improvement of seismic performance of seven story steel building with hysteretic steel dampers under...

The 6 th Civil Engineering Conference in The Asia Region Hotel Brobudur, Jakarta, Indonesia August, 20-22, 2013

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IMPROVEMENT OF SEISMIC PERFORMANCE OF SEVEN STORY STEEL BUILDING WITH HYSTERETIC STEEL DAMPERS UNDER

SEVERE SEISMIC EXCITATION

Daniel R.Teruna*, Taksiah A.Majid**, Bambang Budiono*** *Lecturer, Dept. of Civil Engineering, University of Sumatera Utara, Medan, Indonesia ** Associate Professor, Disaster Research Nexus, School of Civil Engineering, Universiti Sains Malaysia, Penang, Malaysia *** Professor, Dept. of Civil Engineering, Institute of Teknologi Bandung, Bandung, Indonesia

Abstract: The uses of supplementary hysteretic steel dampers have been recognized as effective and inexpensive techniques to reduce seismic responses of structural systems induced by a major earthquake. During a large earthquake event, these dampers will absorb the earthquake input energy to the structure through hysteretic behavior of its elements, where the main members are designed to remain elastic and/or within low inelastic deformation. The purpose of this paper is to study the effectiveness of the hysteretic dampers improving the structural performance of a steel building subjected to a major earthquake excitation. To do this, seven story’s steel building with and without hysteretic steel dampers are investigated using non-linier dynamic time history analysis under a set of selected ground motion records. The ground motions are matched to the response spectrum design of the National Indonesian Standard of seismic hazard map. In this study, hysteretic steel dampers are applied with various stiffness ratio values in the steel bracing of the Chevron types configurations. To quantify the structure’s performance, a damage indicator derived from the energy damage model is introduced and evaluated. Finally, the seismic performance of the building with and without hysteretic steel dampers are discussed and compared.

Keywords: Hysteretic steel damper, energy dissipation, seismic excitation, damage index

INTRODUCTION

In traditional seismic design concept, a structure shall be designed and constructed to withstand seismic forces and its possible combination with other loads without local or global failure. In generally, the seismic forces are determined by reducing real seismic action through reduction factor. Thus, for the estimated seismic responses of a structure, the nonlinear response of the structure is performed, resulting certain damage level in a structure. During severe seismic event, input energy induced by earthquake will be dissipated by inelastic deformation of the structural members, which may lead to building collapse or damage, if the building are not designed and constructed properly. In order to control or minimized damage on a structure under strong earthquake, a number of innovative design concepts for seismic response control of structures have been developed and implemented ( Kamura et al. 2009, Song and Spencer 1992). Passive energy absorber have been recognized as one of the innovative design concept within civil engineering community to improve the seismic performance of the structures. Several review article on passive energy absorber systems have been appeared, including Martinez and Rueda (2002), Hanson (1993), and Syman et al.(2008). The purpose of using passive energy absorber in a structures for seismic protection is to concentrate substantial portion of energy input in specific detail region of the structures and to minimized inelastic deformation on the primary


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structural members such as beams, column, or walls. Currently, the most practical and effective of the energy absorber is known as hysteretic steel damper, which uses the hysteresis of the material of the damper as the source of energy dissipation. A disadvantage of such damper is they absorb seismic energy only when they experienced inelastic deformation. As a result the damper damaged and would need to be replaced. In addition, in the most of cases, floor acceleration is increased because of the period of the system shortens. The use of hysteretic steel damper for controlling seismic performance have been reported by several authors such as Aiken and Kelly (1990), Avedo et al. (2010), Xia and Hanson (1992), Aiken et al. (1993), Li Gang and Li Hongnan (2008), Kobori et al.(1992), Benavent and Climent (2006), and Oh SH et al. (2009). The most commonly adopted to determine seismic performance of a structure is set usually by a limit the maximum inelastic roof displacement, maximum inter-story drift, or the maximum ductility demand. However, many researcher believe that the cumulative plastic deformation occurring in beam-column joint of a structure is directly related to energy dissipated by hysteretic damping (Abbas 2011, Park et al. 1985, 1987, Bojorquez et al.2008, 2010a, 2010b, and Fajfar 1992 ). As a result, damage in structural members is inevitable. Intensive investigation of hysteretic steel damper acting as structural fuse concept have been reported by Vargas and Bruneau (2004, 2008, 2009). In this concept the whole structural members are designed to remain elastic whereas energy input induced by seismic forces is concentrated on hysteretic damper systems. In this paper, the use of hysteretic steel damper of yielding type for enhancing of seismic performance of steel frame were studied. One seven story of steel frame with and without hysteretic steel damper under 4 (four) selected earthquake acceleration were investigated using non-linier time history analysis. These accelerations record were matched to Banda Aceh design spectrum in accordance with Indonesian standard of seismic hazard map, 2010. In oder to quantify the seismic performance of these steel frame, a damage index based on energy damage model approach which is developed by Bojorguez et al. (2008, 2010a) were used as performance criteria. To investigate how hysteretic steel damper influence the response parameters, the stiffness ratio (SR) i.e., ratio between the stiffness kbd of the hysteretic steel damper-braced assembly and the frame stiffness kf is proposed in five variant. Furthermore, the use of damage index provides a measure on the structural damage level, and making a decision on repairing systems with respect to the cost and functional interruption.

ACCELEROGRAM AND DESIGN RESPONSE SPECTRUM In December 26th, 2004 a severe earthquake with a magnitude 9.1 struck Banda Aceh. Because it happened below sea level, the earthquake triggered tsunami. It was reported that more than 126.000 people are dead and 37.000 people missing. Four different accelerogram were selected in order to performed the time history analysis of the building under consideration. These accelerogram were constructed matching a given design acceleration response spectrum of Banda Aceh with site class D. These ground motion details are given in Table 1 and their matching response spectrums are depicted in Figure 1. Table 1. Ground Motion Details

No. Year Earthquake name

Magnitude

Station Number

PGA (g)

Scale Factor

1 1989 Loma Prieta 6.93 Capitola 0.53 1.1 2 1994 Northridge 6.69 Bevery Hills 0.44 0.85 3 1980 Imperial valley 6.53 Elcentro 0.31 1.65 4 1995 Kobe 6.90 Takatori 0.61 1.2


3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3

Sa(g)

T(sec)

BSE-2 Design Spectrum

Loma Prieta

Northridge

Kobe

Imperial Valley

Target

ANALYTICAL MODELING OF HYSTERETIC STEEL DAMPER The force deformation relationship of hysteretic steel damper under cyclic loading has been often simplified by discrete multi-linear model, such as tri-linier model, bilinear model, and elasto perfectly plastic. Hereafter, unless otherwise mentioned, the term hysteretic steel damper refers to the damper or device. In this study, a bilinear model is adopted to characterize the parameter involve in the design of damper. Figure 2 shows the model of a single frame equipped with steel damper, whose frame, two braces support, and damper are modeled as lumped mass connected to ground by non-linear springs, and inherent viscous damping is represented by a linear dashpot (Vargas and Bruneau 2004). For the purpose of discussion, combination of a damper element (device) and two bracing elements that support the device is called as device-brace assembly. The lateral stiffness of the device-brace assembly, kbd, is a function of the lateral stiffness of the braces, kb, and the device stiffness kd. Since these stiffness are connected in series, it can shows that Where B/D is the ratio between the bracing and device stiffness. The lateral stiffness equivalent of a single frame with damper, ks, equal to: Another quantify of interest is ratio of brace-assembly stiffness to the lateral structural story stiffness, kf , is defined as SR (Xia and Hanson 1992), then:

DB

k

kk

k d

db

bd

/1

111

1

+=

+=

d

b

k

kDB =/

f

bd

k

kSR=

fbds kkk +=

(1)

(2)

(3)

(4)

Figure 1. Response spectra of scale ground motion


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Figure 3 deficts a general force-deformation response for SDOF frame with two bilinear springs acting in parallel.The yielding damper concepts that requires yield deformation of the device, ∆yd, should be less than the yield deformation of the bare frame, ∆f. The yield force of the yielding element, denoted by Vy, can be written as: where ∆yd and ∆y are yield deformation of device and device-brace assembly respectively. Equation (5) can be expressed in term of the parameter SR and B/D by considering Eqs. (1) , (2), and (4) in Eq.(5) as: Equation (6) is the basic expression for relationship between the parameters of the assumed bilinear model.Tsai, et al.(1993) recommended the SR value between 4 and 2 are appropriate for short and medium to long vibration period.

m

Frame

Braces

damper

( b )

( c )

( a )

ks

C

m

m

kf

kb kd

C

Figure 2. Model of systems with steel damper (Vargas and Bruneau 2004); (a) a single-story frame, ( b ) equivalent three spring system, ( c ) equivalent one -spring system

(5) ybdyddy kkV ∆=∆=

ydfy DBkSRV ∆

+=/1

1 (6)

Figure 3. Nonlinier modeling of restoring force frame and

damper

V

∆y ∆f

Vys

∆

Vy Vyf

Entire system

Device braced-assembly

Bare frame


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ENERGY BASED DAMAGE INDEX

During the last 15 years the concern in seismic design has been progressively change from force based to performance based. Damage occurred during earthquake seems to be seriously attention of the engineers of many countries, including developed countries, because of design building code may not adopted completely the seismic design philosophy. Currently, energy based approach are often used in earthquake resistant structures design ( Choi and Kim 2006, Kim and Choi 2004, Uang and Bartero 1990, and Ye et al. 2009). In order to quantify performance of a structures during earthquake, drift and damage index are commonly accepted as performance criteria. Damage index model based on cumulative plastic deformation and maximum hysteretic energy demand has been developed by several researcher, such as (Park and And 1985, Park et al. 1987, Cosenza (1993), Mehanny and deierlein 2001, Bojorquez et al. 2008, 2010a, 2010b, and Zahrah and Hall 1984). In this paper, damage index model are proposed by Bojorquez et al. are employed to investigate the damage level of a steel frame with and without damper under four series selected ground motion. Energy based design concept can be written in the following requirement: Since, hysteretic energy, EH is directly related to structural damage, Eqs. (7) can be rewritten in the term of dissipated hysteretic energy as follow : where EHC and EHD are dissipated hysteretic energy and hysteretic energy demand respectively. Then, Energy base damage index is defined as: Here, DI is used as indicator of damage state of structures. When, DI ≥ 1.0 is assumed as condition of failure, and when DI = 0 indicate no structural damage (elastis). The value of DI in the range of between 0 < DI < 1.0, shows some measure of the degree of damage. With assumption that yielding is usually concentrated at both ends of beam; and especially for WF steel shapes, in the flanges. Hysteretic energy capacity of MDOF structures can be estimated in the simplified form (Bojorquez 2008): where Zf is section plastic modulus of the flanges, Fy is yield stress of steel material, θpa is cumulative plastic rotation of the beam ends, Ns is number of stories, Nb is number of bays, and FEHi is energy distribution factor, to account the contribution of each story to the energy dissipation capacity of structure. Based on statistically result, Bojorquez et al.(2008) proposed that cumulative plastic rotation capacity equal to 0.23. Furthermore, based on extensive statical studies of eight steel moment resisting frames due to 31 accelograms recorded of Mexico city, Bojorquez et al.(2008) proposed the energy distribution factor, FEHi as follows: where

demandEnergycapacityEnergy ≥ (7)

HDHC EE ≥

HC

HD

E

EDI =

(8)

(9)

EHiPayf

N

ibHC FFZNE

s

θ∑=

=1

2

{ }1,min EHEH FF =

(10)

(11)


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and h/H is the ratio of the height relative of a particular floor to the base and the total height of the structure, and µ is the expected ductility demand. Based on the results derived from non-linier dynamic and regression analysis, Bojorquez et al.(2010) proposed simplified formula instead of Eq. (11) in order to release the dependency with respect to the ductility demand. The damage index in Eq.(9) can also rewritten in term of ratio between normalized hysteretic energy demand and normalized hysteretic energy capacity. where ENHD and ENHC are normalized hysteretic energy demand and normalized hysteretic energy capacity respectively, and are given as follows: in which Vy = yield strength of system, ∆y = yield displacement. Both of these parameters are derived from capacity curve.

DESCRIPTION OF EVALUATED BUILDINGS • Building Description

To study seismic performance of a structure with and without insertion of hysteretic damper under severe earthquakes, an 7 (seven) story of moment resisting frame (MRF) are considered as depicted in figure 4. In order to have the simulation more reasonable, the structure is designed to withstand realistic gravity load (dead load and live load). The magnitude of gravity load each story is assumed to be 28 kN/m. The relevant data of the structure is listed in table 3. Figure 5 shows the geometry of moment resisting frame equipped with hysteretic damper (DRF). In order to study the influence of damper characteristic in seismic responses, 5 (five) variant of stiffness of damper-brace assembly employed i.e. SR=2, SR= 3, SR=4, SR=5, and the last selected with different SR (SR combination). For a convenience discussion, the fifth of DRF frames denote as DRF1, DRF2, DRF3, DRF4, DRF5 respectively. The SR values for DRF frame with combined SR (DRF5) are selected as follows: two lowest floors were defined SR=3, followed by SR=4 for the next two floors, SR=3 at the fifth floor, and SR=2 for the other upper floors. In this context, the ratio of brace stiffness to damper stiffness are designed for 2 (two) as recommended by Xia et al.(1990). The story stiffness of frame, braces and damper device stiffness for the fifth of DRF are listed in table 4.

( )( )( ) ( )

++−−

+−=

2

39.006.03461.0031.0ln/ln

21

exp/82.20675.0

1µ

µµ

Hhx

HhFEH

( )( ) ( )

−−=2

49.052.0ln/ln

21

exp/33.2

1 Hhx

HhFEH

(12)

NHC

NHDN E

EDI =

yy

HCNHC

yy

HDNHD V

EE

V

EE

∆=

∆= ,

(13)

(14)


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Columns dimension Beams dimension Interior Exterior Interior Exterior

Story 1 W460x286 W460x260 W410x46 W410x67 Story 2 W460x260 W460x213 W410x53 W410x75 Story 3 W460x235 W460x177 W410x53 W410x75 Story 4 W460x193 W460x144 W410x53 W410x75 Story 5 W460x158 W460x128 W410x46 W410x67 Story 6 W460x128 W460x113 W410x46 W410x67 Story 7 W460x113 W460x113 W410x46 W410x67

Structures Story 1 2 3 4 5 6 7

MRF(105N/m) 410 223 175 158 149 141 117

DRF1 (SR=2)

Damper (105N/m)

1230 678 524 474 448 424 350

Brace (105N/m)

2460 1356 1048 948 896 848 700

DRF2 (SR=3)

Damper (105N/m)

1805 1017 786 711 672 636 525

Brace (105N/m)

3810 2034 1572 1422 1344 1272 1050

DRF3 (SR=4)

Damper (105N/m)

2460 1356 1048 948 896 848 700

Brace (105N/m)

4920 2712 2096 1896 1792 1696 1400

DRF4 (SR=5)

Damper (105N/m)

3075 1672 1312 1185 1117 1057 877

Brace (105N/m)

6150 3345 2625 2370 2235 2115 1755

DRF5 (SR=varied)

Damper (105N/m)

1805 1017 1048 948 672 424 350

Brace (105N/m

3810 2034 2096 1896 1344 848 700

Figure 5. Schematic of DRF

8m 8m 6m

Figure 4. Schematic of MRF

8m 8m 6m

4m

6

x3.5

m=

21

m

Table 3. Size of beams and columns

Table 4. Story stiffness, damper and brace stiffness


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• Structural Analysis and Modeling

The computer program ABAQUS was used to perform finite element analysis of the frame under 4 (four) scaled up of acceleration records in accordance with target spectrum reponse evaluated at fundamental period of T1. All beams, column and braces were modeled as one dimensional element of the B21 beam element. Where as, steel damper were modeled as equivalent nonlinier truss element. For design purposes, connection between column and foundation were modeled as fixed support at ground level, where as beam column connection were assumed to be rigid. Steel material was assumed to have an elastic modulus of 200 Gpa, an yield stress of 270 Mpa. Engineering stress and stress was entered, and isotropic hardening model were specified in order to take into account inelastic behavior of the element. Non-linier geometry option was also turn on for account second order effect which relate to P-delta and buckling. In the dynamic analysis, Rayleigh damping was constructed through the first and the third mode of vibration were specified 5% of critical damping. Direct integration method using Newmark-Beta was applied to solve differential equation of motion. Damper device were modeled as bilinier with 5% post yield stiffness ratio. Furthermore, nonlinier static pushover are performed in order to obtained yield strength and yield displacement of MRF and DRF, as shown in figure 6. Table 5 summarize relevant characteristic of MRF and DRF.

Frame Fundamental Period (sec.)

Vy (kN) ∆y (m)

MRF 1.69 613 0.198 DRF1 1.10 1366 0.091 DRF2 1.05 1348 0.083 DRF3 1.01 1338 0.077 DRF4 0.99 1339 0.073 DRF5 1.04 1341 0.081

Δy

Vy

Roof displacement

Base shear

Figure 6. Evaluation of Vy and ∆y from capacity curve

Table 5. Characteristic of Investigated Frames


9

0

1

2

3

4

5

6

7

0 1 2 3

Sto

ry

Interstory Drift (%)

Loma prieta

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

0

1

2

3

4

5

6

7

0 0.5 1 1.5

Sto

ry


Northridge

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

0

1

2

3

4

5

6

7

0 0.5 1 1.5

Sto

ry


Kobe

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2

Sto

ry

Story Drift (%)

Imperial Valley

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

RESULTS AND DISCUSSION

• Inter-story Drift

One of response parameters commonly used as seismic performance indicator is inter-story drift, although the lack of this parameter to predict damage induced by earthquake. Figure 7 shows the inter-story drift for moment resisting frame (MRF) and moment resisting frame with damper (DRF) under 4 selected scaled ground motion. It is observed that inter-story drift reduced significantly due to effect of additional stiffness when a damper device incorporated with MRF. It was also noted that the maximum inter-story drift occurred in the vicinity of middle stories . In addition, the largest inter-story drift occurred under input motion of Loma Prieta, followed by Imperial Valley, Kobe and Northridge. • Input and Hysteretic Energy Demand

Figure 8 and figure 9 show the time history of input energy and hysteretic energy for MRF and DRF frames subjected to 4 (four) ground motion respectively. It is clearly noticed that there are influence of ground motion characteristics and structural properties to the magnitude of total input energy and hysteretic energy . It can be seen that the MRF experienced higher input and hysteretic energy than DRF during Loma Prieta and Kobe earthquake. However, some decrease in the input energy demand under Northridge and Imperial Valley earthquake. Furthermore, there is a variability in magnitude of input energy and hysteretic energy for increasing the stiffness ratio value SR for DRF systems.

Figure 7. Inter-story drift vs Story height


10

0

1

2

3

4

5

0 5 10 15 20 25

Ei (

x105

Nm

)

t(sec)

Northridge

DRF1

DRF2

DRF3

DRF4

DRF MIX

MRF

0

2

4

6

8

10

12

14

16

0 20 40 60

Ei (

x105

Nm

)

t(sec)

Loma prieta

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

0

2

4

6

8

10

0 20 40 60

Ei (

x10

5 N

m)

t(sec)

Kobe

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

0

2

4

6

8

10

0 20 40

Ei (

x105

Nm

)

t(sec)

Imperial Valley

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

0

1

2

3

4

5

6

7

8

9

0 20 40 60

Eh

(x1

05 N

m)

t(sec)

Loma prieta

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

0

0.5

1

1.5

2

0 5 10 15 20 25

Eh(

x105

Nm

)

t(sec)

Northridge

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

0

0.5

1

1.5

2

2.5

3

0 20 40 60

Eh

(x1

05 N

m)

t(sec)

Kobe

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40

Eh

(x1

05 N

m)

t(sec)

Imperial Valley

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

Figure 8. Time history of total input energy

Figure 9. Time history of total hysteretic energy


11

0

1

2

3

4

5

6

7

0 0.5 1

Sto

ry

Eh (x105 Nm)

Kobe DRF1

DRF2

DRF3

DRF4

DRF5

MRF

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6

Sto

ry

Eh (x105 Nm)

Imperial Valley DRF1

DRF2

DRF3

DRF4

DRF5

MRF

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6

Sto

ry

Eh (x105 Nm)

Northridge

DRF1

DRF2

DRF3

DRF4

DRF5

MRF

It is recognize that the damage to a structures depend on amount of hysteretic energy dissipated and on its cumulative effect. Figure 10 present hysteretic energy components, i.e., dissipated by beams elements and damper element along the height of building. The following observation are made: (1) the magnitude and variation of hysteretic energy demand for beams and dampers element are influenced by structural properties and ground motion characteristics. (2) In generally, most of the maximum hysteretic energy demand for beams members occurred vicinity of middle stories (third story). On the contrary, different trend are observed due to Northridge earthquake. Under this earthquake, the maximum hysteretic energy demand resulting from inelastic action of all beams element incorporated in the third floor concentrated close to upper and lower stories. (3) It can be also seen that all DRF systems show the smaller of hysteretic energy demand for beams element compare to MRF system. This behavior can be attributed to the concentrated a large portion of hysteretic energy demand on the damper devices. Therefore, building equipped with hysteretic damper during a major earthquake event remain elastic or minor damage. (4) It should be pointed out that all beams at top floor for DRF system remain elastic, while for MRF system have slightly inelastic deformation.(5) There is no consistent correlation in magnitude and variation through the height of building in energy dissipation by damper device when strength ratio SR increase or decrease. In this context, the ground motion characteristics has a strong influence in the energy dissipation. It can be noticed that distribution of energy dissipated by damper element become relatively similar in shape

(a) Beams element

0

1

2

3

4

5

6

7

0 1 2 3

Sto

ry

Eh (x105 Nm)

Loma prieta

DRF 1

DRF 2

DRF 3

DRF 4

DRF 5


12

0

1

2

3

4

5

6

7

0 0.5 1 1.5

Sto

ry

Eh (x105 Nm)

Loma prieta DRF1

DRF2

DRF3

DRF4

DRF5

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6

Sto

ry

Eh (x105 Nm)

Northridge

DRF 1

DRF 2

DRF 3

DRF 4

DRF 5

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6

Sto

ry

Eh (x105 Nm)

Kobe

DRF1

DRF2

DRF3

DRF4

DRF5

0

1

2

3

4

5

6

7

0 0.5 1 1.5

Sto

ry

Eh (x105 Nm)

Imperial Valley

DRF1

DRF2

DRF3

DRF4

DRF5

Figure 11 illustrate the energy component for MRF and DRF system. It was noted that the total hysteretic energy demand for beams in the DRF system are always less than total hysteretic energy demand for beams in the MRF system. It is confirm that beams in the DRF3 ( damper with SR=3) experienced the smallest hysteretic energy demand, except under Imperial Valley acceleration record, beams in the DRF5 show the smallest one. In addition, Energy absorbed by inelastic deformation of beams element in the DRF can be neglected compare to MRF. In other word, Building with hysteretic damper in place will provide supplement stiffness and damping, hence ensure the increasing of the structure safety. Furthermore studies, the energy dissipated by damper device tend to similar pattern with input energy. Moreover, from consideration of input energy, it can be pointed out that the Loma prieta ground motion is more severely than other ground motions.

GLOBAL DAMAGE INDEX

In this study, seismic performance of the structures in term of global damage index are presented. Tabel 6 indicates calculation of energy capacity of beams. After determining the energy capacity and energy hysteretic demand of the structures, global damage index and damage state are derived. In this context, the relation between degree of damage and damage index as listed in table 7 (Park and Ang), and the results comparison is given in table 8. It was found that seismic performance of DRF definitely improving and resulted no damage in all main members of the structures. it can be also noted that the MRF suffered severe

(b) Dampers element

Figure 10. Distribution of hysteretic energy through

the height of building


13

damage due to Loma Prieta earthquake, reparable state under kobe earhquake, and minor damage or serviceable condition during the Northridge earthquake and the Imperial Valley earthquake.

Story

Fy (Mpa)

θpa (rad)

FEH

Zf (x103 mm3) EHC (Nm)

Exterior beam Interior beam 1

270

0.23

0.15 1038 623 50281 2 0.76 1166 767 292520 3 0.86 1166 767 331009 4 0.72 1166 767 277124 5 0.48 1038 623 160902 6 0.29 1038 623 97212 7 0.18 1038 623 60338

total 1269386

Degree of damage Damage index State of structure Minor 0.0-0.2 Serviceable

Moderate 0.2-0.5 Reparable

Severe 0.5-1.0 Irreparable

collapse >1.0 Loss of building

02468

10121416

MRF DRF 1DRF 2DRF 3DRF 4DRF 5

Ene

rgy

( x1

05 N

m)

Lomaprieta Input Energy

E hys. (Beam)

E hys. (Damper)

Frame System

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

MRF DRF 1 DRF 2 DRF 3 DRF 4 DRF 5

En

erg

y (

x1

05

Nm

)

Northridge

Input Energy

Ehys.(Beam)

E hys. (Damper)

Frame System

0123456789

10


Ene

rgy

( x1

05 N

m)

Kobe

Input Energy

Ehys.(Beam)

Ehys.(Damper)

Frame System

0

2

4

6

8

10


Ene

rgy

( x1

05 N

m)

Imperial valley

Input Energy

Ehys.(Beam )

Ehys.(Damper)

Frame System

Figure 11. Comparison of energy component of the buildings

Tabel 6. Determination of total energy capacity

Tabel 7. Interpretation of damage index


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CONCLUSION

A seven story of steel frames with and without hysteretic steel damper are investigate under a set of four ground accelerations with a series non-linier time history analysis. All these ground motions are matched to response spectrum design according to seismic hazard map Indonesia, 2010. Stiffness ratio SR are main parameter of device-brace assembly in order to study the behavior of the structures subjected to asset of ground motions. From the results, some conclusion can be drawn: 1. Ground motion which matched to the spectrum response design does not always produce the similar response parameters of the building under study. Because the responses of this building are not only influenced by building dynamic properties but also depend on ground motion characteristic, such as duration of motion, Frequency content and intensity of motion 2. The maximum inter-story drift, hysteresis energy demand and its distribution throughout the height of the building showed the similar trend, i.e., occurs approximately in the middle of the story. This phenomenon may be due to responses are dominated by the first mode. 3. Installation hysteretic damper on the MRF can reduce either story drift or hysteretic energy demand of the main members. In this cases, the value of SR 3 in general more effective than others in reducing of response parameters 4. Seismic performance of MRF system shows different state of damage, i.e, between serviceable state to irreparable state. However, all DRF systems show a good performance, i.e., serviceable state or no damage .

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Tabel 8. Damage index and state of structures


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