous. The latter was felt to be particularly significant since its obvious(if limited) velocity dependence calls into question the appropriateness of using a non-linearstatic analysis as the basis for design. At this stage, however, only hysteretic and frictionaldevices have been analysed, partly due to time constraints and partly due to apparent bugs inthe damper element in Sap2000.Hysteretic devices were based on the knee element, which spans diagonally across a beamcolumn joint and connects to a diagonal brace as shown in Figure 2.5(a). The K-braceconfiguration was chosen as previous studies suggest this provides the optimal combination ofenergy dissipation and drift limitation. Knee element properties were based on a tri-linearidealisation of the hysteresis curve presented in Figure 2.1. A series of idealised kneeelements was designed with designations ke300, ke350, ke400 , where the number refers tothe initial yield load in kN. Details of the modelling of the devices are given in Section 5.2.Frictional devices were of the Pall type, positioned at the centre of an X-brace, Figure 2.5(b).Properties were based on a rigid-plastic idealisation of the hysteresis shown in Figure 2.2.Filiatrault and Cherry (1987) have shown that this formulation is only strictly correct if thedevice slips during every cycle of loading, but it is considered sufficiently accurate for thisstudy. Also, the geometric non-linearity referred to above has not been modelled at this stage.A series of idealised friction elements were designed with designations fric300, fric400 ,where the number refers to the slip load in kN.Bulletin no. 24-7-December 2003
BraceBraceFriction elementKnee element(a)(b)Figure 2.5 Dissipative frame layouts: (a) knee braced frame, (b) friction-damped frame3.Design ParametersThe frames presented in Section 4 below were initially designed to two different codes ofpractice – the NEHRP (1997) provisions and the Australian seismic code AS 1170.4 (1993).However, for the purposes of the analyses and assessments performed here, it was decided touse a single earthquake specification, taken from the European code EC8 (2003). This gives aslightly more sophisticated definition of the design earthquake than either of the other codes,and provides a point of comparison that is independent of the original design basis of any ofthe structures.3.1Response spectrum1212101088EC8T 0.2Sa (m/s/s)Sa (m/s/s)Buildings were designed, analysed and assessed against the EC8 (2003) Type 1 designspectrum (for moderate or large events), soil type C (dense sand or gravel, or stiff clay),scaled to a peak ground acceleration of 3.5 m/s2. This represents a reasonably largeearthquake in Europe or the USA, and an exceptionally large event in Australia. The spectrumis shown in Figure 3.1, both in the conventional acceleration vs period format, and in theADRS (acceleration-displacement) format used by ATC 40 (1996).644200123Period (s)T 2.0620T 0.600.10.2Sd (m)0.3Figure 3.1 EC8 design spectrum plotted in conventional and ADRS formatsBulletin no. 24-8-December 20030.4
3.2Generation of Spectrum-Compatible AccelerogramsFor time history analysis, an ensemble of 30 acceleration time histories compatible with theresponse spectrum of Figure 3.1 was created using the program Simqke (Gasparini andVanmarcke, 1976). To create a reasonably harsh, long-duration event, a total duration of 20seconds was specified, comprising a 2 second rise time, 10 seconds of strong motion and an 8second decay.Details of the generation process, plots of the accelerograms and comparisons with the targetspectrum can be found in Appendix A.4.Building DesignsThis section presents the designs of all the buildings chosen for analysis. Four basic buildingswere chosen/designed: 3-, 6- and 10-storey ductile moment resisting frames (MRFs), and a10-storey elastic MRF. Each of the ductile frames was then modified by the addition ofbracing and dissipative elements (both hysteretic and frictional), giving a total of sixdissipative structures.4.1Moment Resisting FramesThe 3-storey frame design was taken from the work of Ramirez et al. (2001). It was designedusing the American NEHRP (1997) guidelines for a peak ground acceleration of 0.4g with aresponse modification (ductility) factor of R 8, and standard American section sizes. In planthe building consists of five 8.23 m bays in each direction. Storey heights are 4.42 m at thefirst floor and 4.3 m at the upper floors. Lateral loads are resisted by three-bay specialmoment resisting frames on each side of the building. The structural details are shown inFigure 4.1. The building has a fundamental period of 1.1 s – this is very long for a 3-storeyframe and perhaps rather unrealistic, but it is likely to provide a good test of the variouspushover analysis methods.The 6-storey frame design was also taken from Ramirez et al. (2001). It has a very similarlayout and the same design criteria as the 3-storey frame. The structural details are shown inFigure 4.2. The building has a fundamental period of 1.9 s, again rather long for a frame ofthis height.The 10-storey frames were loosely based on designs produced by a UQ undergraduate thesisgroup under the authors’ guidance. They were designed in accordance with the Australianseismic code AS 1170.4 (1993) for a peak ground acceleration of 0.33g, using standardAustralian sections (which are similar to British ones). Two buildings were designed, withductility factors of R 1 and R 4.5. The buildings consist of three 6 m bays in eachdirection, with 4 m storey heights. The structural details are shown in Figure 4.3. The R 1building has a natural period of 1.2 s and the R 4.5 building has a natural period of 2.4 s.Bulletin no. 24-9-December 2003
8.23m8.23m8.23mMass per floor: 580 tMass of roof: 320 t8.23m8.23m3-bay perimeter SMRFsAll other joints pinned8.23m8.23m8.23m8.23m8.23mAll columns W14x2114.3mStorey 3: Beams W18x464.3mStorey 2: Beams W21x504.42mStorey 1: Beams W24x62Figure 4.1 Structural details of 3-storey MRFBulletin no. 24- 10 -December 2003
8.23m8.23m8.23mMass per floor: 580 tMass of roof: 320 t8.23m8.23m3-bay perimeter SMRFsAll other joints torey 6: W21x44Storeys 5-6: W14x2114.3mStorey 5: W21x504.3mStorey 4: W24x68Storeys 3-4: W14x2334.3mStorey 3: W24x764.42m4.3mStorey 2: W27x84Storey 1: W27x94Storeys 1-2: W14x257Figure 4.2 Structural details of 6-storey MRFBulletin no. 24- 11 -December 2003
6m6mMass per floor: 195 tMass of roof: 156 t6mPerimeter MRFInternal joints pinned6m6mR 4.5:R 1.0:Storeys 8 - 10Beams: 460UB67.1Columns: 310UC118Storeys 8 - 10Beams: 530UB92.4Columns: 400WC361Storeys 5 - 7Beams: 530UB92.4Columns: 350WC197Storeys 5 - 7Beams: 800WB192Columns: 500WC414Storeys 1 - 4Beams: 610UB101Columns: 350WC280Storeys 1 - 4Beams: 900WB218Columns: Proprietary4m4m4m4m4m4m4m4m4m4m6mFigure 4.3 Structural details of 10-storey MRFsBulletin no. 24- 12 -December 2003
4.2Dissipative framesThe dissipative frames were designed as retrofits to the ductile moment-resisting frames, i.e.bracing and dissipative elements were added to the frames so as to improve their performance,with no attempt made to redesign the main frame elements. In each case the design aims wereto convert a ductile frame into one in which the main members stayed as near to elastic aspossible while the dissipators suffered no ultimate failure (defined as exceeding a limitingdeformation) under the design earthquake, as specified in Section 3.1. For the knee elements,failure was defined as occurring when the extension of a link element representing thecombination of a brace and knee element exceeded 40 mm (corresponding to a knee elementdeformation of 25 mm). For the friction elements, failure was assumed to occur when a linkrepresenting a brace and a friction element exceeded 30 mm (virtually all in the frictionelement).Initial rough sizing of the dissipative elements was performed using the two approximatedesign methods set out in Section 5.4 below, while final design was based on pushoveranalysis using the FEMA 356 (2000) approach, as described in Section 5.3.The dissipator designs and initial elastic periods of the retrofitted buildings are set out inFigures 4.4 – 4.6. The designation ke300 refers to a knee element with in initial yield load of300 kN. Similarly, fric300 refers to a friction element with a slip load of 300 kN. Braces weresized to carry the maximum load in the adjoining dissipator with a factor of safety of 2.0 onyield.The design objective of no yield in the main frame was not achieved in all cases. It was foundthat a point was reached where increasing the dissipator capacity had no beneficial effect, andin some cases was even detrimental. In general, the friction damped frames came closer tomeeting the design objective than the knee braced frames.Knee braced frameFriction damped frameke300fric300ke650fric600ke650fric700T 0.58 sT 0.54 sFigure 4.4 Dissipator designs for 3-storey framesBulletin no. 24- 13 -December 2003
Knee braced frameFriction damped 600ke700fric700ke700fric700T 0.93 sT 0.90 sFigure 4.5 Dissipator designs for 6-storey framesKnee braced frameFriction damped 0ke600fric600ke600fric600T 1.14 sT 1.13 sFigure 4.6 Dissipator designs for 10-storey framesBulletin no. 24- 14 -December 2003
5.Analysis and Design MethodsIn this section the modelling of the frames using Sap2000 is discussed, as are the variouspushover analysis methods investigated and the non-linear time history analysis with whichthe results are compared.5.1Modelling of the StructureIn each case, only a single, planar MRF was modelled. The beams and columns weremodelled using standard frame elements in Sap. Elements were assumed to behave linearlyexcept at pre-defined hinge locations, which were located at 5% of the length from each endof each member. Hinges were assigned a 5% strain hardening ratio and were assumed to failcompletely at a rotational ductility of 6. Floors were assumed to act as rigid diaphragms andto distribute their mass uniformly on the supporting beams.5.2Modelling of the DissipatorsKnee element hysteretic properties were based on a tri-linear idealisation of the hysteresiscurve as shown in Figure 5.1(a). In order to come up with a series of simple, idealised kneeelement properties, it was assumed that both strength and stiffness could be scaled in the sameway for different knee element sizes, so that only the yield forces varied between sections, notthe yield deformations. This is not strictly correct, but the error thus introduced is likely to besmall.The brace connected to a knee element was designed to carry the maximum knee elementforce with a factor of safety of 2 against yielding, assuming mild steel with a yield strength of300 MPa. Braces were assumed not to buckle. For modelling in Sap, a single link elementwas defined representing the combined stiffness of the elastic brace and the yielding kneeelement acting in series. Figure 5.1(b) shows the skeleton curves for a typical knee elementand the corresponding knee/brace link element in a direction along the brace axis.A similar approach was adopted for modelling the friction elements, except that the initialidealisation was simply to elastic-perfectly plastic. Typical curves are shown in Figure 5.2.1000600TestModelForce (kN)Force (kN)300Knee n (mm)2030(a)Link element-30-20-10010Displacement (mm)20(b)Figure 5.1 Modelling of a knee element: (a) Idealisation of hysteresis data, (b) typical skeleton curvesfor a ke500 element and the corresponding ke/brace link element in the 10-storey frameBulletin no. 24- 15 -December 200330
200FrictionelementLinkelement10025Force (kN)Force (kN)5000-100-25-50-200-20-10010Displacement (mm)20-40-20020Displacement (mm)(a)(b)Figure 5.2 Modelling of a friction element: (a) Idealisation of hysteresis data, (b) typical skeletoncurves for a fric300 element and the corresponding element/brace link element in the 10-storey frame5.3Pushover Analysis MethodsDisplacement-based design methods make use of non-linear static, or pushover, analysis(Fajfar and Fischinger, 1988; Lawson et al. 1994; Krawinkler and Seneviratna, 1998).Appropriate lateral load patterns are applied to a numerical model of the structure and theiramplitude is increased in a stepwise fashion. A non-linear static analysis is performed at eachstep, until the building fails. A pushover curve (base shear against top displacement) can thenbe plotted. This is then used together with the design response spectrum to determine the topdisplacement under the design earthquake – termed the target displacement or performancepoint. The non-linear static analysis is then revisited to determine member forces anddeformations at this point.These methods are considered a step forward from the use of linear analysis and ductilitymodified response spectra, because they are based on a more accurate estimate of thedistributed yielding within a structure, rather than an assumed, uniform ductility. Thegeneration of the pushover curve also provides the engineer with a good feel for the nonlinear behaviour of the structure under lateral load. However, it is important to remember thatpushover methods have no rigorous theoretical basis, and may be inaccurate if the assumedload distribution is incorrect. For example, the use of a load pattern based on the fundamentalmode shape may be inaccurate if higher modes are significant, and the use of a any fixed loadpattern may be unrealistic if yielding is not uniformly distributed, so that the stiffness profilechanges as the structure yields.The main differences between the various proposed methods are (i) the choices of loadpatterns to be applied and (ii) the method of simplifying the pushover curve for design use.The methods used in this study are summarised below.Bulletin no. 24- 16 -December 200340
5.3.1EC8 (2003)1.Pushover analysis – apply the following two load patterns:Modal – the acceleration distribution is assumed proportional to the fundamentalmode shape. The inertia force Fi on mass i is then:mi φ iFi m φjj 1(5.1)Fbnjwhere Fb is the base shear, mi the ith storey mass and φi the mode shape coefficient forthe ith floor. If the fundamental mode shape is assumed linear then φi is proportionalto storey height hi and Equation (5.1) can be written as:mi hiFi m hjj 1(5.2)FbnjUniform – the acceleration is assumed constant with height. The inertia forces are thengiven by:miFi Fbn mj 1(5.3)jPlot pushover curve Fb vs d, with maximum displacement dm.2.Convert pushover curves to equivalent SDOF system using:F* FbΓ(5.4)d* dΓ(5.5)nΓ m φj 1j(5.6)n m φj 13.jj2jSimplify to elastic-perfectly plastic as shown in Figure 5.3. Set Fy* equal to maximumload, choose d *y to give equal areas under actual and idealised curves.Bulletin no. 24- 17 -December 2003
F*Fy*Ked*d y*d m*Figure 5.3 Idealisation of pushover curve in EC84.Calculate target displacement of SDOF system under design earthquake:d t* S aT24π 2T Tc(5.7)d t* S aT T2 1 1 (q 1) c 2 T 4π q T Tc(5.8)whereq Sa( F / m* )(5.9)*ynm * m jφ j(5.10)j 1T is the elastic period of the idealised SDOF system, Sa is the spectral accelerationcorresponding to T, and Tc is the corner period of the design response spectrum, i.e.the period at the transition between the constant acceleration and constant velocityparts of the curve.5.Transform target displacement back to that of the original MDOF system usingEquation (5.5).6.Check that dt dm/1.5. Check member strengths and storey drifts are acceptable at thisvalue of dt.Bulletin no. 24- 18 -December 2003
5.3.2 FEMA 356 (2000)1.Pushover analysis – apply the following two load patterns:Modal – use either an acceleration distribution proportional to the fundamental modeshape or a multi-modal load distribution obtained from a response spectrum analysis.If using the fundamental mode shape, the inertia force distribution is given byEquation (1). The fundamental mode shape can be obtained from a modal analysis, oran assumed shape can be used, giving the load distribution:Fi mi hik m hjj 1(5.11)Fbnkjk 1.0T 0.5s 0.75 T20.5 T 2.5s 2.0(5.12)2.5 TEither uniform or adaptive – For the uniform pattern the inertia forces are then givenby Equation (5.3).Plot pushover curve Fb vs d, with maximum displacement dm.2.Simplify to bilinear as shown in Figure 5.4. Choose parameters so as to giveapproximately equal areas under actual and idealised curves. Initial stiffness estimateis governed by the requirement that the actual and idealised curves intersect at 0.6Fy.Post-yield stiffness is governed by the requirement for the curves to meet at the targetdisplacement. This may require some iteration since dt is not determined until later.FbFyα Ke0.6FyKeddydtdmFigure 5.4 Idealisation of pushover curve in FEMA 356Bulletin no. 24- 19 -December 2003
3.Calculate target displacement of MDOF system under design earthquake:Te2d t ΓS a4π 2Te Tc(5.13)Te2 1 Tc d t ΓS a 1 (q 1) 2Te 4π q Te Tc(5.14)Te is the elastic period of the idealised MDOF system and Sa is the spectralacceleration corresponding to Te.4.Check member strengths and storey drifts are acceptable at this value of dt.Note: The main calculation steps are equivalent to the EC8 procedure. The significantdifferences are (a) a slightly wider choice of load patterns and (b) a more realistic idealisationof the pushover curve.5.3.3 Modal pushover (Chopra and Goel, 2002, Chintanapakdee and Chopra, 2003)Proposed as a modification to the FEMA method outlined above.1.Pushover analysis – apply modal load patterns corresponding to the first three modeshapes as determined by eigenvalue analysis. Inertia loads are given by Equation (5.1).Plot
dissipative devices, have been performed using the program Sap2000 (CSI, 2002). The principal aims are to assess (a) the degree of improvement in performance achieved through use of the devices, and (b) the suitability of various displacement-based analysis methods for estimating the seismic response of frames fitted with dissipative devices.
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