a modified friction damper for diagonal bracing of structures

Journal of Constructional Steel Research 87 (2013) 17–30

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Journal of Constructional Steel Research

A modified friction damper for diagonal bracing of structures

Habib Saeed Monir ⁎, Keyvan Zeynali 1

Civil Engineering Department, Urmia University, Urmia, Iran

⁎ Corresponding author. Tel.: +98 9143143125; fax:E-mail addresses: [email protected] (H.S. Monir)

(K. Zeynali).1 Tel.: +98 9143143125; fax: +98 4412773591.

0143-974X/$ – see front matter © 2013 Elsevier Ltd. Alhttp://dx.doi.org/10.1016/j.jcsr.2013.04.004

a b s t r a c t
a r t i c l e i n f o
Article history:Received 6 December 2012Accepted 12 April 2013Available online xxxx

Keywords:DamperFrictionShaking tableEnergy dissipationRetrofit

In this paper, the dynamic behavior of a recently developed friction damper has been demonstrated. It ismade from nine steel stripes and nine high strength steel bolts and is applied in the diagonal bracing of struc-tures. This device has a square geometric shape and should be installed in the square spans. During this re-search work, a prototype of the modified friction damper was tested by a universal machine. Then thedamper was installed inside a SDOF steel frame and tested by the shaking table under several earthquake ex-citations. For numerical assessment of the system, the model of SDOF frame was created in SAP2000 and an-alyzed under the same excitations which had been applied during the shaking table tests. By comparing theresults obtained from SAP2000 to those of experimental tests, the validity of numerical modeling was proved.In order to assess the behavior of damper in multi-story buildings, the model of a four story frame, with andwithout the modified damper, was created in SAP2000 and analyzed under several seismic records. Theresults were indicating that the lateral displacements and the base shears of the multi-story building havebeen significantly reduced by the installation of this modified energy absorber and a considerable energyhas been dissipated by the damping system.

© 2013 Elsevier Ltd. All rights reserved.

1. Introduction

During earthquake ground motions, large amounts of seismicenergy are imported into structures. For preventing the structuralcollapse, conventional design methods allow structural members todissipate the transmitted energy by inelastic cyclic deformations inthe specially considered regions. These methods accept that somedamage may happen, possibly to the extent that the structure is nolonger repairable. In the last two decades, special vibration controlsystems have been developed to increase safety and reduce the dam-ages during earthquakes [1]. These alternative protecting systems aimto control the structural seismic responses and reduce the energy dis-sipation demands on the structural members.

One of the most practical and reliable methods for mitigation ofthe seismic structural responses is the application of passive controlsystems. These systems can be classified as [2]: (1) seismic isolationsystems and, (2) passive energy dissipation devices. Passive energydissipaters absorb some of the vibration energy and reduce the plasticdeformation of structural elements. They consist of precisely placeddampers or replaceable yielding elements that link various parts ofthe framing system [3]. The performed analytical and experimentalstudies on these protective systems strongly affirm their suitabilityfor being applied in structures subjected to the seismic effects.

+98 4412773591., [email protected]

l rights reserved.

Passive energy absorbing devices are classified into two subdivisions:permanent and disposable devices. Permanent devices need no replace-ment after the absorption of energy and remain permanently instructures (although they may need some readjustments after the dissi-pation of energy). However, disposable systems usually need to bereplaced after sever earthquakes. Friction dampers are permanent pas-sive energy absorbing systems and exhibit a hysteretic behavior similarto that of metallic dampers. These devices use the resistance developedbetween moving solid interfaces to dissipate a substantial amount ofthe input energy in the form of heat. During severe seismic excitations,the friction devices yield at the predetermined loads and provide dissipa-tion of energy by friction phenomenon while at the same time shiftingthe structural fundamental mode away of the earthquake resonant fre-quencies. Friction dampers are not vulnerable to the thermal effectsand have a reliable performance with the stable hysteretic behavior [2].

Metal yielding absorbers and friction dampers differ in the usedphenomenon for the dissipation of energy but they have similardesign characteristics. The maximum force developed in a frictiondevice and a metallic damper is controlled by the design slip-loadand the yield load respectively. By considering high limiting loads inthese dampers, the dissipated energy (area under the force–deformationcurve) will be minimal since there will be no slippage within the device.In this case, the structure will behave as a braced frame. If the limitingloads are too low, the dampers will experience large inelastic slippagesbut again the amount of dissipated energy will be negligible [4].

PALL and DAMPTECH companies have presented commerciallymanufactured friction dampers for seismic structural control, whichtheir schematic representations are shown in Fig. 1. In PALL dampers

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Fig. 1. Schematic representation of: (a) Friction device presented by PALL Company and (b) tension-only concentric bracing by DAMPTECH.

18 H.S. Monir, K. Zeynali / Journal of Constructional Steel Research 87 (2013) 17–30

[5], there are translational movements between solid interfaces whilein DAMPTECH devices, the movements are rotational [6].

2. The modified friction damper

In this research, a modified friction damper (MFD) has been devel-oped for the improvement of the seismic behavior of steel structuresunder earthquake excitations. This damper is applied at the intersec-tion of X-shaped diagonal braces and its friction hinges have onlyrotational movements. This causes the friction interfaces to be away

Friction Hinge for dissipation of energy

Simple Hinge for connecting the device to the braces

Fig. 2. Schematic representation of MFD.

Fric

Fig. 3. Cross sect

from environmental effects. Fig. 2 is the schematic representation ofMFD and Fig. 3 is its cross section.

MFD consists of 9 steel strips, 10 circular friction pads and 9 highstrength steel bolts as shown in Fig. 3. Friction pads are located be-tween steel strips and are clamped by bolts to create friction for the

tion pad Disc Spring

ion of MFD.

Fig. 4. The steel plate and the friction pad.

ActuatorLoad Cell

The specimen

Fig. 7. Experimental set-up for universal testing.

19H.S. Monir, K. Zeynali / Journal of Constructional Steel Research 87 (2013) 17–30

dissipation of energy. Fig. 4 shows a steel plate and a friction pad. En-ergy dissipation is provided by the rotation of the steel plates over thefriction pads. Five friction hinges have been considered in the deviceas shown in Fig. 2. This modified damper is installed in the X-shapebracing systems. Four bolts are used to connect the device to thebraces. For the proper performance of MFD, it is necessary for the de-vice to be installed in a square span as shown in Fig. 5a. Square spanconfiguration should be created if the span is rectangular (Fig. 5b).Because the damper is attached to structure by cable connections,therefore, if the device is made rectangular or it is installed in a rect-angular span, there will be some free rotation of the damper duringthe vibrations, due to the created eccentricity between the align-ments of the braces (Fig. 5c). This will result in a large reduction inthe absorption of energy.

3. Experimental work — universal machine tests

3.1. Experimental set up

The device, with the dimensions shown in Fig. 6a, was built at theEarthquake Engineering Laboratory of Urmia University. The stripes in

(a)

The frame

The damper

(c)

The cable

Eccentricity

Fig. 5. Installation of the MFD in (a) a square span, (b) a

(a) Fig. 6. a) Dimensions of the sample M

this specimen were made from ST37 mild steel plates (based on DINstandard) with a 235 MPa yield limit and 370 MPa ultimate stress.The friction pad with the thickness of 10 mm and outer radius of40 mmwas made from PARSLENT brake pads with the regular frictioncoefficient of 0.3–0.4. The device was tested by a universal machineand the objective was to obtain the force–displacement relation of thedamper and validate its energy-dissipation capability. The loading

(b)

The frame

The damper

The frame

The damper

rectangular span and (c) an incorrect composition.

(b)

F F

FD and b) the loading direction.

Fig. 8. (a) The applied displacement loading with 2.5 cm amplitude and (b) its recorded hysteresis load–deflection curve.

Fig. 9. (a) The applied displacement loading with the amplitude of 3.2 cm and (b) its hysteresis load–deflection curve.


direction has been shown in Fig. 6b. The hydraulic displacement-controlled actuator of Urmia University was used for this purpose.Fig. 7 shows the experimental set-up in which a load cell and a LVDThave been used to measure the loadings and the displacements respec-tively. A digital data logger recorded their signals at every 0.02 s.

3.2. Experimental results

The tests were carried out in two series with different clampingforces. In both series, first the device was adjusted to its initial squareshape (Fig. 6b) and then all the friction hinges were equally tightenedby a torque wrench. Afterwards, the device was gone under a series ofdisplacement controlled cyclic loadings with 0.2 Hz frequency and 2.5,3.2 and 5 centimeter amplitudes and their hysteresis load deflection

Fig. 10. (a) The applied displacement loading with the amplit

curves were obtained. In the second series of the experimental tests,the clamping forces of the friction hinges were increased. Then thetests were repeated with the same amplitudes and frequencies of thefirst series. Figs. 8, 9, and 10 show some sample applied loadings andtheir recorded hysteresis load deflection curves. In these curves, theslip-force of the damper at its initial configuration (θ = 45°) was2000 N.

3.3. The load–deflection equation of MFD

Rotational friction moment (M), which will be called here asslip-moment, is the torsion moment which a fiction hinge developswhen slippage starts. The amount of slip-moment depends on thefriction coefficient, the clamping force (Pcl) and the friction area. If

ude of 5 cm and (b) its hysteresis load deflection–curve.

Fig. 11. Geometric parameters of the friction pad.

Fig. 13. The numerical and experimental curves for 2.5 cm displacement amplitude.

Fig. 14. The numerical and experimental curves for 3.2 cm displacement amplitude.


Pcl is the normal pressure which has been created by bolts at any lo-cation between the friction pad and the steel plate, the frictionalforce acting on an elemental area will be μPcldAwhere μ is the frictioncoefficient and dA is the area r.dr.dθ of the element. The moment ofthis elemental friction force about the friction pad center is μPcl rdA,then the total moment becomes ∫ μPcldA. Therefore, the frictionalmoment is equal to:

M ¼ μPcl

2πR∫2π0 ∫R2

R1r:dr:dθ ¼ 2

3μ:Pcl

R32−R3

1

R22−R2

1

: ð1Þ

Fig. 11 shows the geometric properties and surface element of dAon the friction pad.

By attention to Fig. 12 and using virtual work principal, we canestablish Eq. (2) between the slip-load of MFD and slip-moment ofthe friction hinges.

F1� 2� L � dθð Þ � cos θ ¼ M 2dθð Þ ð2Þ

in which “M” is the slip-moment of a single friction hinge, “F1” is theslip-force of the device resulted from the resistance of one frictionhinge only and “L” is the length of steel strips. Angle “θ”, which variesbetween 45° and 90°, has been shown in Fig. 11. Because there are 5symmetric friction hinges in the device, then the overall resistant ofthe device, F, will be equal to 5F1. Therefore:

F ¼ 5ML cos θ

ð3Þ

/2

F

(a)Fig. 12. (a) MFD at the initial form, (b) the deformed device and

because Δ = 2 × L(sin θ − sin 45°), then we have:

F ¼ 5M

Lffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1− Δ

4L þffiffi2

p2

� �2r : ð4Þ

Eq. (4) is used to estimate the slip-moments of the friction hingesMafter determining the slip-force F by universal test. For checking thevalidity of this Equation, at first the slip-moments of the friction hingesin the specimen were computed for both test series by substitutingθ = 45° in Eq. (3). Then the load deflection curves of the device wereobtained by applying Eq. (4) and compared to those of the experimentalresults. Figs. 13 to 15 show some sample curves in this regard. It is seenthat there are good matches between the experimental curves and thecurves obtained by Eq. (4). Therefore, Eq. (4) can be confidently used toestimateM from the universal test results.

4. Experimental work — the shaking table tests

4.1. The experimental setup

In the second step of experimental tests, the device was installedinside a Single Degree Of Freedom (SDOF) steel frame, which itself

/2

F

(b) (c)(c) variation of the angles during the deformation of MFD.

Fig. 15. The numerical and experimental curves for 5 cm displacement amplitude.

Table 1Earthquake records for experimental and analytical works.

Row Earthquake Station Magnitude Latitude Longitude

1 Tabas (1978-09-16) Iran, 9101Tabas

7.35 33.5800 56.9200

2 Imperial Valley(1940-5-19)

Array #9, ElCentro

6.95 32.7940 −115.549

3 Kobe, Japan(1995-01-16)

99999 TOT 6.90 35.4850 134.2400


was located over the shaking table of Urmia University. The responsesof SDOF frame, with and without the damper, were recorded underTabas, Kobe and Elcentro earthquakes. Table 1 shows the details ofthe applied excitations.

The shaking table of Urmia University was used to evaluate theperformance of MFD in the SDOF frame. This table is a single degreeof freedom systemwhich consists of a deck, an actuator which appliesthe excitations and a computer unit which controls the actuator. Thewhole unit has been shown in Fig. 16.

Schematic sketch of the SDOF steel frame has been shown inFig. 17. It is a three dimensional frame which has been installedover the shaking table. In one direction, the excitations are appliedand along the other direction, the frame is braced. The weight of theroof is 115 kg but four point loads can be also applied at the cornersby using steel sinkers. The whole weight of the model was 443 kgduring the tests.

In this shaking table, base excitations are applied by using a horizon-tal computer-controlled actuator. Horizontal accelerations are recordedby the application of two accelerometers at the top and bottom of the

Fig. 16. The shaki

frame. The relative displacement between the top and bottom of theframe is measured by placing an Aluminum box-profile between theshaking table and the roof (with its higher inertia moment axis perpen-dicular to the loading direction) and locating a LVDT between them. Theresponses of SDOF frame are recorded by using a digital data logger. Toavoid out-of-planemovements of the frame, it is laterally braced by foursteel sticks at the back and the front faces (Fig. 17).

In order to adjust the slip-moments of the friction hinges to anydesired value M, at first its equivalent slip-force F is determined bysubstituting θ = 45° in Eq. (3). Then by doing universal machine test-ing, the slip-load of MFD is adjusted to the computed F by applying atorque wrench and tuning the clamping forces of the friction hinges.

4.2. The shaking table test results

Shaking table tests were performed by putting the frame, withoutthe damping system, under Tabas, Kobe and Elcentro earthquake exci-tations and recording its accelerations and drifts. The frame was thenequipped with MFD, as shown in Figs. 18 and 19, and the tests were re-peated with the same excitations. During the shaking table tests, theslip-moments of the friction hinges were adjusted to 20, 35, 50 and60 N-m. By increasing the slip-moments of the friction hinges, themax-imum displacements of the framewere reduced. It was noticed that be-yond (60 N-m), there is no slippage in the friction hinges and thedamper behaves like an ordinary brace.

By attention to Fig. 20, a proper amount for the slip-moments of thefriction hinges could be considered as 50 N-m during the shaking tabletests. Fig. 21 shows the displacement records of the frame under scaledElcentro earthquake records (the scaling was performed under Iranian2800 version 3 code regulations). This figure provides a comparison ofthe peak displacements of the SDOF structure with and without MFD.It can be seen that the damper provides an extra damping to the struc-ture, so that the displacements have been significantly reduced.

5. Finite Element Analysis

5.1. Finite element modeling of the SDOF frame equipped with MFD

In order to analyze the responses of multi-story structures equippedwith the modified damper, at first the finite element model of SDOFsteel frame was created in SAP2000 (Fig. 22). The device was modeledin SAP2000 by using link elements and Fig. 23 shows the details. Forthe braces, no tension cable component was used and for the steelstrips, beam elements were assigned. For the friction hinges, link ele-ments with nonlinear plasticity in R1 direction and rigid properties inthe other directions were considered while for the corner hinges, alinear link with the properties of a simple hinge was assigned. The

Aluminum Box Profile

ng table unit.

285mm

285 mm

MFD

(a)

(b)

(c)

Fig. 17. a) The details of SDOF structure, b) overall location of MFD in SDOF frame and c) the details of the installation of MFD in the frame.


nonlinear moment–rotation relationship for the link element is givenby a multi-linear curve with the following restrictions:

1- One point must be origin, (0,0)2- The points with positive and negative deformationsmust be defined

Fig. 18. Installation of the friction damper inside the SDOF structure.

3- The rotation of these points must increase monotonically4- The moments at a point must have the same sign as the rotation5- The final slope at each end of the curve must not be negative.

Fig. 24 shows the link element properties which were used for thefriction hinges in the SDOF model. Non-linear time history analyses ofSDOF under Tabas and Kobe earthquakes were performed and com-pared to those of the experimental results (Figs. 25 and 26). By atten-tion to these displacement–time curves, it can be concluded that thenumerical results are in close match with laboratory tests.

5.2. Finite Element Analysis of multi-story frames equipped with MFD

In order to assess the behavior of MFD in multi-story buildings, afour story 3-span moment resistant steel frame was considered. Theframe belongs to a geometrically regular building which its typicalheights and widths are shown in Fig. 27. The sections of the frame,shown in Table 2, were made from mild steel ST37 (based on DINstandard). This building was nonlinearly analyzed under scaled

Detail D

Detail A

Detail B

Detail C

Detail D

Detail C

Detail B

Detail A

Steel Cables

Friction Pad

Fig. 19. Description of the device in details.

0

2

4

6

8

10

12

Dis

pla

cem

ent

(mm

)

0 20 40 60 80

Slip-moment (N)

Fig. 20. Variation of the maximum displacement with the yield moment under ElcentroEarthquake.


Tabas, Elcentro and Kobe earthquake excitations. The scaling wasperformed according to Iranian 2800 seismic code, 3rd revision.Large displacement and P-delta effects were included in the analysis.The maximum displacements and base shears were determined foreach earthquake record.

The structurewas then equippedwith themodified friction damper.The sizes of the device in this frame were the same as the SDOF frame

Fig. 21. Roof displacement histories, with and w

(Fig. 6). In general, the size of the device should be sufficient for devel-oping the necessary lateral deformation of the structure. The ultimatedeformationwhich a small damper can develop is less than a bigger sys-tem. Besides, a big device provides more uniform load–deflection curvewhile a small one has some hardening behavior. The braces which con-nect the device to the structure should be considered strong enough toremain elastic during the absorption of energy. These components areselected from circular cross section cables.

Link-elements were used to simulate the behavior of damping sys-tem. The optimal amounts for the slip-moments of the friction hingeswere obtained by conducting a trial and error procedure andperforming several nonlinear dynamic analyses. The minimum baseshear and the minimum relative displacements were the criteria forobtaining the optimal values from these analyses. Figs. 28 and 29show the link element properties which were applied for the frictionhinges of the device in the multi-story model.

The frame with MFD was analyzed under the same earthquake re-cords which were applied for the none-equipped one. The resultshave been shown in Figs. 30 to 35. The comparison of story driftsshows the effectiveness of MFD in mitigation of the structural vibra-tions. This comparison indicates a significant reduction in building re-sponses when it is equipped with MFD. It can be seen that the damperhas provided considerable extra damping to the structure, so the dis-placements of the frame have been significantly reduced.

ithout damper, under 0.9 g Elcentro record.

Fig. 22. The numerical model of the SDOF steel frame.

No tension

bar element

Beam

Element

Link Element-Simple Hinge

Link Element-Friction Hinge

Beam

Element

(a) (b)

Fig. 23. (a) The bracing and (b) the friction damper elements.


6. Conclusions

In this paper, a modified friction damper was introduced and someexperimental works in this regard were presented. The followingconclusion can be drawn:

(1) The introduced damper in this paper, not only provides an ad-ditional structural stiffness, but also it is an effective dissipative

Fig. 24. The link element properties of the

device with good energy dissipating capabilities. The resultsshow that it is feasible to calculate the response of a frameequipped with MFD by finite element method.

(2) Themodified friction damper has reduced the displacements andstory drifts. By attention to time–displacement curves, it can berealized that the average amount of the displacements in a 4story structure for Tabas, Elcentro and Kobe earthquake excita-tions has been reduced by 22%, 25% and 26% factors respectively.

rotation (Rad)

Moment (N.m)

-1 -500 -500 00 501 50

friction hinge in the SDOF steel frame.

Fig. 25. Time–displacement curve the SDOF structure equipped with MFD under Kobe earthquake excitation.

Fig. 26. The time–displacement curve of the SDOF structure with MFD under Tabas earthquake excitation.

Fig. 27. The 4 story structure.

Table 2The properties of structural members (DIN standard).

Middle spanbeam

Sidebeams

Middle spancolumns

Sidecolumns

First floor 2*IPE 22 2*IPE 22 2*IPE 18 2*IPE 16Second floor 2*IPE 22 2*IPE 22 2*IPE 18 2*IPE 16Third floor 2*IPE 22 2*IPE 22 2*IPE 16 2*IPE 14Fourth floor 2*IPE 18 2*IPE 18 2*IPE 16 2*IPE 16


(3) The modified friction damper has reduced the displacement andstory drifts. By attention to time–displacement curves, it can berealized that the average amount of the displacements in a 4story structure for Tabas, Elcentro and Kobe earthquake excita-tions have been reduced by 22%, 25% and 26% factors respectively.

References

[1] Constantinou MC, Soong TT, Dargush GF. Passive energy dissipation systems forstructural design and retrofit. Monograph no. 1. Buffalo, NY: Multidisciplinary Cen-ter for Earthquake Engineering Research; 1998.

rotation (Rad)

Moment (N.m)

-1 -6500 -6500 00 6501 650

Fig. 28. The link element curve applied for the friction hinges in the first and second stories of the multi-story steel frame.

rotation (Rad)

Moment (N.m)

-1 -5000 -5000 00 5001 500

Fig. 29. The link element curve applied for the friction hinges in the third and fourth floors.


[2] Soong TT, Dargush GF. Passive energy dissipation systems in structural engineer-ing. Chichester: John Wiley & Sons; 1997.

[3] Constantinou MC, Symans MD. Seismic response of structures with supplementaldamping. Struct Des Tall Build 1993;2:77–92.

[4] Lopez I, Nijmeijer H. Prediction and validation of the energy dissipation of a frictiondamper. J Sound Vib 2009;328(4–5):396–410.

[5] Pall A, Venzina S, Proulx P, Pall R. Friction dampers for seismic control of CanadianSpace Agency Headquarters. Earthquake Spectra 1993;9(3):547–57.

[6] Mualla IH, Belev B. Performance of steel frames with a new friction damper deviceunder earthquake excitation. Eng Struct 2002;24(3):365–71.

Bas

e S

hea

r (k

N)

1000

800

600

400

200

0.0

-200

-400

-600

-800

-1000

100

80

60

40

20

0

-20

-40

-80

-60

100

Ro

of

Dis

pla

cem

ent

(mm

)F

loo

r N

o

0 1 2 3 4 5 6 7

Time (sec)

0 1 2 3 4 5 6 7

Time (sec)

Maximum Displacement (mm)

0

5

4

3

2

1

020 40 60 80 100 120

Without Damper With Damper



Fig. 30. Effects of the application of MFD in the response of four-story steel frame underElcentro 0.3 g earthquake.

Bas

e S

hea

r (k

N)

Time (sec)

1000

800

600

400

200

0.0

-200

-400

-600

-800

-1000

150

100

0

50

150

-100

-150

4

5

2

3

1

0

0 1 2 3 4 5 6 7

Ro

of

Dis

pla

cem

ent

(mm

)


Flo

or

No

Time (sec)

0 1 2 3 4 5 6 7

0 20 40 60 80 100 120 140




Fig. 31. Effects of the application of MFD in the response of four-story steel frame underElcentro 0.5 g earthquake.


Bas

e S

hea

r (k

N)

Time (sec)

800

600

400

200

0

-200

-400

-600

-8000 1 2 3 4 5 6

Time (sec)

0 1

0 10 20 30 40 50 60 70

2 3 4 5 6

Ro

of

Dis

pla

cem

ent

(mm

)


60

40

20

0

-20

-40

-60

Flo

or

No

5

4

3

2

1

0




Fig. 32. Effects of the application of MFD in the response of four-story steel frame underKobe 0.3 g earthquake.

Bas

e S

hea

r (k

N)

Time (sec)

800

600

400

200

0

-200

-400

-600

-800

100

80

60

40

20

0

-20

-40

-60

-80

-100

0 1 2 3 4 5 6

Time (sec)

0 1 2 3 4 5 6

0 200

1

3

2

4

5

40 60 80 100 120

Ro

of

Dis

pla

cem

ent

(mm

)F

loo

r N

o





Fig. 33. Effects of the application of MFD in the response of four-story steel frame underKobe 0.5 g earthquake.


0 5 10 15 20 25

Time (sec)

Without Damper With DamperB

ase

Sh

ear

(kN

)R

oo

f D

isp

lace

men

t (m

m)


800

600

400

200

0.0

-200

-400

-600

-800

80

60

40

20

0

-20

-40

-60

-80



0 5 10 15 20 25

Time (sec)

Flo

or

No

5

4

3

2

1

00 10 20 30 40 50 60 70 80

Fig. 34. Effects of the application of MFD in the response of four-story steel frame underTabas 0.3 g earthquake.

Ro

of

Dis

pla

cem

ent

(mm

)B

ase

Sh

ear

(kN

)


0

-20

-40

-60

-80

-100

100

60

80

40

20

30

0

-30

-60

-90

-120

-150

120

90

60

0 5 10 15 20 25

Time (sec)


0 5 10 15 20 25

Time (sec)F

loo

r N

o

5

4

3

2

1

00 20 40 60 80 100 120 140



Fig. 35. Effects of the application of MFD in the response of four-story steel frame underTabas 0.5 g earthquake.


a modified friction damper for diagonal bracing of structures

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