Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

ALUMINUM BUCKLING RESTRAINED BRACES FOR SEISMIC RESISTANCE OF

TRUSS MOMENT FRAMES

Vijay Pal Singh1 and Durgesh C. Rai2

ABSTRACT An innovative and unique design of buckling restrained brace (BRB) was developed which gives better energy dissipation potential with delayed buckling to a much larger axial strain than conventional BRBs. The core, which is the yielding element of the BRB, was fabricated using annealed and soft alloys of aluminum for its high ductility, low yield strength and high over-strength. Series of slow cyclic tests were conducted on the Aluminum-core BRBs (Al-BRBs) to study its restraining mechanism, end connection capability and to verify the ability of the Al-BRB to sustain expected cyclic axial forces and deformations. Experimental investigations resulted in an optimum and effective design of Al-BRB with excellent hysteretic behavior and large axial deformation capability. Applicability of the Al-BRB was verified by analytical and experimental studies on truss moment frames (TMFs) with buckling restrained knee brace (BRKB-TMF), designed for large span industrial buildings. The BRKB-TMF was designed using Performance-Based Plastic Design (PBPD) method with a pre-selected target drift and yield mechanism as key performance limit states. Pseudo dynamic tests were performed on a 1:6 reduced scale model of the BRKB-TMF and a total of 21 scaled ground motions with PGA ranging from 0.05g to 3.0g were applied to the model successively. The Al-BRBs showed very satisfactory performance in preventing the damage in truss members and columns by restricting the inelastic activities to itself without causing any significant decrease in the stiffness of the frame. Further, analytical results closely matched with the experimental observed values for various response quantities.

1Frmr. Grad. Student, Dept. of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, India. Currently, Graduate Structural Engineer, W.S. Atkins, Bangalore 560 052, India. 2Professor, Dept. of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, India Singh VP, Rai DC. Aluminum Buckling Restrained Braces for Seismic Resistance of truss moment frames. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

Aluminum Buckling Restrained Braces for Seismic Resistance of Truss

Moment Frames

Vijay Pal Singh1 and Durgesh C. Rai2

ABSTRACT An innovative and unique design of buckling restrained brace (BRB) was developed which gives

better energy dissipation potential with delayed buckling to a much larger axial strain than conventional BRBs. The core, which is the yielding element of the BRB, was fabricated using annealed and soft alloys of aluminum for its high ductility, low yield strength and high over-strength. Series of slow cyclic tests were conducted on the Aluminum-core BRBs (Al-BRBs) to study its restraining mechanism, end connection capability and to verify the ability of the Al-BRB to sustain expected cyclic axial forces and deformations. Experimental investigations resulted in an optimum and effective design of Al-BRB with excellent hysteretic behavior and large axial deformation capability. Applicability of the Al-BRB was verified by analytical and experimental studies on truss moment frames (TMFs) with buckling restrained knee brace (BRKB-TMF), designed for large span industrial buildings. The BRKB-TMF was designed using Performance-Based Plastic Design (PBPD) method with a pre-selected target drift and yield mechanism as key performance limit states. Pseudo dynamic tests were performed on a 1:6 reduced scale model of the BRKB-TMF and a total of 21 scaled ground motions with PGA ranging from 0.05g to 3.0g were applied to the model successively. The Al-BRBs showed very satisfactory performance in preventing the damage in truss members and columns by restricting the inelastic activities to itself without causing any significant decrease in the stiffness of the frame. Further, analytical results closely matched with the experimental observed values for various response quantities.

Introduction

Lateral forces on structures due to earthquake or wind have been of great concern for engineers for a long time. In order to minimize the effect of these lateral forces, braces have been used in the structures, which absorb energy by undergoing inelastic deformations in tension and compression. However, buckling of a brace in compression leads to a sudden loss of stiffness and progressive material degradation which limits the amount of energy dissipated [1]. Buckling Restrained Braces (BRBs) have emerged as a superior alternative to conventional braces because of their unique feature that they don’t buckle when loaded in compression. Hence, they can use the material yielding capacity both in tension and compression. Since BRBs are able to achieve ductile yielding in both directions of loading, they can dissipate much larger amount of energy than conventional braces.

1Frmr. Grad. Student, Dept. of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, India. Currently, Graduate Structural Engineer, W.S. Atkins, Bangalore 560 052, India. 2Professor, Dept. of Civil Engineering, Indian Institute of Technology Kanpur, India Singh VP, Rai DC. Aluminum Buckling Restrained Braces for Seismic Resistance of truss moment frames. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

A typical BRB consists of two main components as shown in Fig. 1(a); (i) the core and (ii) the casing. In the conventional BRB configuration, the core is made from a rectangular plate and the casing typically consists of a mortar filled steel tube. The steel core is coated with a special “debonding material” that prevents the load transfer between the core and the casing. Therefore, the applied axial load is essentially carried by the steel core while the casing prevents the core from buckling. The BRBs have been shown to improve the seismic performance of moment frames [2] and also of truss moment frames when used as a diagonal brace in the special segment of the truss moment frames [3]. The present study concerns with the development of a simple, economical and efficient BRB with soft alloys of Aluminum for the core, which can be used to enhance the seismic performance of truss moment frame when used as a knee brace, referred as buckling restrained knee brace (BRKB-TMF) as shown in Fig. 1(b). Details of the innovative design of Aluminum-core BRB (Al-BRB) suitable for the intended application are shown in Fig. 2. The core section designed to yield in tension and compression is made from rectangular aluminum flat. Aluminum was preferred over steel for fabrication of the core due to its high ductility, low yield strength and high over-strength. The core is sandwiched between two steel flats that are stitched together to form the casing. The core projects outside the casing with eye-bar plates at the ends to facilitate its connection in the structure.

(a) (b)

Figure 1. (a) Different parts of a BRB and its hysteretic behavior comparison with conventional brace (b) BRKB-TMF, proposed structural system

5 5 5

Aluminium core

50 27

15

Casings Stitch plate Stopper

M6 (all dimensions

are in mm)

Eyebar plate

Figure 2. Details of Aluminum-core Buckling Restrained Brace (Al-BRB)

Prototype Building and Design Methodology Prototype building is a single story large span industrial building, located in the seismic zone V (very severe) on stiff soils (type II) as per IS 1893:2002 (Part 1) with 5% damping [4]. The plan view of the building and its elevation along N-S direction are shown in Fig. 3. The building is 90 m long (9 bays @10 m) in the E-W direction and 27 m long (3 bays @ 9 m) in the N-S direction with accessible roof at a height of 9.5 m. The building has eight lateral load resisting truss moment frames with buckling restrained knee braces (BRKB-TMF) in the N-S direction, which is relatively weaker direction. Other frames are gravity frames, which were assumed to resist only gravity load without any contribution in resisting lateral loads.

1

2

3

4

A

A

A

B C D E F G H I J

90 m (9@10 m)

27 m

(3@

9 m

)

N

1.5 m

27 m (3@9 m)

9.5

m

BRB

Section A-A

(a) (b)

Figure 3. (a) Plan view of the study industrial building (b) Elevation view, section A-A Performance based plastic design of BRKB-TMF BRKB-TMF was designed using performance based plastic design method (PBPD), a design approach proposed by Leelataviwat [5] and modified by Lee and Goel [6]. A target drift and yield mechanism is selected prior to the design process and then energy balance equation is used to calculate the base shear generated by the structure after attaining the preselected target drift and yield mechanism. Table 1 summarizes calculations for the base shear using this approach.

Table 1. Design base shear calculations of BRKB-TMF

Yield drift, θy = 0.5%

Target roof drift, θmax = 1.2% Plastic drift, θp= θmax- θy = 0.7% Height of the roof, h = 9.5m Fundamental period, T= 0.085h0.75 = 0.46s Zone factor, Z = 0.4 Assumed Damping, ξ = 5% Spectral acceleraton coefficient, Sa/g = 2.5 Normalised Pseudo Acceleration (g),

.

2a

eZ S

Cg

= =0.5

Structural ductility factor maxs yμ θ θ= = 2.4

Ductility reduction factor, 2 1Rμ μ= − =1.95

Modification factor, 2

2 1s

Rμ

μγ

−= =1

Seismic weight on the roof, W = 3415 kN

Dimensionless parameter, 2

2

8.

ph

T g

θ πα =

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

= 2.53

Base shear per unit weight on the roof, 2 24

2

eCV

W

α α γ− + += = 0.095

Base shear for the whole building, V = 325 kN Partial safety factor, Pf = 1.2 Design base shear per frame, PfV/8 = 48.8 kN

Analysis of the BRKB-TMF The frame was designed based on the principle of virtual work. The BRB was designed to yield at design base shear while other members of the frame were designed for an amplified base shear, i.e., the base shear at which the BRB attains its ultimate strength. This is to ensure that no damage occurs in the frame members, such as chords, diagonal, columns etc. before the failure of BRB occurs. Vertical members of the truss largely carry gravity loads and are unaffected by lateral loads. However, as the truss is connected to columns through gusset plates, the plastic moments are generated at the ends of the top chord due to fixity of the connection, which causes additional forces in the vertical members of the truss.

Reduced Scale Model

Length scale ratio of 1:6 was chosen for the small scale model due to practical limitations. The acceleration was scaled up by 3 to reduce the imposed mass on the model in such a way that the gravity load on the model is similar to that on the prototype. Similarly, various other scale ratios were calculated based on the similitude laws as shown in Table 2. Various member sections used in fabricating the BRKB-TMF are presented in Fig. 4.

Table 2. Modeling scaling requirements

Parameter Factors Dimension Scales Length, L Sl L 1/6 Area, A Sl

2 L2 1/36 Mass, M SeSl

2 M 1/108 Force, F SeSl

2 MLT-2 1/36 Acceleration, a Sa LT-2 3 Frequency, ω Sl

-1/2 T-1 √18 Time, t Sl

1/2 T 1/√18 The 1:6 reduced scale BRBs as shown in Fig. 5(a) were fabricated in the laboratory. Aluminum alloy 6063-T5 with alloying elements of magnesium and silicon was used to manufacture the core of the BRB because of its high ductility, low yield strength and high over-strength etc. After machining, the aluminum core was annealed to reduce its yield strength, as low yield strength allows the use of thicker core which in turn reduces the possibility of local buckling or end connection failure of the BRB. Fig. 5(b) shows the comparison between annealed and un-annealed aluminum tensile coupon test results. The casings of Al-BRB when properly designed and fabricated are not supposed to carry any axial force and they are meant to prevent the buckling of the core of BRB. The ratio of the buckling load of casings to the yield load of the core is used as a criterion to verify the flexural stiffness adequacy of casings. Watanabe et al. suggested that this ratio should be over 1.5 [7]. In the present study, the casing used in the BRB is 5 mm thick steel flat. The core was manufactured by machining aluminum flat of 5 mm thickness and connected to eye-bar plates using M6 bolts. Stoppers were welded to the casing for preventing the relative movement between core and casings in the longitudinal and the transverse directions. Both casings were then joined together by welding stitch plates of 4 mm thickness, which ensures that the core can

freely move inside the casings. Moreover, grease was used as de-bonding material to reduce the friction between core and casings. The BRB was pin connected at both ends with T-sections welded to the column flange and bottom chord of the frame truss as shown in Fig. 4.

1500 mm

250 mm

250 mm

Vertical member (SHS 15x15x1.17 mm)

Diagonal member (Angle 18x18x1.6 mm)

187.5 mm

Bottom & top chord (2 Angles 25x25x1.5 mm)

BRB

Column ISLB 75 @6.1 kg/m

Stiffener

Figure 4. Schematic diagram of the designed model specimen

Core

Casing

M6 bolts

Strain gauge Eye-bar plate

Stopper

0

30

60

90

120

150

180

0 5 10 15 20 25

Str

ess

(MP

a)

Strain (%)

Pin connection

T-section Stitch plate

(a) (b)

Figure 5. (a) Fabrication of Al-BRB (b) Annealed & un-annealed aluminum coupon test results

Cyclic tests of the Al-BRBs Deformation controlled slow cyclic tests were carried out on Al-BRB specimens to assess the effectiveness of the restraining mechanism of casings and also to assess their ability to sustain the expected cyclic loads and deformations. Two Al-BRB specimens were tested under cyclic loading protocols of FEMA 461 [8], and AISC 341 [9] and their performance was quite similar in both the tests. The core buckled about the major axis but the casings adequately restrained the minor axis bucking as shown in Fig. 6(a), (b). Comparison of hysteresis plot of the BRBs using actuator load and stroke data is presented in Fig. 6(c). Maximum strain attained is approximately 6% and peak stresses experienced by the BRB are approximately 80 MPa and 108 MPa in tension and compression, respectively. The BRB showed slightly higher overstrength in compression probably due to striking of the core with stoppers after excessive buckling about the

Un-annealed coupon

Annealed coupon

weak axis as shown in Fig. 6(a) and (b). This issue can be resolved to some extent by providing larger spacing between the core and stoppers. However, it is extremely difficult to completely avoid the coupling of casing and core in compression, especially at large strains. As a result, BRBs typically show higher strength in compression as compared to strength in tension.

-120

-80

-40

0

40

80

120

-8 -6 -4 -2 0 2 4 6 8

FEMA 461AISC 341

Str

ess

(MP

a)

Strain (%)

(a) FEMA 461

(b) AISC 341 (c)

Figure 6. (a),(b) BRBs after the cyclic tests (c) Comparison of the hysteresis curve of the BRBs obtained from the cyclic tests as per FEMA 461 and AISC 341 loading protocols.

Pseudo Dynamic Testing of BRKB-TMF

Pseudo dynamic tests (PsD) were performed on the BRKB-TMF model specimen to assess its capacity and behavior under earthquake type loads. Two frames were fabricated and then connected side by side through X-bracings as shown in Fig. 7. The TaftN21E ground motion of the 1952 Kern County earthquake with a PGA of 0.156g was used for the loading. The response spectrum of this ground motion when scaled to PGA of 0.20g compares well with the response spectrum corresponding to Design Basis Earthquake (DBE) in zone V (PGA 0.18g) of IS 1893, as shown in Figure 8(a). The original duration of the Taft ground motion of 56.16 s was compressed by a factor of 18 to satisfy the similitude requirements as shown in Fig. 8(b).

Actuator

Concrete Slabs

T-section

Stiffener

(a) (b)

Figure 7. (a) PsD test setup for BRKB-TMF (b) BRB mounted on the frame

00.10.20.30.4

0.50.60.70.8

0 0.5 1 1.5 2 2.5 3 3.5 4

Taft 0.20gDBE

Spe

ctra

l Acc

eler

atio

n (g

)

Period (s)

-0.2-0.1

00.10.2

-0.2-0.1

00.10.2

0 10 20 30 40 50 60Time (s)

(a) (b)

Figure 8. (a) Comparison of DBE (PGA 0.20g) for zone V with Taft (PGA 0.20g) (b) Original and compressed (for model) Taft N21E Ground Motion

Overall behavior of BRKB-TMF A total of 21 Taft ground motions of increasing PGA levels from 0.05g (8.3% DBE) to 3.0g (500% DBE) were applied on the BRKB-TMF using the PsD test method. The initial properties of the frame such as mass (665 kg), damping (0.00148) and stiffness (0.545 kN/mm) were provided to the PsD software at the start of the test. Since aluminum core is not very sensitive to the strain rate, therefore, slow speed of the PsD test acted as an advantage in observing closely the behavior of the frame and BRBs during the test runs. Webcams were installed in front of each BRB to continuously monitor their behavior. All the BRBs started yielding at PGA 0.60g (100% DBE) as observed from the hysteretic response described later. The frame specimen experienced more deformation on one side (towards the actuator) as the permanent deformation kept on accumulating during application of the series of ground motions. Consequently, the BRBs close to the actuator experienced mostly compressive stress while the BRBs away from the actuator predominantly underwent tensile deformations. Fig. 9 shows the visual inspection of the BRBs at the conclusion of tests. In-plane buckling was observed in two BRBs which were under compression (1-LF and 1-RF). Casings performed satisfactorily in restraining the out of plane buckling of the core as seen in Fig. 9(b).

BRB 1-LF

BRB 2-LF

BRB 1-RF

BRB 2-RF

(a) Without one of the casings (b) thickness view – no out of plane buckling

Figure 9. Visual inspection of all four Al-BRBs after completion of the tests (LF = Left frame and RF=Right frame)

Acc

eler

atio

n (g

)

Analytical Study Non-linear time history analysis of BRKB-TMF was performed by modeling the frame in SAP2000 [10] as shown in Fig. 10(a). The BRB was modeled as an axial element with a general aluminum section and the cross sectional area same as that provided in the experiment for its core. The total length of the brace is 313 mm, of which the yielding portion of the aluminum core is only 130 mm. Therefore, the remaining part of the brace was made rigid. To provide the non-linear properties of the BRB, a deformation controlled axial plastic hinge was defined at the center of the BRB. A stress-strain backbone curve of four linear segments for the BRB was constructed from the results of the cyclic tests as shown in Fig. 10(b). Ultimate strength of the BRB in compression is approximately 1.25 times of its tensile capacity due to the restraining mechanism of the BRB as observed from the cyclic test results. Plastic hinges were also assigned to other frame members to account for their non-linear behavior.

-150

-100

-50

0

50

100

150

-20 -15 -10 -5 0 5 10 15 20

Cyclic Test

Backbone Curve

Str

ess

(kN

)

Strain (%)

(a) (b)

Figure 10. (a) BRKB-TMF model in SAP2000 for analytical study (b) Backbone curve of BRB obtained from cyclic test results

Base shear response Base shear at various PGA levels of the ground motions obtained from experimental and analytical studies is shown in Fig.11(a) The change in the slope of the experimental curve at PGA 0.60g (100% DBE) indicates the initiation of yielding in the BRBs. The frame attracted base shear at much decreased rate after yielding of the core of BRBs. No major damage was observed in the frame members till Taft 2.70g as the yielding was restricted to the BRBs only. Some minor damages such as local buckling of the end diagonal, top chord and column joint cracks were observed for the Taft 3.0g (500% DBE) ground motion due to closing of the gap between restraining member and eye-bar plate of the BRB as shown in Fig. 11(b). This interlocking eventually led to transfer of some axial load to steel casings, which also resulted in sudden increase in the overall frame stiffness after Taft 2.7g ground motion.

1.5 m

Rigid

Seismic Weight

BRB core (130 mm) Moment

released

Pin connection

1.58

m

00.5

11.5

22.5

33.5

44.5

5

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.3

0 50 100 150 200 250 300 350 400 450 500 550

ExperimentalAnalytical

Bas

e S

hear

(kN

)

PGA (g)

DBE (%)

Eye-bar plate

Casing

(a) (b)

Figure 11. (a) Peak base shear at various PGA levels (b) Closing of the gap between casing and eye-bar plate at PGA 3.0g ground motion

Displacement Response Fig. 12(a) shows the comparison of the peak roof drift (%) obtained from analytical and experimental study for different intensities of the Taft ground motion. Permanent drift kept on accumulating as ground motions were applied successively one after another in the PsD test which led to tilting of the frame towards one side, i.e., towards actuator in this case. The total cumulative permanent drift of the frame after completion of the testing program was recorded as 68 mm. Fig. 12(b) shows the plot of peak base shear and peak roof drift recorded at different PGA levels of ground motions. The ratio of the first stiffness (0.26 kN/mm) and the second stiffness (0.056 kN/mm) of the frame is 4.68, which indicates that frame stiffness did not reduce significantly after yielding of BRBs.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.3

0 50 100 150 200 250 300 350 400 450 500 550

ExperimentalAnalytical

Roo

f Drif

t (%

)

PGA (g)

DBE (%)

00.5

11.5

22.5

33.5

44.5

5

0 5 10 15 20 25 30 35 40 45 50

0 0.5 1 1.5 2 2.5 3

Experimental

Analytical

Pea

k B

ase

She

ar (

kN)

Peak Roof Drift (mm)

Roof Drift (%)

Initial Stiffness (K

1)

Second Stiffness(K

2)

(a) (b)

Figure 12. Comparison of experimental and analytical results (a) Peak roof drift v/s PGA (b) Peak base shear v/s peak roof drift

Energy dissipation Figure 13 shows the hysteresis plots of BRKB-TMF at various intensities of the ground motion. Yielding of the Al-core of the BRB started at TAFT 0.6g ground motion. The demands imposed on the frame members were limited after the yielding of BRBs which continued to dissipate a major portion of energy by yielding in tension and compression. Thus, BRBs restricted the inelastic activities to themselves and were successful in preventing any kind of damage to the

frame members. Fig. 14 shows quadratic trend in the total energy dissipated by the BRKB-TMF with increasing PGA levels of the ground motion.

-4

-2

0

2

4

-4 -3 -2 -1 0 1 2 3 4

-60 -40 -20 0 20 40 60

PGA 0.6g (100% DBE)

Bas

e S

hear

(kN

)

Roof Drift (%)

Roof Drift (mm)

-4

-2

0

2

4

-4 -3 -2 -1 0 1 2 3 4

-60 -40 -20 0 20 40 60

PGA 1.8g (300% DBE)

Bas

e S

hear

(kN

)Roof Drift (%)

Roof Drift (mm)

-4

-2

0

2

4

-4 -3 -2 -1 0 1 2 3 4

-60 -40 -20 0 20 40 60

PGA 3.0g (500% DBE)

Bas

e S

hear

(kN

)

Roof Drift (%)

Roof Drift (mm)

Figure 13. Hysteresis of one of the BRKB-TMF for various intensities of Taft ground motions

0

100

200

300

400

500

600

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.3

0 50 100 150 200 250 300 350 400 450 500 550

Ene

rgy

Dis

sipa

ted

(Nm

)

PGA (g)

DBE (%)

Quadratic fit

R2=0.997

Figure 14. Energy dissipated per frame for the BRKB-TMF with quadratic best fit

Conclusion A novel design of Buckling Restrained Brace (BRB) is proposed which uses annealed and soft alloys of Aluminum in its core for its high ductility, low yield strength and high over-strength. The Aluminum-core BRB (Al-BRB) performed satisfactorily under cyclic loads as per FEMA 461 and AISC 341 loading protocols. The proposed restraining mechanism of the Al-BRB in the form of simple steel plates for the casing was able to prevent the premature buckling of the core and ensured similar behavior in both tension and compression which led to the full and stable hysteretic loops. Moreover, Al-BRB was able to achieve deformation capability in excess of 6%, which is not common with other designs of BRBs. Performance of Al-BRBs in the BRKB-TMF was very satisfactory in terms of preventing the damage in the frame members by restricting the inelastic activities to itself without causing any significant decrease in the stiffness of the frame. The application of Al-BRB increased the energy dissipating capacity of the frame which attracted base shear at a decreased rate after yielding of the aluminum core of the BRB, and eventually reduced the seismic demand on other frame members.

References

1. Xie Q. (2004). State of the art of buckling-restrained braces in Asia. Journal of Constructional Steel Research, 61, 727-748.

2. Mayes RL, Goings C, Naguib W, Harris S, Lovejoy J, Fanucci JP, Bystricky P, Hayes JR. Comparative Performance of Buckling Restrained Braces and Moment Frames. In Proc. 13th World Conference on Earthquake Engineering, 2004, Vancouver, B.C., Canada. Paper No. 2887.

3. Pekcan G, Linke C, Itani AM. Damage Avoidance Design of Special Truss Moment Frames with Energy Dissipating Devices. Journal of Constructional Steel Research, Elsevier, 2009, 65(6), 1374-1384.

4. BIS. IS:1893: Indian Standard Criteria for Earthquake Resistant Design of Structures, Part 1: General provisions and buildings. Bureau of Indian Standards 2002, New Delhi.

5. Leelataviwat S, Goel SC, Stojadinovic B. Toward Performance-Based Seismic Design of Structures. Earthquake Spectra 1999, 15(3), 435-461.

6. Lee, S and Goel, SC. A New Lateral Force Distribution for Seismic Design of Steel Structures. In Proc. U.S.-Japan Workshop on Seismic fracture issue in Steel Structures 2000, San Francisco, CA.

7. Watanabe A, Hitomi Y, Saeki E, Wada A, Fujimoto M. Properties of brace encased in buckling restrained concrete and steel tube. In Proc. 9th World Conference on Earthquake Engineering 1988, Tokyo-Kyoto, Japan, Paper 6-7-4.

8. AISC. Seismic Provisions for Structural Steel Buildings. ANSI/AISC 341-05, American Institute of Steel Construction 2005, , Chicago, IL, USA.

9. FEMA. Interim Testing Protocols for Determining the Seismic Performance Characteristics of Structural and Non-Structural Components. FEMA 461, Federal Emergency Management Agency 2007, Washington, D.C.

10. CSI. “SAP2000 Analysis Reference Manual,” Version 14, Computers and Structures Inc. 2009, Berkeley, California, USA.