Passive structural control strategies using

seismic steel energy dissipators

K.C. Tsai*, Li-Chong Huang* & Ting-Fu-Wang*

"Dept. of Civil Engineering, National Taiwan University

Sinotech Engineering Consultant, Inc.

Taipei, Taiwan, Republic of China

Email: kctsai@ce.ntu.edu.tw

Abstract

The force versus deformation relationships of a steel frame constructed with theproposed hysteretic energy dissipators (HED) are characterized by a tri-linearmodel indicating the distinct yielding of the HED and the frame. The optimalstiffness and strength ratios between the HED and the frame are recognized fromparametric analysis of the nonlinear response spectra. A design algorithm ispresented to illustrate the strategies incorporated into the design of framebuildings for seismic response control, particularly on the reduction of theinelastic deformational demands imposed on the beam-to-column connections ofa six-story example steel moment frame.

1 Introduction

Modern seismic resistant design practice generally adopts a set ofreduced seismic forces to account for the ductility capacity of thestructures [1]. In the meantime, it often requires the compliance ofspecific ductility design provisions in order to assure a ductile behavior ofthe system. However, structural failures of buildings observed followingsome recent earthquakes have suggested that a ductility-based, rather thana performance based, design methodology may be inadequate for modernseismic hazard mitigation of buildings, particularly from the socio-economical point of views. This is evidenced by the brittle fractures of

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welded steel moment connections due to the difficulties of controlling

material properties, construction workmanship and inspections [3]. Thus,in addition to searching for sound technology for the construction ofductility-enhanced members or connections, the general consensus hasbeen on how to find reliable solutions to reduce ductility demandsimposed on these structural components. For this purpose, two types ofenergy absorbing devices have been developed at the National TaiwanUniversity and proven promising in improving the performance ofbuilding structures in resisting severe earthquake excitations [4,6,7].

2 Steel Hysteretic Energy Dissipators (HEDs)

Since the bending curvature of a transverse load applied at the end of atriangular plate is uniform over the full height of the triangular plate, theplate can deform well into the inelastic range without curvatureconcentrations. As shown in Fig. 1, the proposed steel triangular-plateadded damping and stiffness (TADAS) device consists of severaltriangular plates welded to a common base plate. Similarly, a short steelwide flange beam under cantilever load can yield in shear while remainelastic in flexure. As shown in Fig. 2, the proposed shear link energyabsorber (SLEA) consists of a short steel wide flange beam segmentwelded to a end plate. Experimental results (see Figs. 1 and 2) haveconfirmed that properly constructed TADAS and SLEA elements possesshighly predictable mechanical properties, and can sustain a large numberof yielding reversals. Pseudo-dynamic tests of full-scale steel frames havedemonstrated that both these two types of HEDs, increasing the lateralframe stiffness and hysteretic damping, can effectively control theresponses of the structures under severe excitations [4,6].

2.1 Nonlinear Responses of SDOF Frame Systems

The TADAS or SLEA can be conveniently placed between the floorgirder and a pair of braces. Note that the HED-to-brace connections canbe advantageously realized by using vertical slots to separate the gravityand lateral load effects while minimizing the lateral support requirementsat the HED-to-brace joint. Thus, the HED and the moment resisting frame(MRF) are combined in series, and the force versus deformationrelationships of a hysteretic energy dissipated frame (HEDF) can beadequately characterized by a tri-linear model as illustrated in Fig. 3. Forthe purpose of discussion, a system using the TADAS as the HED isadopted.

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-0.30

Figure 1 TADAS device andcyclic response

-15 0 15Rotation (% rad)

Figure 2 SLEA device andcyclic response

30

(Cy) Ry2

(Cs) Ry1

Rymrf(Cymrf)

Rymrf = Ry1 x[1 n-1

1+SR 1+SRXSHR*

System

I

ENGERGYDISSIPATOR

MRF

Ay1 Ay2

Figure 3 Tri-linear force deformation relationships

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In Fig. 3, the elastic lateral stiffness of the TADAS element (includingthe braces) and the MRF are represented by K^ and AT/, respectively. Theeffective stiffness of the system, £,, can be computed from K Ka+Kf.The stiffness ratio (SR) is defined as SR=KJKf. SHRA and SHRp representthe strain hardening effects of the TADAS and the MRF after undergoing

displacements beyond the yield points, Ayj and 4 , respectively. Thesystem's first yield strength and the ultimate strengths are respectivelyidentified as Ryj (yielding of the TADAS) and / (yielding of the MRF).In Fig. 3, the non-dimensional factors C, and Cy are computed bynormalizing Ryi and Ry2, respectively, with respect to the weight, W, of

the system. The strength ratio, 12, is defined as £2=Ry2/Ryi=C/Cs. Sincethe yielding of the TADAS indicates a significant yielding of the entire

system, the strength ratio R is analogous to the overstrength factorinherent in the conventional structural system [8]. The system's post-yield stiffness can be computed from pkl and pk2. It can be found that

pkl =(7+SRxSHRA)/(l +SR) and pk2=(SHRp+SRxSHRA)/(l +SR).

Since it is preferable to allow the HEDs to yield prior to the yielding ofthe MRF, the concept of two-level design procedures prescribed in theJapanese Building Standard Law [1] have been adopted. Accordingly, thepeak ground acceleration (PGA) for the service limit state earthquake is

set at O.OSg (0.2x0.4g) for structures in regions of high seismic risk. Thefirst yield strength index, C,, for a system with specific vibration period,is determined from the corresponding (PGA=0.08g) response spectrumprescribed in the model building code [2] for a given soil condition (e.g.hard site). The system stiffness, #,, is directly related to the vibration

period. Thus, given a specific set of SR and JQ values, the complete tri-linear force versus deformation relationships can then be determined asnoted above (using ,S#&=0.07 and S///?/*=0.02). Using six historicalearthquake ground acceleration records obtained from hard sites,extensive parametric study on energy, ductility and acceleration response

spectrum have been performed for various values of SR and £2 for singledegree of freedom systems [7]. It is concluded that:• For short period structures (T < 0.8 sec.), a SR value ranging from 3 to4 and an Q value of about 2 should be considered. In this manner, theHED can absorb about 50%, while the MRF can absorb about 10% of thetotal earthquake input energy.• For long period structures (T > 2.0 sec.), increasing SR will reduce, butless effectively, the displacement responses. It will also increase the totalenergy input energy and the acceleration responses. If the 12 value is toosmall (e.g. 1.2), the inelastic demands imposed on the MRF may be too

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mat a uiv Ull lilt UlUCi Ul 1 . J IU Z-.J allU all

£1 between 2 and 3 be considered for the long period structures.

•For structures having medium vibration period (0.8 < T < 2.0 sec.), a SR

on the order of 2.5 to 3.5 and an Q of at least greater than 2 should beconsidered.

3 Design Strategies for Response Control

A displacement-based design method, which requires the computation of

the yield displacement (4*) of the MRF have been proposed [4]. Basedon the results of the experimental and analytical studies noted above, theproposed force-based design methodologies are as follows. Since theductility capacity of the proposed HEDs is adequate for seismicapplications, the design procedures can be conveniently constructed bymodifying those for the eccentrically braced frames (EBF) prescribed inthe model building codes [2].

(1). Proportion the MRF without the presence of the HEDs to resist thegravity loads. Compute the elastic story stiffness, A}, for each floor usingthe story drift resulted from a suitable pattern of lateral force distribution.(2). Select a suitable SR value based on the fundamental period estimatedfor the system (MRF + RED).

(3). Compute the required stiffness, %,, of the HED elements from theproduct of SR and AT/. Construct an equivalent concentrically bracedframe (CBF) from the MRF. Let the equivalent CBF have a lateralstiffness ofKa+Kf for each floor.

(4). Compute the design base shear V from V=0.2Z/C for the equivalentCBF, where Z, / and C are defined in the model building codes [2].(5). Compute the story shears by distributing the base shear to each floor.Alternatively, the story shears can be obtained by performing a modalanalysis using the corresponding response spectrum scaled to produce thesame design base shear as that computed in step (4).(6). Compute the story shear resisted by the HEDs based on the relativestiffness. The required HED strength can be computed by multiplying thetotal story shear by a factor of SR/(l+SR) for each floor.(7). Proportion the HEDs and the braces, so that their overall stiffness isclose to Ka and the yield strength of HED is adequate to resist therequired strength computed in step (6). It has been found most cost-effective if the the braces-to-HED stiffness ratio is kept at about 5 [4].(8). Perform a capacity design check for both the braces and thesupporting beam. It is recommended that a strain-hardening factor of 1.5

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be incorporated to estimate the maximum force that can be developed inthe HEDs. Repeat steps 1 through 7 if necessary.(9). Construct a suitable analytical model for the entire system. Performstatic or modal analysis using the lateral forces determined in step 5. Thestory drift angle should not be greater than 0.005 radians and all membersshould remain elastic. As a minimum, the member forces and the lateraldisplacements should be checked following the requirements (Rw=12)prescribed in the model building code [2] for a dual MRF/EBF. The MRFwithout the HED in place should have strength capable of resisting 25%of the prescribed seismic forces.(10). Perform nonlinear static push over analyses to check whether the

overstrength factor 12 is as appropriate as noted previously. Performnonlinear time history analyses to examine whether the rotationaldemands imposed on various members are excessive or not.

4 Using The TADAS for A 6-Story Frame

The frame elevation of the 6-story example frame is given in Fig. 4. Theuniformly distributed gravity loads are assumed 51.2 kN/m and 20 kN/mfor dead load and live load, respectively. The selections of the beams andcolumns are shown in Table 1. The fundamental period of the MRF is1.90 second. The seismic responses of the 6-story frame are to becontrolled by applying the TADAS devices in the center bay.

The stiffness (K<j) and the plastic strength (?,,) of a TADAS can becomputed from K<f=NEBt*/6h* and Pp=NFyBt*/4h, respectively. E and Fyrepresent the young's modulus and yield stress of steel, respectively, fl, t,h and N represent the base width, thickness, height and number oftriangular plates, respectively. Using a S7?=3.0, the overall stiffness of theTADAS/braces are determined from the product of SR and the MRFstiffness, A}, for each floor. An equivalent CBF is constructed in order tocompute the design story shear from the modal analysis. The first twovibration periods of the equivalent CBF are 0.99 and 0.34 seconds,respectively. In this example, in stead of using a PGA=0.08g designearthquake to determine the required plastic strength (Pp) for the TADAS,the code prescribed minimum base shear (Rw=12) is used to scale thestory shear. Accordingly, the TADASs are proportioned to meet thedemands based on the fisrt yield strength Py, where Py=NFyBf/6h.Theselections of the TADAS and the braces considering the required stiffnessand the strength noted above are shown in Table 2.. Except the columnsare A572 Grade 50, all beams, TADAS devices and braces are A36 steel.As shown in Table 2, the actual SR value in each floor is very close to the

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vaiue or j.u. inese analyses or me MKI- ana me equivalentare performed using the ETABS program.

Table 1 Schedule of column and beam sizes

6FL

5FL

4FL

3FL

2FL

1FL

C1&C4

W 12x72

W12x72

W12x72

W12x72

W12x79

W12X79

C2&C3

W18X106

W18X106

Wl 8x106

W18X106

W18xl43

W18X143

B1&B3

W21x50

W21x50

W21x50

W21x50

W21x57

W21x57

B2

W21X57

W21x57

W21x62

W21x62

W21x62

W21X62

Table 2 Schedule of TADAS and brace sizes

6FL

5FL

4FL

3FL

2FL

1FL

Braces

2L6x4xl/2

2L6x4xl/2

2L6x4xl/2

2L6x4xl/2

2L6x4x5/8

2L6x4x5/8

h(mm)240

240

300

300

300

240

t(mm)

50

40

40

40

40

50

B(mm)120

90

110

100

110

100

N

2

5

8

9

10

6

SR

3.15

3.07

3.09

3.01

3.06

3.07

6FL

5FL

4FL

3FL

2FL

1FL

L- 3@8m = 24m ^"*•» sBT

— — _

B2

_ —

B3 /

GsII

Tf©vo

\

Cl C2 C3 C4

Figure 4 Frame Elevation

Nonlinear static and dynamic analyses for both the MRF and the entireadded damping and stiffness frame (ADASF) including the TADAS andbraces are performed using the DRAIN2D+ program [5]. This program is

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2000 -

ROOF DRIFT ANGLE (1/1000)10 20 30 40

MRF El Centre 0.4 g

1600-MRF (with UBC Lateral Force Pattern)0 = 1.33

0.3000-r

300 600 900ROOF DISPL. (mm)

ROOF DRIFT ANGLE (1/1000)5 10 15 20

0.05

0.001200

700

525

O

J ADASF (with UBC Lateral Force Pattern)JO = 3.30

K. =17.84 kN/znmR, =575 IcN C, =0.08Ry =1900 kN Cy =0.27

100 200 300 400 500ROOF DISPL. (mm)

ADASF El Centre 0.4 g

175

700

MRF El Centre 0.4g

10 15TIME (SEC)

600

TIME (SEc5

20

20

i§EL

I

aCO

IO

Figure 5 Nonlinear staticpush over analyses

Figure 6 Extents anddistributions of plastic hinges

Figure 7 Energy distributiontime histories

ELCO

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a suDsiantiany moainea version or me ongmai UKAUN-zD program. Its

main features have included the graphical post-processor, nonlinear staticanalysis capability, computations of periods and mode shapes,

computations of energy distribution time histories in the system and

various elements. The strength of the beams, columns and braces arebased on the AISC, ASD 1989 specifications using nominal materialproperties. The beam-column elements are used for all members exceptthe TAD AS devices are modeled using beam elements with the samestiffness and yield strength as those of the TAD AS. The first twovibration periods obtained from the DRAIN2D+ are 0.98 and 0.34seconds, well represented by the equivalent CBF model using the ETABSprogram.

The static force versus roof displacement curves for the MRF and theAD ASF are shown in Fig. 5, respectively. It is found that for AD ASF thefirst yield strength index, C, and the ultimate yield strength indexes Cy

are 0.074 and 0.267, respectively. The overstrength factor Q for theAD ASF is 3,30, a acceptable value for a system having a mediumvibration period. Using the VBEW2D post-processor, Fig. 6 indicates thatthe maximum plastic hinge rotational demands imposed on the beam-to-column connections for the 6-story MRF are close to 0.01 radians due tothe 1940 El Central Earthquake ground accelerations (NS component)scaled to PGA=0.4g. Under the same earthquake excitations, thenonlinear demands on the beam-to-column connections are completelyeliminated by applying TAD AS devices as shown in Fig. 6. Themaximum rotational demand (at 3FL) imposed on the TAD AS devices isonly about 0.07 radians, well below the rotational capacity commonlyobserved in the TAD AS test specimens [4]. Figure 7 shows the energydistribution time history of the MRF and the AS ASF during the sameearthquake excitation, where E* and Eg are kinetic and elastic strainenergies, respectively. It is evident that the energy absorbed by theTADAS devices is significant and evenly distributed along the height ofthe frame. It is worthy noting that the total input energy in the ADASFcan be less than that observed in the MRF as shown in this example.

5 Conclusions

The following conclusions can be drawn from this study:• Experimental response of well constructed TADAS and SLEA cansustain large inelastic cyclic deformations. Thus, they appear promisingfor seismic resistant constructions of building structures.

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• The nonlinear deformational demands imposed on the beam-to-column

connections of steel MRFs can be effectively mitigated by incorporatingproperly proportioned steel energy absorbers.

• The proposed design strategies incorporate the modern two-levelseismic-resistant design methodologies, ensure to satisfy the service limitstate while facilitate the review of the overstrength factor for controllednonlinear responses.

Acknowledgements

The authors are gratefully acknowledge the financial supports providedby the National Science Council and the Sinotech Foundation forEngineering Science and Technology.

References

[1] IAEE, "Earthquake Resistant Regulations, A World List",International Association of Earthquake Engineering, Tokyo, 1988.

[2] ICBO, International Conference of Building Officials, "UniformBuilding Codes," Whittier, CA, 1994.

[3] SAC, "Interim Guidelines: Evaluation, Repair, Modification andDesign of Welded Steel Moment Frame Structures", Report No.SAC-95-02,SAC Joint Venture, Sacramento, CA, 1995.

[4] Tsai, K.C., Chen, H.W., Hong, C.P. and Su, Y.F., "Design of SteelTriangular Plate Energy Absorbers for Earthquake ResistantConstruction", Earthquake Spectra, EERI, Vol. 9, No. 3, 1993.

[5] Tsai, K.C. and Li, J.W., DRAIN2D+, A General Purpose ComputerProgram for Static and Dynamic Analyses of Inelastic 2DStructures, supplemented with a graphic processor VIEW2D, UserGuide, 1994. (Available in NISEE/Computer Applications, Univ. ofCalifornia, Berkeley)

[6] Tsai, K.C., "Seismic Energy Dissipators for Performance-BasedDesign", Proc., 2™* Int. Workshop on Structural Control, HongKong, 1996

[7] Tsai, K.C. and Wang, R.J., "Shear Links Energy Absorbers forSeismic Energy Dissipation", Proc., the 6th Natl. Conf. OnEarthquake Eng., Seattle, 1998.

[8] Uang, C.M., "Establishing R» and Q Factors for Building SeismicProvisions", J. of Struc. Eng., ASCE, Vol. 117, No. 1, 1991

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