INELASTIC BEHAVIOR OF DUCTILE BUCKLING...

International Conference on Earthquake Engineering and Disaster Mitigation, Jakarta, April 14-15, 2008

INELASTIC BEHAVIOR OF DUCTILE BUCKLING-RESTRAINED BRACED TRUSS-GIRDERS MOMENT FRAMES

H. Sugihardjo1, W. Merati2, A. Surahman2 and M. Moestopo2

1Department of Civil Engineering, Sepuluh Nopember Institute of Technology (ITS), Surabaya, Indonesia

2Department of Civil Engineering, Bandung Institute of Technology (ITB), Bandung, Indonesia Email: [email protected]

ABSTRACT: This paper evaluates the inelastic behavior of three Buckling-Restrained Braces (BRB) and a ductile Buckling-Restrained Braced Truss-Girder Moment Frames (BRBTMF) by analytical and experimental means. The BRB section is a strip plate core A283 grade C steel which has been treated with soft annealing, cased with rectangular hollow section A50 steel as a buckling-restraint material. The BRBTMF proposed in this paper is the modification of The Special Truss Moment Frames (STMF) X-diagonal-type by replacing the X-diagonal with the BRB inverted-V-type to improve its inelastic behavior. From the Nonlinear History Analysis using earthquake records, it can be concluded that in general, the BRBTMF has better inelastic behavior than the other ductile frames. The cumulative ductility factor of the BRBTMF subassemblages has met the requirements of the hysteretic system structure. Based on these preliminary studies, the use of the BRBTMF may be implemented to practice.

1. INTRODUCTION

Indonesia is located in the junction of three tectonic plates, namely Indo-Australia, Pacific, and Eurasian plates. This situation has caused most of the areas in the country are categorized in the high-risk tectonic earthquake zones. It is, therefore, required to design an earthquake-resistant building in Indonesia. Strength, stiffness, ductility, and the ability to dissipate the earthquake energy should be possessed by each earthquake-resistant building. These are the main aspects that should be considered in the building structures. Besides, the structural system, material used in the building as well as the connection system of each structural element are also very important and require serious attention.

A truss-moment frame is one of Moment-Resisting Frame System. If compared with the solid beams, the truss-moment frames have three economical advantages. Goel and Itani (1994b) stated that “It requires simpler connections, it can be applied for longer structural spans and the space within the truss elements can be used as a place for the utility”. The additional advantage is that if the truss system is implemented in Indonesia, where the labor cost is relatively low, the truss beams that require more labor work than the solid beams, is still preferable as a more economical choice. The only disadvantage of this system is that the occurrence of inelastic behavior in the columns and that the beams remain elastic due to the high seismic loading. In the full-scale testing, this type of frames had been proven to perform a sharp degradation on its hysteretic loops (Goel and Itani, 1994a).

To improve the performance of the truss system as the moment-resisting frames under high seismic loading, some Vierendeel’s panels are added in the midspans as the ductile segments. These segments work as fuses (warning system), that has a function to absorb the earthquake energy by means of inelastic flexural deformation. During the earthquake, the induced lateral forces produce the shear forces in the ductile segments resisted by the cords alone until the plastic hinges occurred due to the flexure and thus, forming the yielding mechanism in the frames as shown in Figure 1 (Basha and Goel, 1996).

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X-bracing system Vierendeel-system

ductile segment

plastic hinge plastic hinge

ductile segment

Figure 1 Yield mechanisms of ductile truss-moment frames.

Another system is by using the additional diagonal X-shaped bars (will be called as X-diagonal subsequently) located in the panels around the midspans of the truss-frames (Goel and Itani, 1994b), as shown in Figure 1. The numerical analyses were carried out on the 4-story 7-bay frames. The response indicated that an asymptotical lateral displacement at the top roof and smaller inter-story drifts than those in the regular truss system. The material used in this study can be saved up to 30 to 40 percent. The quasi-static test with full-scale specimens has shown that a consistent behavior in the hysteretic loops. This study is adopted as the Special Truss Moment Frames (STMF) (AISC, 1997) or the Special Steel Truss Moment Frames (SSTMF) (NEHRP, 2000).

In the last decade, a new steel material was developed. It is known as Low Yield Stress Steel. The steel types that can be classified into this group are LY100, LY160 and LY235. It is the form of panel or bracing. The bracing is the shape of flat bars which is stiffened by the box structural steel. It is called as Buckling-Restraint Braces (BRB). This material is mostly used as a hysteretic damper. It has a low yield strength ranges from 90 to 245 MPa (up to one-third of A36). However, the ultimate strain can reach up to 1.5 to 2.5 times the A36 steel’s ultimate strain (Inoue, 2004b; Kamura et al., 2000). The implementation of low yield stress steel as a replacement to the normal steel assures that the plasticity process occurred at the small deformation without significant changes in the bracing and structural stiffness (Kamura et al., 2000). The BRB sectional configuration is in the form of strip plates (or other sections) from low yield or mild steel as core bracing inserted into the box case made from normal steel with or without unbonded material as the lateral stiffening elements. From the BRB configuration, the resulted compressive yielding capacity is relatively similar to the tensile yielding capacity. The application of the ASTM-A36 mild steel as the core bracing also produces consistent hysteretic loops, even though the cumulative ductility factor is lower than that in the low yield steel (Chen and Lu, 1990; Watanabe, et al., 1989).

In the latest code (AISC, 2005), a new structural system called Buckling-Restraint Braces Frames (BRBF), is introduced. The system comprises the solid beams stiffened by the BRB. From the analytical study carried out by Shimokawa and Kamura (1999) on the 11-story 8-bay steel frame structures stiffened by the BRB, it showed that the reduction of lateral displacement could be as high as 50% and the base shear was also reduced although it was relatively small. The study conducted by Kasai et al. (1998) on 14-story building retrofitted with the BRB made from unbonded material (Buckling-Restraint Unbonded Braces), it showed that the reduction of lateral displacement ratio could be up to 60% and up to 30% for the base shear. The conclusion of the study conducted by Clark et al. (2000) on a structure designed based on the target of the lateral displacement ratio and the stiffness, the base shear could still be reduced up to 50% with additional BRB of unbonded material as stiffeners.

From the above overview, it can be seen that the studies conducted was to stiffen the solid beam frame structure with the BRB. The idea was arisen, when the X-diagonal, which has small



compressive capacity in the post-buckling region, was replaced by the BRB with lower yield stress steel and has the compressive yield stress similar to the tensile stress, it is believed that it could improve the seismic response of the frame system. Hence, it is hoped that plasticity could happen earlier in the frame system with bulkier hysteretic loop but stable. The proposed structural system is called the Buckling-Restrained Braced Truss-girder Moment Frames (BRBTMF).

2. ANALYTICAL STUDY

The analytical model in this study was based on the study conducted by Goel and Itani (1994b), and Sugihardjo, et al. (2004), i.e., 4-story 7-bay frame with layout and analytical model of exterior frame in longer direction axes A and D, as seen in Figure 2. This model was modified from the STMF X-diagonal type by replacing the X-diagonals with BRB inverted-V, and has the height of 3962 mm (156 in.) for each story level. The cross-section of the frame elements and yield strength of the steel in this analytical study can assumed equal to those in the previous study, that is it made from A36 steel with fy = 248.2 MPa, as listed in Table 1. The BRB made from LY235 steel with fy = 225 MPa and the cross-sectional area designed using Eq. (1), where Py = tensile yield strength of the X-diagonals; Pcr = buckling strength of the X-diagonals; φ = ratio post-buckling to initial buckling strength of the X-diagonals (assumed to be 0.3).

)()( )( cryBRBycry PPPPP +≤≤Φ+

(1)

The most left-hand side columns of Figure 2(b) represents the stiffness of interior columns. First, the structural elements were designed with the static equivalent method according to the UBC 1988 and the load factors were adopted from AISC-LRFD 1986. These old standards were adopted to trace and compare with the previous study such that the static earthquake loading was equivalent (Goel and Itani, 1994b). The base shear: V = ZICW/Rw with Z = 0.4; I = 1.0; C = 1.94 based on the natural period of the building, T = 0.68 sec and the soil type S3 (Sfactor = 1.2). The total weight of the building W was calculated using the uniformly-distributed load of 3.83 kPa for each story. The structure was designed as SMRF with Rw = 12 (or R = 8.5 (ICBO, 1997)) since it is expected the ductile and stable hysteretic behavior.

The analytical method used was the nonlinear time history analysis. To analyze the yielding energy dissipated by the BRB, an inelastic motion system equation was adopted. In the form of energy equilibrium, this equation is in terms of the kinetic, damping, static (the sum of strain and yielding energies) and input energy equilibrium (Akiyama, 1985; Chopra, 2001) as given in Eq. (2):

∫ ∫ ∫ ∫−=++t t t t

gs dtutumdtuuufdttucdtutum0 0 0 0

2 )(),()()( &&&&&&&&& (2)

Table 1 Comparison of frame systems.

Element STMF X-diagonal BRBTMF

Column (stories 1 and 2) W 14x120 W 14x120

Column (stories 3 and 4) W 14x99 W 14x99

Chords 2L 88.9x88.9x12.7 2L 88.9x88.9x12.7

Outside diagonal 2L 63.5x63.5x7.9 2L 63.5x63.5x7.9

Outside vertical 2L 50.8x50.8x6.4 2L 50.8x50.8x6.4

Inside vertical 2L 31.8x31.8x6.4 2L 31.8x31.8x6.4

X-diagonal L 25.4x25.4x6.4 L 25.4x25.4x6.4

Core of BRB (stripe plate) 60x8

Casing of BRB (rectangular) 2L 50x50x3



A classic way of Rayleigh was used to define the viscous damping of 5%. By using the step-by-step procedure of Newmark, the inelastic motion equation can be solved with the aid of DRAIN2-DX software (Prakash and Powel, 1992). The structure was loaded under several scaled-earthquake records with the following methods: First, using the 1978 NS Miyagi-ken-oki earthquake with PGA 0.4g. This earthquake record was adopted since it could give the maximum dynamic response as in the study on the STMF X-diagonal type. The result obtained will be compared with the result of the previous study by Goel and Itani (1994b). Secondly, for validation purpose, the proposed system will tested under the 1940 NS Elcentro earthquake record with PGA 0,69g, Northridge (Newhall 0 degree) with PGA 0.42g and NS Kobe with PGA 0.58g. The scale factor was chosen such a way that the earthquake response spectra intensity is equivalent to the UBC-S3 velocity response spectra, as shown in Figure 3.

B

7x8484 mm

DC

1 2 3 4 5 6

3X914

4 m

m

7 8

A

BRB (YIELD IN TENSION OR COMPRESSION)

PLASTIC HINGE

(a) (b)

Figure 2 Analytical models (a) Plan (b) Frame A, D and inelastic activities (Miyagi record).

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2

spectra acceleration

periode(sec).5

UBC-S3MIYAGI-0,40G

NRIDGE-0,42GKOBE-0,58GELCENTRO-0,69G

Figure 3 Scaled spectra of records to match UBC soil S3 spectrum.

3. EXPERIMENTAL STUDY

In the experimental work, three BRB and one full-scale BRBTMF frame specimens were tested. The longitudinal layout and cross section of BRB are given in Figure 4. The stiffener plate with thickness of 12 mm at the end of BRB represents a connection plate when BRB has been implemented in the truss. The base plate of 25 mm thick is used as a support to tie with the loading frame. All BRB use the A283 Grade C steel material which has been soft-annealing treated with the yield strength of about 265 MPa and the stiffener was made from a material similar to A50 steel, such that the dimension was smaller than the analytical study. The design of BRB dimension according to the stable hysteretic requirement from Shimokawa and Kamura (1999) was in the safe region of Inoue’s interaction diagram (2004a). The complete result can be seen in Table 2, whereas BRBTMF using BRB 50 × 8 mm with the dimension of the elements equal to the A50 steel, as shown in Figure 4. The cyclic loading history is implemented by strain to the BRB and the drift ratio of BRBTMF from 0.5 to 3% as in Figure 5. The applied strain was up to 3% to know the



BRB’s capacity, although from the earlier analytical study the strain in the BRB was not greater than 2%.

weld 6mm

casing A50

1/2s = 1.2

1/2s = 1.2

bi = 49.0

ti = 7.9

tp = 3.

3

bp = 48

.5

core A28312.0

6.0

gusset A50

base plate 25mm

795

las 630 60 30

40 60 3040 40

A

A

L=709

gusset 12mm

baut 3/4"B

B

A-A B-B

25

60

30 60 3040

40

120

3040 40

30

60

30

(a) Longitudinal layout (b) Section A-A

Figure 4 Details of BRB specimen.

C

plate 12mm

loadcell

2L 50x50x5

762

bolt 4x1in

2L 5

0x 5

0x5

762

roller

A

100

bolt

plate

4x1 in

20 mm

280

250

35

3535 200

35

STRONG W

ALL

2L 90x90x12

2L 60x60x6

STRONG FLOOR

D 2L 90x90x12

762 1778

B

167 in (4242 mm)

brb

brb

2L 5

0x5

0x5

2L 60x

60x6

940

BOLT A325

plate 2x20mm

10x7/8

940a

200

t=8

a

200

180

1373

BOLT 4x1 in

1/2 WF 350x350x12x19

2L 60x

60x6

las 6

6

1778

200

WF 3

50x3

50x

12x1

9

330

t=8

816

ACTUATOR

t=12

1573

250

156 in(3962 mm)210

roller

-4

-3

-2

-1

0

1

2

3

4

0 2 4 6 8 10 12 14 16 18 20 22drift ratio (%)

number of cycle

Figure 5 Test setup for BRBTMF.

Table 2 Dimensions of buckling-restraint braces.

CASING CORE BRB

Width, bi Thickness, ti Width, bp Thickness, tp

LENGTH (mm)

(1)-50x8 49,0 7,9 48,5 3,3 709

(2)-40x8 37,7 7,9 38,8 2,7 707

(3)-50x8 47,8 7,9 46,5 3,3 709

4. RESULTS AND DISCUSSION

From the analytical study, the largest inelastic activity in the structure was due to the Miyagi earthquake. This is because the natural period of the structure was 1.0041, which was located near predominant period of Miyagi earthquake of approximately one (see Figure 3). All the BRB elements experienced the plasticity and the plastic hinges occurred at the end of the ductile segments in the first to third stories, as shown in Figure 2(b). The inelastic response, in the form of



comparison ratio between the story drift due to the Miyagi earthquake and the roof drift due to other earthquake, as shown in Figure 6. In terms of the drift ratio, the BRBTMF could reach up to 67% smaller than that in the X-diagonal-type STMF. It can be seen in general the drift ratio of the proposed frame was smaller than those in the X-diagonal type frame system, Vierendeel, solid frame, and the conventional truss system. In terms of roof drift, the maximum value in the BRBTMF was 275 mm, less 21.6% from the X-diagonal-type STMF (see also Goel and Itani, 1994b). The roof drift history in the BRBTMF was also stable due to the all considered earthquakes with various frequencies.

1

2

3

4

0 1 2 3 4 5 6 7

STOREY

DRIFT RATIO (%)

BRBTMF STMF X-diagonal SOLID FRAMES

CONVENTIONAL VIERENDEEL

(a)drif ratio (b)roof displacement

Figure 6 Inelastic response of BRBTMF.

From the experimental study, the relationship between the load and the displacement in the BRB and BRBTMF was plotted in Figure 7. The magnitude of the cumulative ductility factor, η, of the BRB and BRBTMF specimens can be computed from the comparison between the total energy to the elastic energy and the result are listed in Table 3. It can be seen that the cumulative ductility factor of the BRBTMF satisfied the recommendation for hysteretic structural system, where the practical value η was taken to be greater than 20 (Akiyama, 1985). For BRB, if the cumulative dissipating energy was computed until the failure, all BRBs have the η value greater than 100. This value is sufficient for the BRB elements as elasto-plastic structural components (Shimokawa and Kamura, 1999).

Table 3 Cumulative ductility factor (η) of BRB and BRBTMF.

BRB

Hysteretic energy, (ΣWi) (106 N-mm)

First yield load,Py

(103 N) First yield displacement, dy

(mm) η

BRB-1 20,61 89,67 0,61 377

BRB-2 15,58 66,67 1,11 211

BRB-3 22,83 90,90 1,52 166

BRBTMF 89,73 90,94 20,05 48

The ductility of the structural system can be calculated using the envelope curve obtained from the experiment. From Figure 7(d), by taking the peak points in each cycle and by mean of first yielding point position defined from the energy equilibrium in the strain hardening region, it was obtained the ductility, µ, of 5.98 (see Sugihardjo, et al., 2006). This value is 32.8% greater than that assumed earlier in the preliminary design of STMF X-diagonal type having the ductility of 4.5 when calculated based on 3Rw/8 (Uang, 1991).



(a)BRB-1-50X8 (b) BRB-2-40X8

(c)BRB-3-50X8 (d)BRBTMF

Figure 7 Hysteretic loops of BRB and BRBTMF.

5. CONCLUSIONS

1. From the nonlinear time history analysis, the BRBTMF has the story-drift ratio up to 67% and the roof drift up to 21.6% smaller than that in STMF X-diagonal type due to the Miyagi earthquake. The result satisfied the foregoing studies, that is, the use of BRB will reduce the roof drift and the inter-story drift ratio.

2. From the experimental study, it was proven that the BRBTMF has better ductility. Hence, the reduction factor of the first yielding load, R, could reach up to 11.38 (or Rw =15.94), which is 32.8% greater than the STMF X-diagonal type. The hypothesis that the use of BRB elements will increase the structural ductility is proven. This result also supports the NEHRP (2000) recommendation that the value of R for frame with BRB stiffeners can be increased.

3. From the experimental study on the BRB specimens, it is proven that the proposed model still has a stable hysteretic curve at strain of 2% (or 13,5δy) in cyclic loading. This value is sufficient since the resulted cumulative ductility factor, η = (166-377) > 100, has satisfied the requirement as an elasto-plastic structural element.

4. From the experimental study on the full-scale BRBTMF, it is proven that the structural hysteretic still occurs up to the drift ratio of 3% (or 6δy) in cyclic loading, even though there was stiffness degradation. This value is also sufficient because analytically, the BRBTMF had the drift ratio less than 2%.

5. In terms of the cumulative ductility factor of the BRBTMF specimen, which was 48, the proposed BRBTMF satisfies the requirements as a hysteretic structural system which requires a value greater than 20.

6. For the BRB and BRBTMF specimens, in terms of the comparison of the first yielding force and the cumulative dissipating energy on the relatively similar analytical model, it can be concluded that the model developed using DRAIN-2DX software was accurate.



International Conference on Earthquake Engineering and Disaster Mitigation 2008

6. REFERENCES

AISC (1997, 2005). “Seismic Provisions for Structural Steel Building”, American Institute of Steel Construction, Chicago.

Akiyama, H. (1985). “Earthquake-Resistant Limit-State Design for Building”, University of Tokyo Press.

Basha, H.S. and Goel, S.C. (1996). “Seismic-resistant truss-moment frames with Vierendeel segment”, The 11th World Conference on Earthquake Engineering, paper no. 487.

Bruneau, M., Uang, C.M. and Whittaker, A. (1998). “Ductile Design of Steel Structures”, McGraw-Hill, New York, 411-414.

Chen, C.C. and Lu, L.W., (1990). “Development and experimental investigation of a ductile CBF system”, Proceeding of the 4th National Conference on Earthquake Engineering, Palm Springs, Calif., Vol.2, 578-584.

Chopra, A.K. (2001). “Dynamics of Structures: Theory and Applications to Earthquake Engineering, 2nd ed.”, Prentice Hall, Upper Saddle River, NJ, 265-283.

Clark, P.W., Kasai, K., Aiken, I.D. and Kimura, I. (2000). “Evaluation of design methodologies for structures incorporating steel unbonded braces for energy dissipation”, The 12th World Conference on Earthquake Engineering, paper no. 2240.

Goel, S.C. and Itani, A.M. (1994a). “Seismic behavior of open web truss moment frames”, Journal of Structural Engineering, ASCE, 120(6), 1763-1780.

Goel, S.C. and Itani, A.M. (1994b). “Seismic-resistant special truss-moment frames”, Journal of Structural Engineering, ASCE, 120(6), 1781-1797.

ICBO (1988, 1997). “Uniform Building Code”, International Conference of Building Officials, Whtitier, Calif.

Inoue, K. (2004a). “Hysteresis-type vibrations dampers. Design of hysteresis type dampers”, Steel Construction Today and Tomorrow, The Japan Iron and Steel Federation, June, 4-6.

Inoue, K. (2004b). “Low yield-point steel for steel dampers”, Steel Construction Today and Tomorrow, The Japan Iron and Steel Federation, No.7, June, 7-8.

Kamura, H., Katayama, T., Shimokawa, H. and Okamoto, H. (2000). “Mechanical property of low yield strength steel and energy dissipation characteristics of hysteretic dampers with low yield steel”, US-Joint Meeting for Advanced Steel Structures, 1-4.

NEHRP (2000). “Recommended Provisions for Seismic Regulations for New Buildings and Other Structures”, BSSC, Washington, D.C., 43-75.

Prakash, V. and Powell, G.H. (1992). “DRAIN-2DX”, University of California, Berkeley, California.

Shimokawa, H. and Kamura, H. (1999). “Hysteretic behavior of flat-bar brace stiffened by square steel tube”, The 6th International Conference on Steel & Space Structures, Singapore, 1-4.

Sugihardjo, H., Merati, W., Surahman, A. and Moestopo, M. (2004). “Analytical study of behavior of ductile truss-girder frames with low yield X-diagonal-type as hysteretic damper”, Proceeding of Conference on Earthquake Engineering II, Indonesian Earthquake Association (IEEA), ISBN 979-95620-1-5, Yogyakarta, 67-79 (in Indonesia).

Sugihardjo, H. (2006). “Inelastic Behavior of Ductile Buckling-Restrained Braced Truss-Girders Frames as Component of Storey Buildings”, Dissertation, School of Postgraduate, ITB, Bandung (in Indonesia).

Uang, C.M. (1991). “Establishing R (or Rw) and Cd factors for building seismic provisions”, Journal of Structural Engineering, ASCE, 117(1), 19-28.

Watanabe, A., Hitomi, Y., Saeki, E., Wada, A. and Fujimoto, M. (1989). “Properties of brace encased buckling-restraining concrete and steel tube”, Proceeding of 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, Japan, Vol. IV, 719-724.


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INELASTIC BEHAVIOR OF DUCTILE BUCKLING...

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