damper

Engineering Structures 30 (2008) 1058–1066www.elsevier.com/locate/engstruct

Experimental study of steel slit damper for passive energy dissipation

Ricky W.K. Chana,b, Faris Albermania,∗

a Department of Civil Engineering, University of Queensland, Australiab Department of Building and Construction, City University of Hong Kong, Hong Kong

Received 13 April 2007; received in revised form 12 July 2007; accepted 12 July 2007Available online 15 August 2007

Abstract

This paper summarizes the development of a new steel energy dissipative device designed for earthquake protection of structures. The SteelSlit Damper (SSD) is fabricated from a standard structural wide-flange section with a number of slits cut from the web, in a vierendeel trussarrangement. The device is a weld-free design, thereby eliminating the uncertainties and difficulties encountered in in situ welding. Energy isdissipated through flexural yielding of the vierendeel’s web members when the device is subjected to inelastic cyclic deformation. The performanceof the device was verified by nine tests and the effects of geometrical parameters were investigated. Experiments showed that the device exhibitedstable hysteresis with excellent energy dissipation and ductility. The device yielded at small angular distortion and is thus expected to dissipateenergy early in an earthquake. The structural characteristics of the device are readily determined from fundamental engineering principles, thusthe design can be easily modified or extended to suit particular structural requirements.c© 2007 Elsevier Ltd. All rights reserved.

Keywords: Energy dissipation; Metallic damper; Cyclic tests; Earthquake resistant structure

1. Introduction

The research and development of structural control againstwind and earthquake excitation have achieved significantprogress over the last three decades [1,2]. Structural controlcan broadly be classified into three categories: (1) Passivecontrol systems are those structures equipped with designateddevices or dampers which do not require an external source ofpower, (2) Active control systems are those structures equippedwith real-time processing sensors and force delivery deviceswhich require an external source of power to generate structuralcontrol forces, and (3) Semi-active control systems which uselittle power to change certain structural parameters. Passivecontrol systems, also known as passive energy dissipationsystems, have been considered an effective and inexpensiveway to mitigate earthquake risks to structures. With designatedenergy dissipative devices installed in a structure, a largeportion of the input energy supplied by wind and/or earthquakecan be dissipated; hence the damage to the parent structure is

∗ Corresponding author.E-mail address: [email protected] (F. Albermani).

0141-0296/$ - see front matter c© 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2007.07.005

minimized. Passive devices do not require an external sourceof power, hence the reliability associated with power supplyand computer control during an earthquake event is eliminated.By arranging the devices in a way that facilitates replacement,damaged devices can be replaced with minimum time andcost, hence interruption to human occupancy is minimized—acrucial benefit to the building owners and occupants.

Energy dissipation can be achieved by a number ofmechanisms: friction sliding, yielding of metals, phasetransformation of metals, fluid orificing and deformation ofviscoelastic solid or fluid. In particular, one of the most popularmechanisms for dissipation of energy input to a structure isthrough the yielding of metallic materials. The research inmetallic passive energy dissipative devices has been conductedover the last three decades. Numerous metallic dampers havebeen proposed and installed [3–5]. Popular devices include thehourglass shape ADAS device [6], its variant the triangularshape TADAS [7], Honeycomb damper [8] and BucklingRestrained Brace [9]. These devices are mainly designed tobe incorporated into the bracing system of structural frames.Other devices were developed for installation between beamsand columns in a frame structure [10]. On the other hand, someresearchers have made use of alternative materials in device

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R.W.K. Chan, F. Albermani / Engineering Structures 30 (2008) 1058–1066 1059

Fig. 1. Geometric design of steel slit damper (a) and (b) SL-1 to SL-7, (c) SL-8 and (d) SL-9.

fabrication, such as lead, low-yield steel, copper and shapememory alloys to improve the performance [11–15].

de la Llera et al. [14] described that a good metallic dampermust possess two important characteristics in order for thesedevices to be used in engineering applications: (1) to havestable and large energy dissipative capability; (2) to have arepresentative model of its cyclic behaviour. In line with thesecond aspect, numerous experiment-based and mechanics-based models have been developed [16–19]. While someresearchers used the simpler bilinear model for hystereticresponse [19], others adopted models such as the Bouc–Wenmodel [14] and Ramberg–Osgood model [18]. These modelsare capable of capturing the smooth transition from elastic toinelastic regime observed in experiments.

The design aspect of structures equipped with passivedevices has been considered by many researchers [19–21].Nakashima et al. [21] described that the first yielding,i.e. yielding of the damping mechanism has to be set low, for thepurpose of triggering the energy dissipation as early as possible,and to set the yielding level of the parent structure high for thepurpose of retarding serious structural damage.

This paper summarizes a development of a new metallicpassive device; the steel slit damper SSD. The proposeddevice provides stable and reasonably large energy dissipativecapability, and provides a low-cost alternative to structuraldesigners. The structural behaviour of the proposed SSD isevaluated theoretically, followed by experimental verifications.Eight cyclic tests and one monotonic test were conducted.Results and discussions are presented with emphasis on key

features which affect energy dissipation capability. The conceptof SSD, though of a different configuration, was implementedin a 26-storey building in Japan in 1996 [22].

2. Device design

The basic design of the proposed device is shown in Fig. 1.It is fabricated from a short length of a standard structural wide-flange section with a number of slits cut from the web, leavinga number of strips between the two flanges in a vierendeeltruss arrangement. The slits are rounded at their ends, therebyreducing stress concentration in reentrant-corners. Four boltholes are drilled on each flange for the connection to the parentstructure. The device is a weld-free design, thus eliminating theuncertainties and imperfections associated with welding. Thedevice can be installed on top of an inverted-V brace of a framedstructure as shown in Fig. 2. Under small relative displacementbetween the two supported flanges, the strips behave as a seriesof partially fixed-ended beams and deform in double curvature.The elastic bending moment in the strips is shown in Fig. 3(a).Under sufficient displacement, plastic hinges form at both endsof each strip. Consequently, the mechanical characteristics ofthe slit damper can be described in terms of the strip lengthl0, strip depth b and web thickness t (Fig. 1). Assumingelastic–perfectly-plastic behaviour, the device yield load Pycan be determined based on a plastic mechanism analysis (seeAppendix).

Py =nσy tb2

2l0(1)

1060 R.W.K. Chan, F. Albermani / Engineering Structures 30 (2008) 1058–1066

Fig. 2. A single-storey structure with a damper.

Fig. 3. (a) Bending moment in SSD and (b) Deformed shape of SSD.

where n is the number of strips in the device, l0 is as shown inFig. 1(a) and σy is the material yield stress. The elastic stiffnessof the device kd can be determined by assuming that the stripsare partially fixed at their ends. It is given by,

kd = cnEtb3

l30

(2)

where E is Young’s modulus and c is a stiffness coefficient tobe calibrated from experiments.

3. Experimental verification

The objective of the experiments is to verify the structuralcharacteristics as well as the cyclic performance of the proposeddevice. Attempts were made to identify the key geometricparameters for largest energy dissipation. Particular attentionwas paid to the change in stiffness and equivalent dampingratio. It was assumed that the device is used as a retrofit optionwhere axial force in the device is less significant; hence no axialforce was applied to the specimens in the experiment.

3.1. Specimens

A total of nine specimens similar to Fig. 1(a) were fabricatedat the City University of Hong Kong. To simplify the fabricationprocess, all specimens (each 100 mm long) in this study werecut from a single segment of a structural wide-flange section152 × 152 × 37 Universal Column to BS4449 (depth ×

flange width × web thickness × flange thickness is 161.8 ×

152.2 × 8 × 11.5 mm respectively). Consequently, the webthickness t is identical and material strengths of all specimensmay be assumed equal. Four 16 mm diameter holes were

Table 1Test specimens (units: mm)

Specimen ID Measured dimensions b/ l0 Test regime

t b l0SL-1 8.0 14.9 97.0 0.155 Cyclic

SL-2 15.0 87.1 0.172

SL-3 15.1 77.0 0.195

SL-4 16.9 99.2 0.172

SL-5 16.8 88.3 0.191

SL-6 16.5 79.0 0.215

SL-7 16.6 99.1 0.172 Monotonic

SL-8 16.6 Varies Varies Cyclic

SL-9 16.5

drilled on each flange. Two standard test coupons were takenfrom the web of the section. Coupon tests gave an averagetensile yield stress of 316.5 N/mm2 and an average Modulusof Elasticity of 206.1 kN/mm2. Among the nine specimens,SL-1 to SL-6 aimed at investigating the best geometry of theslit arrangement (i.e. b/ l0 ratio). SL-7 was fabricated withthe identical dimensions of SL-4 and was instrumented todetermine the strain behaviour of the device under monotonicloading. SL-8 and -9 were fabricated with varied slit lengths,as shown in Figs. 1(c) and (d). Each specimen weighedapproximately 2.2 kg. A summary of the specimens are givenin Table 1.

3.2. Test setup, loading history and instrumentation

Based on the existing laboratory conditions, the test setupshown in Fig. 4 was developed. The test specimens wereinstalled between a ground beam and an L-beam, securelyfastened by four M16 bolts (snug tight) on each side. Forceddisplacement was applied by an MTS 100 kN capacitycomputer-controlled actuator quasi-statically to the specimenvia the L-beam. To ensure the verticality of the applied load,a pantograph system was welded to the right hand side ofthe L-beam. To prevent the L-beam from deflecting out-of-plane, lateral supports (with rollers) were provided (not shownfor clarity). However, these supports were later removed asit was noticed that the pantograph system already preventedthe L-beam from deflecting out-of-plane. The complete testsetup rested on a reaction frame which was significantly stiffer.The centreline of the actuator implied an eccentricity to thespecimen, measured 162 mm to the centreline of the specimen.A free-run of the setup (i.e. without the specimen installed) wasperformed, and the result showed that friction and the effect ofgravity were considerably negligible. The test setup was robustand repeatable, and no visible damage occurred after all testswere carried out.

Displacement history for the cyclic tests is shown in Fig. 5.Three cycles were performed at each amplitude: 0.5, 1.0, 1.5,2.5, 5.0, 7.5, 10.0, 12.5, 15.0 and 20.0 mm. The tests werecarried out until the complete failure of specimens.

Displacements of the specimens were measured indepen-dently by a set of LVDTs, marked as 1 through 3 in Fig. 4.


Fig. 4. Test setup.

Fig. 5. Displacement history for cyclic tests.

While LVDT 1 measures the elastic deformation of the support,the difference across LVDT 1 and 2 measured the absolute dis-tortion of the test specimen. With LVDT 3 and the distance be-tween LVDT 2 and 3 measured, in-plane rotation of the L-beamcould be monitored and was found to be negligible.

3.3. Test results and discussion

All eight specimens deformed in a stable manner underthe cyclic tests. The strips deformed in double curvatureas expected. Figs. 6(a)–(h) present the force–displacementhysteresis obtained in the cyclic tests. A positive signrefers to downward force and displacement. Shear strain γ

(i.e. distortion divided by total width of the device) of thespecimens are also shown. It is clear that all specimenshave yielded at small displacement and exhibited very stablehysteretic behaviour with a gradual transition between theelastic and inelastic regime. As seen from Fig. 6, the deviceresponse is usually less than the input displacement (Fig. 5)due to small elastic support displacement. The structuralcharacteristics of the device were determined based on theabsolute deformation of the device as calculated from thedifference between LVDT 1 and 2 (Fig. 4). Specimen SL-1(specimen with the smallest b/ l0 ratio), sustained the lowestforce while specimen SL-6 (specimen with highest b/ l0 ratio)sustained the largest.

Strength degradation started to appear when cracks slowlyformed at the ends of the strips due to stress concentration.On an average this took place after 27 cycles of loading. Theexact location at which these cracks originated differed amongthe specimens. The tests were stopped after one or more stripscompletely fractured and the load sustained was significantlyreduced. The number of cycles Nc sustained by the specimensis tabulated in Table 2. On the other hand, the connection ofthe specimens by four structural bolts on each flange performedsatisfactorily; no significant distortion was observed after thetests.

For specimens SL-8 and -9 with variable slit lengths, cracksfirst appeared in strips on the side adjacent to the shorter slit.As will be discussed in later sections, in terms of strengthand energy dissipation capabilities, these two specimens didnot demonstrate any superior performance. Fig. 7 shows thedamaged device after testing.

3.3.1. Yield and initial stiffnessKey experimental results are tabulated in Table 2.

Experimental yield strength Py,ex is defined as the pointat which there is visible deviation from the initial linearrelationship. The predicted yield load of the device, Py , usingEq. (1) and the measured and calculated properties of eachdevice are also tabulated for comparison. The predicted yieldstrengths using plastic mechanism analysis are generally ingood agreement with the test results.

The average stiffness coefficient c determined from the testswas 0.30, suggesting that the actual stiffness of the strips is 30%of that of a fixed-ended beam. The c values for specimens withsmaller slenderness (SL-3 and -6) were relatively lower than0.3.

A nonlinear finite element (FE) analysis, in which the devicewas represented by solid elements, was carried out and resultwas compared with the monotonic test of specimen SL-7 inFig. 8. The elastic and plastic properties of the material weredirectly obtained from the standard coupon test. As can be seenfrom Fig. 8, the FE model gave very accurate prediction ofthe elastic stiffness but slightly over estimated the elastoplasticresponse. The same FE model gave an out-of-plane stiffnessof 1.27 kN/mm based on the geometry of SL-7, a valuecomparable to a typical cleat-plate type of brace connectionused in practice.

3.3.2. Peak strengths and ductility ratiosBoth the positive (Pmax downward) and negative (Pmin

upward) peak strengths are tabulated in Table 2. Negative peakswere, on an average 13% lower than the positive peak valuesdue to the Bauschinger effect. Due to strain-hardening, themaximum positive peak strengths Pmax obtained are on anaverage 2.0 times higher than the experimental yield Py,ex .Cumulatively, SL-1 (the specimen with the lowest b/ l0 ratio)travelled the longest displacement prior to failure. Ductilityratio is defined by µ = δmax/δy , where δmax is the maximumdisplacement during a stable cycle and δy is the nominalyield displacement (see Appendix). The curves for normalizedstrength Pmax/Py versus ductility are shown in Fig. 9. It is


Fig. 6. Force–displacement hysteresis for cyclic test specimens.

interesting to note that all specimens behaved in a similarfashion. All specimens sustained ductility ratios in the rangeof 29–40. It should be noted that ductility is dependent on thedisplacement history applied, and it will vary if the history ischanged. For the monotonic test SL-7, a ductility ratio over 55was achieved when the test was terminated. It is expected thata higher ductility than this is possible to achieve.

3.3.3. Energy dissipation

The curves for cumulative energy dissipation versuscumulative displacement are shown in Fig. 10. Specimensdissipated negligible energy at the start while the specimenswere loaded in their elastic range. The curves take off asthe specimens were displaced beyond their yield limit. Thesmall wobbles in these curves were caused by the elastic


Fig. 6. (continued)

(a) SL-4. (b) SL-8.

Fig. 7. Specimens at failure.

Table 2Summary of test results (units: kN, mm)

Specimen kd c Py Py,ex Py/Py,ex Pmax Pmin δy δmax µ Nc

SL-1 6.67 0.29 11.83 11.51 1.03 22.61 −19.37 0.49 17.32 35.42 29SL-2 9.31 0.29 13.78 13.09 1.05 25.54 −20.59 0.39 12.05 30.86 27SL-3 12.36 0.26 11.56 15.02 0.77 25.81 −25.98 0.30 11.66 38.49 26SL-4 9.30 0.29 14.34 14.62 0.98 29.61 −23.28 0.45 16.47 36.69 29SL-5 12.54 0.29 16.75 16.11 1.04 31.26 −26.40 0.36 11.92 32.83 26SL-6 13.52 0.23 17.45 17.47 1.00 35.68 −29.79 0.29 11.44 39.19 26SL-7 14.56 0.48 12.94 14.08 0.92 25.71 – 0.46 25.71 55.89 –SL-8 11.02 0.31 14.15 14.80 0.96 29.56 −25.41 0.41 11.88 28.86 27SL-9 10.21 0.25 15.19 15.49 0.98 31.68 −29.41 0.37 11.42 30.81 26

energy released at each cycle. These light-weight specimens(around 2.2 kg each) are capable of dissipating significantamounts of energy (8–10 kJ). Among the specimens, SL-4dissipated the highest energy (10.3 kJ) while SL-3 dissipatedthe least (6.92 kJ). SL-6, which possesses strips with the leastslenderness, dissipated energy with the highest rate but failed ata relatively low cumulated displacement. It is possible to designthe proposed device according to the desired level of energy

dissipation that can be quantified through numerical analysis ofthe entire structure.

3.3.4. Strain distributionsIn order to monitor the strain behaviour of the device, a

monotonic test was carried out. The force–displacement curvefor specimen SL-7 is shown in Fig. 8. The geometry of SL-7is identical to the previously tested SL-4 which dissipated the


Fig. 8. Force–displacement curve of SL-7.

Fig. 9. Envelope curves for test specimens in cyclic tests.

Fig. 10. Cumulative dissipated energy of specimens.

largest amount of energy. A total of 24 high-yield strain-gauges(SG) were attached to the strips (i.e. 6 gauges on each strip).Under monotonic loading, the strain measured at the top andbottom fibres of each strip are shown in Figs. 13(a) and 13(b)respectively. These figures confirm the validity of the plastic

Fig. 11. Effective stiffness and energy dissipated in a cycle.

mechanism analysis and also show that loading is uniformlydistributed between the four strips in the device.

3.3.5. Equivalent stiffness and damping ratiosIt is generally accepted that energy dissipated in cyclic

straining of metals is rate-independent. For practical use it issometimes more preferable to express the device properties inan equivalent viscous system. This is basically a single degreeof freedom oscillator with an equivalent stiffness keff defined as(see Fig. 11),

keff =|Pmax| − |Pmin|

|δmax| − |δmin|. (3)

The damping ratio for the equivalent system, ζeq can beobtained by equating the measured energy dissipated percycle (ED) in the experiment to that of a viscously dampedoscillator [23]. It can be expressed by,

ζeq =1

4π

ED

ES0(4)

where ES0 is the energy stored in an elastic spring with astiffness keff and displacement δmax.

The plots of equivalent damping ratio versus normalizedeffective stiffness keff/kd are shown in Fig. 12 (for differentloading cycles). Each point represents a feasible stiffness andequivalent damping ratio of the proposed device. Effectivestiffness decreases as the device undergoes larger displacement.It can be observed that equivalent damping ratios varyapproximately inversely with effective stiffness. In largedisplacement ranges, the specimens provide a damping ratio inexcess of 50% and in general the device can furnish a dampingratio range between 30% to 50%.

4. Conclusions

This paper describes the development of a new low-coststeel energy dissipative device. The steel slit damper SSDis fabricated from commonly available wide-flange structuralsection. No special fabrication technique is involved; hence thedevice can be easily implemented in practice.


Fig. 12. Equivalent damping ratios of specimens.

Fig. 13(a). Axial strain measured on top of strips of SL-7.

Fig. 13(b). Axial strain measured on bottom of strips of SL-7.

The proposed device dissipates input energy by flexuralyielding of a series of strips, which are created by cuttinga series of slits through the web of a short length wide-flange section. Eight cyclic tests and one monotonic test wereconducted and the main findings are summarized below:

1. Cyclic tests demonstrated stable hysteretic behaviour anddissipated significant amounts of energy (6.9–10.3 kJ) underquasi-static conditions.

2. The yield strength of the device can be easily predictedby plastic mechanism analysis. The elastic stiffness of thedevice can be calibrated empirically. A nonlinear finiteelement analysis gave accurate predictions of the elastic andpost-yield behaviour of the device. Therefore, the design ofthe device can be easily extended to suit particular needs.

3. Due to strain-hardening, the ultimate strength of thespecimens was larger than their respective yield strength bya factor of 2.0. Such strain-hardening effect is beneficial interms of increased energy dissipation.

4. Devices with longer and/or wider slits behave more flexibly.Devices with shorter and/or narrower slits possess higherstiffness, dissipate energy at a higher rate but suffer fromearlier failure.

5. Large plastic strains concentrations at strip ends causethe specimens to fail by fracture. On an average thishappens after more than 27 loading cycles with cumulativedisplacement of over 500 mm.

Acknowledgement

This research is partially funded by the City University ofHong Kong (Project No. 9040797-560).

Appendix. Mechanism analysis of slit damper

The second moment of area I can be calculated by thegeometry of the prismatic strips.

I = tb3/12. (5)

For a unit displacement between the two sides of the device,elastic stiffness against displacement is given by,

kd = cn12E I

l30

= cnEtb3

l30

(6)

where n = number of prismatic strips in the SSDc = stiffness coefficient of device, expressed as a fraction of

fixed-ended stiffnesst = width of stripsb = depth of strips.When movement is sufficiently large, bending moment at the

ends of strips causes the extreme fibres to reach yield stress.Subsequently, plastic hinges form at both ends with a rotationθp. For prismatic beams the full plastic moment Mp is given by,

Mp = σytb2

4. (7)

The ultimate force of the device can be determined based on thecollapse mechanism when all beam end moment become plastichinges. According to the conservation of energy, and assumingan elastic–perfectly-plastic material behaviour;

Pyδp = 2nMpθp. (8)

By using the geometric relationship as shown in Fig. 3,the plastic displacement δp sustained by the damper can beexpressed in terms of plastic rotation θp by

δp = l tan θp. (9)


For small rotation, tan θp ≈ θp, Eq. (9) is reduced to

δp = lθp. (10)

Substituting Eqs. (7) and (10) into (8) gives

Py =2nMp

l0=

nσy tb2

2l0(11)

and nominal yield displacement can be obtained from

δy = 0.5εyl20/b. (12)

References

[1] Soong TT, Dargush GF. Passive energy dissipation systems in structuralengineering. John Wiley & Sons; 1997.

[2] Soong TT, Spencer Jr BF. Supplemental energy dissipation: State-of-the-art and state-of-the-practice. Engineering Structures 2002;24:243–59.

[3] Boardman PR, Wood BJ, Carr AJ. Union House – A cross braced structurewith energy dissipaters. Bulletin of the New Zealand National Society forEarthquake Engineering 1983;16(2).

[4] Martines-Romero E. Experiences on the use of supplemental energydissipaters on building structures. Earthquake Spectra 1993;9(3):581–625.

[5] Perry CL, Fierro EA, Sedarat H, Scholl RE. Seismic upgrade in SanFrancisco using energy dissipation devices. Earthquake Spectra 1993;9(3):559–79.

[6] Bergman DM, Goel SC. Evaluation of cyclic testing of steel plate devicesfor added damping and stiffness. Report no. UMCE87-10. Ann Arbor (MI,USA): The University of Michigan; 1987.

[7] Tsai K, Chen H, Hong C, Su Y. Design of steel triangular plate energyabsorbers for seismic-resistant construction. Earthquake Spectra 1993;9(3):505–28.

[8] Kobori T, Miura Y, Fukusawa E, Yamada T, Arita T, Takenake Y, et al.Development and application of hysteresis steel dampers. In: Proceedingsof 11th world conference on earthquake engineering. 1992. p. 2341–6.

[9] Clark PW, Aiken ID, Tajirian F, Kasai K, Ko E, Kimura I. Designprocedures for buildings incorporating hysteretic damping devices.In: Proc. int. post-SmiRT conf. seminar on seismic isolation. Passiveenergy dissipation and active control of vibrations of structures. 1999.

[10] Koetaka Y, Chusilp P, Zhang Z, Ando M, Suita K, Inoue K, et al.Mechanical property of beam-to-column moment connection withhysteretic dampers for column weak axis. Engineering Structures 2005;27:109–17.

[11] Rodgers GW, Chase JG, Mander JB, Leach NC, Denmead CS. High force-to-volume extrusion dampers and shock absorbers for civil infrastructure.In: Proceedings of 19th Australasian conference on the mechanics ofstructures and materials. 2006.

[12] Nakashima M, Iwai S, Iwata M, Takeuchi T, Konomi S, Akazawa T, et al.Energy dissipation behaviours of shear panels made of low yield steel.Earthquake Engineering and Structural Dynamics 1994;23:1299–313.

[13] Nakashima M. Strain-hardening behaviour of shear panels made of low-yield steel, I: Test. Journal of Structural Engineering 1995;121(12):1742–9.

[14] de la Llera J, Esguerra C, Almazan JL. Earthquake behavior of structureswith copper energy dissipaters. Earthquake Engineering and StructuralDynamics 2004;33:329–58.

[15] Dolce M, Cardone D, Marnetto R. Implementation and testing of passivecontrol devices based on shape memory alloys. Earthquake Engineeringand Structural Dynamics 2000;29:945–68.

[16] Williams MS, Albermani F. Monotonic and cyclic tests on sheardiaphragm dissipaters for steel frames. Advanced Steel Construction2006;2(1):1–21.

[17] Tena-Colunga A. Mathematical modeling of the ADAS energy dissipationdevice. Engineering Structures 1997;19(10):811–21.

[18] Nakashima M, Akazawa T, Tsuji B. Strain-hardening behavior ofshear panels made of low-yield steel, II: Model. Journal of StructuralEngineering, ASCE 1995;121(12):1750–7.

[19] Xia C, Hanson RD. Influence of ADAS element parameters on buildingseismic response. Journal of Structural Engineering, ASCE 1992;118(7):1903–18.

[20] Wu B, Ou JP, Soong TT. Optimal placement of energy dissipationdevices for three-dimensional structures. Engineering Structures 1997;19(2):113–25.

[21] Nakashima M, Saburi K, Tsuji B. Energy input and dissipation behaviorof structures with hysteretic dampers. Earthquake Engineering andStructural Dynamics 1996;25:483–96.

[22] Wada A, Huang YH, Iwata M. Passive damping technology for buildingsin Japan. Proceeding of progress in structural engineering materials, vol.2. 2000. p. 335–50.

[23] Chopra AK. Dynamics of structures: Theory and applications toearthquake engineering. Englewood Cliffs (NJ): Prentice Hall; 1995.

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