Engineering Structures 139 (2017) 1–14

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Engineering Structures

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Cyclic loading test of double K-braced reinforced concrete framesubassemblies with buckling restrained braces

http://dx.doi.org/10.1016/j.engstruct.2017.02.0400141-0296/� 2017 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: m.quzhe@gmail.com (Z. Qu).

Zhe Qu a,⇑, Jinzhen Xie a, Tao Wang a, Shoichi Kishiki b

aKey Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Yanjiao, Sanhe, Hebei 065201, Chinab Structural Engineering Research Center, Tokyo Institute of Technology, Nagatsuta, Midori, Yokohama 226-8503, Japan

a r t i c l e i n f o a b s t r a c t

Article history:Received 4 July 2016Revised 22 December 2016Accepted 14 February 2017

Keywords:Double K-braced framesSeismic damageBuckling restrained braceSteel-to-concrete connectionsReinforced concrete frameMenegotto-Pinto model

Although the unbalanced brace force at the mid-length of columns discourages the use of K- or double K-bracing in concentrically braced frames, this limitation needs re-evaluation when K- or double K-bracingis implemented in buckling restrained braced frames. Unlike ordinary steel braces, buckling restrainedbraces (BRBs) exhibit almost identical behavior in tension and compression, and to arrange BRBs in a dou-ble K configuration may provide an efficient solution of connecting BRBs to reinforced concrete membersby exempting the steel-to-concrete interface from unfavorable tensile force. Three 1/2-scaled one-storyone-span subassemblies were subjected to cyclic loading to examine the above idea. Two of the speci-mens were braced by BRBs in double K configuration, whilst the other was a bare frame for comparison.During the test, the BRBs performed as intended in both tension and compression. The RC frames in thebraced specimens were only moderately damaged at 1% inter-story drift when the BRB cores sustainedlarge plastic strain. The damage patterns of the braced RC frames were similar to that of the bare framethroughout the loading process up to 2% inter-story drift. No cracks were observed at the mid-length ofthe columns or the mid-span of the beams where the BRBs were connected.

� 2017 Elsevier Ltd. All rights reserved.

1. Introduction

Developed in late 1980 s in Japan for seismic protection of steelstructures [1,2], buckling restrained braces (BRBs) have beenincreasingly used in reinforced concrete (RC) structures as wellduring the past decades over the world [3–6]. Although RCmoment-resisting frames exhibit higher lateral stiffness than steelframes do, the effectiveness of using BRBs to mitigate the seismicdamage to RC frames has been demonstrated through both numer-ical analyses and experimental tests (e.g., [5,7,8] among manyothers).

Nevertheless, there remain several challenges when combiningsteel braces with concrete frames. A significant challenge is totransfer the brace tension force to concrete members which areweak in tension. Conventional solutions include attaching orinserting steel braced frames instead of separate braces to RCframes by extensive anchor bolts. This practice is widely used inJapan for the seismic retrofit of existing RC frames and efforts havebeen made to find ways of reducing the number of anchor bolts tolower the cost and environmental impact [9,10]. For new construc-tions, an intuitive solution is to embed some steel parts in concrete

members to receive the brace gusset connections [11], in somecases even making the RC members into steel reinforced concrete(SRC) ones [12]. Recently, several innovative solutions were pro-posed to deal with the unfavorable tension force. Benavent-Climent et al. [13] proposed to use a pair of shear key plates to holdthe corner gusset of a brace, which is not directly connected to con-crete. In such a manner, the axial tension force of BRBs is convertedto almost pure shear force before being transmitted to the con-crete. Similar idea was partially applied by Ichikawa et al. [14] toseparate the tension and shear resistance in the corner gussets ofBRBs in RC frames. Both methods can greatly simplify the local loadtransfer around corner gusset connections, thus making the con-nections more reliable and easier to design.

Another problem comes from the detrimental interactionbetween the gusset plate and the frame members, which is usuallyreferred to as the ‘frame action’ (Fig. 1). Kishiki et al. [15] investi-gated the stress concentration at the toes of corner gussets in steelbraced frames because of the frame action. Such concentratedstress may lead to premature fracture of the gusset plate. Chouand Liu [16] demonstrated in their experimental test that the cor-ner gusset plate could buckle at much lower story drift thanexpected when free-edge stiffeners were absent. Numerical analy-sis showed that the force in the gusset plate resulting from theframe action was on the same order as the brace axial force.

Beam Beam

Col

umn

Col

umn

Gusset plate Gusset plate

)b()a(

Fig. 1. Frame action when (a) frame closes and (b) frame opens.

2 Z. Qu et al. / Engineering Structures 139 (2017) 1–14

Another side effect of the frame action is the considerable over-strength in braced frames [17], which may not be properly takeninto account in the design. While specific design methods can bedeveloped to address the effect of frame action in corner gussets[18], alternative corner gusset configurations were proposed toavoid frame action. Ishii et al. [19] anchored the gusset plates ofBRBs to the side surfaces of RC beam ends by post-tensioned steelrods. Berman and Bruneau [20] proposed an unconstrained gussetconnection for steel constructions, in which the gusset plate is sep-arated with the column by an intended gap and bolted to the beamend. This idea was later applied to RC frames with BRBs by Kham-panit et al. [21] and Qu et al. [22].

To address both the challenges of axial tension force and frameaction, Qu et al. [23] proposed to install BRBs in a zigzag configu-ration in RC frames and eliminate the RC beams in the braced spanso that the braced span forms a Warren truss. In the zigzag config-uration, the BRB gusset plates are anchored on the side surfaces ofbeam-to-column joints by independent shear and tension resistantelements. The axial forces of two adjacent BRBs, which share thesame gusset plate, are expected to counteract each other whenthe structure deforms laterally, so that the demands for the hori-zontal resistance of the connection can be greatly reduced or eveneliminated. However, numerical analysis showed that the highermode vibration of buildings would lead to significant tension forceon the gusset-to-concrete interface [24].

The double-K bracing as shown in Fig. 2 provides a promisingsolution to this problem. Similar to those in zigzag configurations,the BRBs in a double-K configuration share gusset plates. The twoneighboring braces are always acting in opposite directions, that is,one in tension and the other in compression. This mechanism isnot influenced by higher mode vibration because it takes placewithin a single story. Ideally, when BRBs of the same propertiesare used in a single span, there will be little unbalanced tension

RC

Col

umn

Plastic hinge

RC Beam

RC Beam

RC

Col

umn

Fig. 2. Reinforced concrete frames braced

force on the gusset plate. As a result, much less studs or post-installed anchors would be required to transfer the brace axialforce to the concrete. Some unbalanced compression force may risefrom the higher compression strength of BRBs. AISC 341-10 [25]requires that the BRB compression strength should be no greaterthan 1.3 times its tension strength. The same requirement wasincluded in a Chinese specification for BRBs which is to be pub-lished soon. This sets an upper limit for the unbalanced compres-sion force at the mid-length of the beams and columns. Suchcompression force may introduce friction to the connection inter-face, and thus increase the shear capacity of the connection.

In double-K bracing, the gusset connections at the mid-length ofthe beams and columns are free of the detrimental ‘frame action’,and are thus easier to proportion. In addition, the gusset connec-tions are away from the potential ‘plastic hinges’ at the RC beamends, and therefore the inelastic behavior (e.g., concrete cracking,rebar yielding) would not interact with the gusset connections inan unintended manner. For quick construction, the four BRBs andtheir gusset plates in a single span can be prefabricated as an inte-grated energy-dissipating unit ready to be shipped to the site foron-site installation.

The term ‘K-bracing’ has been used in the past to refer to whatwe call inverted V-bracing nowadays e.g. [26]. Nonetheless, AISC341-02 [27] defines K-braced frame as ‘‘an OCBF (ordinary concen-trically braced frame) in which a pair of diagonal braces located onone side of a column is connected to a single point within the clearcolumn height”. In AISC 341-10 [25], this definition is evolved to ‘‘abraced-frame configuration in which braces connect to a column ata location with no out-of-plane support”. By both definition, thebracing configuration in Fig. 2 falls into the category of K-bracing. To emphasize that the ‘K’ needs to appear in pair (thatis, four BRBs in a single span) so that the interfacial tension forcecan be eliminated, the term ‘double-K’ is used in this paper.

CompressionShear

by BRBs in double-K configuration.

Z. Qu et al. / Engineering Structures 139 (2017) 1–14 3

For steel constructions, double K-bracing is prohibited by AISC341-10 [25] for special concentrically braced frames. This is pri-marily because the braces intersect at mid-height of the columnsand their unbalanced force may cause the columns to failure, thustriggering collapse of the building [28]. The same provisions alsoprohibit the use of double K-bracing in buckling restrained bracedframe. However, as already mentioned, the unbalanced force ofintersected BRBs should be small.

In the Chinese seismic code [29], there is only a small sectionregarding the design requirements for structures with energy dis-sipating devices, which does not include any restraint for the use ofspecific bracing configurations. However, in the section for steelstructures in the same code, it is prohibited to use BRBs in a K-bracing configuration. Since no detailed explanation is providedfor this restriction, it is deemed to have been strongly influencedby the AISC provisions.

In Japan, however, it always remains an option to connectbraces within the clear span of columns. As a demonstration ofthe ‘‘damage tolerant structure” concept, buckling restrainedbraces were installed in the perimeter steel frames of a 40-storyoffice building in Tokyo [30]. The brace configuration in a singlespan was similar to that in Fig. 2 but the two adjacent BRBs didnot intersect at the mid-length of the beams/columns. Morerecently, a minimal-disturbance arm damper was proposed inJapan for the seismic retrofit of existing frames. The damper con-nects the mid-span of beams with the upper part of column andthus imposes an additional shear force in the column within itsclear span, whereas the magnitude of this detrimental force onthe column is limited by the strength of the bending plates inthe damper [31].

To assess the seismic performance of double-K braced RCframes with BRBs, cyclic loading tests were performed on threesubassembly specimens and the preliminary results were reportedby [32]. More detailed discussions on the test results are summa-rized in this paper, which would provide substantial evidence tosupport the use of double-K bracing in RC frames with BRBs. It isalso worth noting that a global plastic mechanism that can activatemore energy dissipating devices is usually preferred for all types ofpassively controlled structures including the one with double-Kconfigured BRBs as discussed herein. Additional design effort suchas those introduced by [7,33] is needed in proportioning the pri-mary structural components and the energy dissipating devices.This is beyond the scope of the current discussion but representsa future research interest.

2. Test program

2.1. Specimens

Three 1/2-scaled RC frame subassemblies were subjected tocyclic loading with increasing lateral drift amplitudes to assessthe seismic damage to RC frames and the cyclic performance ofBRBs in double-K configuration. Two of the specimens were bracedby BRBs, whereas the other was a bare frame counterpart for com-parison (Table 1). To simulate the behavior of a middle story in amulti-story building, the RC part in each subassembly consists of

Table 1Specimens.

ID Specimen Steel-to-concrete connection

No.1 Bare RC frame –No.2 Double-K braced RC frame with

BRBsEmbedded shear studs

No.3 Double-K braced RC frame withBRBs

Post-installed chemicalanchors

two beams framing into two columns (Fig. 3). The multi-storybuilding from which the subassemblies were separated wasassumed to be over 24 m high and locate on a site of Intensity 8(i.e., the design level spectral acceleration in short period regionSad = 0.45 g), so that the frames fell into the Seismic Design Cate-gory I per the Chinese seismic code [29]. The design of the RC partsconforms to the Chinese code for concrete structures [35], and astrong column-weak beam concept was applied in proportioningthe beams and columns. In the Chinese seismic code, the sum ofthe flexural strength of columns framing into a joint is requiredto be no less than 1.2 to 1.7 times the sum of the design strengthsof the beams framing into the same joint for bare moment-resisting frames, depending on the Seismic Design Category. Whilethe required amplification factor is 1.7 for bare frames in CategoryI, it is allowed by the code to lower it by at most 0.2 if the structuralis protected by additional energy dissipating devices. Therefore, anamplification factor of no less than 1.5 was adopted in proportion-ing the specimens of the current test. As a result, the beam flexuralreinforcement ratio is about 1.1%, and the column overall longitu-dinal reinforcement ratio is 2.7%. Ductile detailing was provided forboth the beams and columns. The intervals of the beam stirrupsand column hoops were reduced by half in the regions close tothe beam-to-column joints. C40 concrete (40 MPa nominal com-pressive strength of cubes) and HRB400 rebars (400 MPa nominalyield strength) were used for the RC frames. The measured averagecompressive strength of concrete cubes was 49.7 MPa. The mea-sured yield and ultimate strength of the /14 longitudinal rebarswere 563 MPa and 673 MPa, respectively.

Four identical BRBs were installed in a double-K configurationin each braced specimen. The BRBs were manufactured by LeadDynamic Engineering Co., Ltd., a joint-venture by Nippon Steeland another two Chinese local companies. The proportioning ofthe BRBs was controlled by (1) the brace-to-frame strength ratioand (2) the ultimate strain of the BRB steel cores. The steel corewas made of 10 mm thick steel plate of Chinese Q235 steel(commonly-used structural steel of 235 MPa nominal yieldstrength). The nominal axial strength (including an assumed 1.5times over-strength because of strain hardening) of each BRB is200 kN so that the additional lateral strength provided by the BRBsis 338 kN, approximately two times that of the RC frame, which is167 kN per the nominal material strengths.

While the distance between the intersection points of the BRBaxes is 1595 mm, the length of the plastic segment of the BRB steelcore is 500 mm (Fig. 4). As a result, the strain in the plastic segmentof the BRBs would be approximately 1.7% at 1/100 inter-story driftassuming that the elastic deformation of the remaining parts of theBRBs including the connections is negligibly small. It wouldbecome 3.4% at 1/50 inter-story drift. Previous tests on similarBRBs provided by the same company demonstrated stable hys-teretic performance of the BRBs at such strain levels [23].

The equivalent axial stiffness of each brace between the twointersection points is approximately 144.7 kN/mm. The additionalstiffness provided by the braces is thus 122.4 kN/mm, which isapproximately three times that of the bare frame, which is41.6 kN/mm. The high stiffness of the braces corresponds to a1/927 inter-story drift ratio when the BRBs first yield (no strainhardening). Such a yield drift ratio is very small as compared tothat of the bare RC frame, which is estimated to be 1/100 accordingto the empirical equation for yield story drift ratio, IDR = 0.5eyLB/hB,where, ey is the yield strain of rebars, LB and hB are the span lengthand sectional height of beams, respectively [34].

The BRBs were bolted to the gusset plates, which were anchoredto the RC beams or columns by two different methods for the twobraced specimens. In one method proposed for new constructions,M19 shear studs (19 mm in diameter) were welded to the baseplate of the gusset plates, and were embedded in the RC compo-

3000

2000

B

B

CCA

A

A-A section (BRB)

B-B section (Beam)

C-C section (Column)

140

56

Core, PL-10Tube 140-5

Concrete

200

300

300

300

4 14

4 14

@100

5 1414

5 14

@100

900

CL

450@100 @200

1100

300

300

@20

0@

100

@10

0

4M16 bolts for connecting jigs

053053

32.2

x

Fig. 3. Specimen geometry and reinforcement (unit: mm).

30 30680

267 500 26710351595

A

A

B

BIntersection

pointIntersection

point

9090 14

0

10

56 140

A-A

B-B

Polystyrene cushion

Fig. 4. Buckling restrained braces used in test (unit: mm).

4 Z. Qu et al. / Engineering Structures 139 (2017) 1–14

nents (Fig. 5(a)). In the other method, /12 post-installed chemicalanchors were used for the connection to simulate applications inseismic retrofit of existing buildings. In this case, the RC framewas first cast without the BRB gusset plates and cured for 28 days.Then the chemical anchors were installed in the /15 holes drilledin the concrete with epoxy resin, then fit into the tapered holes andwelded to the base plate of gusset base (Fig. 5(b)). Following thecapacity design concept, the number of shear studs and post-installed anchors were determined by the resultant shear force ofthe adjusted BRB strength at the connection interfaces, neglectingthe possible compression or tension force on the interface. The

19 stud

1140 140 140550

80200

80 110

)a(

194

16

50 60 40 40

194

16

64 64

PL10

PL10

18

Fig. 5. Connection details for gusset plates on beams: (a) embedded shear studs for new(unit: mm).

adjusted BRB strength takes into account 50% strain hardeningfor both BRBs connecting to the same gusset plate and another30% over-strength for the BRB in compression. The design of theembedded studs conforms to the provisions on composite beamsin the Chinese code for steel structures [36]. The specified yieldstrength of studs is 215 MPa, and a strain hardening factor of1.67 is applied in calculating the stud ultimate strength. The chem-ical anchor group is designed conforming to the Chinese code forstrengthening concrete structure [37]. The specified shear strengthof the anchor steel is 290 MPa.

12 chemicalanchor

11011010 110 110 110 110 110970

80200

)b(

550 64 64

PL10

PL10

18

construction applications; (b) post-installed anchors for seismic retrofit applications

Z. Qu et al. / Engineering Structures 139 (2017) 1–14 5

2.2. Test setup, loading and measurement

The specimens were mounted on two mechanical pins thatwere firmly fastened on the strong floor (Fig. 6 and 7). Two hori-zontal actuators of 1000 kN capacity were employed to load thespecimens. The upper actuator was displacement-controlled toimpose the desired inter-story drift ratio (IDR) on the specimen,while the lower actuator was force-controlled to fully counteractthe upper actuator so that the bottom mechanical pins werewaived from excessive shear.Fig. 8

End plates were provided at the far ends of the beams and col-umns for connections to the loading jigs. The longitudinal rebarswere welded to the end plates. Four M16 high-strength bolts pro-truded from the outer surface of each end plate, ready to be fas-tened to the steel loading jigs.

Two spherical-headed oil jacks were employed to exert axialforce through steel jigs on top of the columns. Roller cushions wereinstalled between the oil jacks and the overhead reaction beam sothat the jacks could move horizontally along with the top of thecolumns. The steel jigs fastened to the top of the columns wererestrained by pantographs for out-of-plane stability. Before lateralloading, the oil jacks applied 482 kN axial compression force toeach of the columns to simulate the gravity load of upper stories.This corresponds to 20% of the column’s nominal axial strength,and approximately 16% of its actual axial strength. To simulatethe realistic construction process, the BRBs were not fully fasteneduntil the dead load was imposed. During the test, the forces in theoil jacks were constantly adjusted to counteract the overturningmoment resulting from the horizontal loading, so as to maintainconstant axial forces in the lower halves of the columns to protectthe mechanical pins under them.

The additional distributed loads along the beams (e.g., the deadload of slabs and the live loads) were neglected in the test because(1) the inclusion of these load would bring about additional com-plexity of the test setup without making significant difference tothe global behavior of the specimens and (2) these loads wouldresult in more complicated curvature distributions in the beams,

Pantograph

Displacement-controlled actuator

Force-controlled actuator

Oil jack Oil jack

Mechanical pin

Reaction beam

3000

Rea

ctio

n w

all

630

2000

870

780

Roller cushion

West East

Fig. 6. Test

which would make the analysis of the unbalance force of BRBsmore difficult.

Inter-story drift ratios of 1/1200, 1/550, 1/200, 1/100, 1/67 and1/50 were selected as the target amplitudes for the loading proto-col (Fig. 7). Among these, IDR = 1/550 and 1/50 are the lateral diftlimits for RC moment-resisting frames at their serviceability andultimate limit states, respectively, per the Chinese seismic code[29]. IDR = 1/200 corresponds to the drift limit stipulated in theBuilding Standard Law of Japan for serviceability limit state [38].It is also the drift limit in Eurocode 8 for damage limitation of RCframes with brittle nonstructural elements [39]. IDR = 1/100 is usu-ally taken as an inelastic drift limit for passive-controlled struc-tures under major earthquakes in Japan’s seismic design practice.The 1/100 and 1/200 drift limits were adopted in the loading pro-tocol to explore the specimens’ behavior at more levels of deforma-tion, although they are not stipulated in the Chinese codes. Inparticular, the 1/100 drift ratio is regarded as the performance tar-get of the archetype structure under major earthquakes. Twocycles of static loading were performed at each amplitude.

Displacement sensors were used to monitor the deformation ofthe specimens. The locations of the sensors are shown in Fig. 9. Inparticular, two sensors, namely D1 and D2, are used to monitor thestory drift of the specimen. B1–B8 are for the axial deformation ofthe BRBs, R1–R4 are for the end rotations of the lower eastern BRB,and S1–S4 are for the slip of the four gusset plates of BRBs. In addi-tion to the displacement sensors, strain gauges were attached tothe outermost longitudinal rebars at three sections (i.e., both endsand mid-length) of each beam or column. The locations of the sec-tions are also depicted in Fig. 9.

3. Test results

3.1. Global responses

As shown in Fig. 10, compared to the bare frame specimen(No.1), the two braced frame specimens exhibited stable and fullhysteresis throughout the loading process up to 1/50 inter-storydrift ratio. The BRBs started to yield at IDR = 1/604 and 1/560 in

Pantograph

Oil jack

Mechanical pin

Strong floor

setup.

Fig. 7. Photos of specimens ready for loading: (a) No.1 and (b) No.2.

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 1 2 3 4 5 6 7 8 9 10 11 12

1/1200 1/550 1/2001/100

1/671/50

No. of load cycle

Stor

ydr

iftra

tio

Fig. 8. Loading protocol.

Lower east

Upper west

Lower west

Upper east

S1

D2

S2

S3

S4

R1

R2

R3

R4

B1, B2B7, B8

B3, B4B5, B6

D1

Sections where rebar strains are monitoredDisplacement sensors

Beam section

Column section

Strain gaugeon rebar

Fig. 9. Installation of displacement transducers and rebar strain gauges.

6 Z. Qu et al. / Engineering Structures 139 (2017) 1–14

the braced frame with shear studs (No.2) and the one with chem-ical anchors (No.3), respectively. These drift ratios are much largerthan the estimated yield drift ratio of 1/927. This is primarilybecause of the local deformation loss at the brace connections,which will be discussed later in Section 3.4.

On the other hand, the bare frame specimen did not exhibit sig-nificant yielding until IDR = 1/78 in the negative direction and 1/81in the positive direction. Rather than the first yielding of rebars

determined by specific strain readings, these yield drift ratios wereidentified on the skeleton curve as the points where the tangentstiffness was degraded significantly (Fig. 10a). For the current testsetup, the drift ratio includes both the deflection of the RC columnand the rotation of the lower beam-to-column joints which isrelated to the chord rotation of the beams. In this specific case,the story drift associated with the beam chord rotation constitutes

-400

-300

-200

-100

0

100

200

300

400

0.03-1000-800-600-400-200

0200400600800

1000

-0.03 -0.02 -0.01 0 0.01 0.02 -0.03 -0.02 -0.01 0 0.01 0.02 0.03-1000-800-600-400-200

0200400600800

1000

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

Stor

ysh

ear(

kN)

Inter-story drift ratio Inter-story drift ratio Inter-story drift ratio

Lower-eastBRB removed

No.1 Bare frame No.2 Braced frame + shear studs No.3 Braced frame + chemical anchor

Significant yielding

Significant yielding

)c()b()a(

Fig. 10. Force-deformation relationship of specimens: (a) No.1, (b) No.2 and (c) No.3.

Z. Qu et al. / Engineering Structures 139 (2017) 1–14 7

approximately 77% of the total story drift when the frameremained elastic.

For specimen No.3, one of the four BRBs was removed at theunloaded point before the last load cycle of IDR = 1/50. Then theloading was resumed to check the BRB-to-concrete connection per-formance when the force balance of BRBs was broken. The hystere-sis of this last loading cycle is depicted by the dashed line in Fig. 10.The only significant phenomenon was that the peak force droppedby 21% (from 821.4 kN to 650.2 kN) and 18% (from �895.4 kN to�693.8 kN) in the positive and negative loading directions, respec-tively. The damage to the concrete members or the steel-to-concrete connections were not exacerbated by the removal of theBRB.

The BRBs in a double-K configuration are shorter than in otherconfigurations such as V- or inverted-V bracing. This leads toshorter plastic segments and consequently larger plastic strain inthe core if the story drift is the same. The results in Fig. 10 showthat the commercially available BRBs used in the current test suc-cessfully exhibited stable hysteresis. The maximum average strainsin the cores, which were taken as the measured axial deformationdivided by the length of the BRBs’ plastic segments, were approx-imately 3.6% in specimen No.2 and 3.2% in No.3, where the BRB’saxial deformation was measured by displacement sensorsB1 � B8 as shown in Fig. 6. Since these sensors spanned over thewhole lengths of the BRBs including their elastic segments andthe connections, the above strains are upper-bound values forthe actual strains experienced by the plastic segments.

3.2. BRB hysteresis

For the statically undetermined system of the loading setup, theaxial force of individual BRBs could hardly be directly measuredduring the test. To evaluate the force transmitted to the steel-to-concrete connections, the Menegotto-Pinto model is adopted toestimate the BRB axial force from the measured axial deformation,which takes the form of Eq. (1) [40].

r� ¼ be� þ ð1� bÞe�ð1þ e�RÞ1R

ð1Þ

where e⁄ and r⁄ are the normalized strain and stress that are calcu-lated by Eqs. (2) and (3), respectively; b is the strain hardeningratio; R is a parameter that controls the shape of the transitioncurve between the two asymptotes of elastic loading and post-yield hardening branches.

e� ¼ e� ere0 � er

ð2Þ

r� ¼ r� rr

r0 � rrð3Þ

where e and r are strain and stress; e0 and r0 are stress and strain atthe intersection point of the two asymptotes; er and rr are strainand stress at the previous strain reversal.

R is further evaluated by Eq. (4) as below.

R ¼ R0 1� cR1ncR2 þ n

� �ð4Þ

where R0, cR1 and cR2 are experimentally determined parameters; nis the normalized plastic strain as defined in Eq. (5).

n ¼ ep � e0ey

�������� ð5Þ

where ep and ey are plastic strain and yield strain, respectively.Filippou et al. [41] proposed a stress shift to consider the isotro-

pic hardening on the basis of the Menegotto-Pinto model. Beforeevaluating the intersection point (e0, r0), the yield asymptotes isfirst moved parallel to its direction by a stress shift, rst, which iscalculated by Eq. (6).

rst ¼ a1ðemax � emin

2a2eyÞ0:8

ð6Þ

where emax and emin are the absolute maximum and minimumstrains at strain reversal, respectively; a1 and a2 are experimentallydetermined parameters.

The above model is referred to as the Steel02 model (Giuffré-Menegotto-Pinto Model with Isotropic Strain Hardening) in Open-Sees [42]. To capture the characteristics of BRBs which exhibitslightly higher strength in compression than in tension, the modelis modified to allow for different sets of strain hardening parame-ters, b, a1 and a2 for compression and tension.

The model parameters are calibrated against the hystereticcurve of a uniaxially loaded BRB that was the same as those usedin the present subassembly tests (Fig. 11). With the values of theparameters as listed in Table 2, the model gives satisfactory esti-mates of the BRB hysteresis. The deviation between the modeland the test result is slightly larger in compression than in tension.This is because linear strain hardening with a larger slope in com-pression was used to approximately model the complicated behav-ior of compression over-strength of the BRB, which is dependenton the sectional expansion of the steel core and the frictionbetween the core and the outer restraining elements.

The axial forces of the BRBs in the subassemblage specimensduring the loading is calculated corresponding to the measuredBRB axial deformations by the above calibrated model. Althoughthese force results are considered accurate enough for the follow-

(a)

-600

-400

-200

0

200

400

-0.04 -0.02 0 0.02 0.04

TestCalculated

Average strain, (mm/mm)

Ave

rage

stre

ss,

(MPa

)

(b)

200

200

MPa

Over-estimatedUnder-estimatedMaximum error: 8.1%

Calculated Test

Fig. 11. Comparison of model and measured hysteresis of BRB under uniaxial cyclic loading: (a) complete hysteresis and (b) cycle-by-cycle hysteresis.

Table 2Calibrated parameters in hysteresis model.

Parameter Calibrated value

In compression In tension

R0 26 26cR1 0.925 0.925cR2 0.15 0.15b 0.02 0.005a1 0.035 0.04a2 1 1

8 Z. Qu et al. / Engineering Structures 139 (2017) 1–14

ing discussions, it should be noted that their accuracy may be influ-enced by such factors as the scattering of the material propertiesand the BRB end rotations in the subassembly test which did notpresent in the uniaxial calibration test.

3.3. Unbalanced BRB force on connection interface and its influence

The force components on the four steel-to-concrete connectioninterfaces are evaluated through the equilibrium of the BRB axialforce. Fig. 12(a) depicts the hysteresis of the force component nor-mal to the connection interface on the western column of speci-men No.3, which is connected to the lower western (LW) and theupper western (UW) braces. During the second load cycle ofIDR = 1/100, both the tension and compression forces are small ascompared to the BRB’s strength. In particular, the maximum ten-sion force at point C is less than 20 kN, almost negligible in the

design of the shear connection (either of shear studs or chemicalanchors). In Fig. 12(b), it is clear that the compressive normal forcein Fig. 12(a) is primarily a result of the compression over-strengthof the BRBs, whereas the tensile normal force takes the maximumvalue during the transition from elastic loading to yielding, whichis related to the Bauschinger effect.

Similar phenomena can be observed for the second load cycleof IDR = 1/50 except that the magnitude of the normal tensile andcompressive force were increased (Fig. 11). Even though, themaximum tensile force is no greater than 30 kN, which is onlyapproximately 8% of the design shear force of the BRB connec-tions on the columns. It is worth noting that the drift limit ofRC structures with supplemental energy dissipating devices suchas BRBs are usually required to be less than IDR = 1/100 undermajor earthquakes (such as in the Japanese practice), the behav-ior at IDR = 1/50 should be interpreted as beyond-design levelperformance.

The negligible influence of the small normal forces at the mid-length of the columns and beams is also demonstrated by the cur-vature distributions in the RC frames. The curvatures were cap-tured by the strains of the longitudinal rebars at three crosssections of each beam and column. Because the strain readings ofmany rebars, especially those in the beams, became unreliablewhen the deformation approached IDR = 1/100, the results at thesecond load cycle at IDR = 1/200 are given in Fig. 13. At such a driftlevel, the RC members remain essentially elastic and the curva-tures are expected to be small. The curvature distributions in theRC frames of the three specimens are quite similar to one another.

-400

-300

-200

-100

0

100

200

300

400-400

-300

-200

-100

0

100

200

300

400-80

-60

-40

-20

0

20

40

60

50

-300

-200

-100

0

100

200

300-300

-200

-100

0

100

200

300

-80

-60

-40

-20

0

20

40

60

-50 -25 0 25 50-50 -25 0 25

-20 -10 0 10 20-50 -25 0 25 50Inter-story drift (mm)

Forc

eno

rmal

toco

nnec

tion

inte

rfac

eon

colu

mn

(kN

)

UW

brac

eax

ialf

orce

(kN

)

A

B

C

D

A

B

CD

LW braceUW brace

IDR = 1/100

Inter-story drift (mm)

(Comp.)

(Tens.) -300 (Comp.)

-200

-100

0

100

200

300 (Tens.)

LWbr

ace

axia

lfor

ce(k

N)

Inter-story drift (mm)

Forc

eno

rmal

toco

nnec

tion

inte

rfac

eon

colu

mn

(kN

)

UW

brac

eax

ialf

orce

(kN

)A

BC

D

A

B

C

D

IDR = 1/50

)b()a(Inter-story drift (mm)

(Comp.)

(Tens.) -400 (Comp.)

-300

-200

-100

0

100

200

300

400 (Tens.)

LWbr

ace

axia

lfor

ce(k

N)

Fig. 12. Force components normal to steel-to-concrete connection interface on western column of specimen No.3 during different load cycles: (a) normal force hysteresis and(b) axial force of BRBs connected.

Fig. 13. Curvature distributions of RC frames at: (a) IDR = 1/200 and (b) IDR = �1/200 (unit: le/mm).

Z. Qu et al. / Engineering Structures 139 (2017) 1–14 9

10 Z. Qu et al. / Engineering Structures 139 (2017) 1–14

No obvious curvature is observed at the mid-length of the beams orcolumns in specimen No.2 and 3, where the BRBs are intersected.

The apparent damage to the RC frames in the three specimenscorresponded well to their curvature distributions. At the peakdrift of each load cycle, the cracks on the concrete surface weremarked and recorded on a grid that coincides with the rebarsand stirrups (Fig. 14). The crack widths were read by crack scaleson points where the crack crossed the grid lines (Fig. 15). Regard-less of the existence of the BRBs, the crack patterns (both the dis-tribution and widths) of specimens No.2 and 3 were similar to thatof the bare frame specimen (No.1). As intended, most damage wasconcentrated in the beam ends, where major cracks developed andslight concrete spalling was observed at the final stage of the load-ing. Take specimen No.2 for example. Cracks were first observed onthe beams, and no cracks were found on the columns until the sec-ond load cycle of IDR = 1/100. At IDR = 1/100, a few cracks at thebeam ends grew to wider than 0.2 mm. These cracks continuedto open and some of them became wider than 1.0 mm atIDR = 1/50. Cracks on the columns were distributed at the beam-to-column joints and regions close to the joints. The column crackwidths were considerably smaller than those on the beams.

The above results show that the BRBs and their gusset connec-tions in the double-K configuration would not deteriorate the seis-mic performance of the RC frame. The similar levels of damageshould not be interpreted in a way that the BRBs bring no benefitto reduce the structural damage because such a similarity isobserved at the same story drift. The maximum story drift of anRC frame equipped with BRBs would be much less than that of abare frame because of the addition stiffness and energy dissipationprovided by the braces. In such cases, the damage to the RC framebraced by BRBs is expected to be much less than that to a bareframe.

3.4. Deformation loss at BRB-to-concrete connections

It is usually preferred to have stiff brace connections so that thebrace axial deformation is concentrated in the energy dissipatingsegments. In this sense, the effectiveness of brace connectionscan be evaluated in terms of the ‘deformation loss’ in the connec-tion, which is calculated by subtracting the actual deformation of aBRB’s plastic core from its maximum possible deformation whenassuming the rest of the brace and the connections are rigid. Inthe double-K configuration as shown in Fig. 16 in which one-fourth of a single span is taken as a free body, the maximum pos-sible deformation of a BRB, dbm, can be expressed as a function ofthe story drift ratio, IDR, the rotation at the mid-length of thebeam, hb, and the column, hc (Eq. (7)). By assuming that the RCframe remains elastic, R, hb and hc can be calculated by Eqs. (8)–(10).

Fig. 14. Damaged RC members with marked cracks of Specimen No.2 at

dbm ¼ RH2

cosbþ hc

2hcsinbþ hb

2hbsinb ð7Þ

where H is the story height; hc and hb are the depths of the columnand beam, respectively; b is the inclination angle of the brace.

D ¼ RH2

¼ PH2

24HEIc

þ LEIb

� �ð8Þ

hc ¼ PH4

H2EIc

þ L3EIb

� �ð9Þ

hb ¼ PHL24EIb

ð10Þ

where P is the story shear force; L is the span length; E is the con-crete Young’s modulus; Ib and Ic are the moment of inertia of thebeam and column, respectively.

Substituting the specific geometric and material properties ofthe current specimens in Eqs. (7)–(10) gives a simple numericalrelationship between the inter-story drift ratio, IDR, and the max-imum possible brace deformation, dbm = 0.58∙(IDR)∙Hcosb. Thedeformation loss ratio is defined in Eq. (11) by dbm and the mea-sured BRB core deformation dBRB, and is depicted in Fig. 17 for allthe drift amplitudes. The values shown in the figure are the aver-age of the four BRBs in each specimen (in case of No.3 during thesecond load cycle of 1/50 drift, it is the average ratio of the threeremaining BRBs).

Deformation loss ratio ¼ dbm � dBRBdbm

ð11Þ

At small drift amplitudes when the BRBs were essentially elas-tic, the deformation loss took more than 20% of the maximum pos-sible brace deformation. This ratio decreased rapidly at larger driftamplitudes as the BRBs sustained significant plastic deformation.The deformation loss in specimen No.3 is larger than that of No.2at all stages, indicating that the post-installed chemical anchorsexhibited lower stiffness than the embedded studs.

Although the deformation loss may come from various sources,it is predominated by the slip of the gusset plate along the beam/-column’s axis in double-K braced frames in which the tension forceon the connection interface is very limited. Taking the gusset con-nection on the lower beam in specimen No.3 for example, Fig. 18shows that the deformation loss at a single connection (taken ashalf the deformation loss of a brace) and the contribution of gussetslip, ds∙cosb, where ds is the measured gusset slip, are very close toeach other at various drift amplitudes.

The peak gusset slips in specimens No.2 and 3 were almostidentical when the story drift ratio, IDR, was no greater than1/100, although the hysteresis curves were somehow different

end of 1/50 load cycle: (a) lower-east joint and (b) lower-west joint.

Crack width: <0.2mm 0.2 mm ~ 1.0 mm 1.0mm

No.1Bare frame

IDR = 1/100

No.1Bare frameIDR = 1/50

No.2 Braced frame +

Shear studsIDR = 1/100

No.2 Braced frame +

Shear studsIDR = 1/50

No.3 Braced frame +

Chemical anchorIDR = 1/100

No.3 Braced frame +

Chemical anchorIDR = 1/50

Fig. 15. Cracks on RC frames.

1

= (IDR) H/2

Pb

c

L/2

H/2

hb/2

hc/2

EIc

EIb

Fig. 16. Maximum possible axial deformation of braces.

0

0.1

0.2

0.3

0.4

1/120

01/5

501/2

001/1

001/6

71/5

0

Inter-story drift ratio amplitude1/5

0(2)

No.2No.3

Ave

rage

defo

rmat

ion

loss

ratio

Fig. 17. Maximum brace deformation loss at peak story drifts.

Z. Qu et al. / Engineering Structures 139 (2017) 1–14 11

IDR = 1/100

IDR = 1/67

Deformation (mm) Deformation (mm) Deformation (mm) Deformation (mm)

Forc

e (k

N)

BRB axial force deformation loss/2 Gusset shear gusset slip s cos

IDR = 1/550

IDR = 1/200

Fig. 18. Deformation loss and slip at lower gusset connection in specimen No.3.

-600

-400

-200

0

200

400

600

1

No. 2 No. 3

-600

-400

-200

0

200

400

600

-1 -0.5 0 0.5 -4 -2 0 2 4

Lower-eastBRB removed

)mm(pilstessuG)mm(pilstessuG

Gus

sets

hear

forc

e(k

N)

Gus

sets

hear

forc

e(k

N)

(b)(a)

R = 1/100 R = 1/67, 1/50

Fig. 19. Slip of gusset plates on lower beams.

12 Z. Qu et al. / Engineering Structures 139 (2017) 1–14

(Fig. 19(a)). During the remaining load cycles, the gusset slip inspecimen No.2 remained almost the same as in previous loadcycles while that in No.3 was significantly increased (Fig. 19(b)),indicating softening of the chemical anchor connection.

For specimen No.3, one of the BRBs was removed before the sec-ond load cycle of IDR = 1/50. As a result, half of the shear force onthe connected gusset plate was released and the gusset slips werethus decreased as shown by the dashed line in Fig. 19(b). On theother hand, it broke the BRB force balance and subjected the gussetconnection to significant tension force. The latter effect was sooverwhelming that, despite the considerable decrease in gussetslips, the overall deformation loss of BRBs was increased by 43%from 16% in the first 1/50 load cycle to 23% in the second 1/50 cycle(Fig. 17). In other words, the break of BRB force balance by remov-ing one of the braces exaggerate the deformation loss in the con-nections, although it did not cause strength problem in thecurrent test.

3.5. BRB end rotations

In addition to the aforementioned larger core strains in the BRBsin double-K configuration, which are usually shorter than in othercommonly-seen configurations, another possible side effect is lar-ger rotations at the ends of BRBs’ plastic cores, which may havedetrimental effects on the performance of the BRBs [43]. In adouble-K conguration, the BRB end rotation can be decomposed

into components related to (a) lateral drift, D, (b) beam gussetrotation, hb and (c) column gusset rotation, hc, as depicted inFig. 20. The end rotations of a brace at its column-side end andbeam-side end can thus be estimated by Eqs. (12) and (13), respec-tively, assuming that the BRB connections and segments outsidethe core are rigid.

hEC ¼ hEC1 þ hEC2 þ hEC3

¼ �arctanDsinb

Lcore � Dcosb� Lconn

Lcorehb þ 1þ Lconn

Lcore

� �hc ð12Þ

hEB ¼ hEB1 þ hEB2 þ hEB3

¼ arctanDsinb

Lcore � Dcosbþ ð1þ Lconn

LcoreÞhb � Lconn

Lcorehc ð13Þ

where Lcore is the length of the BRB’s plastic core.The estimates given by Eqs. (12) and (13) generally agree well

with the test results measured by pairs of displacement sensorsfor the lower western BRB in each braced specimen (Fig. 21). Linearregression of the test results shows that the column-side end rota-tions are only a small fraction of the inter-story drift ratio, IDR,whereas the beam-side end rotations are slightly larger than IDR.Such level of end rotations is only slightly larger than thosereported in the past literature for commonly-used inverted-V brac-ing [44].

EB1

EC1 EC2

EB2b

EC3EB3

c

LcoreLcore

LconnLcore

)c()b()a(

H/2

L/2

Fig. 20. BRB end rotations because of: (a) story drift, D; (b) beam gusset rotation, hb and (c) column gusset rotation, hc.

-0.04

-0.02

0

0.02

0.04

0.04-0.04

-0.02

0

0.02

0.04

0.04

-0.04

-0.02

0

0.02

0.04

0.04-0.04

-0.02

0

0.02

0.04

-0.04 -0.02 0 0.02-0.04 -0.02 0 0.02

-0.04 -0.02 0 0.02-0.04 -0.02 0 0.02 0.04

Inter-story drift ratio, IDR

Col

umn-

side

end

rota

tion,

EC

(b)(a)

Measured Linear regressionEq. (12) or (13)

2.oN2.oN

3.oN3.oN

Inter-story drift ratio, IDR

Bea

m-s

ide

end

rota

tion,

EB

Bea

m- s

ide

end

rota

tion,

EB

EC = 0.14 IDREB = 1.15 IDR

Col

umn-

side

end

rota

tion,

EC

Tsai et al. 2008 [36]

EC = 0.22 IDR EB = 1.03 IDR

Fig. 21. End rotations of lower western BRB at: (a) column-side end and (b) beam-side end.

Z. Qu et al. / Engineering Structures 139 (2017) 1–14 13

4. Conclusions

Although currently prohibited by steel structure design codesfor seismic applications, double-K bracing is a promising systemfor buckling restrained braced reinforced concrete frames. It cansimplify the design of the BRB-to-concrete connection and helpimprove the seismic performance of these connections.

Three RC frame subassemblies were subjected to cyclic load-ing, two of which were braced by BRBs in double-K configura-tion and one was a bare frame for comparison. TheMenegotto-Pinto model with isotropic hardening was modifiedto simulate the BRB hysteresis so that the forces on the gussetconnections could be explicitly evaluated in the statically unde-termined specimens. The test results confirmed the reliable seis-mic performance of double-K braced RC frames by providing thefollowing findings.

(1) The RC frames sustained quite similar flexural deformationand damage patterns no matter if it is braced or not, giventhat the story drift is the same. The unbalanced force of BRBson the frames had negligible effect on the behavior of the RCframes. Since the maximum story drift of a braced framewith BRBs is always much smaller than that of a bare frameunder the same earthquake excitation, the benefit of usingBRBs to reduce the seismic damage is guaranteed.

(2) The BRB-to-concrete connections were primarily subjected toshear force, which could be well withstood by either embed-ded studs or post-installed chemical anchors. The tensionforce on the connection interface was negligibly small.

(3) The BRBs behaved well in the double-K configuration todevelop full and stable hysteresis. In particular, the end rota-tions of the BRBs in the present test were similar in magni-tude to those in commonly-used inverted-V bracing.

14 Z. Qu et al. / Engineering Structures 139 (2017) 1–14

Although the BRBs in a double-K configuration are usually smal-ler than in other configurations and thus may sustain higher levelsof plastic strain in the cores, it would not bring about difficultiesfor practical design because the currently available BRBs usuallyexhibit superior low-cycle fatigue performance.

Acknowledgements

The experimental investigation is sponsored by the NationalNatural Science Foundation of China (No. 51308514 and No.51478441). The financial support is highly appreciated.

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