4th International Conference on Earthquake Engineering Taipei, Taiwan

October 12-13, 2006

Paper No. 133

THE USE OF PASSIVE DAMPERS AND CONVENTIONAL STRENGTHENING METHODS FOR THE REHABILITATION OF AN

EXISTING STEEL STRUCTURE

Payam Tehrani1 and Shahrokh Maalek2

ABSTRACT In this study, the effect of the use of several rehabilitation methods to improve the seismic performance of an existing 9 story steel structure has been investigated using nonlinear dynamic analyses. These methods include the use of the EBF systems; RC Shear Walls and use of Passive energy dissipators such as metallic TADAS, viscous, viscoelastic and friction dampers. Each damping system has been modeled in the structure for several damping ratios and damper properties. In nonlinear dynamic analyses, the response of the structure to seven scaled earthquake records matched to the design spectrum has been obtained and the average value of the, base shears and dissipated energy in the structural members have been used for the comparison. The results demonstrate that the use of the passive dampers in the structures, in comparison with conventional methods of strengthening, substantially reduces the base shear and damages in the structure. Keywords: Seismic Rehabilitation, Passive Dampers, Nonlinear Dynamic Analysis

INTRODUCTION Strong earthquakes induce high amount of energy to the affected structures. If this energy can be controlled and dissipated in a manner independent of the structural components, the seismic performance and response of the structure will be substantially improved. This objective can be achieved by using passive control of the structures or base isolation techniques. In this study the effect of using passive dampers in comparison with the use of conventional strengthening methods in improving the seismic performance of a vulnerable steel structure has been investigated.

1. PASSIVE DAMPERS In recent years, the use of passive dampers for the purpose of the rehabilitation and the improvement of the seismic performance of existing structures and also enhancing the design of new structures has been increased rapidly. The common types of these dampers include metallic dampers, viscous dampers, visco-elastic dampers and friction dampers, among others. The maximum responses of the structures equipped with these dampers are the function of different factors such as the cyclic behavior of these dampers and also the frequency content of the input earthquake records. This study is carried out to investigate the privileges of the use of passive dampers in the structures, in comparison with the use of the conventional strengthening methods such as the use of Bracings and shear walls. In this regard, the effect of the application of these devices on the responses of an existing steel structure has been investigated by means of nonlinear dynamic analyses.

1 Graduate Student of Structural Engineering, University of Tehran, Tehran, Iran, payam.tehrani@gmail.com 2 Faculty of Engineering, Civil Engineering Department, University of Tehran, Tehran , Iran, maalek@ut.ac.ir

For nonlinear dynamic analyses seven earthquake records that have been matched to the used acceleration spectrum corresponding to FEMA356 provisions have been used. Regarding to FEMA356 provisions, when using seven or more earthquake records, the average value of the responses may be used rather than the maximum values (FEMA356, 2000). In the following, the introduction of the investigated structure and various alternative methods of its retrofit have been introduced. At the same time, the assumptions for constructing a computer model for the structure have been discussed. Finally, the results have been presented.

2. INTRODUCTION OF THE INVESTIGATED STRUCTURE The investigated existing structure in this research is a nine story steel building located in Tehran-Iran. In Figure 1 the plan of the structure is presented. The structure In the Y direction consists of four spans of 4.8m .Connections in this direction are of a specific type which was prevalent in Iran in the past (1960-1990). In this type of connection, which is known as the saddle or the bypass connection, the beams directly pass in pairs from the both edges of column and they are connected to the columns by means of angles at top and bottom. Previous researches on the behavior of these connections indicate that these type of connections act like semi-rigid connections that are continuous over the node of the connection. A bilinear moment-rotation model can be used for this connection. The plastic moment and rotational stiffness of the connection can be calculated with regard to the depth of the beams and the length of the connection angles. The saddle connections in this structure include angles at the top and the bottom of the size L100x10mm with the length of 30cm. In the Y directions also two relatively weak shear walls exist. Steel Reinforcement plates at the edge connections are also used. The beams in axes of 1 and 8 are INP220 types, and in axes 2, 3, 6 and 7 are INP240 and in the axes 4and 5 are INP260, according to the German standard. In the other direction the structure has seven spans of 7m. The beams in this direction are castellated beams of CNP200 with restrained connections. The beams at center and edges include steel reinforcement plates. In modeling of the structure, to deal with the effects of variation in the beam cross sections, additional nodes have been defined. Also, the columns are double INP profiles with strengthening top and bottom plates. The bracings of the existing structure are shown in figure 2

Figure 1. The typical floor plan of the existing structure

Figure 2. Bracings of the structure in X direction axis C (right) and in Y direction axes 1 and 8(left)

Figure 3. Capacity - demand spectrum for the existing structure in Y direction for CP and LS levels

Figure 4. Capacity - demand spectrum for the existing structure in X direction for CP and LS levels

3. THE ASSUMPTIONS FOR THE NONLINEAR ANALYSIS OF THE STRUCTURE

The existing structure was modeled in three dimensions in Perform-3D software and several nonlinear static analyses were performed on the model. The evaluation of the structural elements was undertaken according to provisions given in FEMA356. In this regard the structural elements are divided into two main groups, namely: deformation-controlled and force-controlled elements (FEMA356, 2000).The initial nonlinear static analyses of the original structure in the X direction, demonstrate that the plastic hinges were formed in the castellated beams in the region between two reinforcing plates at the web of the beams, where there was no infill plates available. Hence there was no expectation for the castellated beams to resist large plastic deformations without web buckling or the formation of a vierendeel type of mechanism at this region. Therefore, in the proposed model, the region with no infill plates was considered as a force-controlled region under the applied forces .So when the applied moments in these regions exceed elastic limits, the beam at these points is conservatively assumed to lose its strength. Regarding to the results obtained in this stage, it was observed that the shear wall in the Y direction is failed by concrete crushing. Therefore the saw tooth shape is obtained in the capacity curve of the structure. The remarkable strength loss was seen in the capacity curve that causes increase in the target displacement of the structure. The demand-capacity spectra of the structure are shown in figure 3 and 4. Even in life safety performance level, shear walls and also columns have not sufficient capacities; in addition, the target displacement of the structure is far more than the permissible displacements. Also, in the most of the connections, plastic deformations exceed from the acceptable limits and the link beams in the eccentric bracings have not enough capacity while their plastic rotation violate the limitation given in FEMA356 instruction manual; therefore, in accordance with FEMA356 guidelines , the structure is vulnerable and need to be rehabilitated. Also, in the X-direction, some weaknesses are found in the bracings, columns and castellated beams that even in the life safety performance level, result in large deformations in the structure.

3-1.The Characteristics of the Spectrum In this work, the three-lined spectrum was used based on ATC40 and FEMA356 with the assumption of soil type Se. Also CV and CA were considered at BSE-1 Earthquake Hazard Level as 0.35 and 0.51 respectively. For BSE-2 Earthquake Hazard Level these values were determined as 0.525 and 0.74 respectively (Applied Technology Council, ATC40, 1996).

3-2.The Locations of Bracings or Dampers In all of the methods used with the consideration of the building limitations, it was found that in the Y direction, the addition of new bracings was only possible at the 1 and 8 axes. The bracings were set at the edge spans DE and AB (see figure 1). In the X direction, the bracings were set in axes A and E at spans between the axes of 2-3 and 6-7. 3-3.The Modeling of the Saddle (Bypass) Connections The saddle connection can be modeled using panel zone element that acts like a semi rigid connection. In this model the rigidity effects and connection strength is considered nonlinearly and the continuity of the beam at the joints can also be modeled. The moment-rotation diagram for this connection is considered to be bilinear. With the attention to the previous test results and the existing relationships for this connection, the rigidity and strength of this type of connection has been estimated (Moghadam, 2005). The rotational stiffness of connections for the beams No. 220, 240 and 260 are considered as 35000, 38000 and 42000 KN.m/rad respectively. Also the yielding moments of these connections are assumed to be of the order of 110, 130 and 150 KN.m respectively. Figure 5 shows a typical saddle (bypass) connection.

Figure 5. Typical saddle (bypass) connection

4. THE RETROFITTING METHODS

In this research, two groups of strengthening methods were considered: the first group is related to the relatively modern methods based on the use of passive control devices that include metallic dampers, friction dampers, viscous dampers and visco-elastic dampers. On the other hand the conventional strengthening methods such as the use of bracings and shear walls were also investigated. The concept of these methods follows. 4-1.The Use of the TADAS Metallic Dampers This damper consists of some triangular steel plates (Fig.6). The characteristics of these dampers (SR and U values) for structure in X and Y directions are determined regarding to guidelines in Reference 6 (Tsai, Chen, Hong, and Su, 1993). SR and U values are defined as the relative strength and stiffness of the metallic TADAS dampers to the original frame of the structure respectively. Also the strain hardening effect of the damper is considered by taking the slope of 5% in its bilinear force-displacement model. Therefore by calculating the relative yielding displacements of the floors of the frame (∆y2) and the stiffness of each floor, the stiffness and yielding force of the TADAS damper can be obtained and considered in the computational model. In the X direction the characteristics of the damper is calculated for 4 different values of U and SR. With regard to the low rigidity of the frame in this direction, the SR=4 gives a more reliable results. By the reduction of the U value and increasing

the yielding force of the damper, the effect of the damper is reduced; because, the columns can not carry the applied loads and are out of the elastic mode. For the structure in the Y direction, also for three different values of U, the damper characteristics are calculated and the results are presented.

Figure 6. TADAS damper (Tsai, Chen, Hong, and Su, 1993) 4-2.The Use of the Visco-Elastic (VE) Dampers A typical VE damper is presented in Figure 7.The structure is subjected to three different percentage of critical damping for each direction separately. The VE damper is modeled as the parallel dashpot and spring (Kelvin model). Based on the relationships presented for VE dampers, the percentage of critical damping in the structure induced by VE dampers can be calculated regarding to equation 1 (Zhang and Soong, 1992).

Figure 7. VE damper

)1(2 2

2

iϖωηε −= (1)

Where η, ω and ϖi are loss factor, frequency of the original structure at mode i and the frequency of the structure with damper in the i th mode respectively. In this case, with the assumption of uniform distribution of the dampers, installed to the structure, the graph of variation of frequency of the structure in relation to increasing rigidity due to the addition of the visco-elastic dampers were calculated and drawn for each of the two directions. To draw this diagram, the diagonal bracings with different values of stiffness were added, the analysis gives the alternative period for each stiffness value. For the consideration of the effect of the bracing rigidity on the performance of the visco-elastic dampers, the effective loss factor for the composed system of bracing and damper, in the series form can be obtained from the following equation:

1.

2 ++=− n

nb η

ηην (2)

Where n is the relative stiffness of bracing with respect to the stiffness of the visco-elastic damper and η ν-b is the effective loss factor. By substituting the effective loss factor (η ν-b) instead of η in equation1, the amount of damping in the structure can be obtained. For modeling purposes, it is sufficient to find

the equivalent stiffness and damping of VE dampers regarding to a desirable percentage of critical damping. In this study the coefficient η is considered to be equal to 1.12 (Soong and Dargush, 1997). An investigation of these diagrams, in the Y direction gives the maximum percentage of damping as 10% of the critical damping. Therefore the structure in the Y direction for 3 different percentages of damping, i.e.: 4, 7, and 10% were investigated. On the other hand, in the X direction, with considerably less rigidity, the dampers can produce up to 30% of the critical damping. 4-3.The Use of the Viscous Dampers In order to model the viscous dampers, the spring and damper in series can be used (Maxwell model). The dampers have been distributed in the structure uniformly with the assumption of linear behavior.

Figure 8. Viscous damper

In the nonlinear static analysis of the structure equipped with viscous damper in the X direction, it was observed that even with high damping ratio of 50 percent of the critical damping, the capacity curve of the structure has negative gradient that indicates the instability of the structure in this direction, in theory. Regarding the fact, that the viscous dampers do not add any rigidity and stiffness to the structure, after the failure of the castellated beams, in the region with no infill plates, the structure becomes unstable. Therefore the viscous damper was used in the Y direction, only. In this direction the study included the analyses with the consideration of 3 different percentages of damping ratio as 10, 30 and 40 percent of the critical damping. A typical viscous damper is presented in fig.8. 4-4. Friction Dampers For damper modeling, the model given by Pall has been used in this work (Pall And Marsh, 1982). Therefore, to determine the optimum slipping load of the friction dampers, the structure was analyzed for the different values of slip loads from 150 to 900 KN in each direction and the relevant results are presented. It is estimated that the load slip of 300 KN in each direction gives the more realistic results, since, the amount of energy dissipated by the dampers is in the highest level and much less damages are expected to occur in the other parts of the structure.

Figure 9. Friction damper

In order to prevent the formation of the plastic hinges in the shear wall, in the first floor, the friction damper with the slip load of 700 KN was used. A typical pall friction damper is presented in figure 9. 4-5.The Use of the Reinforced Concrete Shear Wall Another method of the rehabilitation is the use of reinforced concrete (RC) shear wall. For nonlinear modeling of the shear walls, the location and depth of the moment plastic hinge must be determined.

First, one should identify whether the shear wall is controlled by shear or bending, in this project, the shear walls are controlled by bending. Also in the analyses one should consider that the applied shear forces do not exceed from the maximum bearing shear. The amount of the maximum shear which can be carried out by the existing shear walls is calculated as 5500 KN. Therefore, in the nonlinear model of the wall in the software, the height of the plastic hinge should be determined. Regarding to the instruction given by FEMA-356 and ATC-40, the length of the plastic hinge is considered to be the minimum of the values of the half of the wall section depth and the half of the story height. To evaluate the performance of the shear wall based on FEMA356 and ATC40, the maximum rotation of the plastic hinge must satisfy the limitation presented for the maximum permissible hinge rotation in the wall at the different levels of performance (Fig.10). In the PERFORM-3D software a similar but slightly more precise method has been used to determine the performance of the shear walls. In this program, after determination of the length of the plastic hinge in the wall with the use of an appropriate relationship, the program calculates the maximum strain due to compression and tension produced in concrete and steel bars. Then it compares those strains with the maximum permissible strain of the material in different performance levels. The effect of concrete cracking is also considered in the analyses.

Figure 10. Plastic hinge rotation in shear wall

Therefore in the two perpendicular directions of the structure, the analyses were undertaken with the consideration of two alternatives: the use of one and also two shear walls in the structure. These walls have been initially designed with the aid of ETABS program and then modeled in PERFORM-3D software, to perform a nonlinear analysis. 4-6.The Use of the Eccentric Braced Frame (EBF System) The eccentric bracing cannot be used in the X direction because of the existence of the castellated beams at this direction without a comprehensive strengthening of the webs of the beams. Even if the infill plates for the castellated beams are used in the link beam region with web stiffeners, it is expected to be a time consuming task. Therefore, the eccentric bracing is used only in Y direction. In this direction this bracing is used for three values of eccentricity. The plastic shear and moment of the link beams have been calculated as 515 KN and 155 KN.m respectively. As a result of the analysis, the critical eccentric values for the link beams have been calculated as 0.48 and 0.78 m. This means that when the length of the link beam is less than 0.48m, it yields in shear, and if this length exceeds 0.78 m it is controlled by plastic bending.

5. THE NONLINEAR DYNAMIC ANALYSES Based on the above, for each of the rehabilitation schemes of the structure a realistic model has been prepared and several nonlinear dynamic analyses have been performed on the models. The nonlinear dynamic analyses were performed using seven scaled earthquake records matched to the spectrum under consideration. These records include Naghan (Iran, 1977), Tabas (Iran, 1978), Abhar (Iran, 1991), Elcentro (1940), Park field (1966), Taft (Kern County, 1952), and San Fernando (1971) earthquakes. Figures 11 and 12 show the elastic response spectra and average response spectrum for these records.

Elastic Response Spectrum of Earthquake Records Scaled to g

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0.01 0.1 1 10

Period (Sec)

Spec

tral A

ccel

erat

ion(

g)

Tabas

Naghan

Abhar

Elcentro

Taft

San fernando

park field

Figure 11. Elastic Response Spectrum of the Earthquake Records Scaled to g

Avarage spectrum Response of Scaled Earthquake Records

0

0.5

1

1.5

2

2.5

3

0.1 0.6 1.1 1.6 2.1 2.6 3.1 3.6 4.1 4.6

Period (Sec)

Spec

tral A

cceleration (g

)

Used Spectrum ( CP LEVEL)

Avarage spectrum of Scaled Earthquake Records

Figure 12. Average spectrum response of the seven records compatible with the design spectrum In the Diagrams 1 to 2 the base shears of the structure for the use of various devices is presented. By the comparison of these diagrams one can find out that the variation of the base shear forces is much higher in the X direction in comparison to Y direction. This is because of the existence of the stiff shear walls in this direction that decrease the effect of dampers to reduce the base shear of the structure. However these diagrams show that with the application of passive dampers, the base shears will be reduced, particularly in the X direction. Diagrams 3 to 4 show the average percentage of dissipated energy in the structural elements in response to the 7 earthquake records. Dissipated energy in the structural elements has been used as a damage index parameter that reflects the damages in the elements. In this regard, the more dissipated energy in the elements, the more damages are expected. In diagram 3, the results show that the amount of dissipated energy in the VE dampers with the 30% of critical damping is maximum. This means that most of the earthquake energy is dissipated via the VE dampers while the other structural elements remain almost elastic. Also in this case the structural damages in the columns are minimal. In addition, this diagram shows that the use of friction damper with the slip load of 300 KN can lead to the same results. In the diagram 4, the results show that the amount of dissipated energy in the viscous damper with the 20% of critical damping is maximum. In this case the damages in the columns and saddle (bypass) connections are minimal. This is because of the fact that viscous dampers exert their maximum forces in out of phase with displacement. So when the structure undergoes to its maximum deformations, no force is exerted by the viscous dampers to the structure. This desirable characteristic of viscous dampers is especially suitable for the existing structures that may have not enough capacity to carry out the exerted forces.

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12359 11431 1137714529

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11401 1251414291

1621917871

29030

33714

0

5000

10000

15000

20000

25000

30000

35000

40000

U=2

SR

=2

U=1

SR

=4

U=2

SR

=4

U=3

SR

=4

10%

DA

MPI

NG

20%

DA

MPI

NG

30%

DA

MPI

NG

150

KN

300

KN

500

KN

700

KN

900

KN

1 W

ALL

2 W

ALL

S

TADAS DAMPER VISCOELASTICDAMPER

FRICTION DAMPER SHEARWALL

Bas

e Sh

ear

(KN

)

Diagram 1.Comparison of the maximum base shears for the use of various devices (X direction)

20200

18030 17807 17159 1739718261

16497 16946 17329

1492915764

1663317779

2012118844 18613

2424125914

0

5000

10000

15000

20000

25000

30000

U=1

SR

=2

U=2

SR

=2

U=3

SR

=24%

DA

MPI

NG

7%D

AM

PIN

G10

%D

AM

PIN

G10

%D

AM

PIN

G30

%D

AM

PIN

G45

%D

AM

PIN

G

300

KN

500

KN

700

KN

900

KN

e =4

0 cm

e =1

00 c

m

e =1

50 c

m

1 W

ALL

2 W

ALL

S

TADASDAMPER

VISCOELASTICDAMPER

VISCOUSDAMPER

FRICTION DAMPER ECCENTERICDAMPER

SHEARWALL

Bas

e Sh

ear

(KN

)

Diagram 2.Comparison of the maximum base shears for the use of various devices (Y direction)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

U=2

SR=

2

U=1

SR=

4

U=2

SR=

4

U=3

SR=

4

10%

DA

MPI

NG

20%

DA

MPI

NG

30%

D

AM

PIN

G

150K

N

300K

N

500

KN

700K

N

900

KN

1 W

ALL

2 W

ALL

S

TADAS DAMPER VISCOELASTICDAMPER

FRICTION DAMPER SHEAR WALL

Perc

enta

ge o

f diss

ipat

ed e

nerg

y

Damper

Shear Wall

Beams

Columns

`

Diagram 3.Average dissipated energy in each element for the use of various devices (X direction)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%U

=1 S

R=2

U=2

SR=

2

U=3

SR=

2

4%D

AM

PIN

G

7%D

AM

PIN

G

10%

DA

MPI

NG

10%

DA

MPI

NG

20 %

DA

MPI

NG

30 %

DA

MPI

NG

45%

DA

MPI

NG

150

KN

300

KN

500

KN

700

KN

900

KN

e =4

0 cm

e =1

00 c

m

e =1

50 c

m

1 W

ALL

2 W

ALL

S

TADAS DAMPER VISCOELASTICDAMPER

VISCOUS DAMPER FRICTION DAMPER ECCENTERICBRACE

SHEARWALL

Perc

enta

ge o

f dis

sipa

ted

ener

gyColumns Beams Bypass Connections Shear Walls Dampers

Diagram 4.Average dissipated energy in each element for the use of various devices (Y direction)

6. CONCLUSIONS

With the consideration of the case study under investigation and the alternative methods of rehabilitation suggested here, we may summarize the following concluding remarks.

The comparison of the results indicates that the use of passive dampers for the purpose of the seismic rehabilitation of the existing structures is quite valuable. With the application of the passive energy absorbers in the structures, the earthquake energy is dissipated via these devices while the other structural elements can remain undamaged. On the other hand the comparison of the base shears induced in the structure, demonstrates that the use of the passive dampers in the structures can substantially reduce the base shear and base moment and usually eliminates the expensive works on foundation strengthening or local retrofitting.

The use of the viscous dampers is particularly useful for the structures that contain weak columns. Because this type of damper exerts its maximum forces in out of phase with displacement, most of the columns remain elastic. Also fewer damages are expected in the connections.

REFERENCES

1- Applied Technology Council (1996); “Seismic Evaluation and Retrofit of Concrete Buildings”, ATC40, Volume 1, Report No.SSC 96-01, Seismic Safety Commission, Redwood City, CA.

2-Federal Emergency Management Agency, NEHRP.(2000); “Pre Standard and Commentary for the Seismic Rehabilitation of Buildings”, FEMA356, Washington, D.C.,

3- Moghadam, H. (2005). Earthquake Engineering, Farahang Press, Tehran.

4-Pall, A. S., Marsh, C. (1982); “Response of Friction Damped Braced Frames”.ASCE, J. of Structural Eng., 108(ST6), 1313-1326

5- Soong, T.T and Dargush, G.F. (1997); Passive Energy Dissipation Systems in Structural Engineering, JOHN WIELY &SONS Ltd, Chichester.

6- Tsai, K.C., Chen, H.W., Hong, C.P and Su, Y.F. (1993), “Design of steel Triangular Plate Energy Absorbers for Seismic-Resistant Construction”. Earthquake Spectra, 19(3), 505-528

7- Zhang, R.H., Soong, T.T. (1992). “Seismic Design of ViscoElastic Dampers for Structural Applications”, ASCE, J. of Structural Eng., 118(5), 1375-1391