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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
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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
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
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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
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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
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
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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
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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
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%,
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%)
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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%)
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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
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
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
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