Behaviour of fibre-reinforced beams with diagonal ...earthquake.hanyang.ac.kr/journal/2015/Behaviour of fibre reinforced... · u maximum shear force obtained from hysteretic curve

Behaviour of fibre-reinforcedbeams with diagonal reinforcementSang Whan HanProfessor, Department of Architectural Engineering, Hanyang University,Seoul, Korea

Chang Seok LeeGraduate student, Department of Architectural Engineering, HanyangUniversity, Seoul, Korea

Hyun Wook KwonGraduate student, Department of Architectural Engineering, HanyangUniversity, Seoul, Korea

Ki Hak LeeProfessor, Department of Architectural Engineering at Sejong University,Seoul, Korea

Myung Su ShinProfessor, School of Urban and Environment Engineering at UNIST, Ulsan,Korea

Diagonal reinforced coupling (DRC) beams can provide excellent strength, stiffness and energy dissipation capacities.

However, fabricating DRC beams at construction sites is difficult due to reinforcement congestion and interference

among the reinforcements due to the complex arrangement required by current design provisions. The objective of

this study is to simplify the reinforcement details of DRC beams by reducing the transverse reinforcement around the

beam perimeter that is required for the confinement of DRC beams. This is achieved by using high-performance

fiber-reinforced cement composites (HPFRCC) for DRC beams. Experiments are conducted using six specimens under

reversed cyclic loads to evaluate the hysteretic behaviours of the HPFRCC DRC beams. The test results show that the

use of HPFRCC in DRC beams is very effective, providing a confinement effect with transverse reinforcement. HPFRCC

DRC beams with half the transverse reinforcement required by ACI 318-11 provide almost identical energy dissipation

capacities as concrete DRC beams detailed according to ACI 318-11.

NotationAct cross-sectional area of coupling beamAvd area of reinforcement in each group of diagonal barsbw beam web widthdb nominal diameter of barF forceFmax maximum forceFmin minimum forcefc′ compressive strength of concreteh height of beamk1, k2 first and second cycle stiffnessesLn length of beamVf volumetric ratio of fibresVu maximum shear force obtained from hysteretic curveΔ driftΔmax maximum driftΔmin minimum driftθ drift ratio obtained from hysteretic curveθf drift ratio at failure obtained from hysteretic curveθu maximum drift ratio obtained from hysteretic curveθy yield drift ratio obtained from hysteretic curve

IntroductionShear walls are commonly used as structural walls to resistlateral forces such as winds and earthquakes. Two shear wallscan be coupled by coupling beams, leading to a more efficient

and cost-effective structural system than shear walls withoutcoupling beams (Lee and Kim, 2013). During earthquakes,coupling beams may experience repeated large shear defor-mations. If coupling beams in a coupled wall system avoidbrittle failure, most of the energy caused by an earthquake canbe dissipated by the coupling beams. Therefore, the seismicperformance of coupled shear wall systems strongly dependson the energy dissipation capacity of the coupling beams(Taranath, 2010).

Paulay and Binney (1974) developed a coupling beam withdiagonal reinforcement. Previous experimental research studies(Barney et al., 1980; Paulay and Binney, 1974; Tassios et al.,1996) reported that diagonal reinforced coupling (DRC) con-crete beams provided energy dissipation capacities significantlylarger than conventionally reinforced coupling beams, whilethey retained their strength and stiffness during cyclic loadingwith large displacement amplitudes.

ACI 318-11 (ACI, 2011) section 21·9·6 provides two confine-ment options for DRC beams. For the first option, each diag-onal element consists of a cage of longitudinal and transversereinforcement (Figure 1(a)). At least four reinforcements arerequired for each diagonal element. A simpler transversereinforcement was introduced in ACI 318-11 (ACI, 2011)section 21·9·7·4 (d). As seen in Figure 1(b), transversereinforcement for the second confinement option is only

1287

Magazine of Concrete ResearchVolume 67 Issue 24

Behaviour of fibre-reinforced beams withdiagonal reinforcementHan, Lee, Kwon, Lee and Shin

Magazine of Concrete Research, 2015, 67(24), 1287–1300http://dx.doi.org/10.1680/macr.14.00194Paper 1400194Received 26/06/2014; revised 19/05/2015; accepted 03/06/2015Published online ahead of print 22/07/2015

ICE Publishing: All rights reserved

Downloaded by [ Newcastle University] on [23/09/16]. Copyright © ICE Publishing, all rights reserved.

placed around the beam perimeter rather than around thediagonal elements.

Even though the use of the second confinement option makesthe reinforcement detail simpler, construction difficulties dueto reinforcement congestion and interference still exist. In par-ticular, construction difficulty becomes more serious when theshear stress on coupling beams is large and the beam isslender. Harries et al. (2005) reported that placing reinforce-ment in coupling beams becomes practically impossible as thebeam shear stress approaches 0 � 5 ffiffiffiffiffi

f 0cp

.

Research studies (Fortney et al., 2008; Galano and Vignoli,2005) were conducted to develop simple reinforcement detailsfor coupling beams. Canbolat et al. (2005) developed high-performance cementitious composite (HPFRCC) couplingbeams to reduce reinforcement in coupling beams. Kuang andBaczkowski (2009) conducted experimental tests of large-scale,steel-fibre-reinforced concrete (SFRC) coupling beams. Theydemonstrated that HPFRCC coupling beams providedsuperior damage tolerance and stiffness retention capacities. Itwas reported that steel fibre in concrete can significantlyincrease the shear strength of structural concrete (Casanovaet al., 1994; Lim et al., 1987). Many studies were conducted toinvestigate the effect of the fibres on the mechanical behaviourof concrete (Aslani and Nejadi, 2013; Tadepalli et al., 2014;Yan et al., 2013). To evaluate the cyclic performance of acoupled wall system containing HPFRCC coupling beams,Lequesne (2011) tested a four-storey coupled wall specimenwith HPFRCC coupling beams. However, to date, no researchhas been conducted investigating the confinement effect ofHPFRCC in coupling beams detailed according to ACI 318-11,section 21·9·7·4 (ACI, 2011).

In this study, experiments were conducted on DRC beamsdetailed according to the second confinement option specifiedin ACI 318-11, section 21·9·7·4(d). Six DRC beam specimens

were constructed with beam aspect ratios (Ln/h) of 2·0 and 3·5,and they were subjected to reversed cyclic loads, where Ln

is the beam length and h is the overall height of the beam.Naish et al. (2009) reported that residential and commercialbuildings have slender coupling beams with large aspect ratios(Ln/h) ranging from 2·4 to 3·33. Among the six specimens,two DRC concrete specimens satisfying the requirement ofthe reinforcement details specified in ACI 318-11, section21·9·7·4(d) were used as control specimens, and four HPFRCCDRC specimens were fabricated – of which two had half thetransverse reinforcement used in control specimens and twohad no transverse reinforcement. Although the contributionof fibres could be directly measured by comparing the testresults of DRC specimens with and without fibres, which hadhalf the transverse reinforcement used in control specimens,the DRC specimens without fibre were not made because offunding and time limitations. From the experimental results,the hysteretic behaviour of the HPFRCC DRC beams wasevaluated.

Experimental programme

Test specimens and test set-upExperiments were conducted using six half-scale diagonalreinforced coupling (DRC) beam specimens subjected toreversed cyclic loads. The main test variables were the appli-cation of HPFRCC, the amount of lateral reinforcementaround the beam perimeter, and the beam aspect ratios (2·0and 3·5).

Among the six specimens, two were control concrete DRCspecimens (RC-2·0 and RC-3·5) without fibres, with aspectratios of 2·0 and 3·5, respectively, which satisfy the secondconfinement option specified in ACI 318, section 21·9·7·4(Figure 1(b)). The FRC-0–2·0 and FRC-0–3·5 HPFRCC DRCbeam specimens had the same diagonal reinforcement as thecontrol specimens, but they did not have any lateral

Avd Avd

bw

≥ bw/2

α α

h

ln ln

A

(a) (b)

A B

B

Section A–A

bw

Section B–B

21.9.7.4(c) 21.9.7.4(d)≤ 350 mm

21.9.7.4(d)≤ 200 mm≤ min(150 mm, 6db)

21.9.7.4(c)≤ 350 mm

21.9.7.4(d)≤ 200 mm

Figure 1. Two confinement options for DRC beams specified inACI 318-11: (a) first confinement option; (b) second confinementoption

1288




reinforcement (no confinement reinforcement) around thebeam perimeter and they were made using HPFRCC insteadof normal concrete. From the test results of these specimens,the contribution of HPFRCC on the DRC beams could bedemonstrated. The FRC-0·5–2·0 and FRC-0·5–3·5 specimensare HPFRCC DRC beams, which had the same diagonalreinforcement as the control specimens with half of the lateralreinforcement used in the control specimens. It is noted thatthe purpose of this study was to observe the contribution offibres to the cyclic performance of DRC beams. To estimatethe amount of the contribution by the fibres accurately, morespecimens should be made with a wide range of test variables.Polyvinyl acetate (PVA) fibres at volume fraction (Vf ) of 2%were used for the HPFRCC DRC beam specimens. Thematerial mix and test results for HPFRCC will be discussed ina later section. The amount of diagonal reinforcement wasdetermined to make the maximum shear stress of the beamequal to 0 � 5 ffiffiffiffiffi

f 0cp

(MPa). Table 1 summarises the dimensionsand reinforcement details of the specimens. Figure 2 shows thereinforcement arrangement of the DRC specimens.

Quality control for members using HPFRCC at constructionsites is more difficult than for concrete members. Thus,precast DRC beam specimens were made and tested. Shearkeys were provided at the interface between the beam and stub.Concrete with a compressive strength of 60MPa was used toconstruct the stubs and sufficient reinforcement was placedin the stubs to avoid failure before the DRC beam specimensfailed.

Figure 3 shows the test set-up. A specimen was placed verti-cally and a loading frame was installed. The stubs at both endsof the coupling beam specimens were fixed to the strong floorand loading frame. Quasi-static reversed cyclic loading wasapplied to the specimen by an actuator through the loadingframe. Two cycles were applied for each drift loading ampli-tude, ranging from 0·25% to 12%, as shown in Figure 3. Toachieve a zero moment (inflection point) at the beam mid-span, the actuator was installed at the left-hand vertical girder(A) to make the line of force meet the mid-span of the beam(Figure 3). The right-hand vertical steel girder (B) was madefor balancing the gravity load against the left-hand verticalgirder (A). Four rollers were installed on two strong columns(C and D) to prevent rotation of the top of the beam speci-men. Two strong columns were anchored to the strong floor.Thus, only horizontal displacement was introduced throughthe test set-up, as shown in Figure 3. Stopper blocks wereplaced at the top and bottom stubs of the beam specimensto prevent slip between the beam, loading frame and strongfloor.

Lateral loads were measured by a load cell installed in theactuator. The lateral displacement was measured by linearvariable differential transformers (LVDTs). As shown inFigure 4, vertical and diagonal LVDTs were used to estimateSp

ecim

enWidth:

mm

Heigh

t:mm

Span

:mm

Aspectratio

:L n/h

Ang

le,α

:de

grees

Diago

nalb

ars

Long

itudina

lbars

Tran

sverse

bars

Diameter:

mm

No.

ofba

rsDiameter:

mm

No.

ofba

rsDiameter:

mm

Spacing:

mm

RC-2·0

250

525

1050

2·0

20·4

22·2

813

1412

·712

0FC

-0–2·0

250

525

1050

2·0

20·4

22·2

8Xa

XX

XFC

-0·5–2·0

250

525

1050

2·0

20·4

22·2

813

1412

·725

0RC

-3·5

250

300

1050

3·5

8·9

25·4

813

1012

·711

0FC

-0–3·5

250

300

1050

3·5

8·9

25·4

8X

XX

XFC

-0·5–3·5

250

300

1050

3·5

8·9

25·4

813

1012

·725

0

a Xde

notesno

reinforcem

ent.

Table

1.Su

mmaryof

testspecim

ens

1289




the deformations associated with flexure and shear forces.Strain gauges were installed at various locations of the diag-onal and transverse reinforcement, as shown in Figure 2.

Material testsTo investigate the material properties of HPFRCC and normalconcrete, compressive and tensile tests were conducted. PVAfibres were used in HPFRCC. The properties of the PVA fibreare summarised in Table 2. The volume ratio (Vf) of the fibresin HPFRCC was 2%. Trial mixes for HPFRCC having a

compressive strength ( fc′) of 40MPa were made and compres-sive strength tests were conducted, from which the best mixwas identified, as summarised in Table 3. Three specimens fornormal concrete and HPFRCC were made and tested. Thediameter and height of the specimens were 100mm and200 mm, respectively. Figure 5(a) shows the stress–strain curvesobtained from the compressive tests. The compressive strengthsof the HPFRCC and concrete specimens exceeded 40MPa.The HPFRCC specimens failed at 65% larger strains than theconcrete specimens. However, the secant elastic modulus of the

1050 1050

150

250

250

250

250

525

525

250

525

300

300

1050 1050

1050 1050

A A

A A

5050

50

50

45

150150

4 - D22

4 - D25

A' A'

30

A A

A' A'

A' A'

A–A'

250

300 50 30

A–A'

A–A'

Normalconcrete

Normalconcrete

HPFRCCfibre 2%

HPFRCCfibre 2%

HPFRCCfibre 2%

HPFRCCfibre 2%

(a) (d)

(e)(b)

(c) (f)

25

4 - D22(diagonal)

4 - D25(diagonal)

D13@120D13@110

150

20·44º 8·89º

D13@250D13@250

Strain gauge, unit: mm

Figure 2. Reinforcement details and strain gauge layout for testspecimens: (a) RC-2·0; (b) FC-0–2·0; (c) FC-0·5–2·0; (d) RC-3·5;(e) FC-0–3·5; (f) FC-0·5–3·5

1290




HPFRCC specimens was 40% less than that of the concretespecimens.

To evaluate the tensile performance of HPFRCC, a directtensile test was conducted using three dog-bone type

specimens, which had sectional dimensions of 25 mm�50mmand a gauge length of 200mm, as shown in Figure 5(b). Thetest results are summarised in Table 4. Figure 5(b) shows thestress–strain curve obtained from the tests. The HPFRCCspecimens behaved in a very ductile manner prior to failure.

14B

DC

A

Actuator

Stub

Strong floor

Anchored tothe floor

Couplingbeam

Reac

tion

wal

l Roller

12108642

–2–4–6–8

–10–12–14

0 5 10 15 20 25 30Cycles

Drif

t ra

tio, θ

: %

35

0

Figure 3. Test set-up and loading history

BottomBottom

(a) (b)

B1 B1

T2

L8

L12

L4L2L6L8

L4L2

L6L5

L1 L3

L7

L5

L1 L3

D1

D2

D3

D4D2

D1

L11

L7

L10

L9

T2

T1 T1

Ln/h = 2·0Ln/h = 2·0

TopTop

Figure 4. LVDT locations in specimen

1291




Multiple cracks were detected on the specimen surface due tothe bridging effect of the fibres. In the final stage of loading,the width of one particular crack of the specimen increaseddue to the loss of the bridging effect of the fibres and loss ofits tensile strength. The maximum strain was 2·5%, and strain

hardening was observed, which is an advantageous property ofHPFRCC (Naaman and Reinhardt, 1996).

In the coupling beam specimens, reinforcement with diametersof 13 mm (D13), 22 mm (D22) and 25mm (D25) was used.The mechanical properties obtained from the tensile tests forreinforcement are summarised in Table 5.

Analysis of the test results

Hysteretic curvesFigure 6 shows the hysteretic curves obtained from the test,relating shear force and drift ratio. The abscissa of the graph isthe drift ratio (θ), which was calculated as the lateral drift ofthe coupling beam divided by the beam span length, and theordinate is the shear force normalised by

ffiffiffiffiffif 0c

pAct, where Act is

the cross-sectional area of the coupling beam. In Table 6, theimportant test results are summarised, including the yield driftratio (θy), maximum shear force (Vu), maximum drift ratio(θu), and drift ratio at failure (θf) obtained from the hystereticcurves. The yield and maximum drift ratios were determinedaccording to the method used by Pan and Moehle (1989). Themaximum drift ratio, θu, is defined as the drift ratio when theshear strength decreases by 20%.

Tensilestrength:MPa

Elasticmodulus:

GPaDiameter:

mmLength:mm

Volumefraction,Vf: %

1600 25 0·039 12 2·0

Table 2. PVA fibre properties

CementFlyash

Silicafume Water

Filler:Calciumcarbonate

Super-plasticiser

489 374·9 32·6 366·8 684·6 3·3

Table 3. HPFRCC mixture proportion (kg/m3)

f 'c = 44 MPa

εcu = 0·23%

50Concrete

f 'c = 41 MPa

εcu = 0·46%

5

4

3

2

1

0 0 0·5 1·5 2·51·0 2·0 3·0

HPFRCC

40

30

Com

pres

sive

str

ess:

MPa

Tens

ile s

tree

s: M

Pa

20

10

0 0 0·1

(a) (b)

0·2 0·3Compressive strain: % Tensile strain: %

0·4 0·5 0·6

Figure 5. Result of material test: (a) compression test of concreteand HPFRCC; (b) direct tensile test of HPFRCC

MaterialsCompressive strength,

fc′: MPaMaximum compressive

strain, εcu:%Direct tensilestress: MPa

Maximum tensilestrain:%

Concrete 44 0·23 — —

HPFRCC 41 0·46 4·3 2·5

Table 4. Compressive strength of concrete and HPFRCC

1292




The control concrete DRC specimens RC-2·0 and RC-3·5 withaspect ratios of 2·0 and 3·5, respectively, detailed according tothe second confinement option for DRC concrete beams speci-fied in ACI 318-11 (ACI, 2011), showed stable hysteretic behav-iour (Figures 6(a) and 6(d)). The strength and stiffness of thesetwo specimens did not deteriorate until the drift ratios reached5% and 7%, respectively. Their drift ratios, θu and θf, were5·2% and 7·0% (RC-2·0), and 9·8% and 10·0% (RC-3·5),respectively.

Figures 6(b) and 6(e) show the hysteretic curves of the FC-0–2·0 and FC-0–3·5 HPFRCC DRC beam specimens with aspectratios of 2·0 and 3·5, respectively. Note that these specimenshad the same amount of diagonal reinforcement as the controlspecimens, but did not have lateral reinforcement (Figures 2(b)and 2(e)). They showed stable hysteretic behaviour before a

sudden strength drop occurred at a drift ratio of 4%. The driftratios, θu and θf, were 4·0% and 5·0% (FC-0–2·0), and 4·1%and 5·0% (FC-0–3·5), respectively. For these specimens, θuand θf did not vary with respect to aspect ratio. Even thoughthese specimens failed earlier than the corresponding controlspecimens, HPFRCC in the FC-0–2·0 and FC-0–3·5 specimensprovided a confinement effect until the drift ratio reached4·0%. However, it is noted that the load capacities of fibre-only beams were considerably lower than those of reinforcedconcrete DRC beams with shear reinforcement. For example,the load capacity of RC-2·0 was 1087 kN, whereas that ofFC-0–2·0 was 775 kN. This indicates that the whole transversereinforcement in DRC beams could not be replaced solely byfibres.

The FC-0·5–2·0 and FC-0·5–2·0 HPFRCC DRC specimenshaving half the lateral reinforcement used in the control speci-mens had almost identical hysteretic behaviour to the controlspecimens, as shown in Figures 6(c) and 6(f). They demon-strated hysteretic behaviour as stable as the control specimens.Their drift ratios, θu and θf, were 5·9% and 7·0% (FC-0·5–2·0),and 9·9% and 10·0% (FC-0·5–3·5), respectively. The driftratios, θu, of these specimens were slightly higher than the cor-responding control specimens, which can be attributed to thecontribution of the fibres. Thus, DRC beams with half thetransverse reinforcement and fibres had almost identical

Re-barBar diameter:

mmYield stress, fy:

MPaTensile strength,

fst: MPa

D13 12·7 506 620D22 22·2 438 587D25 25·4 442 607

Table 5. Mechanical properties of reinforcement

Vu = 1087 kNVy = 1004 kN 0·8 Vu

0·8 Vu

0·8 Vu

0·8 Vu

Vf = 606 kN

Vu = 775 kNVy = 739 kN

Vf = 468 kN

Vf = 432 kN Vf = 401 kN

Vy = 1086 kN

Vy = 743 kN

Vu = 1117 kN

Vu = 909 kN

θy = 2·0% θy = 1·4%

θf = 7·0% θf = 5·0%

θy = 2·0% θy = 1·4%θu = 6·2% θu = 4·7%

θu = 5·2% θu= 4·0%θf = 7·0%

Vu = 507 kNVy = 437 kN

0·8Vu

0·8 Vu

Vf = 421 kN

Vf = 348 kN

Vy = 469 kNVu = 504 kN

θy = 2·0%

θy = 2·0%θ u

= 9·8%

θ u =

10·1

%

θ u =

9·9%

θ f =

10·0

%

θf = 5·0%

0·8 Vu

0·8 Vu

Vu = 437 kNVy = 430 kN

Vf = 207 kN

Vf = 300 kN

Vy = 441 kNVu = 452 kN

θy = 2·0%

θf = 5·0%

θy = 2·0%θu= 5·0%

θu = 4·1%θf = 5·0%

0·8 Vu

Vu = 484 kNVy = 466 kN

Vf = 385 kN

Vf = 340 kN

Vy = 531 kNVu = 562 kN

θy = 2·5%

θy = 2·3% θ f = 1

0·0%

θ u =

9·9%

θu = 10·0%

0·8 Vu

0·8Vu

0·8Vu

Vu = 1073 kNVy = 987 kN

Vf = 751 kN

Vf = 746 kN

Vy = 1078 kNVu = 1163 kN

θy = 2·0%

θf = 7·0%

θy = 2·0%

θu = 5·9%

θu = 6·1%θf = 7·1%

1200(a) (b) (c)

(d) (e) (f)

1000

800

600

400

200

–200

Shea

r fo

rce:

kN

Shea

r fo

rce:

kN

–400

–600

–800

600

500

400

300

200

100

–100

–200

–300

–400

–500

–600–10 –8 –6 –4 –2 0

Drift ratio: % Drift ratio: % Drift ratio: %2 4 6 8 10 –10 –8 –6 –4 –2 0 2 4 6 8 10 –10 –8 –6 –4 –2 0 2 4 6 8 10

–1·2

–1·0

–0·8

–0·6

–0·4

Nor

mal

ised

she

ar s

tres

s, V

u /

f c A

cw

–0·2

0

0·2

0·4

0·6

0·8

1·0

1·2–1·4

–1·2

–1·0

–0·8

–0·6

–0·4

–0·2

0

0·2

0·4

0·6

0·8

1·0

1·2

1·4

0

–1000

0N

orm

alis

ed s

hear

str

ess,

Vu /

f c A

cw

Figure 6. Hysteretic curves: : (a) RC-2·0; (b) FC-0–2·0; (c) FC-0·5–2·0; (d) RC-3·5; (e) FC-0–3·5; (f) FC-0·5–3·5

1293




strength and drift capacity to reinforced concrete DRC beamsdesigned according to ACI 318-11 (Figure 1(b)).

Figures 7(a) and 7(b) show the Vu and θu values of the speci-mens. HPFRCC DRC beam specimens with half the lateralreinforcement used in the control specimens provided Vu andθu values as large as those of the corresponding control

specimens. The contribution of fibres in DRC beams could beevaluated more accurately by comparing the test results offibre-reinforced specimens FC-0·5–2·0 and FC-0·5–3·5 withhalf the transverse reinforcement used in control specimens,and the specimens with half the transverse reinforcement andno fibres. However, specimens having half the transversereinforcement and no fibres were not made in this experimentalprogramme, owing to the funding limit as mentioned earlier.Nevertheless, the contribution of fibres was clearly observed inHPFRCC specimens FC-0–2·0 and FC-0–3·5, which did nothave transverse reinforcement. Even though they did notprovide Vu and θu values as large as those of the correspondingcontrol specimens, their drift capacities were substantial, andwere larger than 4%. With an increase in the aspect ratio, Vu

decreased and θu increased except for the HPFRCC specimenwithout lateral reinforcement.

Cracking pattern and failureFigure 8 shows the crack distributions of the specimens withan aspect ratio of 2·0 at a drift ratio (θ) of 2·0% and 5%, andat failure. In the control concrete DRC specimen, RC-2·0, thehorizontal crack was first detected near the interface betweenthe beam and stub at a drift ratio of 0·25%. With an increasein the loading amplitude, horizontal cracks near the interfacewere transformed into diagonal cracks. At a drift ratio of 1%,

RC-2·00

200

400

504437 484

0

2·0

4·0

6·0

Drif

t ra

tio, θ

u: %

Drif

t ra

tio, θ

u: %

Shea

r fo

rce,

Vu:

kn

Shea

r fo

rce,

Vu:

kn

8·0

9·8

4·1

9·910·0

12·0

600

800

1000

1087

775

107312·0

10·0

8·0

6·0

4·0

5·2

4·0

5·9

2·0

0

1200

0

200

400

600

800

1000

1200

FC-0–2·0

(a) (b)

(c) (d)

FC-0·5–2·0 RC-2·0 FC-0–2·0 FC-0·5–2·0

RC-0–3·5 FC-0–3·5 FC-0·5–3·5RC-3·5 FC-0–3·5 FC-0·5–3·5

Figure 7. Comparison of maximum strengths and ultimate driftsof specimens: (a) maximum shear strength (Ln/h = 2·0); (b) ultimatedrift ratio (Ln/h = 2·0); (c) maximum shear strength (Ln/h = 3·5);(d) ultimate drift ratio (Ln/h = 3·5)

Specimen Vy: kN θy: % Vu: kN θu: % θf: %

RC-2·0 (+) 1004 2·0 1087 6·2 7·0(−) 1086 2·0 1117 5·2 7·0

FC-0–2·0 (+) 739 1·4 775 4·7 5·0(−) 743 1·4 909 4·0 5·0

FC-0·5–2·0 (+) 981 2·0 1073 5·9 7·1(−) 1078 2·0 1163 6·1 7·0

RC-3·5 (+) 437 2·0 507 9·8 10·1(−) 469 2·0 504 9·9 10·0

FC-0–3·5 (+) 430 2·0 437 5·0 5·0(−) 441 1·9 452 4·1 5·0

FC-0·5–3·5 (+) 466 2·3 484 9·9 10·0(−) 531 2·5 562 10·0 10·1

Table 6. Summary of experimental test results

1294




many diagonal cracks were formed over the entire beamsurface. When the drift ratios were 2·0% and 5·0%, the diag-onal crack widths were as large as 1·5 mm and 4·8 mm,respectively. The diagonal reinforcement yielded at a drift ratio

of 2%. At a drift ratio of 7·0%, the cover concrete of the speci-men at the beam top fell off (Figure 8(c)) and diagonal barswere fractured. Considering that the specimen did not lose itsstrength until the diagonal bars fractured, the second

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 8. Crack progression and failures of specimens havingLn/h=2·0: (a) 2·0% drift; (b) 5·0% drift; (c) at failure (7·0%);(d) 2·0% drift; (e) 4·0% drift; (f) at failure (5·0%); (g) 2·0% drift;(h) 5·0% drift; (i) at failure (7·0%)

1295




confinement option specified in ACI 318-11 provided a satis-factory confinement effect for the concrete DRC beams.

HPFRCC DRC specimen FC-0·5–2·0 with half the lateralreinforcement used in the control specimen showed similar

crack patterns at the initial loading stages. As the loadingamplitude increased, more cracks were formed and distributedon the beam surface (Figures 9(g)–9(i)) compared to thecontrol specimen. At drift ratios of 2·0% and 5·0%, the largestcrack widths were 0·5 mm and 1·4 mm, respectively, which are

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 9. Crack progression and failures of specimens havingLn/h=3·5: (a) 2·0% drift; (b) 5·0% drift; (c) at failure (10%);(d) 2·0% drift; (e) 4·0% drift; (f) at failure (5·0%); (g) 2·0% drift;(h) 5·0% drift; (i) at failure (10%)

1296




much smaller than those of the control specimen, and can beattributed to the bridging effect of the fibres. At a drift ratio of7%, diagonal bars were fractured but no concrete cover fell off,unlike in the control specimen.

In the FC-0–2·0 HPFRCC specimen without lateral reinforce-ment, an initial horizontal crack was detected near the inter-face between the beam and stub at a drift ratio of 0·25%, anddiagonal cracks were detected near the beam mid-span at adrift ratio of 0·5%. At a drift ratio of 1·5%, diagonal crackspassed through the entire beam surface. At drift ratios of 2·0%and 4·0%, the crack widths were as large as 3·4 mm and15mm (Figures 8(d) and 8(e)), respectively. Finally, the speci-men lost strength at a drift ratio of 5·0% (Figure 8(f)). Nofracture occurred in the diagonal bars, but yielding occurred inthe bars. This indicates that the application of HPFRCC forDRC beams without lateral reinforcement provides someamount of a confinement effect, but it is not as large as thatprovided by the RC-2·0 and FC-0·5–2·0 specimens. Thus,HPFRCC alone cannot replace the entire amount of lateralreinforcement for DRC beams, even though it provides a sig-nificant amount of confinement.

The crack patterns of the specimens with an aspect ratio of 3·5were similar to those of the specimens with an aspect ratio of2·0 (Figure 9). However, more flexural cracks were detected onthe beams with an aspect ratio of 3·5. For the RC-3·5 controlspecimen, at a drift ratio of 10% the cover concrete near thebeam ends severely fell off (Figure 9(c)), while the diagonalbars and lateral reinforcement were simultaneously fractured.Subsequently, the specimen lost its strength. The FC-0·5–3·5

HPFRCC specimen also failed due to fracture of the diagonalbars at a drift ratio of 10% (Figure 9(i)) and more cracks weredetected in it than in the control specimen. The FC-0–3·5HPFRCC specimen failed due to large cracks passing throughthe entire beam at a drift ratio of 5% (Figure 9(f)), while nofracture was detected on the diagonal bars.

In summary, fibres in DRC beams made some contribution tothe confinement, which was observed from the test results offibre-only DRC beams. Even though specimens FC-0–2·0 andFC-0–3·5 were fibre-only DRC beams, they had drift capacitiesgreater than 4%, a drift limit for special moment framemembers. Despite the large compression force in the fibre-onlyDRC beams induced by diagonal reinforcement during thetest, the beams did not split in early loading stages. At thestage of failure, the diagonal reinforcement in the beamsexperienced yielding, but no fracture. This indicated that fibresin the DRC beams made some contribution to the confine-ment, but the contribution of fibres was not as excellent as thatof transverse reinforcement in the control DRC beams.

Cyclic strength, stiffness deterioration and energydissipation capacitiesTo estimate the cyclic strength deterioration of all specimens,envelope curves were extracted from the hysteretic curvesshown in Figure 6, as plotted in Figure 10. Irrespective of theaspect ratio, the control specimens and HPFRCC specimenswith half the lateral reinforcement required for the controlspecimens had similar cyclic strengths and stiffness deterio-ration characteristics. After their maximum strength, the

Ln/h = 2·0 Ln/h = 3·51200

1000

800

600

400

200

–200

–400

–600

–800

–1000

–1200

Drift ratio: %

(a) (b)

Shea

r fo

rce:

kN

Drift ratio: %

–10 –8 –6 –4 –2 0 2 4 6 8 10 –10 –8 –6 –4 –2 00

100

–100

–200

–300

–400

–500

–600

200

300

400

500

600

2 4 6

RC-3·5FC-0–3·5FC-0·5–3·5

RC-2·0FC-0–2·0FC-0·5–2·0

8 100

Figure 10. Envelope curves: (a) Ln/h = 2·0; (b) Ln/h = 3·5

1297




specimens having an aspect ratio of 2 experienced a moresevere cyclic strength drop than the specimens with an aspectratio of 3·5 (Figures 10(a) and 10(b)). The HPFRCC speci-mens without lateral reinforcement were not as strong as thecorresponding control specimens. The strength drop in thesespecimens started at an earlier loading stage than in thecontrol specimens. Even though fibre-only DRC specimenshad lower load capacity than control specimens with transversereinforcement, the load capacity of the fibre-only beamexceeded the capacity calculated using the strength equation

specified in ACI 318-11 (ACI, 2011). The load capacity ofFC-0–2·0 was 775 kN, whereas the strength calculated usingthe equation in ACI 318-11 (ACI, 2011) was 634 kN. For speci-men FC-0–3·5, tested and calculated strengths were 437 kNand 382 kN, respectively.

The cyclic stiffness deterioration of all specimens is plottedin Figure 11. The stiffness was determined by connecting thepeak positive and negative displacements, as shown inFigure 11(a). Similarly to the strength deterioration results, the

00

0·1

0·2

0·3

0·4

0·5

0·6

0·7

0·8

0·9

1·0

Nor

mal

ised

stif

fnes

s

1 2 3 4 5 6 7 0 1 2 3 4 5 6Drift ratio: %Drift ratio: %

(a) (b)

7 8 9 10 11 12

Ln/h = 2·0 Ln/h = 3·5

RC-2·0FC-0–2·0FC-0·5–2·0

F

k1 : First cycle stiffness

k2 : Second cycle stiffness

RC-3·5FC-0–3·5FC-0·5–3·5

k1

k2

Figure 11. Normalised peak-to-peak stiffness: (a) Ln/h = 2·0;(b) Ln/h = 3·5

00·0

1·0

2·0

3·0

4·0

5·0

6·0

7·0

Energy dissipationarea per cycle

F

Fmax

Fmin

8·0

9·0

Ener

gy: ×

105

kN m

m

1 2 3 4 5 6 7 0 1 2 3 4 5 6Drift ratio: %Drift ratio: %

(a) (b)

7 8 9 10 11 12 13

Ln/h = 2·0 Ln/h = 3·5

RC-2·0FC-0–2·0FC-0·5–2·0

F

RC-3·5FC-0–3·5FC-0·5–3·5

∆min∆max

∆

Figure 12. Cumulative energy dissipation: (a) Ln/h = 2·0;(b) Ln/h = 3·5

1298




HPFRCC specimens with half the lateral reinforcement usedin the control specimens had almost identical cyclic stiffnessdeterioration characteristics to the corresponding control speci-mens, which may be attributed to the stiffness retentioneffect provided by the fibres. The HPFRCC specimens withoutlateral reinforcement experienced more rapid cyclic stiffnessdeterioration than the corresponding control specimens.

Figure 12 shows the cumulative dissipated energy at each driftratio. A similar observation to the cyclic stiffness and strengthdeterioration results was made. The HPFRCC specimens withhalf the lateral reinforcement had almost identical energy dissi-pation capacities to the corresponding control specimens,whereas the HPFRCC specimens without lateral reinforcementhad much lower energy dissipation capacities than the otherspecimens.

Summary and conclusionsIn this study, an evaluation was made of the cyclic perform-ance of HPFRCC DRC beams with less transverse reinforce-ment than required by the second option of confinementreinforcement in ACI 318-11 (ACI, 2011). The experimentswere conducted using six specimens. The conclusions of thetest results are as follows.

(a) The concrete DRC beam specimens detailed accordingto the second confinement option in ACI 318-11 (ACI,2011) provided excellent cyclic performance. The speci-mens with aspect ratios of 2·0 and 3·5 failed at large driftratios of 7% and 10%, respectively.

(b) The HPFRCC DRC beam specimens without lateralreinforcement had a drift capacity of 4% irrespective ofthe beam aspect ratio. This is attributed to the confine-ment effect of HPFRCC. However, HPFRCC alonewithout lateral reinforcement cannot provide as muchof the confinement effect as provided by the controlspecimens. The specimens lost their strength prior tofracture of the diagonal bars. Thus, HPFRCC aloneprovided a significant amount of confinement effect,but it cannot replace the entire lateral reinforcement forDRC beams.

(c) The HPFRCC specimens with half the lateral reinforce-ment used in the control specimens provided almost iden-tical drifts, strengths and energy dissipation capacities asthe control specimens. These specimens lost their strengthwhen the diagonal bars fractured as observed in thecontrol specimens. The cyclic deterioration characteristicsof their strength and stiffness, as well as energy dissipa-tion capacities, were also similar to those of the controlspecimens. Thus, the use of HPFRCC in DRC beamsmay significantly reduce the amount of lateral reinforce-ment without a loss of cyclic performance. To draw amore complete conclusion, more tests need to beconducted.

AcknowledgementsThe authors would like to acknowledge the financial supportprovided by the National Research Foundation of Korea (no.2014R1A2A1A11049488).

REFERENCES

ACI (American Concrete Institute) (2011) ACI 318-11: Buildingcode requirements for structural concrete and commentary.ACI, Farmington Hills, MI, USA.

Aslani F and Nejadi S (2013) Mechanical characteristics of self-compacting concrete with and without fibres. Magazine ofConcrete Research 65(10): 608–622, http://dx.doi.org/10.1680/macr.12.00153.

Barney GB, Shiu KN, Rabbat BG et al. (1980) Behavior ofCoupling Beams Under Load Reversals. Portland CementAssociation, Skokie, IL, USA, RD068.01B.

Canbolat BA, Parra-Montesinos GJ and Wight JK (2005)Experimental study on seismic behavior of high-performance fiber-reinforced cement composite couplingbeams. ACI Structural Journal 102(1): 159–166.

Casanova P, Rossi P and Schaller I (1994) Can steel fibers replacetransverse reinforcements in reinforced concrete beams.ACI Materials Journal 94(5): 341–354.

Fortney PJ, Rassati GA and Sharooz BM (2008) Investigation oneffect of transverse reinforcement on performance ofdiagonally reinforced coupling beams. ACI StructuralJournal 105(6): 781–788.

Galano L and Vignoli A (2005) Seismic behavior of shortcoupling beams with different reinforcement layouts. ACIStructural Journal 97(6): 876–885.

Harries KA, Fortney PJ, Shahrooz BM and Brienen PJ (2005)Practical design of diagonally reinforced concrete couplingbeams – critical review of ACI 318 requirements. ACIStructural Journal 102(6): 876–882.

Kuang JS and Baczkowski BJ (2009) Steel-fibre-reinforcedconcrete coupling beams subjected to monotonic loading.Magazine of Concrete Research 61(1): 35–41, http://dx.doi.org/10.1680/macr.2008.00019.

Lee J and Kim J (2013) Seismic performance evaluation ofstaggered wall structures using FEMA P695 procedure.Magazine of Concrete Research 65(17): 1023–1033, http://dx.doi.org/10.1680/macr.12.00237.

Lequesne R (2011) Behavior and Design of High-PerformanceFiber-Reinforced Concrete Coupling Beams and Couple-Wall Systems. PhD thesis, Department of CivilEngineering, University of Michigan at Ann Arbor, AnnArbor, MI, USA.

Lim TY, Paramasivam P and Lee SL (1987) Shear and momentcapacity of reinforced steel-fibre-concrete beams. Magazineof Concrete Research 39(140): 148–160, http://dx.doi.org/10.1680/macr.1987.39.140.148.

Naaman AE and Reinhardt HW (1996) Characterization of highperformance fiber reinforced cement composites –HPFRCC. High performance fiber reinforced cement

1299




http://dx.doi.org/10.1680/macr.12.00153









http://dx.doi.org/10.1680/macr.1987.39.140.148



composite 2 (HPFRCC 2). Proceedings of the2nd International RILEM Workshop. E&FN Spon,London, UK, pp. 1–23.

Naish D, Wallace JW, Fry JA and Klemencic R (2009) ReinforcedConcrete Link Beams: Alternative Details for ImprovedConstruction. Structural and Geotechnical EngineeringLaboratory, University of California at Los Angeles,Los Angeles, CA, USA, UCLA-SGEL Report 2009-06.

Pan A and Moehle JP (1989) Lateral displacement ductility ofreinforced concrete flat plates. ACI Structural Journal86(3): 250–258.

Paulay T and Binney JR (1974) Diagonally reinforced concretebeams of shear walls. In ACI Special Publication 42.American Concrete Institute, Farmington Hills, MI, USA,pp. 579–598.

Tadepalli PR, Dhonde HB, Mo YL and Hsu TTC (2014) Shearbehaviour of prestressed steel fibre concrete box-beams.Magazine of Concrete Research 66(2): 90–105, http://dx.doi.org/10.1680/macr.13.00101.

Taranath BS (2010) Reinforced Concrete Design of TallBuildings. CRC Press, Boca Raton, FL, USA.

Tassios TP, Moretti M and Bezas A (1996) On thebehavior and ductility of reinforced concrete couplingbeams of shear walls. ACI Structural Journal 93(6):711–720.

Yan L, Xing Y, Zhang J and Li J (2013) High-temperaturemechanical properties and microscopic analysis ofnano-silica steel fibre RC. Magazine of Concrete Research65(24): 1472–1479, http://dx.doi.org/10.1680/macr.13.00143.

WHAT DO YOU THINK?

To discuss this paper, please submit up to 500 words tothe editor at [email protected]. Your contribution willbe forwarded to the author(s) for a reply and, if con-sidered appropriate by the editorial panel, will be pub-lished as a discussion in a future issue of the journal.

1300










Documents

Behaviour of fibre-reinforced beams with diagonal ...earthquake.hanyang.ac.kr/journal/2015/Behaviour of fibre reinforced... · u maximum shear force obtained from hysteretic curve