Buckling-Restrained-Lug Connection for Energy Dissipation

1. INTRODUCTIONUnder extreme loading conditions such as anearthquake event considerable amount of energy isimparted to a structure. Rather than designing thestructure to remain elastic under such extremeconditions, dissipation of the input energy is anattractive option for mitigating the associated risk(Soong et al. 2002; Symans et al. 2008). In thistechnique a considerable amount of input energy isdiverted to designated energy dissipating devices,leaving the parent structure, especially the gravity-load-carrying-systems, relatively intact. Under moderateloading events the structure can easily be repaired whileunderstrong loading events, life-safety could beenhanced. Various strategies and designs of energydissipating devices have been proposed, tested andimplemented particularly in earthquake-prone regionssuch as Japan, US, New Zealand and Taiwan.

Advances in Structural Engineering Vol. 16 No. 1 2013 11

Buckling-Restrained-Lug Connection for Energy

Dissipation

Ricky W.K. Chan1,* and Faris Albermani2

1School of Civil, Environmental and Chemical Engineering, RMIT University, Melbourne, Australia2School of Civil Engineering, University of Queensland, Australia

Abstract: Under extreme loading conditions such as an earthquake event considerableamount of energy is imparted to a structure. To protect the structure and to minimizedamages, a method is to divert a portion of the input energy into designated energydissipating devices. A new energy dissipation device is presented in this paper. Thedevice is referred to as Buckling-Restrained-Lug (BRL) which can be incorporated instructural joints. The device is composed of a short segment of a steel strut embeddedinside a mortar filled jacket which makes the BRL’s capacity governed by the squashload under axial tension or compression. The BRL dissipates energy through axialyielding of the steel strut. Analytical, finite element modeling and experimental resultsof the proposed BRL are presented and compared. Implementation of the BRL in abeam-to-column connection that results in a dissipative partial-moment-resisting jointis proposed. Based on the obtained results, the paper advocates the consideration of theBRL as a viable, compact and low-cost passive energy dissipation device.

Key words: earthquake engineering, energy dissipation, buckling restrained lug.

A number of different energy dissipatingmechanisms have been proposed; which includeyielding and phase-transformation of metals, sloshingof fluid and friction. Among the many devicesproposed, passive devices which do not rely onexternal power source remain the most widely used.Devices which utilize flexural deformation of metalsinclude ADAS (Bergman et al. 1987), TADAS (Tsai etal. 1993) and SSD (Chan et al. 2008; Ghabraie et al.2010). Shear deformation of metal plates has been usedto develop Yielding Shear Panel Device (YSPD)(Chan et al. 2009). On the other hand, BucklingRestrained Brace (BRB), or Unbonded Brace, makesuse of plastic axial deformation of metal componentsto dissipate energy. The BRB was first proposed inJapan (Watanabe et al. 1988), and since it wasintroduced to the US in 1999 it has attractedconsiderable research interest (Clark et al. 1999).

*Corresponding author. Email address: [email protected]; Fax: +613-9639-0138; Tel: +613-9925-9975.

Black et al. (2004) carried out component testing ofBRB specimens and reported excellent stability andgood energy dissipation characteristics. Sabelli et al.(2003) reported on seismic demands of framebuildings with BRBs. Fahnestock et al. (2007) andTsai et al. (2008) carried out full-scale BRB frametests. More recently, Takeuchi et al. (2010)investigated effect of various buckling restraintconditions on strength and ductility and Chou et al.(2010) investigated a sandwiched restraining memberarrangement. Takeuchi et al. (2010) reported that theBRB has been implemented in more than two hundredbuildings. BRB may be regarded as a superior braceelement which possesses the structural efficiency ofconcentric-braced frames (CBF) while at the sametime remedy the buckling vulnerability and low energydissipating capability of conventional CBFs. BRBdevices are typically installed as brace members withinrectangular steel frames, hence a typical BRB withconcrete-filled jacket weighs hundreds of kilograms.Installation will require lifting machinery whichcomplicates replacement of damaged units followingan extreme event. Due to their very high strengths(typically in excess of 1000 kN), structural elementssupporting these devices will require strengthening(Tsai et al. 2008).

On the other hand, moment-resisting frames (MRF)have always been a popular structural scheme for theirarchitectural flexibility. However, the 1994Northridge and the 1995 Kobe earthquakes revealedmany cases of premature brittle failures in MRFwelded moment connections (Mazzolani et al. 1996).In the US, a large scale research program was initiatedto study these pre-Northridge connections (SAC 1996;Uang et al. 2000). Improvements such as reinforcedconnections using haunches and reduced beamsections have been suggested and tested. Connectiondesign continued to attract much research attentionsince good energy dissipation can be achieved withproper detailing of structural connections. RecentlyAbolmaali et al. (2009) investigated the energydissipation characteristics of 48 full-scale connectionspecimens. They concluded that at large rotations,significant damage to beams and/or columns isinevitable.

The investigation presented in this paper aimed todevelop a novel energy dissipating device namedBuckling Restrained Lug (BRL) which is smaller,lighter, lower in strength and easier to replace thanBRB. The BRL device is envisaged to be incorporatedin beam-to-column or column-to-base connections asshown in Figure 1(a). The relatively smaller size andweight of the proposed BRL device facilitates its

replacement following extreme loading events. TheBRL device is configured such that it does not interruptgravity-load path, hence the structure may remain fullyfunctional during the replacement of damaged BRLunits. This paper first presents the device design,followed by a finite element investigation, experimentalresults and a proposal for implementing BRL in beam-to-column connections.

2. DESIGN OF THE BRL DEVICEFigure 2 illustrates the basic design of the BRL. Theyielding steel core strut consists of a short segment of astandard reinforcement bar (rebar) threaded at bothends. This core strut is snug tight to proprietarymechanical couplers at both ends. The couplers arewelded to a mild steel connection lugs. A single bolthole on the connection lug allows a pin-to-pinconnection of the device, eliminating any possiblerotational demand on the strut. In order to restrain globalbuckling of the rebar strut, it is embedded in a squarealuminum tube (jacket) in-filled with cement mortar.The rebar strut is unbonded from the surrounding mortarby a thin polyethylene sheath wrapped around the rebar.In addition, a longitudinal clearance between theconnecting lugs and the jacket and between the innerend of each coupler and the mortar filling is provided toallow for axial deformation of the rebar strut. Theconnecting lugs are designed with sufficient strength topreclude local yielding. The length and diameter of therebar strut can be selected according to strength demandand geometric requirements of the application at hand.

12 Advances in Structural Engineering Vol. 16 No. 1 2013

Buckling-Restrained-Lug Connection for Energy Dissipation

l2

l1

1

2 C

BA

Od

φ

ColumnBRL

Beam

BRL

(a)

(b)

θ

θ

Figure 1. (a) Proposed BRL application and (b) geometry of

deformed shape

2.1. Preliminary Design of BRLAssuming a frictionless interface between the rebar strutand restraining mortar jacket, the yield strength andelastic stiffness of the BRL can be obtained from,

(1)

(2)

where Fy and kd are the device’s yield strength andelastic stiffness respectively, Ai, Ei, fy and Li are the corestrut cross-sectional area, elasticity modulus, yieldstress and unthreaded length respectively.

To obtain a stable axial force-displacement hysteresisresponse under tension and compression, the bucklingcapacity of the device has to be higher than the yieldstrength of the core strut. For the BRL device, twogoverning fundamental buckling modes can beidentified; namely (1) global flexural buckling of theentire device and (2) snaking buckling of the rebar strut.

For the global flexural buckling mode, a lower-boundbuckling load is the Euler buckling load of the jackettube (neglecting any contribution from the infill mortarand core strut).

(3)

where Eo, Io, Lo and ro are the Young’s modulus, secondmoment of area, length and radius of gyration of theouter jacket respectively.

PE I

L

E A

L

r

cro o

o1

2

2

20 0

0

0

2= =

π π

kE A

Ldi i

i=

F f Ay y i=

In the snaking buckling mode, the core strut behavesas a compressive strut embedded in an elastic medium.The restraint stiffness of the elastic medium, β can beapproximated by the elastic flexural stiffness of theflange of the jacket (assuming fixed edges along theflange) and neglecting the contribution from the mortar,

(4)

where If is the second moment of area of the flangeplate of outer jacket per unit length (t3/12), b and t arethe breadth and wall thickness of flange plate of thejacket tube.

Accordingly, the critical snaking buckling load canbe obtained using energy method and is independent ofthe end conditions of the device (Black et al. 2004).

(5)

where Ii is second moment of area of the core strut.To illustrate the influence of geometric and material

parameters on the above two types of buckling, a non-dimensional parameter J is defined as the ratio of axialstiffness of core strut to jacket,

(6)

where Ao is cross-sectional area of jacket.If Pcr1 is normalized with respect to yield strength of

BRL, it could be shown that,

(7)

P

F

E

JfL

r

cr

y

i

yo

o

12

2=

π

J E A E Ai i o o= /

P E Icr i i2 2= β

β =192

3

E I

bo f


Ricky W.K. Chan and Faris Albermani

Connecting lug

Coupler Core steel

Aluminium tube

Mortar filling

Fillet weld

Aluminum tubeMortar

Core steel

Figure 2. BRL device

Similarly, the normalized critical snaking bucklingload Pcr 2 can be expressed in terms of J.

(8)

In Figure 3, Eqns 7 and 8 are plotted against modified

jacket slenderness for Pcr1 and flange

slenderness for Pcr 2. Geometric and

material parameters in experiments are used whenplotting these curves: fy = 364 MPa, Ei = 200 GPa,Ao = 475 mm2 and Ai = 113 mm2. It can be observed thatwith an increase in slenderness, critical load decreasesrapidly. The parameter J has a significant influence onbuckling strength of BRL. An increase in J tends toreduce buckling load of the BRL device – as the axialstiffness of the inner core strut increases in relation tothat of the outer jacket, strength of BRL is more likelyto be governed by buckling rather then yielding. TheJ value of the BRL sample used in experiment (12 mmsteel core strut and 50 × 50 × 2.5 mm aluminum jacket)is approximately 0.71. If a 20 mm diameter steel corestrut is used instead the J value will increase toapproximately 1.98. From this buckling analysis it isclear that it is beneficial to use a small diameter innercore and a stiff outer jacket. However, it should be notedthat the diameter of inner core dictates the yield strengthand stiffness of device and it is typically governed bystrength and stiffness requirement as per actualapplication.

2.2. Sensitivity AnalysisA static monotonic nonlinear analysis of the BRL wasconducted prior to the conduct of physical testing toascertain the sensitivity of the device to various

b t fy/ / 250

L r fo o y/ / 250

P

F

E

f

A

JA

b

tcr

y

i

y

i

o

234

=

−

ππ

geometric and material parameters. A finite elementmodel of the rebar strut, the couplers and the lugs wasgenerated using ABAQUS (Simulia 2009). The rebarcore is modeled as a strut embedded in elastic mediumfoundation. The model is generated using eight nodesreduced integration solid elements (C4D8R) with vonMises isotropic hardening plasticity. The materialproperties were based on tension tests conducted on thesteel rebar element and were; 205 GPa elasticitymodulus, 0.3 Poisson’s ratio, yield and ultimate stressof 364 and 505 MPa respectively (250 MPa yield stressis used for lugs and couplers). The center-to-centerlength of connecting lugs, L, is 420 mm and the lengthLi, and diameter of the unthreaded steel core bar was300 and 12 mm respectively. A simple pin endcondition is assumed at the connection hole of each lugwith the lug being restrained against out-of-planedisplacement. The stiffness of the elastic mediumaround the steel rebar strut is approximated as in Eqn 4using 50 × 50 × 2.5 mm aluminum SHS jacket whichgives βo = 192 MPa. A 50 mm compressivelongitudinal displacement corresponding to 16.7%axial strain was incrementally imposed at one end ofthe model to predict the device’s response. To facilitatenonlinear analysis, geometric imperfection based on thefundamental buckling mode shown in Figure 4 isimposed first. Various imperfection amplitudes (δ )were used in the analysis. Figure 5 illustrates typicaldeformed shapes of the model at various stages ofcompression. Initially plasticity is localized at mid-spanof the rebar strut up to 4% strain. This is followed bythe formation of a second plastic zone between the mid-span and the loaded end while the rest of the modelremains below yield stress.

Various values of initial imperfection amplitudes (δ )and stiffness of the surrounding elastic medium β usedin this study are shown in Table 1. The effect of



Modified slenderness

0 50 100 150 200

Pcr

/ F

y

0

0.2

0.4

0.6

0.8

1

1.2

Pcr1Pcr 2

J = 1.4

J = 2.0

J = 0.8

J = 0.2

J = 0.2

Squash load

Figure 3. Buckling of BRL Figure 4. Fundamental buckling mode

increasing the initial geometric imperfection (for aconstant β ) on the axial load carrying capacity of theBRL is shown in Figure 6(a). The axial load carryingcapacity is normalized by the squash load from Eqn 1.The amplitude of initial imperfection has clear influenceon the buckling capacity and steepness of the post-buckling path, with little effect on pre-buckling stiffnessand post-buckling reserve capacity.

Figure 6(b) shows the effect of the stiffness of thesurrounding elastic medium β (for constantimperfection amplitude) on the axial load carryingcapacity of the BRL. The effect of β is more evident inthe post-buckling reserve capacity with little effect onbuckling load or pre-buckling stiffness. The case forβ/βo = 3 is equivalent to having steel rather than

aluminum SHS jacket, the resulting increase inbuckling load is only 3%.

3. EXPERIMENTAL VERIFICATIONTo verify theoretical and numerical predictions,specimens made from 12 mm and 16 mm diameterrebars were fabricated. Accurate threading of the rebarswas carried out to match the chosen mechanicalcouplers (Lenton Weldable Couplers C12, Lenton2006). The rebars were then snug tight to the couplers atboth ends and the couplers were welded to 20 mm thicklugs. A 300 mm unthreaded rebar length (Li) was usedin the experiment. Different jacket options wereexplored; PVC pipe, steel and aluminum SHS (all filledwith cement mortar). A 50 × 50 × 2.5 mm aluminumSHS (βo = 192 MPa) filled with cement mortar waschosen for its satisfactory performance, relative lightweight and durability.

Standard tensile test of 12 and 16 mm diameter rebarsgave yield stress fy of 364 and 312 MPa respectively.Preparation of specimens is shown in Figure 7. Tominimize friction between the rebar strut and thesurrounding mortar, the rebars were wrapped with thinpolyethylene plastic sheath. Two foam blocks wereplaced on the inner sides of the couplers to create a smallvoid in the mortar filling. The foam blocks allowedcompressive axial displacement of the couplers insidemortar filling. Mortar was then cast around the rebar



+3.640e + 08+3.337e − 08+3.033e − 08+2.730e − 08+2.427e − 08+2.123e − 08+1.820e − 08+1.517e − 08+1.213e − 08+9.100e − 07+6.067e − 07+3.033e − 07+0.000e − 00

(Ave. Crit.: 75%)S, Mises

= 1%

= 2%

= 3%

= 4%

= 5%

= 10%

ε

ε

ε

ε

ε

ε

Figure 5. Typical results of FE modeling (β = β0 and δ = 1 mm)

Table 1. Parameters for FE analyses

Parameter Values

δo 1 mmδo /Li 0.0033βo 192 MPaδ /δo 0.1, 0.5, 1, 5, 10β /βo 0.33, 0.5, 1, 2, 3

0

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

00.10.20.30.40.50.60.70.8

0.02

0.02

0.04

0.04

0.06

0.06

0.08

0.08

0.1 0.12 0.14 0.16

0.1 0.12 0.14 0.16

Strain

Strain

Nor

m. s

tren

gth

(F/F

y)N

orm

. str

engt

h ( F

/Fy)

(a)

(b)

/ 0 = 0.1δ δ/ 0 = 0.5δ δ

/ 0 = 5δ δ/ 0 = 10δ δ

/ 0 = 1δ δ

/ 0 = 3ββ/ 0 = 2ββ/ 0 = 1ββ

/ 0 = 0.5ββ

/ 0 = 0.33ββ

Figure 6. (a) Effect of initial imperfection magnitude (β = β 0); (b)

Effect of restrain stiffness (δ = 1 mm)

core with the rebar maintained at the centre of the SHSjacket by temporary plastic spacers. As a result castingof mortar was carried out at three stages. The specimenwas vibrated on a shake table to eliminate air voids andthen cured for 28 days prior to tests.

Displacement-control cyclic tests were conductedusing MTS testing machine with the test specimensecured in the machine using two M20 bolts as shown inFigure 8. A 100 kN load cell and two LVDTs were usedto monitor the applied load and axial displacement. Aramped reverse-cycle displacement history composed ofa total of 24 cycles with 8 different amplitudes (0.5, 1.0,1.5, 2.5, 5.0, 7.5, 10, 12.5 mm and three repeated cyclesper each amplitude) as shown in Figure 9 was applied ata rate of 0.5 mm/sec (strain rate 0.0016/sec).

3.1. Test ResultsTwo types of specimens were tested; BRL12 using a12 mm diameter rebar and BRL16 using a 16 mmdiameter rebar (both with 50 × 50 × 2.5 mm aluminumSHS jacket). The hysteretic response of these twodevices is shown in Figure 10 where positiveforce/displacement indicating compression. Each teststarts from zero by applying a compressivedisplacement. Also shown in Figure 10 are theanalytical results from Eqns 1 and 2, for comparison.Table 2 summarizes the key experimental results. InTable 2, the experimental yield strength ± Fy is taken at

the deviation from the initial linear response and theexperimental stiffness is obtained from averaging thestiffness of the experimental unloading paths.Cumulative energy dissipation is calculated fromnumerical integration of the experimental force-displacement response shown in Figure 11.

3.1.1. Specimen BRL12Very little force was recorded during the first sixloading cycles (3 cycles at 0.5 mm followed by another3 cycles at 1 mm) indicating slippage at the pinconnection. This is followed by a linear response up tothe yield strength which agrees very well with thesquash load from Eqn 1 (42.2 vs 41.2 kN). A stablehysteretic response is obtained until the 21st loadingcycle (3rd cycle at 10 mm amplitude) where a suddendrop in the capacity is obtained as shown in Figure 10(a).



Vibrationtable

Figure 7. Preparation of core rebar and aluminum tube jacket

Hydraulicactuator

Cleat

Specimen

LVDT2

LVDT1

Figure 8. Test setup

−15

−10

−5

0

5

10

15

Dis

plac

emen

t (m

m)

0 10 20 30 40 50

Figure 9. Displacement history applied to specimens

This was attributed to the onset of snaking buckling ofthe steel strut inside the jacket. Further cycling resultedin steady strength degradation, crushing of thesurrounding mortar, bulging of the aluminum jackettube and eventually full fracture of the rebar strut at theinterface with the mechanical coupler as shown inFigure 12(a). No evidence of slippage at the couplers orfatigue cracks at the welded connections was found.

As seen from Figure 10(a), the squash load (Eqn 1)gives a reasonable estimate of the device capacity bothin compression (positive force) and in tension (negativeforce) as was intended. A clear hardening effect can beseen in the compression capacity and the experimental

tension to compression yield (–Fy / + Fy) ratio is nearly57%. The compression/tension bias can be attributed tothe resulting dislocations in the surrounding mortar thattook place under the first phase of loading from zerowhich was compression.

The average experimental stiffness from theunloading paths is 53–75% of the elastic stiffness fromEqn 2 (using Li = 300 or L = 420 mm strut length,respectively) and is higher than the one obtained fromthe loading paths. Pinching of the hysteretic responsearound zero-force is attributed to the pin-joint slippage.Figure 11 shows the cumulative energy dissipationobtained from BRL12. At the end of the test (21 cycleswith close to 300 mm cumulative axial displacement)the dissipated energy is 6.8 kJ. This is equivalent to thepeak kinetic energy of a 100t mass oscillating at 1 Hzwith 59 mm amplitude.

3.1.2. Specimen BRL16Figure 10(b) shows the experimental load-displacementresponse of BRL16 and Figure 12(b) shows this deviceafter testing. Testing was terminated at the end of the 3rd

cycle at 7.5 mm amplitude (a total of 18 cycles) sincethe device capacity approached that of the load cell usedin the test. Again the squash load (Eqn 1) givesreasonable approximation of the device capacity underboth compression and tension. BRL16 displayed a similarcompression/tension bias as was observed in BRL12,



Table 2. Summary of experimental results

Analytical Experimental

kd

Fy Pcr1 Pcr2 Eqn 2 kStrut Dia. Eqn 1 Eqn 3 Eqn 5 (kN/mm) +Fy –Fy +Pmax –Pmax (kN/mm) E

Specimen (mm) (kN) (kN) (kN) 1. (kN) (kN) (kN) (kN) 2. (kJ)

BRL12 12 41.2 6621 395 75 42.2 23.9 74.7 44.3 40 6.8BRL16 16 62.7 6621 703 134 61.2 37.7 100 75.7 54 5.3

ExperimentEquation 1 & 2

ExperimentEqn 1 & 2

For

ce (

kN)

For

ce (

kN)

Displacement (mm)

Displacement (mm)

100

−100

80

−80

60

−60

40

−40

20

−20

0

100

−100

80

−80

60

−60

40

−40

20

−20

0

−10 −8 −6 −4 −2 0 2 4 6 8 10

−10 −8 −6 −4 −2 0 2 4 6 8 10

(a)

(b)

Figure 10. Force displacement hysteresis for: (a) Specimen BRB 12

and (b) BRB 16

Ene

rgy

(kJ)

1

0

2

3

4

5

6

7

0 50 100 150 200 250 300

BRL16 BRL12

Cumulative displacement (mm)

Figure 11. Cumulative energy dissipation

but to a lesser extent. As seen in Figure 12(b) thespecimen remained relatively intact at the end of the testwith some crushing of the surrounding mortar in thevicinity of the coupler. At the end of the test (18 cycleswith close to 200 mm cumulative axial displacement)the dissipated energy was 5.33 kJ. As seen in Figure 11,BRL16 dissipated energy at a higher rate than BRL12.

4. PROPOSED IMPLEMENTATIONEnergy dissipation devices can be strategicallyincorporated in the parent structure to maximize energydissipation and minimize structural damage. Onepossible implementation of the proposed BRL device is atbeam-to-column joints in MRF structure. In this case apivot joint is used to connect the beam (through the web’smid-height) to the column as shown in Figure 1(a). TwoBRL devices are incorporated between the top andbottom flanges of the beam and the inner flange of thecolumn, with provision of adequate web stiffeners toavoid crushing or buckling of web plate. In thisarrangement the BRL devices deform either in tensionor compression while the beam undergoes in-plane

rotation. The pin supports shear force such that the BRLare not part of the gravity load path; this facilitates thereplacement of a damaged device following an extremeloading event.

Under service load, the BRL elastic stiffness providesthe necessary moment resistance at the joint. In theevent of extreme loading, energy is dissipated at thejoint through plastic axial deformations of the steel strutin the BRL under tension and compression, while thebeam and the column remain elastic. Unlike existingstrategies for beam-to-column joints in MRF such asreduced-beam section (or dog-bone section) where aplastic hinge is designed to form in the beam itself, theproposed connection scheme shift the plasticdeformation away from the beam to the sacrificial BRL.Further, when compared with conventional energydissipation strategies where the dissipation isconcentrated in one or few locations (such as TunedMass Dampers), the proposed system distributes theenergy dissipation throughout the entire structure, hencereducing the demand on primary structural elements.

Figure 1(b) shows the proposed joint under an anti-clockwise rotation φ. Consider the BRL deviceconnecting point A and B. Due to the beam rotation, thisdevice exerts an axial compression force F. This forcecreates a bending moment about pivot O which can bewritten as dFsinθ1. Similarly, the BRL connecting Cand D exerts an equal but opposite axial tension –F, andconsequently creates a bending moment dFsinθ2. Withθ1 = θ2 = θ, the moment resistant of the joint can bewritten as,

M = 2dFsinθ (9)

where F is the axial force (tension/compression) in theBRL. The limiting moment capacity, Mp, of the jointcan be obtained by substituting F in Eqn 9 by Fy fromEqn 1, i.e.

(10)

For a semi-rigid joint, the moment-rotationrelationship of the joint can be written as

M = Krφ (11)

where kr is the rotational stiffness of the joint. Relatingthe axial deformation of the BRL to joint rotation φ, therotation φy corresponding to the onset of plastic responseof the BRL can be approximated by

(12)φyy i

i

y

id

f l

E d

f

E≅

∆=

≅

− − −tan tan tan1 1 1

M dfp y i= 2 Α sinθ



Y16

(a)

(b)

Figure 12. Failure mode of: (a) BRL12 and (b) BRL16

where ∆ is the axial deformation of the BRL device. Therotational stiffness, kr, of the joint is evaluated from

(13)

As an example, let the joint shown in Figure 1 becomposed of 310UB46 beam, 200UC46.2 column andtwo BRL12 devices with d = 429 mm, l = 420 mm andθ = 37o. Using the above equations, one can obtain thatMp = 21.26 kNm, φy = 1.819 × 10–3 rad and kr = 11.7 ×103 kNm/rad. By setting the maximum stroke, ∆, of theBRL device to 13 mm for example, a maximum jointrotation φ of 0.05 rad is obtained. Accordingly andassuming an elastic-perfectly plastic response, thetheoretical hysteretic moment-rotation response of thejoint can be constructed as shown in Figure 13. At thisrotation magnitude 4.07 kJ of energy is dissipated by theBRL devices in one complete cycle.

5. CONCLUSIONSAn investigation of a novel metallic energy dissipater,the buckling restrained lug BRL, is presented in thispaper. The BRL dissipates energy through plastic axialdeformation of a short steel strut embedded in a mortarfilled jacket tube. The BRL capacity is governed by thesquash load under axial tension or compression. Thestrut element is made using a standard reinforcement bar,threaded on both ends and snug tight to mechanicalcouplers. The strut and the couplers are embedded insidea jacket composed of aluminum square hollow sectionfilled with mortar. The device is cost effective and easyto fabricate. Sensitivity analysis using FE modeling wasconducted. This has shown the amplitude of geometricimperfection has influence on the buckling capacity withlittle effect on the post-buckling reserve capacity and thatthe stiffness of the restraining jacket has little effect onthe buckling capacity.

KM

rp

y

=φ

Cyclic test of BRL specimens demonstratedreasonably stable force-displacement hysteresis loopsand stable energy dissipation. Minor pinching ofhysteresis loops was observed and was caused byslippage at the pin connection end of the device.Preliminary design of the BRL can be made usingsimple basic equations. An implementation of the BRLin a beam-to-column joint in MRF is presented.Replacement of damaged BRLs following extremeloading event is simplified since the device is compactand is not part of the gravity load path. It also has theadvantage of distributing energy dissipationthroughout the structure.

ACKNOWLEDGMENTSMechanical couplers and threading of reinforcementbars were provided by Erico Products Australia Pty. Ltd.Their support is gratefully acknowledged.

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−30

−20

−0.06 −0.04 −0.02

−10

0

10

0.02 0.04 0.06

20

30

(rad)

M (

kNm

)

φ

Figure 13. M-φ relationship of beam-column connection

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NOTATIONAi cross sectional area of inner core strutAo cross sectional area of outer jacketBRL abbreviation for buckling restrained lugb breadth of flange plate of outer jacketd distance from beam pivot to BRL connection pinE dissipated energyEi Young’s modulus of inner core strutEo Young’s modulus of outer jacketF axial force in BRLFy yield strength of BRLfy yield stress of core strutIf second moment of area of flange of outer jacketJ ratio between axial stiffness of inner core to outer

jacketkd elastic stiffness of BRL device (analytical)k elastic stiffness of BRL samples (measured)kr rotational stiffnessLi unthreaded length of inner core strutLo length of outer jacketl centre to centre length between BRL connection pinl1 upper BRL lengthl2 lower BRL lengthM bending momentMp plastic momentPcr1 critical load – overall bucklingPcr2 critical load – snaking bucklingPmax maximum load ∆ axial displacement of BRLro radius of gyration of outer jackett thickness of flange of outer jacketβ stiffness of elastic mediumβ stiffness of elastic medium in experimentδ initial imperfection magnitudeφ beam in-plane rotation angleφy beam in-plane rotation angle at yieldθ angle between two specific points in a BRL

beam-column joint



Buckling-Restrained-Lug Connection for Energy Dissipation

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