Research ArticleFlexural Strength Evaluation of Reinforced Concrete Memberswith Ultra High Performance Concrete
Baek-Il Bae1 Hyun-Ki Choi2 and Chang-Sik Choi3
1Research Institute of Industrial Science Hanyang University 17 Haengdang-Dong Seongdong-Gu Seoul 04763 Republic of Korea2Department of Fire and Disaster Prevention Engineering Kyungnam University Gyeongsangnam-do 51767 Republic of Korea3Department of Architectural Engineering Hanyang University 17 Haengdang-Dong Seongdong-Gu Seoul 04763 Republic of Korea
Correspondence should be addressed to Hyun-Ki Choi chk7796kyungnamackr
Received 25 September 2015 Revised 5 December 2015 Accepted 7 December 2015
Academic Editor Stefano Sorace
Copyright copy 2016 Baek-Il Bae et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Flexural strength evaluation models for steel fiber reinforced ultra high strength concrete were suggested and evaluated with testresults Suggested flexural strength models were composed of compression stress blocks and tension stress blocks Rectangularstress block triangular stress block and real distribution shape of stress were used on compression side Under tension rectangularstress block distributed to whole area of tension side and partial area of tension side was used The last model for tension side isrealistic stress distribution All these models were verified with test result which was carried out in this study Test was conductedby four-point loading with 2000 kN actuator for slender beam specimen Additional verifications were carried out with previousresearches on flexural strength of steel fiber reinforced concrete or ultra high strength concrete Total of 21 test specimens wereevaluated As a result of comparison for flexural strength of section neutral axis depth at ultimate state models with triangularcompression stress block and strain-softening type tension stress block can be used as exact solution for ultra high performanceconcrete For the conservative and convenient design of section modified rectangular stress block model can be used with strainsoftening type tension stress block
1 Introduction
Usually flexural strength of normal strength concrete mem-bers is designed using rectangular stress block parametersCurrent design codes provide the rectangular stress blockparameters for simplified design methodology Howeverthese stress blocks are determined by tests of reinforcedconcrete columns and they have apparent limitations Rect-angular stress block can be used because the shape of stress-strain relation of concrete is similar to the trapezoid How-ever shape of stress-strain relationship of concrete changedinto triangle as increase of compressive strength of concreteFor this reason rectangular stress block parameters dependon the compressive strength of concrete For example thecurrent ACI code [1] suggests that higher value of com-pressive strength of concrete can be used as 085 times thespecified compressive strength of concrete And the depthof rectangular stress block has the lower bound of 065 at76MPa of compressive strength of concrete Ultimate strain
of concrete is suggested by value of 0003 These values aredetermined from test results of normal strength concreteHowever depending on the compressive strength mechan-ical properties and failure type of concrete are changed
Generally after experiencing peak stress sudden dropof load resistance can be observed Ultra high strengthconcrete also failed with this failure mode Making brittlefailure of ultra high strength concrete matrix more ductileunder compression steel fiber can be included in the matrixInclusion of steel fiber can change the explosive failure of ultrahigh strength concrete and provide higher tensile strengthand deformability So steel fiber is usually used for ultra highstrength concrete matrix
Ultra high performance concrete usually has muchhigher compressive strength and tensile strength than normalstrength concrete generally ranging from 100 to 200MPaShape of stress distribution in compression side of sectionand tensile strength of concrete shall be considered insection design Design guidelines for ultra high performance
Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2016 Article ID 2815247 10 pageshttpdxdoiorg10115520162815247
2 Advances in Materials Science and Engineering
concrete suggested the way to design the section of membersuggested stress-strain relation However stress-strain rela-tion for ultra high performance concrete needs specific testresults not using stress blocks or assumptions Therefore inthis study various types of compression and tension stressblock combinations were evaluated with experimental resultand previous research results for easy and safe design of ultrahigh performance concrete members
2 Review of Current Design Codesfor Flexural Strength of Ultra HighPerformance Concrete
Reinforced concrete members using normal strength con-crete are designed with an assumption that stress distributioncan be shapedwith rectangle and concrete cannot transfer thetensile stress However these assumptions cannot be appliedto flexural strength calculation of ultra high performanceconcrete members Since ultra high performance concretehas much higher compressive strength than normal strengthconcrete and usually reinforcedwith steel fiber shape of stressdistribution in compression side will be changed and tensilestress distribution in tension side should be considered inorder to calculate the flexural strength of section Some ofdesign guidelines for high strength concrete or steel fiberreinforced concrete have different assumptions for flexuralstrength calculationThey can be categorized into two groupsone uses stress block parameters and the other uses specifiedstress-strain relation of concrete
Current design code ACI318 [1] suggests that flexuralstrength of reinforced concrete section can be calculated by
119872119899= 119860119904119891119910(119889 minus
119886
2) (1)
In this equation 119886 depth of rectangular stress blockcan be determined by using stress block parameter 120573
1 For
compressive strength of concrete between 17 and 28MPa 085can be used as the value of 120573
1 1205731shall be decreased linearly
a rate of 005 for each 7MPa of compressive strength ofconcrete above 28MPa of compressive strength of concreteThe smallest value of 120573
1is 065
As can be seen in ACI318 [1] current design code provi-sions did not consider the effect of steel fiber Some of designguidelines suggested the way to calculate flexural strength ofsteel fiber reinforced concrete section ACI 544 committee [2]provides the flexural strength equations by adopting researchresults of Henager and Doherty [3] especially for rectangularsection member
119872119899= 119860119904119891119910(119889 minus
119886
2) + 120590119905119887 (ℎ minus 119890) (
ℎ
2+
119890
2minus
119886
2) (2)
where 119872119899is nominal flexural strength of section 119891
119910is yield
strength of steel rebar 119889 is effective depth of section 119886 isdepth of stress block ℎ is height of section 119890 = (120576
119904(fibers) +
0003)(1198880003) 120576119904is strain in tension side 120576
119904(fiber) = 120590
119891119864119904
119888 is neutral axis depth and tensile strength of steel fiberreinforced concrete can be calculated using
120590119905= 000772
119897119891
119889119891
120588119891119865be (3)
where 119897119891is length of steel fiber 119889
119891is diameter of steel fiber 120588
119891
is percent by volume of steel fiber and 119865be is bond efficiencyfactor
Imam et al [4] suggested the modified ACI 544 [2]model which can be used as steel fiber reinforced concretewith high strength matrix Imam et al investigated the bondstress between steel fiber and matrix They suggested thattensile stress block height coefficient should be changed into002 According to this modification tensile strength can becalculated using
120590119905= 2119865 119865 =
119897119891
119889119891
119881119891120578119891 (4)
where119881119891means volume fraction of steel fiber (= 120588
119891100) and
120578119891is fiber factor (10sim12) Moment capacity of section can be
determined according to ACI 544 [2] (2)Lim et al [5] suggested that stress block parameters
should be reevaluated with change of matrix and steel fiberThey use 120572
1as 090 because steel fiber can provide more
ductility under compression either Tensile strength of steelfiber reinforced concrete can be determined using
120590119905119906
= 1205781015840
01205781119881119891119897119891
120591119906
2119903 (5)
where 1205781015840
0is steel fiber orientation factor 120578
1is length efficiency
factor 120591119906is average ultimate bond stress at the fiber-matrix
interface and 119903 is the ratio of the fiber cross-sectional areato its perimeter Since Lim et al [5] developed their modelwith plasticity approach they use whole area over the neutralaxis as compressive stress block Neglecting cover thicknessand considering tensile stress block in tension side of sectionneutral axis depth 119909 can be calculated using
119909 =
119889120590119905119906
+ 119891119910119887
1205721120590119888119906
+ 120590119905119906
(6)
where 120590119888119906
is compressive strength of concrete 119887 is width ofsection and 119891
119910is yield strength of reinforcement From (6)
internal moment arm can be calculated
ℎ = 119889 minus119909
2 (7)
where 119889 is effective depth of section Using (5) (6) and (7)flexural capacity of section can be calculated by using
119872119906= 119891119910ℎ + 120590119905119906
119887
2(ℎ2
minus1199092
4) (8)
Although stress block approach is easy to use for flexuralstrength calculation it cannot consider the difference ofconcrete with higher strength matrix or other characteristics
Advances in Materials Science and Engineering 3
⟨Strain distribution⟩ ⟨Stress distribution⟩
Compression
Tension
ACI318 ACI544 Lim et al
Figure 1 Previously suggested stress block combination
Flexural strength calculation models for normal strengthconcrete and steel fiber reinforced concrete were illustratedin Figure 1 The main difference between normal strengthconcrete model and steel fiber reinforced concrete model isexistence of tensile stress block Difference among steel fiberreinforced concrete models is the range of tensile stress dis-tribution However they are not exact models because stressdistribution might be changed with compressive strength ofmatrix and tensile stress distribution is more comprehensivethan used in Figure 1
For the exact solution for flexural strength of sectioncomprehensive stress-strain relations are directly applied tocalculate the flexural strength of section The representativemodels considering real stress distribution are provided byRILEM 120590 minus 120576 method [9] EC2 flexural analysis [10] andAFGC-Setra guideline [11] They can provide more accuratevalue than flexural strength model made up of stress blocksHowever they need more comprehensive computation pro-cess and some material test
3 Flexura Strength Calculation Model
According to the material test about ultra high performanceconcrete most of stress-strain relation shapes are triangularunder compression Therefore under compression triangu-lar stress block may be used for the design of ultra highperformance concrete flexural members Previous research[12] suggested rectangular stress block parameters for highstrength and ultra high strength concrete However most ofcode provisions use the rectangular stress block parametersbecause they mainly focused on the use for normal strengthconcrete They consider the shape of stress-strain relationusing various value of 120573
1 depending on compressive strength
of concrete Rectangular stress block slightly overestimatesthe flexural strength of concrete member especially for highreinforcement ratio and compressive strength of concrete Ascan be seen in Section 2 tensile stress block for steel fiberreinforced concrete has been shown in various shape andsize Therefore designing ultra high performance concretemembers stress block parameters should be reorganized
In this study three types of stress block parameterswere considered ACI stress block parameters stress blockparameters from UHPC member design guideline and tri-angular stress block determined by maximum compressive
b
dh
As
e c
120576cu fcu
120576f
120576s
120576tuftb
ft
fy
Section Assumed Assumedstrain distribution stress distribution
Figure 2 Strain and stress distribution of ultra high performanceconcrete section
strength and corresponding strain resulting from materialtests Tensile behavior of steel fiber reinforced concrete wasdivided into strain hardening strain softening and fullyplastic behavior three types In this study tensile stress blockswere composed of these three types of tensile behavior of steelfiber reinforced concrete
Strain and stress distribution of ultra high performanceconcrete section were shown in Figure 2 In this study threetypes of stress blocks were used under compression andtension respectively Total of 9 types of flexural strengthmodels were investigated These models were illustrated inFigure 3 The most important design parameter for flexuralstrength is neutral axis depth Neutral axis depth for 9 typesof flexural strength model was developed as follows
1198881198881
=
119860119904119891119910minus 120574ℎ119891
119905119887
051198911015840119888119887 minus 05 (120578 minus 1) 119891
119905119887 minus 120574120578119891
119905119887
1198881198882
=
119860119904119891119910+ 05 (1 + 120574) 119891
119905119887ℎ
051198911015840119888119887 minus 05 (120578 minus 1) 119891
119905119887 + 05120578 (1 + 120574) 119891
119905119887
1198881198883
=
119860119904119891119910+ 120574119891119905ℎ119887
051198911015840119888119887 + 120574120578119891
119905119887
1198881198884
=
119860119904119891119910+ 120574119891119905119887ℎ
1205721ACI119891
1015840
1198881205731ACI119887 minus 05 (120578 minus 1) 119891
119905119887 + 120574120578119891
119905119887
4 Advances in Materials Science and Engineering
fcu
ftb
ft
fy
(a) Type 1
fcu
ftb
ft
fy
(b) Type 2
fcu
fy
1205741ft
(c) Type 3
ftb
ft
fy
1205731A
CIc
1205721ACIfcu
(d) Type 4
ftb
ft
fy
1205731A
CIc
1205721ACIfcu
(e) Type5
fy
1205741ft
1205731A
CIc
1205721ACIfcu
(f) Type 6
ftb
ft
fy
1205731U
HPC
c1205721UHPCfcu
(g) Type 7
ftb
ft
fy
1205731U
HPC
c
1205721UHPCfcu
(h) Type 8
fy
1205741ft
1205731U
HPC
c
1205721UHPCfcu
(i) Type 9
Figure 3 Stress block models
1198881198885
=
119860119904119891119910+ 05 (1 + 120574) 119891
119905119887ℎ
1205721ACI119891
1015840
1198881205731ACI119887 minus 05 (120578 minus 1) 119891
119905119887 + 05120578 (1 + 120574) 119891
119905119887
1198881198886
=
119860119904119891119910+ 120574119891119905ℎ119887
1205721ACI119891
1015840
1198881205731ACI119887 + 120574120578119891
119905119887
1198881198887
=
119860119904119891119910+ 120574119891119905119887ℎ
1205721UHPC119891
1015840
1198881205731UHPC119887 minus 05 (120578 minus 1) 119891
119905119887 + 120574120578119891
119905119887
1198881198888
=
119860119904119891119910+ 05 (1 + 120574) 119891
119905119887ℎ
1205721UHPC119891
1015840
1198881205731UHPC119887 minus 05 (120578 minus 1) 119891
119905119887 + 05120578 (1 + 120574) 119891
119905119887
1198881198889
=
119860119904119891119910+ 120574119891119905ℎ119887
1205721UHPC119891
1015840
1198881205731UHPC119887 + 120574120578119891
119905119887
(9)
where 1198911015840
119888is compressive strength of concrete 119860
119904is area of
tensile rebar 119891119910is yield strength of steel rebar 119891
119905is ultimate
tensile strength of concrete 120574 is ratio between post crackingtensile strength and ultimate tensile strength 120578 can be definedby 120576119891120576119888119906
+ 1 1205721and 120572
1UHPC are rectangular stress blockparameter for compressive strength of concrete for normalstrength concrete andUHPC respectively 120573
1and 1205731UHPC are
stress block depth parameter for normal strength concreteand UHPC respectively 119887 is width of section and 119889 is
effective depth of section 120576119891for 120578 is strain corresponding
to ultimate tensile strength and 120576119888119906
is ultimate compressivestrain of concrete
The most difficult and controversial part is the determi-nation of tensile strength of fiber reinforced concrete Swamyand Al-Tarsquoan [13] suggested the equation according to thecomposite theory as follows
119891119905= 0970119891
119903(1 minus 119881
119891) + 2119881
119891
119871119891
119863119891
(10)
where 119891119903is modulus of rupture of concrete and other
variables are fiber geometry defined in Section 2Using neutral axis depth defined in (9) considering
shape of stress block nominal flexural strength of ultra highperformance concrete members can be calculated as follows
Case 1 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 119891
119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(11)
Advances in Materials Science and Engineering 5
Table 1 Mix proportions
119908119887
Weight ratio Steel fiber Admixture 119891119888119896
Cement Water Silica fume Sand Filler (Micro Silica)() (kg) (MPa)
017 1 021 024 104 031 2 108 200
Case 2 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 119891
119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 +
ℎ minus 119890
3) + 119860
119904119891119910(119889 minus 119888)
(12)
Case 3 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 120574119891
119905(ℎ minus 119890) (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(13)
Cases 4 7 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 119891119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(14)
Cases 5 8 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 119891119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 +
ℎ minus 119890
2) + 119860
119904119891119910(119889 minus 119888)
(15)
Cases 6 9 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 120574119891119905(ℎ minus 119890) (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(16)
4 Flexural Behavior of Ultra HighPerformance Concrete Members
41 Test Plan In order to verify the applicability of sug-gested models ultra high performance concrete beam wastested Average ultimate compressive strength of standardcylinder was 216MPa Splitting strength of standard cylinderis distributed between 72sim195MPa Mix proportions forultra high performance concrete are summarized in Table 1Mechanical properties of concrete and rebar used in thisstudy were summarized in Tables 2 and 3 respectively
Table 2 Mechanical characteristics of rebar
MaterialsYield
strength(MPa)
Yieldstrain(120576119910)
Tensilestrength(MPa)
Poissonrsquosratio
D25 422 00021 621 028D10 384 00019 568 027
Preventing premature shear failure of specimen total spanof test specimen is reinforced by stirrups with spacing of150mm Stirrups were not located between two loadingpoints 2000 kN actuator was used for test and shear-span todepth ratio was 65 In order to verify the neutral axis depthcalculation model which was shown in (9) strain gages forconcrete were mounted at the concrete surface Strain gagesfor steel also can be attached to reinforcement at the centerof test specimen Details of test specimens were illustrated inFigure 4
42 Test Results Test specimens have shown the flexuralfailure pattern Because of inclusion of steel fiber cracklocalization did not occur until crushing of concrete occurredat extreme compression fiber After initial crack occurredcrackswere spread to outside themaximumbendingmomentarea After yielding of reinforcement diagonal tension crackwas not observed and cracks were spread to supports Atdeflection 98mm crushing of concrete occurred and crackswere propagated to crushing area with opening of initialcrack Final stage of failure and load-deflection relation wereshown in Figures 5(a) and 5(b) respectively Maximumload was 179 kN which occurred after yielding of reinforce-ment Analyzing strain gauges attached to concrete andreinforcement neutral axis depth was 123mm at peak loadstage
Neutral axis depth is important index for reinforcedconcrete members because flexural strength and ductilitycan highly depend on the neutral axis depth of sectionNeutral axis depth can be measured by test using the valueof strain gauge attached to compression fiber and tensionreinforcements Since strain gauge attached to extreme tensileand compression fiber failed before experiencing peak loadstrain of compression and tension reinforcement were usedCurvature at first yield of tension reinforcement was 00122(1m) and peak load curvature was 0019 (1m) Neutral axisdepth was 925mm and 1228mm from extreme compressionfiber respectively As shown in Figure 6 change of neutralaxis depth occurred after yielding of tension reinforcementAfter experiencing peak load neutral axis depth did notchange until crushing of concrete in compression side ofsection occurred
6 Advances in Materials Science and Engineering
Table 3 Mechanical characteristics of concrete
Stress state Ultimate strength(MPa) Youngrsquos modulus (MPa) Ultimatecracking
strain (permil) Poissonrsquos ratio
Compression 216 54306 3738 (120576119888119906) 026
Tension 98 0221 (120576119905)
350
300
50
150 1900 1900
5-D25
2-D10 Load Load
500 150
Strain gage
Strain gage
D10150 A
A
concrete
rebar
(a) Setting and measurement planSection A-A
5-D25
D10
200
240
6050
350
(b) Section
Figure 4 Details of test specimen
Table 4 Comparison between test results and assumed model
Model 119888 120576119904
119872119899
119875119899
(mm) (permil) (kNm) (kN)Type 1 9088 123 363 202Type 2 8598 13 296 164Type 3 9503 118 425 235Type 4 6876 163 356 197Type 5 7872 142 297 164Type 6 8739 128 433 240Type 7 9130 122 316 175Type 8 9813 114 308 170Type 9 10228 110 353 197Test results 93 910 322 179119888 neutral axis depth 120576
119904 strain at tensile reinforcement atmid length of beam
119872119899 nominal flexural strength of section (predicted value) and 119875
119899 load for
119872119899
43 Validation of Flexural StrengthModel Verifying suitabil-ity of flexural strength models test results were comparedwith assumed flexural strength model Comparison resultswere listed in Table 4 As expected model type 1 which hastriangular stress block has shown comparatively high accu-racy However this model overestimated moment capacity ofsection Overestimation of this model was caused by largearea of tensile stress block and higher value of momentarm Higher value of moment arm can be derived by theexistence of residual strength Model type 2 also has shownacceptable accuracy but this model underestimated momentcapacity Underestimation of this model was caused by therelatively low level of tensile stress block area and lower valueof moment arm for tensile stress block This smaller momentarm was derived by the end of the stress block Model type3 which has rectangular tensile stress block has shown lowaccuracy and overestimation
Generally rectangular stress block has shown deeperneutral axis depth from compression fiber than triangularstress block moment arm has lower value than the casesof triangular stress block types Model types with ACI
rectangular stress block have low accuracy on neutral axisdepth tensile strain of reinforcements andmoment capacityThis phenomenonwas caused by the larger area of stress blockthan triangular stress block However Models with ultrahigh performance concrete stress block parameters whichare derived from test results [12] have shown relatively highaccuracy with all types of tensile stress block This modelespecially predicts neutral axis depth more accurately thanother models As discussed above the most accurate tensilestress block was also stress block including residual strengthof concrete
Considering low ductility which is caused by explosivefailure of ultra high strength concrete the most appropriatemodel for design of flexural strength is type 8whichwasmod-elled by UHPC-rectangular stress block parameters undercompression and tension softening considering model undertension Type 7 also can be used for design purposes butin this case strength reduction factor is carefully consideredwith material properties
5 Validation of Flexural Strength Models withPrevious Researches
For the verification of wide range applicability of assumedmodel existing test results [6ndash8] of ultra high performanceconcrete members were compared with assumed modelsBecause a few number of specimens exist only 22 test resultswere compared with suggested model Specifications forcollected test results were shown in Table 5 Test results fromeach research were summarized in Table 5 All test specimensexperienced yielding of reinforcement before reaching peakload They failed with flexural failure at the center of thespecimens Collected test specimens have 027 to 236 oftensile reinforcement ratio and 80sim200MPa of compressivestrength of concrete Fiber contents were distributed from05 to 20
According to the test results of Ashour et al [6] effect ofthe fibers to flexural strength is independent of the amount ofreinforcement but additional moment is proportional to con-crete compressive strength Therefore compressive strength
Advances in Materials Science and Engineering 7
(a) Final stage of failure
Load
s (kN
)
220
200
180
160140120100806040200
160
140
120
100
80
60
40
20
0
Deflection (mm)
Peak strengthType 1 202 kN
Type 7 175kN
Type 1 Type 7
fcu
ftb
ft
fy
ftb
ft
fy
1205731U
HPC
c
1205721UHPCfcu
(b) Load-deflection relation
Figure 5 Test results
Neu
tral
axis
(mm
)
350
300
250
200
150
100
50
0
000
000
001 002
002
003 004
004
005
Curvature (1m)
Yielding ofreinforcement
93mm Peak load
Extreme tensile fiber
Extreme compression fiber
Measurement 1 compression steelMeasurement 2 compression fiber
Type 7 973mm
Figure 6 Change of neutral axis depth
of concrete should be considered in flexural strength modelDancygier and Savir [7] investigated flexural strength of fiberreinforced concrete with conventional reinforcement ratiolower than 1 Fiber length which affects reinforcing index(RI = 119881
119891119871119891119863119891 where119881
119891is fibre volume fraction 119871
119891is fiber
length and119863119891is fiber diameter) directly changes the flexural
strength of section Generally fiber length changes the failuremode of fiber reinforced concrete under bending especiallyafter peak load Therefore material behavior under tensionshould be considered for flexural strength calculation Yang etal [8] investigated about placing method and reinforcementratio especially for ultra high performance concrete whichhave compressive strength around 200MPa According tothis research reinforcement ratio also affects the flexuralstrength and ductility although members have much higher
compressive strength of concrete Some of test results did notevaluate prediction methods previously investigated [2 4 5]
Therefore all assumed models were examined with testresults Comparison of test results with flexural strengthmodels was shown in Figures 7(a)ndash7(d) and descriptive sta-tistical data were shown in Table 6 Existing flexural strengthmodel which was reviewed in this paper only has accuracywhen using comparatively lower compressive strength ofconcrete (80sim100MPa) as shown in Figure 7(a)The varianceof this model increases with increase of compressive strengthof concrete As shown in Figures 7(b) and 7(c) types 1to 6 still have overestimated the flexural strength of ultrahigh performance concreteHowever when tension softeningmodel was applied accuracy comparatively increased Types7 to 9 which use the newly developed rectangular stressblock show more accuracy and safety rather than the other9 models Types 7 and 8 especially have high accuracy overthe range of ultra high performance concrete Because type8 which uses tension softening model underestimates theflexural capacity it would be used for safe design of ultra highperformance concrete members
6 Conclusion
The following conclusions can be made from the statisticalinvestigation analytical works and tests for FRUHSC forflexural strength
(1) Stress distribution of ultra high performance concreteunder compression shaped as triangle Under tensilestress stress distribution of ultra high performanceconcrete can be varied with fiber contents or shape
(2) Nine-flexural strengthmodels were evaluated For theconservative estimation ultimate strain at compres-sion fiber was assumed to be 0003 These flexuralstrength models were evaluated using assumed stressdistribution
8 Advances in Materials Science and Engineering
Table 5 Previous test results
Specimen 119887 ℎ 119889 119860119904119905
120588 119891119888119906
119881119891
119863119891
119871119891
119891119910
119875119906
(mm) (mm) (mm) (mm2) () (MPa) () (mm) (mm) (MPa) (kN)Ashour et al [6]
B-05-M2 200 250 215 509 118 82 05 08 60 530 491B-10-M2 200 250 215 509 118 87 1 08 60 530 542B-05-M3 200 250 215 763 178 82 05 08 60 530 695B-10-M3 200 250 215 763 178 87 1 08 60 530 714B-05-M4 200 250 215 1018 237 82 05 08 60 530 881B-10-M4 200 250 215 1018 237 87 1 08 60 530 897B-05-H2 200 250 215 509 118 107 05 08 60 530 485B-10-H2 200 250 215 509 118 111 1 08 60 530 537B-05-H3 200 250 215 763 178 107 05 08 60 530 696B-10-H3 200 250 215 763 178 111 1 08 60 530 741B-05-H4 200 250 215 1018 237 107 05 08 60 530 891B-10-H4 200 250 215 1018 237 111 1 08 60 530 935
Dancygier and Savir [7]H5-F2-1 35 200 300 273 151 028 129 075 09 35 480 236H5-F2-1 60 200 300 273 151 028 124 075 09 60 480 273H8-F2-1 35 200 300 273 302 055 124 075 09 35 480 389H8-F2-1 60 200 300 273 302 055 122 075 09 60 480 372H5-F2-1 35 3 200 300 273 151 028 122 075 09 35 616 281
Yang et al [8]R12-1 180 270 235 253 060 191 2 02 13 400 770R13-1 180 270 235 380 090 192 2 02 13 400 863R14-1 180 270 235 507 120 197 2 02 13 400 1031R23-2 180 270 220 760 120 196 2 02 13 400 1165119887 beam width ℎ beam height 119889 effective depth of beam 119860
119904119905 tensile reinforcement area 120588 reinforcement ratio 119891
119888119906 compressive strength of concrete 119881
119891
volume fraction of steel fiber119863119891 fiber diameter 119871
119891 fiber length 119891
119910 yield strength of reinforcement and 119875
119906 test results (load at ultimate failure)
Table 6 Descriptive statistics on collected test data(testprediction)
ID Mean Median SD Var COV IAEACI544 124 106 034 0115 027 1720Imam 122 101 045 0201 037 1983Lim 113 104 026 0068 023 1415Type 1 081 090 020 0040 024 3356Type 2 118 107 029 0086 025 1672Type 3 070 076 016 0024 022 4654Type 4 087 091 014 0021 016 1563Type 5 118 106 030 0091 025 1662Type 6 069 075 015 0023 022 4918Type 7 090 095 015 0021 016 1030Type 8 111 107 024 0060 022 1142Type 9 073 077 014 0021 020 3558SD standard variation Var variance COV coefficient of variation and IAEintegrated absolute error
(3) The most accurate model of ultra high performanceconcrete under compression is triangular Becauseultra high performance concrete has large elastic areafailure occurred with the same time experiencing
ultimate strength However for the safe design ofsection flexural strength model which uses modifiedrectangular stress blocks considering mechanicalcharacteristics of UHPC should be used
(4) Evaluating validation process using test result ofthis study and previous researches existing flexuralstrength calculation models cannot accurately andsafely predict the flexural strength of ultra highstrength concrete specimens especially for compres-sive strength larger than 100MPa However flexuralstrength model suggested in this study can pro-vide conservative and highly accurate (10 of error)results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by a grant (15CTAP-C097356-01) from Creative Challenge Research Program fundedby Ministry of Land Infrastructure and Transport of
Advances in Materials Science and Engineering 9
Test
valu
eth
eorit
ical
val
ue35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
ACI544mdashAshour (1)ImammdashAshour (1)LimmdashAshour (1)ACI544mdashAshour (2)ImammdashAshour (2)
LimmdashAshour (2)ACI544mdashYangImammdashYangLimmdashYang
(a) Existing modelTe
st va
lue
theo
ritic
al v
alue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 1mdashAshourType 2mdashAshourType 3mdashAshourType 1mdashDancygierType 2mdashDancygier
Type 3mdashDancygierType 1mdashYangType 2mdashYangType 3mdashYang
(b) Assumed types 1sim3
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 4mdashAshourType 5mdashAshourType 6mdashAshourType 4mdashDancygierType 5mdashDancygier
Type 6mdashDancygierType 4mdashYangType 5mdashYangType 6mdashYang
(c) Assumed types 4sim6
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 7mdashAshourType 8mdashAshourType 9mdashAshourType 7mdashDancygierType 8mdashDancygier
Type 9mdashDancygierType 7mdashYangType 8mdashYangType 9mdashYang
(d) Assumed types 7sim9
Figure 7 Applicability verification for prediction model
Korean government and National Research Foundation ofKorea(NRF) funded by the Ministry of Science ICT andFuture Planning (no NRF-2014R1A2A1A11051049)
References
[1] ACI Committee ldquoBuilding code requirements for structuralconcrete and commentaryrdquo ACI 318-11 American ConcreteInstitute Farmington Hills Mich USA 2011
[2] American Concrete Institute Committee 544 ldquoDesign con-siderations for steel fiber reinforced concreterdquo InternationalConcrete Abstracts Portal vol 85 no 5 pp 563ndash579 1988
[3] C H Henager and T J Doherty ldquoAnalysis of reinforced fibrousconcrete beamsrdquo Journal of the Structural Division vol 102 no1 pp 177ndash188 1976 ASCE Proceedings
[4] M Imam L Vandewalle and F Mortelmans ldquoShear-momentanalysis of reinforced high strength concrete beams containingsteel fibresrdquo Canadian Journal of Civil Engineering vol 22 no3 pp 462ndash470 1995
[5] T Y Lim P Paramasivan and S L Lee ldquoShear and momentcapacity of reinforced steel fiber concrete beamsrdquo Magazine ofConcrete Research vol 39 no 140 pp 148ndash160 1987
[6] S A Ashour F F Wafa and M I Kamal ldquoEffect of theconcrete compressive strength and tensile reinforcement ratio
10 Advances in Materials Science and Engineering
on the flexural behavior of fibrous concrete beamsrdquo EngineeringStructures vol 22 no 9 pp 1145ndash1158 2000
[7] A N Dancygier and Z Savir ldquoFlexural behavior ofHSFRCwithlow reinforcement ratiosrdquo Engineering Structures vol 28 no 11pp 1503ndash1512 2006
[8] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010
[9] RILEM and Final recommendations of TC 162-TDF ldquoTest anddesign methods for steel fibre reinforced concrete 120590-120576 designmethodrdquoMaterials and Structures vol 36 pp 560ndash565 2003
[10] European Committee for Standardization Eurocode 2 (EC2)Design of Concrete Structures 2004
[11] AFGCGroupe de Travail BFUP SETRA-AFGCUltra High Per-formance Fiber-Reinforced Concretes Interim Recommendation2002
[12] B I Bae C S Choi and H K Choi ldquoEvaluation of rectangularstress block parameters of reactive powder concrete membersrdquoJournal of the Architectural Institute of Korea vol 28 no 7 pp3ndash11 2012
[13] R N Swamy and S A Al-Tarsquoan ldquoDeformation and ultimatestrength in flexure of reinforced concrete beamsmadewith steelfibre concreterdquo Journal of the American Concrete Institute vol78 no 5 pp 395ndash405 1981
Submit your manuscripts athttpwwwhindawicom
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2 Advances in Materials Science and Engineering
concrete suggested the way to design the section of membersuggested stress-strain relation However stress-strain rela-tion for ultra high performance concrete needs specific testresults not using stress blocks or assumptions Therefore inthis study various types of compression and tension stressblock combinations were evaluated with experimental resultand previous research results for easy and safe design of ultrahigh performance concrete members
2 Review of Current Design Codesfor Flexural Strength of Ultra HighPerformance Concrete
Reinforced concrete members using normal strength con-crete are designed with an assumption that stress distributioncan be shapedwith rectangle and concrete cannot transfer thetensile stress However these assumptions cannot be appliedto flexural strength calculation of ultra high performanceconcrete members Since ultra high performance concretehas much higher compressive strength than normal strengthconcrete and usually reinforcedwith steel fiber shape of stressdistribution in compression side will be changed and tensilestress distribution in tension side should be considered inorder to calculate the flexural strength of section Some ofdesign guidelines for high strength concrete or steel fiberreinforced concrete have different assumptions for flexuralstrength calculationThey can be categorized into two groupsone uses stress block parameters and the other uses specifiedstress-strain relation of concrete
Current design code ACI318 [1] suggests that flexuralstrength of reinforced concrete section can be calculated by
119872119899= 119860119904119891119910(119889 minus
119886
2) (1)
In this equation 119886 depth of rectangular stress blockcan be determined by using stress block parameter 120573
1 For
compressive strength of concrete between 17 and 28MPa 085can be used as the value of 120573
1 1205731shall be decreased linearly
a rate of 005 for each 7MPa of compressive strength ofconcrete above 28MPa of compressive strength of concreteThe smallest value of 120573
1is 065
As can be seen in ACI318 [1] current design code provi-sions did not consider the effect of steel fiber Some of designguidelines suggested the way to calculate flexural strength ofsteel fiber reinforced concrete section ACI 544 committee [2]provides the flexural strength equations by adopting researchresults of Henager and Doherty [3] especially for rectangularsection member
119872119899= 119860119904119891119910(119889 minus
119886
2) + 120590119905119887 (ℎ minus 119890) (
ℎ
2+
119890
2minus
119886
2) (2)
where 119872119899is nominal flexural strength of section 119891
119910is yield
strength of steel rebar 119889 is effective depth of section 119886 isdepth of stress block ℎ is height of section 119890 = (120576
119904(fibers) +
0003)(1198880003) 120576119904is strain in tension side 120576
119904(fiber) = 120590
119891119864119904
119888 is neutral axis depth and tensile strength of steel fiberreinforced concrete can be calculated using
120590119905= 000772
119897119891
119889119891
120588119891119865be (3)
where 119897119891is length of steel fiber 119889
119891is diameter of steel fiber 120588
119891
is percent by volume of steel fiber and 119865be is bond efficiencyfactor
Imam et al [4] suggested the modified ACI 544 [2]model which can be used as steel fiber reinforced concretewith high strength matrix Imam et al investigated the bondstress between steel fiber and matrix They suggested thattensile stress block height coefficient should be changed into002 According to this modification tensile strength can becalculated using
120590119905= 2119865 119865 =
119897119891
119889119891
119881119891120578119891 (4)
where119881119891means volume fraction of steel fiber (= 120588
119891100) and
120578119891is fiber factor (10sim12) Moment capacity of section can be
determined according to ACI 544 [2] (2)Lim et al [5] suggested that stress block parameters
should be reevaluated with change of matrix and steel fiberThey use 120572
1as 090 because steel fiber can provide more
ductility under compression either Tensile strength of steelfiber reinforced concrete can be determined using
120590119905119906
= 1205781015840
01205781119881119891119897119891
120591119906
2119903 (5)
where 1205781015840
0is steel fiber orientation factor 120578
1is length efficiency
factor 120591119906is average ultimate bond stress at the fiber-matrix
interface and 119903 is the ratio of the fiber cross-sectional areato its perimeter Since Lim et al [5] developed their modelwith plasticity approach they use whole area over the neutralaxis as compressive stress block Neglecting cover thicknessand considering tensile stress block in tension side of sectionneutral axis depth 119909 can be calculated using
119909 =
119889120590119905119906
+ 119891119910119887
1205721120590119888119906
+ 120590119905119906
(6)
where 120590119888119906
is compressive strength of concrete 119887 is width ofsection and 119891
119910is yield strength of reinforcement From (6)
internal moment arm can be calculated
ℎ = 119889 minus119909
2 (7)
where 119889 is effective depth of section Using (5) (6) and (7)flexural capacity of section can be calculated by using
119872119906= 119891119910ℎ + 120590119905119906
119887
2(ℎ2
minus1199092
4) (8)
Although stress block approach is easy to use for flexuralstrength calculation it cannot consider the difference ofconcrete with higher strength matrix or other characteristics
Advances in Materials Science and Engineering 3
⟨Strain distribution⟩ ⟨Stress distribution⟩
Compression
Tension
ACI318 ACI544 Lim et al
Figure 1 Previously suggested stress block combination
Flexural strength calculation models for normal strengthconcrete and steel fiber reinforced concrete were illustratedin Figure 1 The main difference between normal strengthconcrete model and steel fiber reinforced concrete model isexistence of tensile stress block Difference among steel fiberreinforced concrete models is the range of tensile stress dis-tribution However they are not exact models because stressdistribution might be changed with compressive strength ofmatrix and tensile stress distribution is more comprehensivethan used in Figure 1
For the exact solution for flexural strength of sectioncomprehensive stress-strain relations are directly applied tocalculate the flexural strength of section The representativemodels considering real stress distribution are provided byRILEM 120590 minus 120576 method [9] EC2 flexural analysis [10] andAFGC-Setra guideline [11] They can provide more accuratevalue than flexural strength model made up of stress blocksHowever they need more comprehensive computation pro-cess and some material test
3 Flexura Strength Calculation Model
According to the material test about ultra high performanceconcrete most of stress-strain relation shapes are triangularunder compression Therefore under compression triangu-lar stress block may be used for the design of ultra highperformance concrete flexural members Previous research[12] suggested rectangular stress block parameters for highstrength and ultra high strength concrete However most ofcode provisions use the rectangular stress block parametersbecause they mainly focused on the use for normal strengthconcrete They consider the shape of stress-strain relationusing various value of 120573
1 depending on compressive strength
of concrete Rectangular stress block slightly overestimatesthe flexural strength of concrete member especially for highreinforcement ratio and compressive strength of concrete Ascan be seen in Section 2 tensile stress block for steel fiberreinforced concrete has been shown in various shape andsize Therefore designing ultra high performance concretemembers stress block parameters should be reorganized
In this study three types of stress block parameterswere considered ACI stress block parameters stress blockparameters from UHPC member design guideline and tri-angular stress block determined by maximum compressive
b
dh
As
e c
120576cu fcu
120576f
120576s
120576tuftb
ft
fy
Section Assumed Assumedstrain distribution stress distribution
Figure 2 Strain and stress distribution of ultra high performanceconcrete section
strength and corresponding strain resulting from materialtests Tensile behavior of steel fiber reinforced concrete wasdivided into strain hardening strain softening and fullyplastic behavior three types In this study tensile stress blockswere composed of these three types of tensile behavior of steelfiber reinforced concrete
Strain and stress distribution of ultra high performanceconcrete section were shown in Figure 2 In this study threetypes of stress blocks were used under compression andtension respectively Total of 9 types of flexural strengthmodels were investigated These models were illustrated inFigure 3 The most important design parameter for flexuralstrength is neutral axis depth Neutral axis depth for 9 typesof flexural strength model was developed as follows
1198881198881
=
119860119904119891119910minus 120574ℎ119891
119905119887
051198911015840119888119887 minus 05 (120578 minus 1) 119891
119905119887 minus 120574120578119891
119905119887
1198881198882
=
119860119904119891119910+ 05 (1 + 120574) 119891
119905119887ℎ
051198911015840119888119887 minus 05 (120578 minus 1) 119891
119905119887 + 05120578 (1 + 120574) 119891
119905119887
1198881198883
=
119860119904119891119910+ 120574119891119905ℎ119887
051198911015840119888119887 + 120574120578119891
119905119887
1198881198884
=
119860119904119891119910+ 120574119891119905119887ℎ
1205721ACI119891
1015840
1198881205731ACI119887 minus 05 (120578 minus 1) 119891
119905119887 + 120574120578119891
119905119887
4 Advances in Materials Science and Engineering
fcu
ftb
ft
fy
(a) Type 1
fcu
ftb
ft
fy
(b) Type 2
fcu
fy
1205741ft
(c) Type 3
ftb
ft
fy
1205731A
CIc
1205721ACIfcu
(d) Type 4
ftb
ft
fy
1205731A
CIc
1205721ACIfcu
(e) Type5
fy
1205741ft
1205731A
CIc
1205721ACIfcu
(f) Type 6
ftb
ft
fy
1205731U
HPC
c1205721UHPCfcu
(g) Type 7
ftb
ft
fy
1205731U
HPC
c
1205721UHPCfcu
(h) Type 8
fy
1205741ft
1205731U
HPC
c
1205721UHPCfcu
(i) Type 9
Figure 3 Stress block models
1198881198885
=
119860119904119891119910+ 05 (1 + 120574) 119891
119905119887ℎ
1205721ACI119891
1015840
1198881205731ACI119887 minus 05 (120578 minus 1) 119891
119905119887 + 05120578 (1 + 120574) 119891
119905119887
1198881198886
=
119860119904119891119910+ 120574119891119905ℎ119887
1205721ACI119891
1015840
1198881205731ACI119887 + 120574120578119891
119905119887
1198881198887
=
119860119904119891119910+ 120574119891119905119887ℎ
1205721UHPC119891
1015840
1198881205731UHPC119887 minus 05 (120578 minus 1) 119891
119905119887 + 120574120578119891
119905119887
1198881198888
=
119860119904119891119910+ 05 (1 + 120574) 119891
119905119887ℎ
1205721UHPC119891
1015840
1198881205731UHPC119887 minus 05 (120578 minus 1) 119891
119905119887 + 05120578 (1 + 120574) 119891
119905119887
1198881198889
=
119860119904119891119910+ 120574119891119905ℎ119887
1205721UHPC119891
1015840
1198881205731UHPC119887 + 120574120578119891
119905119887
(9)
where 1198911015840
119888is compressive strength of concrete 119860
119904is area of
tensile rebar 119891119910is yield strength of steel rebar 119891
119905is ultimate
tensile strength of concrete 120574 is ratio between post crackingtensile strength and ultimate tensile strength 120578 can be definedby 120576119891120576119888119906
+ 1 1205721and 120572
1UHPC are rectangular stress blockparameter for compressive strength of concrete for normalstrength concrete andUHPC respectively 120573
1and 1205731UHPC are
stress block depth parameter for normal strength concreteand UHPC respectively 119887 is width of section and 119889 is
effective depth of section 120576119891for 120578 is strain corresponding
to ultimate tensile strength and 120576119888119906
is ultimate compressivestrain of concrete
The most difficult and controversial part is the determi-nation of tensile strength of fiber reinforced concrete Swamyand Al-Tarsquoan [13] suggested the equation according to thecomposite theory as follows
119891119905= 0970119891
119903(1 minus 119881
119891) + 2119881
119891
119871119891
119863119891
(10)
where 119891119903is modulus of rupture of concrete and other
variables are fiber geometry defined in Section 2Using neutral axis depth defined in (9) considering
shape of stress block nominal flexural strength of ultra highperformance concrete members can be calculated as follows
Case 1 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 119891
119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(11)
Advances in Materials Science and Engineering 5
Table 1 Mix proportions
119908119887
Weight ratio Steel fiber Admixture 119891119888119896
Cement Water Silica fume Sand Filler (Micro Silica)() (kg) (MPa)
017 1 021 024 104 031 2 108 200
Case 2 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 119891
119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 +
ℎ minus 119890
3) + 119860
119904119891119910(119889 minus 119888)
(12)
Case 3 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 120574119891
119905(ℎ minus 119890) (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(13)
Cases 4 7 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 119891119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(14)
Cases 5 8 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 119891119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 +
ℎ minus 119890
2) + 119860
119904119891119910(119889 minus 119888)
(15)
Cases 6 9 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 120574119891119905(ℎ minus 119890) (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(16)
4 Flexural Behavior of Ultra HighPerformance Concrete Members
41 Test Plan In order to verify the applicability of sug-gested models ultra high performance concrete beam wastested Average ultimate compressive strength of standardcylinder was 216MPa Splitting strength of standard cylinderis distributed between 72sim195MPa Mix proportions forultra high performance concrete are summarized in Table 1Mechanical properties of concrete and rebar used in thisstudy were summarized in Tables 2 and 3 respectively
Table 2 Mechanical characteristics of rebar
MaterialsYield
strength(MPa)
Yieldstrain(120576119910)
Tensilestrength(MPa)
Poissonrsquosratio
D25 422 00021 621 028D10 384 00019 568 027
Preventing premature shear failure of specimen total spanof test specimen is reinforced by stirrups with spacing of150mm Stirrups were not located between two loadingpoints 2000 kN actuator was used for test and shear-span todepth ratio was 65 In order to verify the neutral axis depthcalculation model which was shown in (9) strain gages forconcrete were mounted at the concrete surface Strain gagesfor steel also can be attached to reinforcement at the centerof test specimen Details of test specimens were illustrated inFigure 4
42 Test Results Test specimens have shown the flexuralfailure pattern Because of inclusion of steel fiber cracklocalization did not occur until crushing of concrete occurredat extreme compression fiber After initial crack occurredcrackswere spread to outside themaximumbendingmomentarea After yielding of reinforcement diagonal tension crackwas not observed and cracks were spread to supports Atdeflection 98mm crushing of concrete occurred and crackswere propagated to crushing area with opening of initialcrack Final stage of failure and load-deflection relation wereshown in Figures 5(a) and 5(b) respectively Maximumload was 179 kN which occurred after yielding of reinforce-ment Analyzing strain gauges attached to concrete andreinforcement neutral axis depth was 123mm at peak loadstage
Neutral axis depth is important index for reinforcedconcrete members because flexural strength and ductilitycan highly depend on the neutral axis depth of sectionNeutral axis depth can be measured by test using the valueof strain gauge attached to compression fiber and tensionreinforcements Since strain gauge attached to extreme tensileand compression fiber failed before experiencing peak loadstrain of compression and tension reinforcement were usedCurvature at first yield of tension reinforcement was 00122(1m) and peak load curvature was 0019 (1m) Neutral axisdepth was 925mm and 1228mm from extreme compressionfiber respectively As shown in Figure 6 change of neutralaxis depth occurred after yielding of tension reinforcementAfter experiencing peak load neutral axis depth did notchange until crushing of concrete in compression side ofsection occurred
6 Advances in Materials Science and Engineering
Table 3 Mechanical characteristics of concrete
Stress state Ultimate strength(MPa) Youngrsquos modulus (MPa) Ultimatecracking
strain (permil) Poissonrsquos ratio
Compression 216 54306 3738 (120576119888119906) 026
Tension 98 0221 (120576119905)
350
300
50
150 1900 1900
5-D25
2-D10 Load Load
500 150
Strain gage
Strain gage
D10150 A
A
concrete
rebar
(a) Setting and measurement planSection A-A
5-D25
D10
200
240
6050
350
(b) Section
Figure 4 Details of test specimen
Table 4 Comparison between test results and assumed model
Model 119888 120576119904
119872119899
119875119899
(mm) (permil) (kNm) (kN)Type 1 9088 123 363 202Type 2 8598 13 296 164Type 3 9503 118 425 235Type 4 6876 163 356 197Type 5 7872 142 297 164Type 6 8739 128 433 240Type 7 9130 122 316 175Type 8 9813 114 308 170Type 9 10228 110 353 197Test results 93 910 322 179119888 neutral axis depth 120576
119904 strain at tensile reinforcement atmid length of beam
119872119899 nominal flexural strength of section (predicted value) and 119875
119899 load for
119872119899
43 Validation of Flexural StrengthModel Verifying suitabil-ity of flexural strength models test results were comparedwith assumed flexural strength model Comparison resultswere listed in Table 4 As expected model type 1 which hastriangular stress block has shown comparatively high accu-racy However this model overestimated moment capacity ofsection Overestimation of this model was caused by largearea of tensile stress block and higher value of momentarm Higher value of moment arm can be derived by theexistence of residual strength Model type 2 also has shownacceptable accuracy but this model underestimated momentcapacity Underestimation of this model was caused by therelatively low level of tensile stress block area and lower valueof moment arm for tensile stress block This smaller momentarm was derived by the end of the stress block Model type3 which has rectangular tensile stress block has shown lowaccuracy and overestimation
Generally rectangular stress block has shown deeperneutral axis depth from compression fiber than triangularstress block moment arm has lower value than the casesof triangular stress block types Model types with ACI
rectangular stress block have low accuracy on neutral axisdepth tensile strain of reinforcements andmoment capacityThis phenomenonwas caused by the larger area of stress blockthan triangular stress block However Models with ultrahigh performance concrete stress block parameters whichare derived from test results [12] have shown relatively highaccuracy with all types of tensile stress block This modelespecially predicts neutral axis depth more accurately thanother models As discussed above the most accurate tensilestress block was also stress block including residual strengthof concrete
Considering low ductility which is caused by explosivefailure of ultra high strength concrete the most appropriatemodel for design of flexural strength is type 8whichwasmod-elled by UHPC-rectangular stress block parameters undercompression and tension softening considering model undertension Type 7 also can be used for design purposes butin this case strength reduction factor is carefully consideredwith material properties
5 Validation of Flexural Strength Models withPrevious Researches
For the verification of wide range applicability of assumedmodel existing test results [6ndash8] of ultra high performanceconcrete members were compared with assumed modelsBecause a few number of specimens exist only 22 test resultswere compared with suggested model Specifications forcollected test results were shown in Table 5 Test results fromeach research were summarized in Table 5 All test specimensexperienced yielding of reinforcement before reaching peakload They failed with flexural failure at the center of thespecimens Collected test specimens have 027 to 236 oftensile reinforcement ratio and 80sim200MPa of compressivestrength of concrete Fiber contents were distributed from05 to 20
According to the test results of Ashour et al [6] effect ofthe fibers to flexural strength is independent of the amount ofreinforcement but additional moment is proportional to con-crete compressive strength Therefore compressive strength
Advances in Materials Science and Engineering 7
(a) Final stage of failure
Load
s (kN
)
220
200
180
160140120100806040200
160
140
120
100
80
60
40
20
0
Deflection (mm)
Peak strengthType 1 202 kN
Type 7 175kN
Type 1 Type 7
fcu
ftb
ft
fy
ftb
ft
fy
1205731U
HPC
c
1205721UHPCfcu
(b) Load-deflection relation
Figure 5 Test results
Neu
tral
axis
(mm
)
350
300
250
200
150
100
50
0
000
000
001 002
002
003 004
004
005
Curvature (1m)
Yielding ofreinforcement
93mm Peak load
Extreme tensile fiber
Extreme compression fiber
Measurement 1 compression steelMeasurement 2 compression fiber
Type 7 973mm
Figure 6 Change of neutral axis depth
of concrete should be considered in flexural strength modelDancygier and Savir [7] investigated flexural strength of fiberreinforced concrete with conventional reinforcement ratiolower than 1 Fiber length which affects reinforcing index(RI = 119881
119891119871119891119863119891 where119881
119891is fibre volume fraction 119871
119891is fiber
length and119863119891is fiber diameter) directly changes the flexural
strength of section Generally fiber length changes the failuremode of fiber reinforced concrete under bending especiallyafter peak load Therefore material behavior under tensionshould be considered for flexural strength calculation Yang etal [8] investigated about placing method and reinforcementratio especially for ultra high performance concrete whichhave compressive strength around 200MPa According tothis research reinforcement ratio also affects the flexuralstrength and ductility although members have much higher
compressive strength of concrete Some of test results did notevaluate prediction methods previously investigated [2 4 5]
Therefore all assumed models were examined with testresults Comparison of test results with flexural strengthmodels was shown in Figures 7(a)ndash7(d) and descriptive sta-tistical data were shown in Table 6 Existing flexural strengthmodel which was reviewed in this paper only has accuracywhen using comparatively lower compressive strength ofconcrete (80sim100MPa) as shown in Figure 7(a)The varianceof this model increases with increase of compressive strengthof concrete As shown in Figures 7(b) and 7(c) types 1to 6 still have overestimated the flexural strength of ultrahigh performance concreteHowever when tension softeningmodel was applied accuracy comparatively increased Types7 to 9 which use the newly developed rectangular stressblock show more accuracy and safety rather than the other9 models Types 7 and 8 especially have high accuracy overthe range of ultra high performance concrete Because type8 which uses tension softening model underestimates theflexural capacity it would be used for safe design of ultra highperformance concrete members
6 Conclusion
The following conclusions can be made from the statisticalinvestigation analytical works and tests for FRUHSC forflexural strength
(1) Stress distribution of ultra high performance concreteunder compression shaped as triangle Under tensilestress stress distribution of ultra high performanceconcrete can be varied with fiber contents or shape
(2) Nine-flexural strengthmodels were evaluated For theconservative estimation ultimate strain at compres-sion fiber was assumed to be 0003 These flexuralstrength models were evaluated using assumed stressdistribution
8 Advances in Materials Science and Engineering
Table 5 Previous test results
Specimen 119887 ℎ 119889 119860119904119905
120588 119891119888119906
119881119891
119863119891
119871119891
119891119910
119875119906
(mm) (mm) (mm) (mm2) () (MPa) () (mm) (mm) (MPa) (kN)Ashour et al [6]
B-05-M2 200 250 215 509 118 82 05 08 60 530 491B-10-M2 200 250 215 509 118 87 1 08 60 530 542B-05-M3 200 250 215 763 178 82 05 08 60 530 695B-10-M3 200 250 215 763 178 87 1 08 60 530 714B-05-M4 200 250 215 1018 237 82 05 08 60 530 881B-10-M4 200 250 215 1018 237 87 1 08 60 530 897B-05-H2 200 250 215 509 118 107 05 08 60 530 485B-10-H2 200 250 215 509 118 111 1 08 60 530 537B-05-H3 200 250 215 763 178 107 05 08 60 530 696B-10-H3 200 250 215 763 178 111 1 08 60 530 741B-05-H4 200 250 215 1018 237 107 05 08 60 530 891B-10-H4 200 250 215 1018 237 111 1 08 60 530 935
Dancygier and Savir [7]H5-F2-1 35 200 300 273 151 028 129 075 09 35 480 236H5-F2-1 60 200 300 273 151 028 124 075 09 60 480 273H8-F2-1 35 200 300 273 302 055 124 075 09 35 480 389H8-F2-1 60 200 300 273 302 055 122 075 09 60 480 372H5-F2-1 35 3 200 300 273 151 028 122 075 09 35 616 281
Yang et al [8]R12-1 180 270 235 253 060 191 2 02 13 400 770R13-1 180 270 235 380 090 192 2 02 13 400 863R14-1 180 270 235 507 120 197 2 02 13 400 1031R23-2 180 270 220 760 120 196 2 02 13 400 1165119887 beam width ℎ beam height 119889 effective depth of beam 119860
119904119905 tensile reinforcement area 120588 reinforcement ratio 119891
119888119906 compressive strength of concrete 119881
119891
volume fraction of steel fiber119863119891 fiber diameter 119871
119891 fiber length 119891
119910 yield strength of reinforcement and 119875
119906 test results (load at ultimate failure)
Table 6 Descriptive statistics on collected test data(testprediction)
ID Mean Median SD Var COV IAEACI544 124 106 034 0115 027 1720Imam 122 101 045 0201 037 1983Lim 113 104 026 0068 023 1415Type 1 081 090 020 0040 024 3356Type 2 118 107 029 0086 025 1672Type 3 070 076 016 0024 022 4654Type 4 087 091 014 0021 016 1563Type 5 118 106 030 0091 025 1662Type 6 069 075 015 0023 022 4918Type 7 090 095 015 0021 016 1030Type 8 111 107 024 0060 022 1142Type 9 073 077 014 0021 020 3558SD standard variation Var variance COV coefficient of variation and IAEintegrated absolute error
(3) The most accurate model of ultra high performanceconcrete under compression is triangular Becauseultra high performance concrete has large elastic areafailure occurred with the same time experiencing
ultimate strength However for the safe design ofsection flexural strength model which uses modifiedrectangular stress blocks considering mechanicalcharacteristics of UHPC should be used
(4) Evaluating validation process using test result ofthis study and previous researches existing flexuralstrength calculation models cannot accurately andsafely predict the flexural strength of ultra highstrength concrete specimens especially for compres-sive strength larger than 100MPa However flexuralstrength model suggested in this study can pro-vide conservative and highly accurate (10 of error)results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by a grant (15CTAP-C097356-01) from Creative Challenge Research Program fundedby Ministry of Land Infrastructure and Transport of
Advances in Materials Science and Engineering 9
Test
valu
eth
eorit
ical
val
ue35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
ACI544mdashAshour (1)ImammdashAshour (1)LimmdashAshour (1)ACI544mdashAshour (2)ImammdashAshour (2)
LimmdashAshour (2)ACI544mdashYangImammdashYangLimmdashYang
(a) Existing modelTe
st va
lue
theo
ritic
al v
alue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 1mdashAshourType 2mdashAshourType 3mdashAshourType 1mdashDancygierType 2mdashDancygier
Type 3mdashDancygierType 1mdashYangType 2mdashYangType 3mdashYang
(b) Assumed types 1sim3
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 4mdashAshourType 5mdashAshourType 6mdashAshourType 4mdashDancygierType 5mdashDancygier
Type 6mdashDancygierType 4mdashYangType 5mdashYangType 6mdashYang
(c) Assumed types 4sim6
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 7mdashAshourType 8mdashAshourType 9mdashAshourType 7mdashDancygierType 8mdashDancygier
Type 9mdashDancygierType 7mdashYangType 8mdashYangType 9mdashYang
(d) Assumed types 7sim9
Figure 7 Applicability verification for prediction model
Korean government and National Research Foundation ofKorea(NRF) funded by the Ministry of Science ICT andFuture Planning (no NRF-2014R1A2A1A11051049)
References
[1] ACI Committee ldquoBuilding code requirements for structuralconcrete and commentaryrdquo ACI 318-11 American ConcreteInstitute Farmington Hills Mich USA 2011
[2] American Concrete Institute Committee 544 ldquoDesign con-siderations for steel fiber reinforced concreterdquo InternationalConcrete Abstracts Portal vol 85 no 5 pp 563ndash579 1988
[3] C H Henager and T J Doherty ldquoAnalysis of reinforced fibrousconcrete beamsrdquo Journal of the Structural Division vol 102 no1 pp 177ndash188 1976 ASCE Proceedings
[4] M Imam L Vandewalle and F Mortelmans ldquoShear-momentanalysis of reinforced high strength concrete beams containingsteel fibresrdquo Canadian Journal of Civil Engineering vol 22 no3 pp 462ndash470 1995
[5] T Y Lim P Paramasivan and S L Lee ldquoShear and momentcapacity of reinforced steel fiber concrete beamsrdquo Magazine ofConcrete Research vol 39 no 140 pp 148ndash160 1987
[6] S A Ashour F F Wafa and M I Kamal ldquoEffect of theconcrete compressive strength and tensile reinforcement ratio
10 Advances in Materials Science and Engineering
on the flexural behavior of fibrous concrete beamsrdquo EngineeringStructures vol 22 no 9 pp 1145ndash1158 2000
[7] A N Dancygier and Z Savir ldquoFlexural behavior ofHSFRCwithlow reinforcement ratiosrdquo Engineering Structures vol 28 no 11pp 1503ndash1512 2006
[8] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010
[9] RILEM and Final recommendations of TC 162-TDF ldquoTest anddesign methods for steel fibre reinforced concrete 120590-120576 designmethodrdquoMaterials and Structures vol 36 pp 560ndash565 2003
[10] European Committee for Standardization Eurocode 2 (EC2)Design of Concrete Structures 2004
[11] AFGCGroupe de Travail BFUP SETRA-AFGCUltra High Per-formance Fiber-Reinforced Concretes Interim Recommendation2002
[12] B I Bae C S Choi and H K Choi ldquoEvaluation of rectangularstress block parameters of reactive powder concrete membersrdquoJournal of the Architectural Institute of Korea vol 28 no 7 pp3ndash11 2012
[13] R N Swamy and S A Al-Tarsquoan ldquoDeformation and ultimatestrength in flexure of reinforced concrete beamsmadewith steelfibre concreterdquo Journal of the American Concrete Institute vol78 no 5 pp 395ndash405 1981
Submit your manuscripts athttpwwwhindawicom
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Biomaterials
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Advances in
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Nano
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Journal ofNanomaterials
Advances in Materials Science and Engineering 3
⟨Strain distribution⟩ ⟨Stress distribution⟩
Compression
Tension
ACI318 ACI544 Lim et al
Figure 1 Previously suggested stress block combination
Flexural strength calculation models for normal strengthconcrete and steel fiber reinforced concrete were illustratedin Figure 1 The main difference between normal strengthconcrete model and steel fiber reinforced concrete model isexistence of tensile stress block Difference among steel fiberreinforced concrete models is the range of tensile stress dis-tribution However they are not exact models because stressdistribution might be changed with compressive strength ofmatrix and tensile stress distribution is more comprehensivethan used in Figure 1
For the exact solution for flexural strength of sectioncomprehensive stress-strain relations are directly applied tocalculate the flexural strength of section The representativemodels considering real stress distribution are provided byRILEM 120590 minus 120576 method [9] EC2 flexural analysis [10] andAFGC-Setra guideline [11] They can provide more accuratevalue than flexural strength model made up of stress blocksHowever they need more comprehensive computation pro-cess and some material test
3 Flexura Strength Calculation Model
According to the material test about ultra high performanceconcrete most of stress-strain relation shapes are triangularunder compression Therefore under compression triangu-lar stress block may be used for the design of ultra highperformance concrete flexural members Previous research[12] suggested rectangular stress block parameters for highstrength and ultra high strength concrete However most ofcode provisions use the rectangular stress block parametersbecause they mainly focused on the use for normal strengthconcrete They consider the shape of stress-strain relationusing various value of 120573
1 depending on compressive strength
of concrete Rectangular stress block slightly overestimatesthe flexural strength of concrete member especially for highreinforcement ratio and compressive strength of concrete Ascan be seen in Section 2 tensile stress block for steel fiberreinforced concrete has been shown in various shape andsize Therefore designing ultra high performance concretemembers stress block parameters should be reorganized
In this study three types of stress block parameterswere considered ACI stress block parameters stress blockparameters from UHPC member design guideline and tri-angular stress block determined by maximum compressive
b
dh
As
e c
120576cu fcu
120576f
120576s
120576tuftb
ft
fy
Section Assumed Assumedstrain distribution stress distribution
Figure 2 Strain and stress distribution of ultra high performanceconcrete section
strength and corresponding strain resulting from materialtests Tensile behavior of steel fiber reinforced concrete wasdivided into strain hardening strain softening and fullyplastic behavior three types In this study tensile stress blockswere composed of these three types of tensile behavior of steelfiber reinforced concrete
Strain and stress distribution of ultra high performanceconcrete section were shown in Figure 2 In this study threetypes of stress blocks were used under compression andtension respectively Total of 9 types of flexural strengthmodels were investigated These models were illustrated inFigure 3 The most important design parameter for flexuralstrength is neutral axis depth Neutral axis depth for 9 typesof flexural strength model was developed as follows
1198881198881
=
119860119904119891119910minus 120574ℎ119891
119905119887
051198911015840119888119887 minus 05 (120578 minus 1) 119891
119905119887 minus 120574120578119891
119905119887
1198881198882
=
119860119904119891119910+ 05 (1 + 120574) 119891
119905119887ℎ
051198911015840119888119887 minus 05 (120578 minus 1) 119891
119905119887 + 05120578 (1 + 120574) 119891
119905119887
1198881198883
=
119860119904119891119910+ 120574119891119905ℎ119887
051198911015840119888119887 + 120574120578119891
119905119887
1198881198884
=
119860119904119891119910+ 120574119891119905119887ℎ
1205721ACI119891
1015840
1198881205731ACI119887 minus 05 (120578 minus 1) 119891
119905119887 + 120574120578119891
119905119887
4 Advances in Materials Science and Engineering
fcu
ftb
ft
fy
(a) Type 1
fcu
ftb
ft
fy
(b) Type 2
fcu
fy
1205741ft
(c) Type 3
ftb
ft
fy
1205731A
CIc
1205721ACIfcu
(d) Type 4
ftb
ft
fy
1205731A
CIc
1205721ACIfcu
(e) Type5
fy
1205741ft
1205731A
CIc
1205721ACIfcu
(f) Type 6
ftb
ft
fy
1205731U
HPC
c1205721UHPCfcu
(g) Type 7
ftb
ft
fy
1205731U
HPC
c
1205721UHPCfcu
(h) Type 8
fy
1205741ft
1205731U
HPC
c
1205721UHPCfcu
(i) Type 9
Figure 3 Stress block models
1198881198885
=
119860119904119891119910+ 05 (1 + 120574) 119891
119905119887ℎ
1205721ACI119891
1015840
1198881205731ACI119887 minus 05 (120578 minus 1) 119891
119905119887 + 05120578 (1 + 120574) 119891
119905119887
1198881198886
=
119860119904119891119910+ 120574119891119905ℎ119887
1205721ACI119891
1015840
1198881205731ACI119887 + 120574120578119891
119905119887
1198881198887
=
119860119904119891119910+ 120574119891119905119887ℎ
1205721UHPC119891
1015840
1198881205731UHPC119887 minus 05 (120578 minus 1) 119891
119905119887 + 120574120578119891
119905119887
1198881198888
=
119860119904119891119910+ 05 (1 + 120574) 119891
119905119887ℎ
1205721UHPC119891
1015840
1198881205731UHPC119887 minus 05 (120578 minus 1) 119891
119905119887 + 05120578 (1 + 120574) 119891
119905119887
1198881198889
=
119860119904119891119910+ 120574119891119905ℎ119887
1205721UHPC119891
1015840
1198881205731UHPC119887 + 120574120578119891
119905119887
(9)
where 1198911015840
119888is compressive strength of concrete 119860
119904is area of
tensile rebar 119891119910is yield strength of steel rebar 119891
119905is ultimate
tensile strength of concrete 120574 is ratio between post crackingtensile strength and ultimate tensile strength 120578 can be definedby 120576119891120576119888119906
+ 1 1205721and 120572
1UHPC are rectangular stress blockparameter for compressive strength of concrete for normalstrength concrete andUHPC respectively 120573
1and 1205731UHPC are
stress block depth parameter for normal strength concreteand UHPC respectively 119887 is width of section and 119889 is
effective depth of section 120576119891for 120578 is strain corresponding
to ultimate tensile strength and 120576119888119906
is ultimate compressivestrain of concrete
The most difficult and controversial part is the determi-nation of tensile strength of fiber reinforced concrete Swamyand Al-Tarsquoan [13] suggested the equation according to thecomposite theory as follows
119891119905= 0970119891
119903(1 minus 119881
119891) + 2119881
119891
119871119891
119863119891
(10)
where 119891119903is modulus of rupture of concrete and other
variables are fiber geometry defined in Section 2Using neutral axis depth defined in (9) considering
shape of stress block nominal flexural strength of ultra highperformance concrete members can be calculated as follows
Case 1 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 119891
119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(11)
Advances in Materials Science and Engineering 5
Table 1 Mix proportions
119908119887
Weight ratio Steel fiber Admixture 119891119888119896
Cement Water Silica fume Sand Filler (Micro Silica)() (kg) (MPa)
017 1 021 024 104 031 2 108 200
Case 2 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 119891
119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 +
ℎ minus 119890
3) + 119860
119904119891119910(119889 minus 119888)
(12)
Case 3 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 120574119891
119905(ℎ minus 119890) (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(13)
Cases 4 7 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 119891119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(14)
Cases 5 8 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 119891119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 +
ℎ minus 119890
2) + 119860
119904119891119910(119889 minus 119888)
(15)
Cases 6 9 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 120574119891119905(ℎ minus 119890) (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(16)
4 Flexural Behavior of Ultra HighPerformance Concrete Members
41 Test Plan In order to verify the applicability of sug-gested models ultra high performance concrete beam wastested Average ultimate compressive strength of standardcylinder was 216MPa Splitting strength of standard cylinderis distributed between 72sim195MPa Mix proportions forultra high performance concrete are summarized in Table 1Mechanical properties of concrete and rebar used in thisstudy were summarized in Tables 2 and 3 respectively
Table 2 Mechanical characteristics of rebar
MaterialsYield
strength(MPa)
Yieldstrain(120576119910)
Tensilestrength(MPa)
Poissonrsquosratio
D25 422 00021 621 028D10 384 00019 568 027
Preventing premature shear failure of specimen total spanof test specimen is reinforced by stirrups with spacing of150mm Stirrups were not located between two loadingpoints 2000 kN actuator was used for test and shear-span todepth ratio was 65 In order to verify the neutral axis depthcalculation model which was shown in (9) strain gages forconcrete were mounted at the concrete surface Strain gagesfor steel also can be attached to reinforcement at the centerof test specimen Details of test specimens were illustrated inFigure 4
42 Test Results Test specimens have shown the flexuralfailure pattern Because of inclusion of steel fiber cracklocalization did not occur until crushing of concrete occurredat extreme compression fiber After initial crack occurredcrackswere spread to outside themaximumbendingmomentarea After yielding of reinforcement diagonal tension crackwas not observed and cracks were spread to supports Atdeflection 98mm crushing of concrete occurred and crackswere propagated to crushing area with opening of initialcrack Final stage of failure and load-deflection relation wereshown in Figures 5(a) and 5(b) respectively Maximumload was 179 kN which occurred after yielding of reinforce-ment Analyzing strain gauges attached to concrete andreinforcement neutral axis depth was 123mm at peak loadstage
Neutral axis depth is important index for reinforcedconcrete members because flexural strength and ductilitycan highly depend on the neutral axis depth of sectionNeutral axis depth can be measured by test using the valueof strain gauge attached to compression fiber and tensionreinforcements Since strain gauge attached to extreme tensileand compression fiber failed before experiencing peak loadstrain of compression and tension reinforcement were usedCurvature at first yield of tension reinforcement was 00122(1m) and peak load curvature was 0019 (1m) Neutral axisdepth was 925mm and 1228mm from extreme compressionfiber respectively As shown in Figure 6 change of neutralaxis depth occurred after yielding of tension reinforcementAfter experiencing peak load neutral axis depth did notchange until crushing of concrete in compression side ofsection occurred
6 Advances in Materials Science and Engineering
Table 3 Mechanical characteristics of concrete
Stress state Ultimate strength(MPa) Youngrsquos modulus (MPa) Ultimatecracking
strain (permil) Poissonrsquos ratio
Compression 216 54306 3738 (120576119888119906) 026
Tension 98 0221 (120576119905)
350
300
50
150 1900 1900
5-D25
2-D10 Load Load
500 150
Strain gage
Strain gage
D10150 A
A
concrete
rebar
(a) Setting and measurement planSection A-A
5-D25
D10
200
240
6050
350
(b) Section
Figure 4 Details of test specimen
Table 4 Comparison between test results and assumed model
Model 119888 120576119904
119872119899
119875119899
(mm) (permil) (kNm) (kN)Type 1 9088 123 363 202Type 2 8598 13 296 164Type 3 9503 118 425 235Type 4 6876 163 356 197Type 5 7872 142 297 164Type 6 8739 128 433 240Type 7 9130 122 316 175Type 8 9813 114 308 170Type 9 10228 110 353 197Test results 93 910 322 179119888 neutral axis depth 120576
119904 strain at tensile reinforcement atmid length of beam
119872119899 nominal flexural strength of section (predicted value) and 119875
119899 load for
119872119899
43 Validation of Flexural StrengthModel Verifying suitabil-ity of flexural strength models test results were comparedwith assumed flexural strength model Comparison resultswere listed in Table 4 As expected model type 1 which hastriangular stress block has shown comparatively high accu-racy However this model overestimated moment capacity ofsection Overestimation of this model was caused by largearea of tensile stress block and higher value of momentarm Higher value of moment arm can be derived by theexistence of residual strength Model type 2 also has shownacceptable accuracy but this model underestimated momentcapacity Underestimation of this model was caused by therelatively low level of tensile stress block area and lower valueof moment arm for tensile stress block This smaller momentarm was derived by the end of the stress block Model type3 which has rectangular tensile stress block has shown lowaccuracy and overestimation
Generally rectangular stress block has shown deeperneutral axis depth from compression fiber than triangularstress block moment arm has lower value than the casesof triangular stress block types Model types with ACI
rectangular stress block have low accuracy on neutral axisdepth tensile strain of reinforcements andmoment capacityThis phenomenonwas caused by the larger area of stress blockthan triangular stress block However Models with ultrahigh performance concrete stress block parameters whichare derived from test results [12] have shown relatively highaccuracy with all types of tensile stress block This modelespecially predicts neutral axis depth more accurately thanother models As discussed above the most accurate tensilestress block was also stress block including residual strengthof concrete
Considering low ductility which is caused by explosivefailure of ultra high strength concrete the most appropriatemodel for design of flexural strength is type 8whichwasmod-elled by UHPC-rectangular stress block parameters undercompression and tension softening considering model undertension Type 7 also can be used for design purposes butin this case strength reduction factor is carefully consideredwith material properties
5 Validation of Flexural Strength Models withPrevious Researches
For the verification of wide range applicability of assumedmodel existing test results [6ndash8] of ultra high performanceconcrete members were compared with assumed modelsBecause a few number of specimens exist only 22 test resultswere compared with suggested model Specifications forcollected test results were shown in Table 5 Test results fromeach research were summarized in Table 5 All test specimensexperienced yielding of reinforcement before reaching peakload They failed with flexural failure at the center of thespecimens Collected test specimens have 027 to 236 oftensile reinforcement ratio and 80sim200MPa of compressivestrength of concrete Fiber contents were distributed from05 to 20
According to the test results of Ashour et al [6] effect ofthe fibers to flexural strength is independent of the amount ofreinforcement but additional moment is proportional to con-crete compressive strength Therefore compressive strength
Advances in Materials Science and Engineering 7
(a) Final stage of failure
Load
s (kN
)
220
200
180
160140120100806040200
160
140
120
100
80
60
40
20
0
Deflection (mm)
Peak strengthType 1 202 kN
Type 7 175kN
Type 1 Type 7
fcu
ftb
ft
fy
ftb
ft
fy
1205731U
HPC
c
1205721UHPCfcu
(b) Load-deflection relation
Figure 5 Test results
Neu
tral
axis
(mm
)
350
300
250
200
150
100
50
0
000
000
001 002
002
003 004
004
005
Curvature (1m)
Yielding ofreinforcement
93mm Peak load
Extreme tensile fiber
Extreme compression fiber
Measurement 1 compression steelMeasurement 2 compression fiber
Type 7 973mm
Figure 6 Change of neutral axis depth
of concrete should be considered in flexural strength modelDancygier and Savir [7] investigated flexural strength of fiberreinforced concrete with conventional reinforcement ratiolower than 1 Fiber length which affects reinforcing index(RI = 119881
119891119871119891119863119891 where119881
119891is fibre volume fraction 119871
119891is fiber
length and119863119891is fiber diameter) directly changes the flexural
strength of section Generally fiber length changes the failuremode of fiber reinforced concrete under bending especiallyafter peak load Therefore material behavior under tensionshould be considered for flexural strength calculation Yang etal [8] investigated about placing method and reinforcementratio especially for ultra high performance concrete whichhave compressive strength around 200MPa According tothis research reinforcement ratio also affects the flexuralstrength and ductility although members have much higher
compressive strength of concrete Some of test results did notevaluate prediction methods previously investigated [2 4 5]
Therefore all assumed models were examined with testresults Comparison of test results with flexural strengthmodels was shown in Figures 7(a)ndash7(d) and descriptive sta-tistical data were shown in Table 6 Existing flexural strengthmodel which was reviewed in this paper only has accuracywhen using comparatively lower compressive strength ofconcrete (80sim100MPa) as shown in Figure 7(a)The varianceof this model increases with increase of compressive strengthof concrete As shown in Figures 7(b) and 7(c) types 1to 6 still have overestimated the flexural strength of ultrahigh performance concreteHowever when tension softeningmodel was applied accuracy comparatively increased Types7 to 9 which use the newly developed rectangular stressblock show more accuracy and safety rather than the other9 models Types 7 and 8 especially have high accuracy overthe range of ultra high performance concrete Because type8 which uses tension softening model underestimates theflexural capacity it would be used for safe design of ultra highperformance concrete members
6 Conclusion
The following conclusions can be made from the statisticalinvestigation analytical works and tests for FRUHSC forflexural strength
(1) Stress distribution of ultra high performance concreteunder compression shaped as triangle Under tensilestress stress distribution of ultra high performanceconcrete can be varied with fiber contents or shape
(2) Nine-flexural strengthmodels were evaluated For theconservative estimation ultimate strain at compres-sion fiber was assumed to be 0003 These flexuralstrength models were evaluated using assumed stressdistribution
8 Advances in Materials Science and Engineering
Table 5 Previous test results
Specimen 119887 ℎ 119889 119860119904119905
120588 119891119888119906
119881119891
119863119891
119871119891
119891119910
119875119906
(mm) (mm) (mm) (mm2) () (MPa) () (mm) (mm) (MPa) (kN)Ashour et al [6]
B-05-M2 200 250 215 509 118 82 05 08 60 530 491B-10-M2 200 250 215 509 118 87 1 08 60 530 542B-05-M3 200 250 215 763 178 82 05 08 60 530 695B-10-M3 200 250 215 763 178 87 1 08 60 530 714B-05-M4 200 250 215 1018 237 82 05 08 60 530 881B-10-M4 200 250 215 1018 237 87 1 08 60 530 897B-05-H2 200 250 215 509 118 107 05 08 60 530 485B-10-H2 200 250 215 509 118 111 1 08 60 530 537B-05-H3 200 250 215 763 178 107 05 08 60 530 696B-10-H3 200 250 215 763 178 111 1 08 60 530 741B-05-H4 200 250 215 1018 237 107 05 08 60 530 891B-10-H4 200 250 215 1018 237 111 1 08 60 530 935
Dancygier and Savir [7]H5-F2-1 35 200 300 273 151 028 129 075 09 35 480 236H5-F2-1 60 200 300 273 151 028 124 075 09 60 480 273H8-F2-1 35 200 300 273 302 055 124 075 09 35 480 389H8-F2-1 60 200 300 273 302 055 122 075 09 60 480 372H5-F2-1 35 3 200 300 273 151 028 122 075 09 35 616 281
Yang et al [8]R12-1 180 270 235 253 060 191 2 02 13 400 770R13-1 180 270 235 380 090 192 2 02 13 400 863R14-1 180 270 235 507 120 197 2 02 13 400 1031R23-2 180 270 220 760 120 196 2 02 13 400 1165119887 beam width ℎ beam height 119889 effective depth of beam 119860
119904119905 tensile reinforcement area 120588 reinforcement ratio 119891
119888119906 compressive strength of concrete 119881
119891
volume fraction of steel fiber119863119891 fiber diameter 119871
119891 fiber length 119891
119910 yield strength of reinforcement and 119875
119906 test results (load at ultimate failure)
Table 6 Descriptive statistics on collected test data(testprediction)
ID Mean Median SD Var COV IAEACI544 124 106 034 0115 027 1720Imam 122 101 045 0201 037 1983Lim 113 104 026 0068 023 1415Type 1 081 090 020 0040 024 3356Type 2 118 107 029 0086 025 1672Type 3 070 076 016 0024 022 4654Type 4 087 091 014 0021 016 1563Type 5 118 106 030 0091 025 1662Type 6 069 075 015 0023 022 4918Type 7 090 095 015 0021 016 1030Type 8 111 107 024 0060 022 1142Type 9 073 077 014 0021 020 3558SD standard variation Var variance COV coefficient of variation and IAEintegrated absolute error
(3) The most accurate model of ultra high performanceconcrete under compression is triangular Becauseultra high performance concrete has large elastic areafailure occurred with the same time experiencing
ultimate strength However for the safe design ofsection flexural strength model which uses modifiedrectangular stress blocks considering mechanicalcharacteristics of UHPC should be used
(4) Evaluating validation process using test result ofthis study and previous researches existing flexuralstrength calculation models cannot accurately andsafely predict the flexural strength of ultra highstrength concrete specimens especially for compres-sive strength larger than 100MPa However flexuralstrength model suggested in this study can pro-vide conservative and highly accurate (10 of error)results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by a grant (15CTAP-C097356-01) from Creative Challenge Research Program fundedby Ministry of Land Infrastructure and Transport of
Advances in Materials Science and Engineering 9
Test
valu
eth
eorit
ical
val
ue35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
ACI544mdashAshour (1)ImammdashAshour (1)LimmdashAshour (1)ACI544mdashAshour (2)ImammdashAshour (2)
LimmdashAshour (2)ACI544mdashYangImammdashYangLimmdashYang
(a) Existing modelTe
st va
lue
theo
ritic
al v
alue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 1mdashAshourType 2mdashAshourType 3mdashAshourType 1mdashDancygierType 2mdashDancygier
Type 3mdashDancygierType 1mdashYangType 2mdashYangType 3mdashYang
(b) Assumed types 1sim3
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 4mdashAshourType 5mdashAshourType 6mdashAshourType 4mdashDancygierType 5mdashDancygier
Type 6mdashDancygierType 4mdashYangType 5mdashYangType 6mdashYang
(c) Assumed types 4sim6
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 7mdashAshourType 8mdashAshourType 9mdashAshourType 7mdashDancygierType 8mdashDancygier
Type 9mdashDancygierType 7mdashYangType 8mdashYangType 9mdashYang
(d) Assumed types 7sim9
Figure 7 Applicability verification for prediction model
Korean government and National Research Foundation ofKorea(NRF) funded by the Ministry of Science ICT andFuture Planning (no NRF-2014R1A2A1A11051049)
References
[1] ACI Committee ldquoBuilding code requirements for structuralconcrete and commentaryrdquo ACI 318-11 American ConcreteInstitute Farmington Hills Mich USA 2011
[2] American Concrete Institute Committee 544 ldquoDesign con-siderations for steel fiber reinforced concreterdquo InternationalConcrete Abstracts Portal vol 85 no 5 pp 563ndash579 1988
[3] C H Henager and T J Doherty ldquoAnalysis of reinforced fibrousconcrete beamsrdquo Journal of the Structural Division vol 102 no1 pp 177ndash188 1976 ASCE Proceedings
[4] M Imam L Vandewalle and F Mortelmans ldquoShear-momentanalysis of reinforced high strength concrete beams containingsteel fibresrdquo Canadian Journal of Civil Engineering vol 22 no3 pp 462ndash470 1995
[5] T Y Lim P Paramasivan and S L Lee ldquoShear and momentcapacity of reinforced steel fiber concrete beamsrdquo Magazine ofConcrete Research vol 39 no 140 pp 148ndash160 1987
[6] S A Ashour F F Wafa and M I Kamal ldquoEffect of theconcrete compressive strength and tensile reinforcement ratio
10 Advances in Materials Science and Engineering
on the flexural behavior of fibrous concrete beamsrdquo EngineeringStructures vol 22 no 9 pp 1145ndash1158 2000
[7] A N Dancygier and Z Savir ldquoFlexural behavior ofHSFRCwithlow reinforcement ratiosrdquo Engineering Structures vol 28 no 11pp 1503ndash1512 2006
[8] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010
[9] RILEM and Final recommendations of TC 162-TDF ldquoTest anddesign methods for steel fibre reinforced concrete 120590-120576 designmethodrdquoMaterials and Structures vol 36 pp 560ndash565 2003
[10] European Committee for Standardization Eurocode 2 (EC2)Design of Concrete Structures 2004
[11] AFGCGroupe de Travail BFUP SETRA-AFGCUltra High Per-formance Fiber-Reinforced Concretes Interim Recommendation2002
[12] B I Bae C S Choi and H K Choi ldquoEvaluation of rectangularstress block parameters of reactive powder concrete membersrdquoJournal of the Architectural Institute of Korea vol 28 no 7 pp3ndash11 2012
[13] R N Swamy and S A Al-Tarsquoan ldquoDeformation and ultimatestrength in flexure of reinforced concrete beamsmadewith steelfibre concreterdquo Journal of the American Concrete Institute vol78 no 5 pp 395ndash405 1981
Submit your manuscripts athttpwwwhindawicom
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Biomaterials
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Advances in
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MaterialsJournal of
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Nano
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Journal ofNanomaterials
4 Advances in Materials Science and Engineering
fcu
ftb
ft
fy
(a) Type 1
fcu
ftb
ft
fy
(b) Type 2
fcu
fy
1205741ft
(c) Type 3
ftb
ft
fy
1205731A
CIc
1205721ACIfcu
(d) Type 4
ftb
ft
fy
1205731A
CIc
1205721ACIfcu
(e) Type5
fy
1205741ft
1205731A
CIc
1205721ACIfcu
(f) Type 6
ftb
ft
fy
1205731U
HPC
c1205721UHPCfcu
(g) Type 7
ftb
ft
fy
1205731U
HPC
c
1205721UHPCfcu
(h) Type 8
fy
1205741ft
1205731U
HPC
c
1205721UHPCfcu
(i) Type 9
Figure 3 Stress block models
1198881198885
=
119860119904119891119910+ 05 (1 + 120574) 119891
119905119887ℎ
1205721ACI119891
1015840
1198881205731ACI119887 minus 05 (120578 minus 1) 119891
119905119887 + 05120578 (1 + 120574) 119891
119905119887
1198881198886
=
119860119904119891119910+ 120574119891119905ℎ119887
1205721ACI119891
1015840
1198881205731ACI119887 + 120574120578119891
119905119887
1198881198887
=
119860119904119891119910+ 120574119891119905119887ℎ
1205721UHPC119891
1015840
1198881205731UHPC119887 minus 05 (120578 minus 1) 119891
119905119887 + 120574120578119891
119905119887
1198881198888
=
119860119904119891119910+ 05 (1 + 120574) 119891
119905119887ℎ
1205721UHPC119891
1015840
1198881205731UHPC119887 minus 05 (120578 minus 1) 119891
119905119887 + 05120578 (1 + 120574) 119891
119905119887
1198881198889
=
119860119904119891119910+ 120574119891119905ℎ119887
1205721UHPC119891
1015840
1198881205731UHPC119887 + 120574120578119891
119905119887
(9)
where 1198911015840
119888is compressive strength of concrete 119860
119904is area of
tensile rebar 119891119910is yield strength of steel rebar 119891
119905is ultimate
tensile strength of concrete 120574 is ratio between post crackingtensile strength and ultimate tensile strength 120578 can be definedby 120576119891120576119888119906
+ 1 1205721and 120572
1UHPC are rectangular stress blockparameter for compressive strength of concrete for normalstrength concrete andUHPC respectively 120573
1and 1205731UHPC are
stress block depth parameter for normal strength concreteand UHPC respectively 119887 is width of section and 119889 is
effective depth of section 120576119891for 120578 is strain corresponding
to ultimate tensile strength and 120576119888119906
is ultimate compressivestrain of concrete
The most difficult and controversial part is the determi-nation of tensile strength of fiber reinforced concrete Swamyand Al-Tarsquoan [13] suggested the equation according to thecomposite theory as follows
119891119905= 0970119891
119903(1 minus 119881
119891) + 2119881
119891
119871119891
119863119891
(10)
where 119891119903is modulus of rupture of concrete and other
variables are fiber geometry defined in Section 2Using neutral axis depth defined in (9) considering
shape of stress block nominal flexural strength of ultra highperformance concrete members can be calculated as follows
Case 1 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 119891
119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(11)
Advances in Materials Science and Engineering 5
Table 1 Mix proportions
119908119887
Weight ratio Steel fiber Admixture 119891119888119896
Cement Water Silica fume Sand Filler (Micro Silica)() (kg) (MPa)
017 1 021 024 104 031 2 108 200
Case 2 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 119891
119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 +
ℎ minus 119890
3) + 119860
119904119891119910(119889 minus 119888)
(12)
Case 3 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 120574119891
119905(ℎ minus 119890) (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(13)
Cases 4 7 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 119891119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(14)
Cases 5 8 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 119891119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 +
ℎ minus 119890
2) + 119860
119904119891119910(119889 minus 119888)
(15)
Cases 6 9 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 120574119891119905(ℎ minus 119890) (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(16)
4 Flexural Behavior of Ultra HighPerformance Concrete Members
41 Test Plan In order to verify the applicability of sug-gested models ultra high performance concrete beam wastested Average ultimate compressive strength of standardcylinder was 216MPa Splitting strength of standard cylinderis distributed between 72sim195MPa Mix proportions forultra high performance concrete are summarized in Table 1Mechanical properties of concrete and rebar used in thisstudy were summarized in Tables 2 and 3 respectively
Table 2 Mechanical characteristics of rebar
MaterialsYield
strength(MPa)
Yieldstrain(120576119910)
Tensilestrength(MPa)
Poissonrsquosratio
D25 422 00021 621 028D10 384 00019 568 027
Preventing premature shear failure of specimen total spanof test specimen is reinforced by stirrups with spacing of150mm Stirrups were not located between two loadingpoints 2000 kN actuator was used for test and shear-span todepth ratio was 65 In order to verify the neutral axis depthcalculation model which was shown in (9) strain gages forconcrete were mounted at the concrete surface Strain gagesfor steel also can be attached to reinforcement at the centerof test specimen Details of test specimens were illustrated inFigure 4
42 Test Results Test specimens have shown the flexuralfailure pattern Because of inclusion of steel fiber cracklocalization did not occur until crushing of concrete occurredat extreme compression fiber After initial crack occurredcrackswere spread to outside themaximumbendingmomentarea After yielding of reinforcement diagonal tension crackwas not observed and cracks were spread to supports Atdeflection 98mm crushing of concrete occurred and crackswere propagated to crushing area with opening of initialcrack Final stage of failure and load-deflection relation wereshown in Figures 5(a) and 5(b) respectively Maximumload was 179 kN which occurred after yielding of reinforce-ment Analyzing strain gauges attached to concrete andreinforcement neutral axis depth was 123mm at peak loadstage
Neutral axis depth is important index for reinforcedconcrete members because flexural strength and ductilitycan highly depend on the neutral axis depth of sectionNeutral axis depth can be measured by test using the valueof strain gauge attached to compression fiber and tensionreinforcements Since strain gauge attached to extreme tensileand compression fiber failed before experiencing peak loadstrain of compression and tension reinforcement were usedCurvature at first yield of tension reinforcement was 00122(1m) and peak load curvature was 0019 (1m) Neutral axisdepth was 925mm and 1228mm from extreme compressionfiber respectively As shown in Figure 6 change of neutralaxis depth occurred after yielding of tension reinforcementAfter experiencing peak load neutral axis depth did notchange until crushing of concrete in compression side ofsection occurred
6 Advances in Materials Science and Engineering
Table 3 Mechanical characteristics of concrete
Stress state Ultimate strength(MPa) Youngrsquos modulus (MPa) Ultimatecracking
strain (permil) Poissonrsquos ratio
Compression 216 54306 3738 (120576119888119906) 026
Tension 98 0221 (120576119905)
350
300
50
150 1900 1900
5-D25
2-D10 Load Load
500 150
Strain gage
Strain gage
D10150 A
A
concrete
rebar
(a) Setting and measurement planSection A-A
5-D25
D10
200
240
6050
350
(b) Section
Figure 4 Details of test specimen
Table 4 Comparison between test results and assumed model
Model 119888 120576119904
119872119899
119875119899
(mm) (permil) (kNm) (kN)Type 1 9088 123 363 202Type 2 8598 13 296 164Type 3 9503 118 425 235Type 4 6876 163 356 197Type 5 7872 142 297 164Type 6 8739 128 433 240Type 7 9130 122 316 175Type 8 9813 114 308 170Type 9 10228 110 353 197Test results 93 910 322 179119888 neutral axis depth 120576
119904 strain at tensile reinforcement atmid length of beam
119872119899 nominal flexural strength of section (predicted value) and 119875
119899 load for
119872119899
43 Validation of Flexural StrengthModel Verifying suitabil-ity of flexural strength models test results were comparedwith assumed flexural strength model Comparison resultswere listed in Table 4 As expected model type 1 which hastriangular stress block has shown comparatively high accu-racy However this model overestimated moment capacity ofsection Overestimation of this model was caused by largearea of tensile stress block and higher value of momentarm Higher value of moment arm can be derived by theexistence of residual strength Model type 2 also has shownacceptable accuracy but this model underestimated momentcapacity Underestimation of this model was caused by therelatively low level of tensile stress block area and lower valueof moment arm for tensile stress block This smaller momentarm was derived by the end of the stress block Model type3 which has rectangular tensile stress block has shown lowaccuracy and overestimation
Generally rectangular stress block has shown deeperneutral axis depth from compression fiber than triangularstress block moment arm has lower value than the casesof triangular stress block types Model types with ACI
rectangular stress block have low accuracy on neutral axisdepth tensile strain of reinforcements andmoment capacityThis phenomenonwas caused by the larger area of stress blockthan triangular stress block However Models with ultrahigh performance concrete stress block parameters whichare derived from test results [12] have shown relatively highaccuracy with all types of tensile stress block This modelespecially predicts neutral axis depth more accurately thanother models As discussed above the most accurate tensilestress block was also stress block including residual strengthof concrete
Considering low ductility which is caused by explosivefailure of ultra high strength concrete the most appropriatemodel for design of flexural strength is type 8whichwasmod-elled by UHPC-rectangular stress block parameters undercompression and tension softening considering model undertension Type 7 also can be used for design purposes butin this case strength reduction factor is carefully consideredwith material properties
5 Validation of Flexural Strength Models withPrevious Researches
For the verification of wide range applicability of assumedmodel existing test results [6ndash8] of ultra high performanceconcrete members were compared with assumed modelsBecause a few number of specimens exist only 22 test resultswere compared with suggested model Specifications forcollected test results were shown in Table 5 Test results fromeach research were summarized in Table 5 All test specimensexperienced yielding of reinforcement before reaching peakload They failed with flexural failure at the center of thespecimens Collected test specimens have 027 to 236 oftensile reinforcement ratio and 80sim200MPa of compressivestrength of concrete Fiber contents were distributed from05 to 20
According to the test results of Ashour et al [6] effect ofthe fibers to flexural strength is independent of the amount ofreinforcement but additional moment is proportional to con-crete compressive strength Therefore compressive strength
Advances in Materials Science and Engineering 7
(a) Final stage of failure
Load
s (kN
)
220
200
180
160140120100806040200
160
140
120
100
80
60
40
20
0
Deflection (mm)
Peak strengthType 1 202 kN
Type 7 175kN
Type 1 Type 7
fcu
ftb
ft
fy
ftb
ft
fy
1205731U
HPC
c
1205721UHPCfcu
(b) Load-deflection relation
Figure 5 Test results
Neu
tral
axis
(mm
)
350
300
250
200
150
100
50
0
000
000
001 002
002
003 004
004
005
Curvature (1m)
Yielding ofreinforcement
93mm Peak load
Extreme tensile fiber
Extreme compression fiber
Measurement 1 compression steelMeasurement 2 compression fiber
Type 7 973mm
Figure 6 Change of neutral axis depth
of concrete should be considered in flexural strength modelDancygier and Savir [7] investigated flexural strength of fiberreinforced concrete with conventional reinforcement ratiolower than 1 Fiber length which affects reinforcing index(RI = 119881
119891119871119891119863119891 where119881
119891is fibre volume fraction 119871
119891is fiber
length and119863119891is fiber diameter) directly changes the flexural
strength of section Generally fiber length changes the failuremode of fiber reinforced concrete under bending especiallyafter peak load Therefore material behavior under tensionshould be considered for flexural strength calculation Yang etal [8] investigated about placing method and reinforcementratio especially for ultra high performance concrete whichhave compressive strength around 200MPa According tothis research reinforcement ratio also affects the flexuralstrength and ductility although members have much higher
compressive strength of concrete Some of test results did notevaluate prediction methods previously investigated [2 4 5]
Therefore all assumed models were examined with testresults Comparison of test results with flexural strengthmodels was shown in Figures 7(a)ndash7(d) and descriptive sta-tistical data were shown in Table 6 Existing flexural strengthmodel which was reviewed in this paper only has accuracywhen using comparatively lower compressive strength ofconcrete (80sim100MPa) as shown in Figure 7(a)The varianceof this model increases with increase of compressive strengthof concrete As shown in Figures 7(b) and 7(c) types 1to 6 still have overestimated the flexural strength of ultrahigh performance concreteHowever when tension softeningmodel was applied accuracy comparatively increased Types7 to 9 which use the newly developed rectangular stressblock show more accuracy and safety rather than the other9 models Types 7 and 8 especially have high accuracy overthe range of ultra high performance concrete Because type8 which uses tension softening model underestimates theflexural capacity it would be used for safe design of ultra highperformance concrete members
6 Conclusion
The following conclusions can be made from the statisticalinvestigation analytical works and tests for FRUHSC forflexural strength
(1) Stress distribution of ultra high performance concreteunder compression shaped as triangle Under tensilestress stress distribution of ultra high performanceconcrete can be varied with fiber contents or shape
(2) Nine-flexural strengthmodels were evaluated For theconservative estimation ultimate strain at compres-sion fiber was assumed to be 0003 These flexuralstrength models were evaluated using assumed stressdistribution
8 Advances in Materials Science and Engineering
Table 5 Previous test results
Specimen 119887 ℎ 119889 119860119904119905
120588 119891119888119906
119881119891
119863119891
119871119891
119891119910
119875119906
(mm) (mm) (mm) (mm2) () (MPa) () (mm) (mm) (MPa) (kN)Ashour et al [6]
B-05-M2 200 250 215 509 118 82 05 08 60 530 491B-10-M2 200 250 215 509 118 87 1 08 60 530 542B-05-M3 200 250 215 763 178 82 05 08 60 530 695B-10-M3 200 250 215 763 178 87 1 08 60 530 714B-05-M4 200 250 215 1018 237 82 05 08 60 530 881B-10-M4 200 250 215 1018 237 87 1 08 60 530 897B-05-H2 200 250 215 509 118 107 05 08 60 530 485B-10-H2 200 250 215 509 118 111 1 08 60 530 537B-05-H3 200 250 215 763 178 107 05 08 60 530 696B-10-H3 200 250 215 763 178 111 1 08 60 530 741B-05-H4 200 250 215 1018 237 107 05 08 60 530 891B-10-H4 200 250 215 1018 237 111 1 08 60 530 935
Dancygier and Savir [7]H5-F2-1 35 200 300 273 151 028 129 075 09 35 480 236H5-F2-1 60 200 300 273 151 028 124 075 09 60 480 273H8-F2-1 35 200 300 273 302 055 124 075 09 35 480 389H8-F2-1 60 200 300 273 302 055 122 075 09 60 480 372H5-F2-1 35 3 200 300 273 151 028 122 075 09 35 616 281
Yang et al [8]R12-1 180 270 235 253 060 191 2 02 13 400 770R13-1 180 270 235 380 090 192 2 02 13 400 863R14-1 180 270 235 507 120 197 2 02 13 400 1031R23-2 180 270 220 760 120 196 2 02 13 400 1165119887 beam width ℎ beam height 119889 effective depth of beam 119860
119904119905 tensile reinforcement area 120588 reinforcement ratio 119891
119888119906 compressive strength of concrete 119881
119891
volume fraction of steel fiber119863119891 fiber diameter 119871
119891 fiber length 119891
119910 yield strength of reinforcement and 119875
119906 test results (load at ultimate failure)
Table 6 Descriptive statistics on collected test data(testprediction)
ID Mean Median SD Var COV IAEACI544 124 106 034 0115 027 1720Imam 122 101 045 0201 037 1983Lim 113 104 026 0068 023 1415Type 1 081 090 020 0040 024 3356Type 2 118 107 029 0086 025 1672Type 3 070 076 016 0024 022 4654Type 4 087 091 014 0021 016 1563Type 5 118 106 030 0091 025 1662Type 6 069 075 015 0023 022 4918Type 7 090 095 015 0021 016 1030Type 8 111 107 024 0060 022 1142Type 9 073 077 014 0021 020 3558SD standard variation Var variance COV coefficient of variation and IAEintegrated absolute error
(3) The most accurate model of ultra high performanceconcrete under compression is triangular Becauseultra high performance concrete has large elastic areafailure occurred with the same time experiencing
ultimate strength However for the safe design ofsection flexural strength model which uses modifiedrectangular stress blocks considering mechanicalcharacteristics of UHPC should be used
(4) Evaluating validation process using test result ofthis study and previous researches existing flexuralstrength calculation models cannot accurately andsafely predict the flexural strength of ultra highstrength concrete specimens especially for compres-sive strength larger than 100MPa However flexuralstrength model suggested in this study can pro-vide conservative and highly accurate (10 of error)results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by a grant (15CTAP-C097356-01) from Creative Challenge Research Program fundedby Ministry of Land Infrastructure and Transport of
Advances in Materials Science and Engineering 9
Test
valu
eth
eorit
ical
val
ue35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
ACI544mdashAshour (1)ImammdashAshour (1)LimmdashAshour (1)ACI544mdashAshour (2)ImammdashAshour (2)
LimmdashAshour (2)ACI544mdashYangImammdashYangLimmdashYang
(a) Existing modelTe
st va
lue
theo
ritic
al v
alue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 1mdashAshourType 2mdashAshourType 3mdashAshourType 1mdashDancygierType 2mdashDancygier
Type 3mdashDancygierType 1mdashYangType 2mdashYangType 3mdashYang
(b) Assumed types 1sim3
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 4mdashAshourType 5mdashAshourType 6mdashAshourType 4mdashDancygierType 5mdashDancygier
Type 6mdashDancygierType 4mdashYangType 5mdashYangType 6mdashYang
(c) Assumed types 4sim6
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 7mdashAshourType 8mdashAshourType 9mdashAshourType 7mdashDancygierType 8mdashDancygier
Type 9mdashDancygierType 7mdashYangType 8mdashYangType 9mdashYang
(d) Assumed types 7sim9
Figure 7 Applicability verification for prediction model
Korean government and National Research Foundation ofKorea(NRF) funded by the Ministry of Science ICT andFuture Planning (no NRF-2014R1A2A1A11051049)
References
[1] ACI Committee ldquoBuilding code requirements for structuralconcrete and commentaryrdquo ACI 318-11 American ConcreteInstitute Farmington Hills Mich USA 2011
[2] American Concrete Institute Committee 544 ldquoDesign con-siderations for steel fiber reinforced concreterdquo InternationalConcrete Abstracts Portal vol 85 no 5 pp 563ndash579 1988
[3] C H Henager and T J Doherty ldquoAnalysis of reinforced fibrousconcrete beamsrdquo Journal of the Structural Division vol 102 no1 pp 177ndash188 1976 ASCE Proceedings
[4] M Imam L Vandewalle and F Mortelmans ldquoShear-momentanalysis of reinforced high strength concrete beams containingsteel fibresrdquo Canadian Journal of Civil Engineering vol 22 no3 pp 462ndash470 1995
[5] T Y Lim P Paramasivan and S L Lee ldquoShear and momentcapacity of reinforced steel fiber concrete beamsrdquo Magazine ofConcrete Research vol 39 no 140 pp 148ndash160 1987
[6] S A Ashour F F Wafa and M I Kamal ldquoEffect of theconcrete compressive strength and tensile reinforcement ratio
10 Advances in Materials Science and Engineering
on the flexural behavior of fibrous concrete beamsrdquo EngineeringStructures vol 22 no 9 pp 1145ndash1158 2000
[7] A N Dancygier and Z Savir ldquoFlexural behavior ofHSFRCwithlow reinforcement ratiosrdquo Engineering Structures vol 28 no 11pp 1503ndash1512 2006
[8] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010
[9] RILEM and Final recommendations of TC 162-TDF ldquoTest anddesign methods for steel fibre reinforced concrete 120590-120576 designmethodrdquoMaterials and Structures vol 36 pp 560ndash565 2003
[10] European Committee for Standardization Eurocode 2 (EC2)Design of Concrete Structures 2004
[11] AFGCGroupe de Travail BFUP SETRA-AFGCUltra High Per-formance Fiber-Reinforced Concretes Interim Recommendation2002
[12] B I Bae C S Choi and H K Choi ldquoEvaluation of rectangularstress block parameters of reactive powder concrete membersrdquoJournal of the Architectural Institute of Korea vol 28 no 7 pp3ndash11 2012
[13] R N Swamy and S A Al-Tarsquoan ldquoDeformation and ultimatestrength in flexure of reinforced concrete beamsmadewith steelfibre concreterdquo Journal of the American Concrete Institute vol78 no 5 pp 395ndash405 1981
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Advances in Materials Science and Engineering 5
Table 1 Mix proportions
119908119887
Weight ratio Steel fiber Admixture 119891119888119896
Cement Water Silica fume Sand Filler (Micro Silica)() (kg) (MPa)
017 1 021 024 104 031 2 108 200
Case 2 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 119891
119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 +
ℎ minus 119890
3) + 119860
119904119891119910(119889 minus 119888)
(12)
Case 3 Consider
119872119899= (
119891119888119896119888119887
2)
2
3119888 + 120574119891
119905(ℎ minus 119890) (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(13)
Cases 4 7 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 119891119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(14)
Cases 5 8 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 119891119905(119890 minus 119888) 119887
2
3(119890 minus 119888)
+ 120574119891119905(ℎ minus 119890) 119887 (119890 +
ℎ minus 119890
2) + 119860
119904119891119910(119889 minus 119888)
(15)
Cases 6 9 Consider
119872119899= (11988611198911198881198961205731119888119887)
119888
2+ 120574119891119905(ℎ minus 119890) (119890 minus 119888 +
ℎ minus 119890
2)
+ 119860119904119891119910(119889 minus 119888)
(16)
4 Flexural Behavior of Ultra HighPerformance Concrete Members
41 Test Plan In order to verify the applicability of sug-gested models ultra high performance concrete beam wastested Average ultimate compressive strength of standardcylinder was 216MPa Splitting strength of standard cylinderis distributed between 72sim195MPa Mix proportions forultra high performance concrete are summarized in Table 1Mechanical properties of concrete and rebar used in thisstudy were summarized in Tables 2 and 3 respectively
Table 2 Mechanical characteristics of rebar
MaterialsYield
strength(MPa)
Yieldstrain(120576119910)
Tensilestrength(MPa)
Poissonrsquosratio
D25 422 00021 621 028D10 384 00019 568 027
Preventing premature shear failure of specimen total spanof test specimen is reinforced by stirrups with spacing of150mm Stirrups were not located between two loadingpoints 2000 kN actuator was used for test and shear-span todepth ratio was 65 In order to verify the neutral axis depthcalculation model which was shown in (9) strain gages forconcrete were mounted at the concrete surface Strain gagesfor steel also can be attached to reinforcement at the centerof test specimen Details of test specimens were illustrated inFigure 4
42 Test Results Test specimens have shown the flexuralfailure pattern Because of inclusion of steel fiber cracklocalization did not occur until crushing of concrete occurredat extreme compression fiber After initial crack occurredcrackswere spread to outside themaximumbendingmomentarea After yielding of reinforcement diagonal tension crackwas not observed and cracks were spread to supports Atdeflection 98mm crushing of concrete occurred and crackswere propagated to crushing area with opening of initialcrack Final stage of failure and load-deflection relation wereshown in Figures 5(a) and 5(b) respectively Maximumload was 179 kN which occurred after yielding of reinforce-ment Analyzing strain gauges attached to concrete andreinforcement neutral axis depth was 123mm at peak loadstage
Neutral axis depth is important index for reinforcedconcrete members because flexural strength and ductilitycan highly depend on the neutral axis depth of sectionNeutral axis depth can be measured by test using the valueof strain gauge attached to compression fiber and tensionreinforcements Since strain gauge attached to extreme tensileand compression fiber failed before experiencing peak loadstrain of compression and tension reinforcement were usedCurvature at first yield of tension reinforcement was 00122(1m) and peak load curvature was 0019 (1m) Neutral axisdepth was 925mm and 1228mm from extreme compressionfiber respectively As shown in Figure 6 change of neutralaxis depth occurred after yielding of tension reinforcementAfter experiencing peak load neutral axis depth did notchange until crushing of concrete in compression side ofsection occurred
6 Advances in Materials Science and Engineering
Table 3 Mechanical characteristics of concrete
Stress state Ultimate strength(MPa) Youngrsquos modulus (MPa) Ultimatecracking
strain (permil) Poissonrsquos ratio
Compression 216 54306 3738 (120576119888119906) 026
Tension 98 0221 (120576119905)
350
300
50
150 1900 1900
5-D25
2-D10 Load Load
500 150
Strain gage
Strain gage
D10150 A
A
concrete
rebar
(a) Setting and measurement planSection A-A
5-D25
D10
200
240
6050
350
(b) Section
Figure 4 Details of test specimen
Table 4 Comparison between test results and assumed model
Model 119888 120576119904
119872119899
119875119899
(mm) (permil) (kNm) (kN)Type 1 9088 123 363 202Type 2 8598 13 296 164Type 3 9503 118 425 235Type 4 6876 163 356 197Type 5 7872 142 297 164Type 6 8739 128 433 240Type 7 9130 122 316 175Type 8 9813 114 308 170Type 9 10228 110 353 197Test results 93 910 322 179119888 neutral axis depth 120576
119904 strain at tensile reinforcement atmid length of beam
119872119899 nominal flexural strength of section (predicted value) and 119875
119899 load for
119872119899
43 Validation of Flexural StrengthModel Verifying suitabil-ity of flexural strength models test results were comparedwith assumed flexural strength model Comparison resultswere listed in Table 4 As expected model type 1 which hastriangular stress block has shown comparatively high accu-racy However this model overestimated moment capacity ofsection Overestimation of this model was caused by largearea of tensile stress block and higher value of momentarm Higher value of moment arm can be derived by theexistence of residual strength Model type 2 also has shownacceptable accuracy but this model underestimated momentcapacity Underestimation of this model was caused by therelatively low level of tensile stress block area and lower valueof moment arm for tensile stress block This smaller momentarm was derived by the end of the stress block Model type3 which has rectangular tensile stress block has shown lowaccuracy and overestimation
Generally rectangular stress block has shown deeperneutral axis depth from compression fiber than triangularstress block moment arm has lower value than the casesof triangular stress block types Model types with ACI
rectangular stress block have low accuracy on neutral axisdepth tensile strain of reinforcements andmoment capacityThis phenomenonwas caused by the larger area of stress blockthan triangular stress block However Models with ultrahigh performance concrete stress block parameters whichare derived from test results [12] have shown relatively highaccuracy with all types of tensile stress block This modelespecially predicts neutral axis depth more accurately thanother models As discussed above the most accurate tensilestress block was also stress block including residual strengthof concrete
Considering low ductility which is caused by explosivefailure of ultra high strength concrete the most appropriatemodel for design of flexural strength is type 8whichwasmod-elled by UHPC-rectangular stress block parameters undercompression and tension softening considering model undertension Type 7 also can be used for design purposes butin this case strength reduction factor is carefully consideredwith material properties
5 Validation of Flexural Strength Models withPrevious Researches
For the verification of wide range applicability of assumedmodel existing test results [6ndash8] of ultra high performanceconcrete members were compared with assumed modelsBecause a few number of specimens exist only 22 test resultswere compared with suggested model Specifications forcollected test results were shown in Table 5 Test results fromeach research were summarized in Table 5 All test specimensexperienced yielding of reinforcement before reaching peakload They failed with flexural failure at the center of thespecimens Collected test specimens have 027 to 236 oftensile reinforcement ratio and 80sim200MPa of compressivestrength of concrete Fiber contents were distributed from05 to 20
According to the test results of Ashour et al [6] effect ofthe fibers to flexural strength is independent of the amount ofreinforcement but additional moment is proportional to con-crete compressive strength Therefore compressive strength
Advances in Materials Science and Engineering 7
(a) Final stage of failure
Load
s (kN
)
220
200
180
160140120100806040200
160
140
120
100
80
60
40
20
0
Deflection (mm)
Peak strengthType 1 202 kN
Type 7 175kN
Type 1 Type 7
fcu
ftb
ft
fy
ftb
ft
fy
1205731U
HPC
c
1205721UHPCfcu
(b) Load-deflection relation
Figure 5 Test results
Neu
tral
axis
(mm
)
350
300
250
200
150
100
50
0
000
000
001 002
002
003 004
004
005
Curvature (1m)
Yielding ofreinforcement
93mm Peak load
Extreme tensile fiber
Extreme compression fiber
Measurement 1 compression steelMeasurement 2 compression fiber
Type 7 973mm
Figure 6 Change of neutral axis depth
of concrete should be considered in flexural strength modelDancygier and Savir [7] investigated flexural strength of fiberreinforced concrete with conventional reinforcement ratiolower than 1 Fiber length which affects reinforcing index(RI = 119881
119891119871119891119863119891 where119881
119891is fibre volume fraction 119871
119891is fiber
length and119863119891is fiber diameter) directly changes the flexural
strength of section Generally fiber length changes the failuremode of fiber reinforced concrete under bending especiallyafter peak load Therefore material behavior under tensionshould be considered for flexural strength calculation Yang etal [8] investigated about placing method and reinforcementratio especially for ultra high performance concrete whichhave compressive strength around 200MPa According tothis research reinforcement ratio also affects the flexuralstrength and ductility although members have much higher
compressive strength of concrete Some of test results did notevaluate prediction methods previously investigated [2 4 5]
Therefore all assumed models were examined with testresults Comparison of test results with flexural strengthmodels was shown in Figures 7(a)ndash7(d) and descriptive sta-tistical data were shown in Table 6 Existing flexural strengthmodel which was reviewed in this paper only has accuracywhen using comparatively lower compressive strength ofconcrete (80sim100MPa) as shown in Figure 7(a)The varianceof this model increases with increase of compressive strengthof concrete As shown in Figures 7(b) and 7(c) types 1to 6 still have overestimated the flexural strength of ultrahigh performance concreteHowever when tension softeningmodel was applied accuracy comparatively increased Types7 to 9 which use the newly developed rectangular stressblock show more accuracy and safety rather than the other9 models Types 7 and 8 especially have high accuracy overthe range of ultra high performance concrete Because type8 which uses tension softening model underestimates theflexural capacity it would be used for safe design of ultra highperformance concrete members
6 Conclusion
The following conclusions can be made from the statisticalinvestigation analytical works and tests for FRUHSC forflexural strength
(1) Stress distribution of ultra high performance concreteunder compression shaped as triangle Under tensilestress stress distribution of ultra high performanceconcrete can be varied with fiber contents or shape
(2) Nine-flexural strengthmodels were evaluated For theconservative estimation ultimate strain at compres-sion fiber was assumed to be 0003 These flexuralstrength models were evaluated using assumed stressdistribution
8 Advances in Materials Science and Engineering
Table 5 Previous test results
Specimen 119887 ℎ 119889 119860119904119905
120588 119891119888119906
119881119891
119863119891
119871119891
119891119910
119875119906
(mm) (mm) (mm) (mm2) () (MPa) () (mm) (mm) (MPa) (kN)Ashour et al [6]
B-05-M2 200 250 215 509 118 82 05 08 60 530 491B-10-M2 200 250 215 509 118 87 1 08 60 530 542B-05-M3 200 250 215 763 178 82 05 08 60 530 695B-10-M3 200 250 215 763 178 87 1 08 60 530 714B-05-M4 200 250 215 1018 237 82 05 08 60 530 881B-10-M4 200 250 215 1018 237 87 1 08 60 530 897B-05-H2 200 250 215 509 118 107 05 08 60 530 485B-10-H2 200 250 215 509 118 111 1 08 60 530 537B-05-H3 200 250 215 763 178 107 05 08 60 530 696B-10-H3 200 250 215 763 178 111 1 08 60 530 741B-05-H4 200 250 215 1018 237 107 05 08 60 530 891B-10-H4 200 250 215 1018 237 111 1 08 60 530 935
Dancygier and Savir [7]H5-F2-1 35 200 300 273 151 028 129 075 09 35 480 236H5-F2-1 60 200 300 273 151 028 124 075 09 60 480 273H8-F2-1 35 200 300 273 302 055 124 075 09 35 480 389H8-F2-1 60 200 300 273 302 055 122 075 09 60 480 372H5-F2-1 35 3 200 300 273 151 028 122 075 09 35 616 281
Yang et al [8]R12-1 180 270 235 253 060 191 2 02 13 400 770R13-1 180 270 235 380 090 192 2 02 13 400 863R14-1 180 270 235 507 120 197 2 02 13 400 1031R23-2 180 270 220 760 120 196 2 02 13 400 1165119887 beam width ℎ beam height 119889 effective depth of beam 119860
119904119905 tensile reinforcement area 120588 reinforcement ratio 119891
119888119906 compressive strength of concrete 119881
119891
volume fraction of steel fiber119863119891 fiber diameter 119871
119891 fiber length 119891
119910 yield strength of reinforcement and 119875
119906 test results (load at ultimate failure)
Table 6 Descriptive statistics on collected test data(testprediction)
ID Mean Median SD Var COV IAEACI544 124 106 034 0115 027 1720Imam 122 101 045 0201 037 1983Lim 113 104 026 0068 023 1415Type 1 081 090 020 0040 024 3356Type 2 118 107 029 0086 025 1672Type 3 070 076 016 0024 022 4654Type 4 087 091 014 0021 016 1563Type 5 118 106 030 0091 025 1662Type 6 069 075 015 0023 022 4918Type 7 090 095 015 0021 016 1030Type 8 111 107 024 0060 022 1142Type 9 073 077 014 0021 020 3558SD standard variation Var variance COV coefficient of variation and IAEintegrated absolute error
(3) The most accurate model of ultra high performanceconcrete under compression is triangular Becauseultra high performance concrete has large elastic areafailure occurred with the same time experiencing
ultimate strength However for the safe design ofsection flexural strength model which uses modifiedrectangular stress blocks considering mechanicalcharacteristics of UHPC should be used
(4) Evaluating validation process using test result ofthis study and previous researches existing flexuralstrength calculation models cannot accurately andsafely predict the flexural strength of ultra highstrength concrete specimens especially for compres-sive strength larger than 100MPa However flexuralstrength model suggested in this study can pro-vide conservative and highly accurate (10 of error)results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by a grant (15CTAP-C097356-01) from Creative Challenge Research Program fundedby Ministry of Land Infrastructure and Transport of
Advances in Materials Science and Engineering 9
Test
valu
eth
eorit
ical
val
ue35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
ACI544mdashAshour (1)ImammdashAshour (1)LimmdashAshour (1)ACI544mdashAshour (2)ImammdashAshour (2)
LimmdashAshour (2)ACI544mdashYangImammdashYangLimmdashYang
(a) Existing modelTe
st va
lue
theo
ritic
al v
alue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 1mdashAshourType 2mdashAshourType 3mdashAshourType 1mdashDancygierType 2mdashDancygier
Type 3mdashDancygierType 1mdashYangType 2mdashYangType 3mdashYang
(b) Assumed types 1sim3
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 4mdashAshourType 5mdashAshourType 6mdashAshourType 4mdashDancygierType 5mdashDancygier
Type 6mdashDancygierType 4mdashYangType 5mdashYangType 6mdashYang
(c) Assumed types 4sim6
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 7mdashAshourType 8mdashAshourType 9mdashAshourType 7mdashDancygierType 8mdashDancygier
Type 9mdashDancygierType 7mdashYangType 8mdashYangType 9mdashYang
(d) Assumed types 7sim9
Figure 7 Applicability verification for prediction model
Korean government and National Research Foundation ofKorea(NRF) funded by the Ministry of Science ICT andFuture Planning (no NRF-2014R1A2A1A11051049)
References
[1] ACI Committee ldquoBuilding code requirements for structuralconcrete and commentaryrdquo ACI 318-11 American ConcreteInstitute Farmington Hills Mich USA 2011
[2] American Concrete Institute Committee 544 ldquoDesign con-siderations for steel fiber reinforced concreterdquo InternationalConcrete Abstracts Portal vol 85 no 5 pp 563ndash579 1988
[3] C H Henager and T J Doherty ldquoAnalysis of reinforced fibrousconcrete beamsrdquo Journal of the Structural Division vol 102 no1 pp 177ndash188 1976 ASCE Proceedings
[4] M Imam L Vandewalle and F Mortelmans ldquoShear-momentanalysis of reinforced high strength concrete beams containingsteel fibresrdquo Canadian Journal of Civil Engineering vol 22 no3 pp 462ndash470 1995
[5] T Y Lim P Paramasivan and S L Lee ldquoShear and momentcapacity of reinforced steel fiber concrete beamsrdquo Magazine ofConcrete Research vol 39 no 140 pp 148ndash160 1987
[6] S A Ashour F F Wafa and M I Kamal ldquoEffect of theconcrete compressive strength and tensile reinforcement ratio
10 Advances in Materials Science and Engineering
on the flexural behavior of fibrous concrete beamsrdquo EngineeringStructures vol 22 no 9 pp 1145ndash1158 2000
[7] A N Dancygier and Z Savir ldquoFlexural behavior ofHSFRCwithlow reinforcement ratiosrdquo Engineering Structures vol 28 no 11pp 1503ndash1512 2006
[8] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010
[9] RILEM and Final recommendations of TC 162-TDF ldquoTest anddesign methods for steel fibre reinforced concrete 120590-120576 designmethodrdquoMaterials and Structures vol 36 pp 560ndash565 2003
[10] European Committee for Standardization Eurocode 2 (EC2)Design of Concrete Structures 2004
[11] AFGCGroupe de Travail BFUP SETRA-AFGCUltra High Per-formance Fiber-Reinforced Concretes Interim Recommendation2002
[12] B I Bae C S Choi and H K Choi ldquoEvaluation of rectangularstress block parameters of reactive powder concrete membersrdquoJournal of the Architectural Institute of Korea vol 28 no 7 pp3ndash11 2012
[13] R N Swamy and S A Al-Tarsquoan ldquoDeformation and ultimatestrength in flexure of reinforced concrete beamsmadewith steelfibre concreterdquo Journal of the American Concrete Institute vol78 no 5 pp 395ndash405 1981
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
6 Advances in Materials Science and Engineering
Table 3 Mechanical characteristics of concrete
Stress state Ultimate strength(MPa) Youngrsquos modulus (MPa) Ultimatecracking
strain (permil) Poissonrsquos ratio
Compression 216 54306 3738 (120576119888119906) 026
Tension 98 0221 (120576119905)
350
300
50
150 1900 1900
5-D25
2-D10 Load Load
500 150
Strain gage
Strain gage
D10150 A
A
concrete
rebar
(a) Setting and measurement planSection A-A
5-D25
D10
200
240
6050
350
(b) Section
Figure 4 Details of test specimen
Table 4 Comparison between test results and assumed model
Model 119888 120576119904
119872119899
119875119899
(mm) (permil) (kNm) (kN)Type 1 9088 123 363 202Type 2 8598 13 296 164Type 3 9503 118 425 235Type 4 6876 163 356 197Type 5 7872 142 297 164Type 6 8739 128 433 240Type 7 9130 122 316 175Type 8 9813 114 308 170Type 9 10228 110 353 197Test results 93 910 322 179119888 neutral axis depth 120576
119904 strain at tensile reinforcement atmid length of beam
119872119899 nominal flexural strength of section (predicted value) and 119875
119899 load for
119872119899
43 Validation of Flexural StrengthModel Verifying suitabil-ity of flexural strength models test results were comparedwith assumed flexural strength model Comparison resultswere listed in Table 4 As expected model type 1 which hastriangular stress block has shown comparatively high accu-racy However this model overestimated moment capacity ofsection Overestimation of this model was caused by largearea of tensile stress block and higher value of momentarm Higher value of moment arm can be derived by theexistence of residual strength Model type 2 also has shownacceptable accuracy but this model underestimated momentcapacity Underestimation of this model was caused by therelatively low level of tensile stress block area and lower valueof moment arm for tensile stress block This smaller momentarm was derived by the end of the stress block Model type3 which has rectangular tensile stress block has shown lowaccuracy and overestimation
Generally rectangular stress block has shown deeperneutral axis depth from compression fiber than triangularstress block moment arm has lower value than the casesof triangular stress block types Model types with ACI
rectangular stress block have low accuracy on neutral axisdepth tensile strain of reinforcements andmoment capacityThis phenomenonwas caused by the larger area of stress blockthan triangular stress block However Models with ultrahigh performance concrete stress block parameters whichare derived from test results [12] have shown relatively highaccuracy with all types of tensile stress block This modelespecially predicts neutral axis depth more accurately thanother models As discussed above the most accurate tensilestress block was also stress block including residual strengthof concrete
Considering low ductility which is caused by explosivefailure of ultra high strength concrete the most appropriatemodel for design of flexural strength is type 8whichwasmod-elled by UHPC-rectangular stress block parameters undercompression and tension softening considering model undertension Type 7 also can be used for design purposes butin this case strength reduction factor is carefully consideredwith material properties
5 Validation of Flexural Strength Models withPrevious Researches
For the verification of wide range applicability of assumedmodel existing test results [6ndash8] of ultra high performanceconcrete members were compared with assumed modelsBecause a few number of specimens exist only 22 test resultswere compared with suggested model Specifications forcollected test results were shown in Table 5 Test results fromeach research were summarized in Table 5 All test specimensexperienced yielding of reinforcement before reaching peakload They failed with flexural failure at the center of thespecimens Collected test specimens have 027 to 236 oftensile reinforcement ratio and 80sim200MPa of compressivestrength of concrete Fiber contents were distributed from05 to 20
According to the test results of Ashour et al [6] effect ofthe fibers to flexural strength is independent of the amount ofreinforcement but additional moment is proportional to con-crete compressive strength Therefore compressive strength
Advances in Materials Science and Engineering 7
(a) Final stage of failure
Load
s (kN
)
220
200
180
160140120100806040200
160
140
120
100
80
60
40
20
0
Deflection (mm)
Peak strengthType 1 202 kN
Type 7 175kN
Type 1 Type 7
fcu
ftb
ft
fy
ftb
ft
fy
1205731U
HPC
c
1205721UHPCfcu
(b) Load-deflection relation
Figure 5 Test results
Neu
tral
axis
(mm
)
350
300
250
200
150
100
50
0
000
000
001 002
002
003 004
004
005
Curvature (1m)
Yielding ofreinforcement
93mm Peak load
Extreme tensile fiber
Extreme compression fiber
Measurement 1 compression steelMeasurement 2 compression fiber
Type 7 973mm
Figure 6 Change of neutral axis depth
of concrete should be considered in flexural strength modelDancygier and Savir [7] investigated flexural strength of fiberreinforced concrete with conventional reinforcement ratiolower than 1 Fiber length which affects reinforcing index(RI = 119881
119891119871119891119863119891 where119881
119891is fibre volume fraction 119871
119891is fiber
length and119863119891is fiber diameter) directly changes the flexural
strength of section Generally fiber length changes the failuremode of fiber reinforced concrete under bending especiallyafter peak load Therefore material behavior under tensionshould be considered for flexural strength calculation Yang etal [8] investigated about placing method and reinforcementratio especially for ultra high performance concrete whichhave compressive strength around 200MPa According tothis research reinforcement ratio also affects the flexuralstrength and ductility although members have much higher
compressive strength of concrete Some of test results did notevaluate prediction methods previously investigated [2 4 5]
Therefore all assumed models were examined with testresults Comparison of test results with flexural strengthmodels was shown in Figures 7(a)ndash7(d) and descriptive sta-tistical data were shown in Table 6 Existing flexural strengthmodel which was reviewed in this paper only has accuracywhen using comparatively lower compressive strength ofconcrete (80sim100MPa) as shown in Figure 7(a)The varianceof this model increases with increase of compressive strengthof concrete As shown in Figures 7(b) and 7(c) types 1to 6 still have overestimated the flexural strength of ultrahigh performance concreteHowever when tension softeningmodel was applied accuracy comparatively increased Types7 to 9 which use the newly developed rectangular stressblock show more accuracy and safety rather than the other9 models Types 7 and 8 especially have high accuracy overthe range of ultra high performance concrete Because type8 which uses tension softening model underestimates theflexural capacity it would be used for safe design of ultra highperformance concrete members
6 Conclusion
The following conclusions can be made from the statisticalinvestigation analytical works and tests for FRUHSC forflexural strength
(1) Stress distribution of ultra high performance concreteunder compression shaped as triangle Under tensilestress stress distribution of ultra high performanceconcrete can be varied with fiber contents or shape
(2) Nine-flexural strengthmodels were evaluated For theconservative estimation ultimate strain at compres-sion fiber was assumed to be 0003 These flexuralstrength models were evaluated using assumed stressdistribution
8 Advances in Materials Science and Engineering
Table 5 Previous test results
Specimen 119887 ℎ 119889 119860119904119905
120588 119891119888119906
119881119891
119863119891
119871119891
119891119910
119875119906
(mm) (mm) (mm) (mm2) () (MPa) () (mm) (mm) (MPa) (kN)Ashour et al [6]
B-05-M2 200 250 215 509 118 82 05 08 60 530 491B-10-M2 200 250 215 509 118 87 1 08 60 530 542B-05-M3 200 250 215 763 178 82 05 08 60 530 695B-10-M3 200 250 215 763 178 87 1 08 60 530 714B-05-M4 200 250 215 1018 237 82 05 08 60 530 881B-10-M4 200 250 215 1018 237 87 1 08 60 530 897B-05-H2 200 250 215 509 118 107 05 08 60 530 485B-10-H2 200 250 215 509 118 111 1 08 60 530 537B-05-H3 200 250 215 763 178 107 05 08 60 530 696B-10-H3 200 250 215 763 178 111 1 08 60 530 741B-05-H4 200 250 215 1018 237 107 05 08 60 530 891B-10-H4 200 250 215 1018 237 111 1 08 60 530 935
Dancygier and Savir [7]H5-F2-1 35 200 300 273 151 028 129 075 09 35 480 236H5-F2-1 60 200 300 273 151 028 124 075 09 60 480 273H8-F2-1 35 200 300 273 302 055 124 075 09 35 480 389H8-F2-1 60 200 300 273 302 055 122 075 09 60 480 372H5-F2-1 35 3 200 300 273 151 028 122 075 09 35 616 281
Yang et al [8]R12-1 180 270 235 253 060 191 2 02 13 400 770R13-1 180 270 235 380 090 192 2 02 13 400 863R14-1 180 270 235 507 120 197 2 02 13 400 1031R23-2 180 270 220 760 120 196 2 02 13 400 1165119887 beam width ℎ beam height 119889 effective depth of beam 119860
119904119905 tensile reinforcement area 120588 reinforcement ratio 119891
119888119906 compressive strength of concrete 119881
119891
volume fraction of steel fiber119863119891 fiber diameter 119871
119891 fiber length 119891
119910 yield strength of reinforcement and 119875
119906 test results (load at ultimate failure)
Table 6 Descriptive statistics on collected test data(testprediction)
ID Mean Median SD Var COV IAEACI544 124 106 034 0115 027 1720Imam 122 101 045 0201 037 1983Lim 113 104 026 0068 023 1415Type 1 081 090 020 0040 024 3356Type 2 118 107 029 0086 025 1672Type 3 070 076 016 0024 022 4654Type 4 087 091 014 0021 016 1563Type 5 118 106 030 0091 025 1662Type 6 069 075 015 0023 022 4918Type 7 090 095 015 0021 016 1030Type 8 111 107 024 0060 022 1142Type 9 073 077 014 0021 020 3558SD standard variation Var variance COV coefficient of variation and IAEintegrated absolute error
(3) The most accurate model of ultra high performanceconcrete under compression is triangular Becauseultra high performance concrete has large elastic areafailure occurred with the same time experiencing
ultimate strength However for the safe design ofsection flexural strength model which uses modifiedrectangular stress blocks considering mechanicalcharacteristics of UHPC should be used
(4) Evaluating validation process using test result ofthis study and previous researches existing flexuralstrength calculation models cannot accurately andsafely predict the flexural strength of ultra highstrength concrete specimens especially for compres-sive strength larger than 100MPa However flexuralstrength model suggested in this study can pro-vide conservative and highly accurate (10 of error)results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by a grant (15CTAP-C097356-01) from Creative Challenge Research Program fundedby Ministry of Land Infrastructure and Transport of
Advances in Materials Science and Engineering 9
Test
valu
eth
eorit
ical
val
ue35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
ACI544mdashAshour (1)ImammdashAshour (1)LimmdashAshour (1)ACI544mdashAshour (2)ImammdashAshour (2)
LimmdashAshour (2)ACI544mdashYangImammdashYangLimmdashYang
(a) Existing modelTe
st va
lue
theo
ritic
al v
alue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 1mdashAshourType 2mdashAshourType 3mdashAshourType 1mdashDancygierType 2mdashDancygier
Type 3mdashDancygierType 1mdashYangType 2mdashYangType 3mdashYang
(b) Assumed types 1sim3
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 4mdashAshourType 5mdashAshourType 6mdashAshourType 4mdashDancygierType 5mdashDancygier
Type 6mdashDancygierType 4mdashYangType 5mdashYangType 6mdashYang
(c) Assumed types 4sim6
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 7mdashAshourType 8mdashAshourType 9mdashAshourType 7mdashDancygierType 8mdashDancygier
Type 9mdashDancygierType 7mdashYangType 8mdashYangType 9mdashYang
(d) Assumed types 7sim9
Figure 7 Applicability verification for prediction model
Korean government and National Research Foundation ofKorea(NRF) funded by the Ministry of Science ICT andFuture Planning (no NRF-2014R1A2A1A11051049)
References
[1] ACI Committee ldquoBuilding code requirements for structuralconcrete and commentaryrdquo ACI 318-11 American ConcreteInstitute Farmington Hills Mich USA 2011
[2] American Concrete Institute Committee 544 ldquoDesign con-siderations for steel fiber reinforced concreterdquo InternationalConcrete Abstracts Portal vol 85 no 5 pp 563ndash579 1988
[3] C H Henager and T J Doherty ldquoAnalysis of reinforced fibrousconcrete beamsrdquo Journal of the Structural Division vol 102 no1 pp 177ndash188 1976 ASCE Proceedings
[4] M Imam L Vandewalle and F Mortelmans ldquoShear-momentanalysis of reinforced high strength concrete beams containingsteel fibresrdquo Canadian Journal of Civil Engineering vol 22 no3 pp 462ndash470 1995
[5] T Y Lim P Paramasivan and S L Lee ldquoShear and momentcapacity of reinforced steel fiber concrete beamsrdquo Magazine ofConcrete Research vol 39 no 140 pp 148ndash160 1987
[6] S A Ashour F F Wafa and M I Kamal ldquoEffect of theconcrete compressive strength and tensile reinforcement ratio
10 Advances in Materials Science and Engineering
on the flexural behavior of fibrous concrete beamsrdquo EngineeringStructures vol 22 no 9 pp 1145ndash1158 2000
[7] A N Dancygier and Z Savir ldquoFlexural behavior ofHSFRCwithlow reinforcement ratiosrdquo Engineering Structures vol 28 no 11pp 1503ndash1512 2006
[8] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010
[9] RILEM and Final recommendations of TC 162-TDF ldquoTest anddesign methods for steel fibre reinforced concrete 120590-120576 designmethodrdquoMaterials and Structures vol 36 pp 560ndash565 2003
[10] European Committee for Standardization Eurocode 2 (EC2)Design of Concrete Structures 2004
[11] AFGCGroupe de Travail BFUP SETRA-AFGCUltra High Per-formance Fiber-Reinforced Concretes Interim Recommendation2002
[12] B I Bae C S Choi and H K Choi ldquoEvaluation of rectangularstress block parameters of reactive powder concrete membersrdquoJournal of the Architectural Institute of Korea vol 28 no 7 pp3ndash11 2012
[13] R N Swamy and S A Al-Tarsquoan ldquoDeformation and ultimatestrength in flexure of reinforced concrete beamsmadewith steelfibre concreterdquo Journal of the American Concrete Institute vol78 no 5 pp 395ndash405 1981
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Advances in Materials Science and Engineering 7
(a) Final stage of failure
Load
s (kN
)
220
200
180
160140120100806040200
160
140
120
100
80
60
40
20
0
Deflection (mm)
Peak strengthType 1 202 kN
Type 7 175kN
Type 1 Type 7
fcu
ftb
ft
fy
ftb
ft
fy
1205731U
HPC
c
1205721UHPCfcu
(b) Load-deflection relation
Figure 5 Test results
Neu
tral
axis
(mm
)
350
300
250
200
150
100
50
0
000
000
001 002
002
003 004
004
005
Curvature (1m)
Yielding ofreinforcement
93mm Peak load
Extreme tensile fiber
Extreme compression fiber
Measurement 1 compression steelMeasurement 2 compression fiber
Type 7 973mm
Figure 6 Change of neutral axis depth
of concrete should be considered in flexural strength modelDancygier and Savir [7] investigated flexural strength of fiberreinforced concrete with conventional reinforcement ratiolower than 1 Fiber length which affects reinforcing index(RI = 119881
119891119871119891119863119891 where119881
119891is fibre volume fraction 119871
119891is fiber
length and119863119891is fiber diameter) directly changes the flexural
strength of section Generally fiber length changes the failuremode of fiber reinforced concrete under bending especiallyafter peak load Therefore material behavior under tensionshould be considered for flexural strength calculation Yang etal [8] investigated about placing method and reinforcementratio especially for ultra high performance concrete whichhave compressive strength around 200MPa According tothis research reinforcement ratio also affects the flexuralstrength and ductility although members have much higher
compressive strength of concrete Some of test results did notevaluate prediction methods previously investigated [2 4 5]
Therefore all assumed models were examined with testresults Comparison of test results with flexural strengthmodels was shown in Figures 7(a)ndash7(d) and descriptive sta-tistical data were shown in Table 6 Existing flexural strengthmodel which was reviewed in this paper only has accuracywhen using comparatively lower compressive strength ofconcrete (80sim100MPa) as shown in Figure 7(a)The varianceof this model increases with increase of compressive strengthof concrete As shown in Figures 7(b) and 7(c) types 1to 6 still have overestimated the flexural strength of ultrahigh performance concreteHowever when tension softeningmodel was applied accuracy comparatively increased Types7 to 9 which use the newly developed rectangular stressblock show more accuracy and safety rather than the other9 models Types 7 and 8 especially have high accuracy overthe range of ultra high performance concrete Because type8 which uses tension softening model underestimates theflexural capacity it would be used for safe design of ultra highperformance concrete members
6 Conclusion
The following conclusions can be made from the statisticalinvestigation analytical works and tests for FRUHSC forflexural strength
(1) Stress distribution of ultra high performance concreteunder compression shaped as triangle Under tensilestress stress distribution of ultra high performanceconcrete can be varied with fiber contents or shape
(2) Nine-flexural strengthmodels were evaluated For theconservative estimation ultimate strain at compres-sion fiber was assumed to be 0003 These flexuralstrength models were evaluated using assumed stressdistribution
8 Advances in Materials Science and Engineering
Table 5 Previous test results
Specimen 119887 ℎ 119889 119860119904119905
120588 119891119888119906
119881119891
119863119891
119871119891
119891119910
119875119906
(mm) (mm) (mm) (mm2) () (MPa) () (mm) (mm) (MPa) (kN)Ashour et al [6]
B-05-M2 200 250 215 509 118 82 05 08 60 530 491B-10-M2 200 250 215 509 118 87 1 08 60 530 542B-05-M3 200 250 215 763 178 82 05 08 60 530 695B-10-M3 200 250 215 763 178 87 1 08 60 530 714B-05-M4 200 250 215 1018 237 82 05 08 60 530 881B-10-M4 200 250 215 1018 237 87 1 08 60 530 897B-05-H2 200 250 215 509 118 107 05 08 60 530 485B-10-H2 200 250 215 509 118 111 1 08 60 530 537B-05-H3 200 250 215 763 178 107 05 08 60 530 696B-10-H3 200 250 215 763 178 111 1 08 60 530 741B-05-H4 200 250 215 1018 237 107 05 08 60 530 891B-10-H4 200 250 215 1018 237 111 1 08 60 530 935
Dancygier and Savir [7]H5-F2-1 35 200 300 273 151 028 129 075 09 35 480 236H5-F2-1 60 200 300 273 151 028 124 075 09 60 480 273H8-F2-1 35 200 300 273 302 055 124 075 09 35 480 389H8-F2-1 60 200 300 273 302 055 122 075 09 60 480 372H5-F2-1 35 3 200 300 273 151 028 122 075 09 35 616 281
Yang et al [8]R12-1 180 270 235 253 060 191 2 02 13 400 770R13-1 180 270 235 380 090 192 2 02 13 400 863R14-1 180 270 235 507 120 197 2 02 13 400 1031R23-2 180 270 220 760 120 196 2 02 13 400 1165119887 beam width ℎ beam height 119889 effective depth of beam 119860
119904119905 tensile reinforcement area 120588 reinforcement ratio 119891
119888119906 compressive strength of concrete 119881
119891
volume fraction of steel fiber119863119891 fiber diameter 119871
119891 fiber length 119891
119910 yield strength of reinforcement and 119875
119906 test results (load at ultimate failure)
Table 6 Descriptive statistics on collected test data(testprediction)
ID Mean Median SD Var COV IAEACI544 124 106 034 0115 027 1720Imam 122 101 045 0201 037 1983Lim 113 104 026 0068 023 1415Type 1 081 090 020 0040 024 3356Type 2 118 107 029 0086 025 1672Type 3 070 076 016 0024 022 4654Type 4 087 091 014 0021 016 1563Type 5 118 106 030 0091 025 1662Type 6 069 075 015 0023 022 4918Type 7 090 095 015 0021 016 1030Type 8 111 107 024 0060 022 1142Type 9 073 077 014 0021 020 3558SD standard variation Var variance COV coefficient of variation and IAEintegrated absolute error
(3) The most accurate model of ultra high performanceconcrete under compression is triangular Becauseultra high performance concrete has large elastic areafailure occurred with the same time experiencing
ultimate strength However for the safe design ofsection flexural strength model which uses modifiedrectangular stress blocks considering mechanicalcharacteristics of UHPC should be used
(4) Evaluating validation process using test result ofthis study and previous researches existing flexuralstrength calculation models cannot accurately andsafely predict the flexural strength of ultra highstrength concrete specimens especially for compres-sive strength larger than 100MPa However flexuralstrength model suggested in this study can pro-vide conservative and highly accurate (10 of error)results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by a grant (15CTAP-C097356-01) from Creative Challenge Research Program fundedby Ministry of Land Infrastructure and Transport of
Advances in Materials Science and Engineering 9
Test
valu
eth
eorit
ical
val
ue35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
ACI544mdashAshour (1)ImammdashAshour (1)LimmdashAshour (1)ACI544mdashAshour (2)ImammdashAshour (2)
LimmdashAshour (2)ACI544mdashYangImammdashYangLimmdashYang
(a) Existing modelTe
st va
lue
theo
ritic
al v
alue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 1mdashAshourType 2mdashAshourType 3mdashAshourType 1mdashDancygierType 2mdashDancygier
Type 3mdashDancygierType 1mdashYangType 2mdashYangType 3mdashYang
(b) Assumed types 1sim3
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 4mdashAshourType 5mdashAshourType 6mdashAshourType 4mdashDancygierType 5mdashDancygier
Type 6mdashDancygierType 4mdashYangType 5mdashYangType 6mdashYang
(c) Assumed types 4sim6
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 7mdashAshourType 8mdashAshourType 9mdashAshourType 7mdashDancygierType 8mdashDancygier
Type 9mdashDancygierType 7mdashYangType 8mdashYangType 9mdashYang
(d) Assumed types 7sim9
Figure 7 Applicability verification for prediction model
Korean government and National Research Foundation ofKorea(NRF) funded by the Ministry of Science ICT andFuture Planning (no NRF-2014R1A2A1A11051049)
References
[1] ACI Committee ldquoBuilding code requirements for structuralconcrete and commentaryrdquo ACI 318-11 American ConcreteInstitute Farmington Hills Mich USA 2011
[2] American Concrete Institute Committee 544 ldquoDesign con-siderations for steel fiber reinforced concreterdquo InternationalConcrete Abstracts Portal vol 85 no 5 pp 563ndash579 1988
[3] C H Henager and T J Doherty ldquoAnalysis of reinforced fibrousconcrete beamsrdquo Journal of the Structural Division vol 102 no1 pp 177ndash188 1976 ASCE Proceedings
[4] M Imam L Vandewalle and F Mortelmans ldquoShear-momentanalysis of reinforced high strength concrete beams containingsteel fibresrdquo Canadian Journal of Civil Engineering vol 22 no3 pp 462ndash470 1995
[5] T Y Lim P Paramasivan and S L Lee ldquoShear and momentcapacity of reinforced steel fiber concrete beamsrdquo Magazine ofConcrete Research vol 39 no 140 pp 148ndash160 1987
[6] S A Ashour F F Wafa and M I Kamal ldquoEffect of theconcrete compressive strength and tensile reinforcement ratio
10 Advances in Materials Science and Engineering
on the flexural behavior of fibrous concrete beamsrdquo EngineeringStructures vol 22 no 9 pp 1145ndash1158 2000
[7] A N Dancygier and Z Savir ldquoFlexural behavior ofHSFRCwithlow reinforcement ratiosrdquo Engineering Structures vol 28 no 11pp 1503ndash1512 2006
[8] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010
[9] RILEM and Final recommendations of TC 162-TDF ldquoTest anddesign methods for steel fibre reinforced concrete 120590-120576 designmethodrdquoMaterials and Structures vol 36 pp 560ndash565 2003
[10] European Committee for Standardization Eurocode 2 (EC2)Design of Concrete Structures 2004
[11] AFGCGroupe de Travail BFUP SETRA-AFGCUltra High Per-formance Fiber-Reinforced Concretes Interim Recommendation2002
[12] B I Bae C S Choi and H K Choi ldquoEvaluation of rectangularstress block parameters of reactive powder concrete membersrdquoJournal of the Architectural Institute of Korea vol 28 no 7 pp3ndash11 2012
[13] R N Swamy and S A Al-Tarsquoan ldquoDeformation and ultimatestrength in flexure of reinforced concrete beamsmadewith steelfibre concreterdquo Journal of the American Concrete Institute vol78 no 5 pp 395ndash405 1981
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
8 Advances in Materials Science and Engineering
Table 5 Previous test results
Specimen 119887 ℎ 119889 119860119904119905
120588 119891119888119906
119881119891
119863119891
119871119891
119891119910
119875119906
(mm) (mm) (mm) (mm2) () (MPa) () (mm) (mm) (MPa) (kN)Ashour et al [6]
B-05-M2 200 250 215 509 118 82 05 08 60 530 491B-10-M2 200 250 215 509 118 87 1 08 60 530 542B-05-M3 200 250 215 763 178 82 05 08 60 530 695B-10-M3 200 250 215 763 178 87 1 08 60 530 714B-05-M4 200 250 215 1018 237 82 05 08 60 530 881B-10-M4 200 250 215 1018 237 87 1 08 60 530 897B-05-H2 200 250 215 509 118 107 05 08 60 530 485B-10-H2 200 250 215 509 118 111 1 08 60 530 537B-05-H3 200 250 215 763 178 107 05 08 60 530 696B-10-H3 200 250 215 763 178 111 1 08 60 530 741B-05-H4 200 250 215 1018 237 107 05 08 60 530 891B-10-H4 200 250 215 1018 237 111 1 08 60 530 935
Dancygier and Savir [7]H5-F2-1 35 200 300 273 151 028 129 075 09 35 480 236H5-F2-1 60 200 300 273 151 028 124 075 09 60 480 273H8-F2-1 35 200 300 273 302 055 124 075 09 35 480 389H8-F2-1 60 200 300 273 302 055 122 075 09 60 480 372H5-F2-1 35 3 200 300 273 151 028 122 075 09 35 616 281
Yang et al [8]R12-1 180 270 235 253 060 191 2 02 13 400 770R13-1 180 270 235 380 090 192 2 02 13 400 863R14-1 180 270 235 507 120 197 2 02 13 400 1031R23-2 180 270 220 760 120 196 2 02 13 400 1165119887 beam width ℎ beam height 119889 effective depth of beam 119860
119904119905 tensile reinforcement area 120588 reinforcement ratio 119891
119888119906 compressive strength of concrete 119881
119891
volume fraction of steel fiber119863119891 fiber diameter 119871
119891 fiber length 119891
119910 yield strength of reinforcement and 119875
119906 test results (load at ultimate failure)
Table 6 Descriptive statistics on collected test data(testprediction)
ID Mean Median SD Var COV IAEACI544 124 106 034 0115 027 1720Imam 122 101 045 0201 037 1983Lim 113 104 026 0068 023 1415Type 1 081 090 020 0040 024 3356Type 2 118 107 029 0086 025 1672Type 3 070 076 016 0024 022 4654Type 4 087 091 014 0021 016 1563Type 5 118 106 030 0091 025 1662Type 6 069 075 015 0023 022 4918Type 7 090 095 015 0021 016 1030Type 8 111 107 024 0060 022 1142Type 9 073 077 014 0021 020 3558SD standard variation Var variance COV coefficient of variation and IAEintegrated absolute error
(3) The most accurate model of ultra high performanceconcrete under compression is triangular Becauseultra high performance concrete has large elastic areafailure occurred with the same time experiencing
ultimate strength However for the safe design ofsection flexural strength model which uses modifiedrectangular stress blocks considering mechanicalcharacteristics of UHPC should be used
(4) Evaluating validation process using test result ofthis study and previous researches existing flexuralstrength calculation models cannot accurately andsafely predict the flexural strength of ultra highstrength concrete specimens especially for compres-sive strength larger than 100MPa However flexuralstrength model suggested in this study can pro-vide conservative and highly accurate (10 of error)results
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This research was supported by a grant (15CTAP-C097356-01) from Creative Challenge Research Program fundedby Ministry of Land Infrastructure and Transport of
Advances in Materials Science and Engineering 9
Test
valu
eth
eorit
ical
val
ue35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
ACI544mdashAshour (1)ImammdashAshour (1)LimmdashAshour (1)ACI544mdashAshour (2)ImammdashAshour (2)
LimmdashAshour (2)ACI544mdashYangImammdashYangLimmdashYang
(a) Existing modelTe
st va
lue
theo
ritic
al v
alue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 1mdashAshourType 2mdashAshourType 3mdashAshourType 1mdashDancygierType 2mdashDancygier
Type 3mdashDancygierType 1mdashYangType 2mdashYangType 3mdashYang
(b) Assumed types 1sim3
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 4mdashAshourType 5mdashAshourType 6mdashAshourType 4mdashDancygierType 5mdashDancygier
Type 6mdashDancygierType 4mdashYangType 5mdashYangType 6mdashYang
(c) Assumed types 4sim6
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 7mdashAshourType 8mdashAshourType 9mdashAshourType 7mdashDancygierType 8mdashDancygier
Type 9mdashDancygierType 7mdashYangType 8mdashYangType 9mdashYang
(d) Assumed types 7sim9
Figure 7 Applicability verification for prediction model
Korean government and National Research Foundation ofKorea(NRF) funded by the Ministry of Science ICT andFuture Planning (no NRF-2014R1A2A1A11051049)
References
[1] ACI Committee ldquoBuilding code requirements for structuralconcrete and commentaryrdquo ACI 318-11 American ConcreteInstitute Farmington Hills Mich USA 2011
[2] American Concrete Institute Committee 544 ldquoDesign con-siderations for steel fiber reinforced concreterdquo InternationalConcrete Abstracts Portal vol 85 no 5 pp 563ndash579 1988
[3] C H Henager and T J Doherty ldquoAnalysis of reinforced fibrousconcrete beamsrdquo Journal of the Structural Division vol 102 no1 pp 177ndash188 1976 ASCE Proceedings
[4] M Imam L Vandewalle and F Mortelmans ldquoShear-momentanalysis of reinforced high strength concrete beams containingsteel fibresrdquo Canadian Journal of Civil Engineering vol 22 no3 pp 462ndash470 1995
[5] T Y Lim P Paramasivan and S L Lee ldquoShear and momentcapacity of reinforced steel fiber concrete beamsrdquo Magazine ofConcrete Research vol 39 no 140 pp 148ndash160 1987
[6] S A Ashour F F Wafa and M I Kamal ldquoEffect of theconcrete compressive strength and tensile reinforcement ratio
10 Advances in Materials Science and Engineering
on the flexural behavior of fibrous concrete beamsrdquo EngineeringStructures vol 22 no 9 pp 1145ndash1158 2000
[7] A N Dancygier and Z Savir ldquoFlexural behavior ofHSFRCwithlow reinforcement ratiosrdquo Engineering Structures vol 28 no 11pp 1503ndash1512 2006
[8] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010
[9] RILEM and Final recommendations of TC 162-TDF ldquoTest anddesign methods for steel fibre reinforced concrete 120590-120576 designmethodrdquoMaterials and Structures vol 36 pp 560ndash565 2003
[10] European Committee for Standardization Eurocode 2 (EC2)Design of Concrete Structures 2004
[11] AFGCGroupe de Travail BFUP SETRA-AFGCUltra High Per-formance Fiber-Reinforced Concretes Interim Recommendation2002
[12] B I Bae C S Choi and H K Choi ldquoEvaluation of rectangularstress block parameters of reactive powder concrete membersrdquoJournal of the Architectural Institute of Korea vol 28 no 7 pp3ndash11 2012
[13] R N Swamy and S A Al-Tarsquoan ldquoDeformation and ultimatestrength in flexure of reinforced concrete beamsmadewith steelfibre concreterdquo Journal of the American Concrete Institute vol78 no 5 pp 395ndash405 1981
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Advances in Materials Science and Engineering 9
Test
valu
eth
eorit
ical
val
ue35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
ACI544mdashAshour (1)ImammdashAshour (1)LimmdashAshour (1)ACI544mdashAshour (2)ImammdashAshour (2)
LimmdashAshour (2)ACI544mdashYangImammdashYangLimmdashYang
(a) Existing modelTe
st va
lue
theo
ritic
al v
alue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 1mdashAshourType 2mdashAshourType 3mdashAshourType 1mdashDancygierType 2mdashDancygier
Type 3mdashDancygierType 1mdashYangType 2mdashYangType 3mdashYang
(b) Assumed types 1sim3
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 4mdashAshourType 5mdashAshourType 6mdashAshourType 4mdashDancygierType 5mdashDancygier
Type 6mdashDancygierType 4mdashYangType 5mdashYangType 6mdashYang
(c) Assumed types 4sim6
Test
valu
eth
eorit
ical
val
ue
35
30
25
20
15
10
05
00
Compressive strength of concrete (MPa)80 100 120 140 160 180 200
Underestimation
Overestimation
Type 7mdashAshourType 8mdashAshourType 9mdashAshourType 7mdashDancygierType 8mdashDancygier
Type 9mdashDancygierType 7mdashYangType 8mdashYangType 9mdashYang
(d) Assumed types 7sim9
Figure 7 Applicability verification for prediction model
Korean government and National Research Foundation ofKorea(NRF) funded by the Ministry of Science ICT andFuture Planning (no NRF-2014R1A2A1A11051049)
References
[1] ACI Committee ldquoBuilding code requirements for structuralconcrete and commentaryrdquo ACI 318-11 American ConcreteInstitute Farmington Hills Mich USA 2011
[2] American Concrete Institute Committee 544 ldquoDesign con-siderations for steel fiber reinforced concreterdquo InternationalConcrete Abstracts Portal vol 85 no 5 pp 563ndash579 1988
[3] C H Henager and T J Doherty ldquoAnalysis of reinforced fibrousconcrete beamsrdquo Journal of the Structural Division vol 102 no1 pp 177ndash188 1976 ASCE Proceedings
[4] M Imam L Vandewalle and F Mortelmans ldquoShear-momentanalysis of reinforced high strength concrete beams containingsteel fibresrdquo Canadian Journal of Civil Engineering vol 22 no3 pp 462ndash470 1995
[5] T Y Lim P Paramasivan and S L Lee ldquoShear and momentcapacity of reinforced steel fiber concrete beamsrdquo Magazine ofConcrete Research vol 39 no 140 pp 148ndash160 1987
[6] S A Ashour F F Wafa and M I Kamal ldquoEffect of theconcrete compressive strength and tensile reinforcement ratio
10 Advances in Materials Science and Engineering
on the flexural behavior of fibrous concrete beamsrdquo EngineeringStructures vol 22 no 9 pp 1145ndash1158 2000
[7] A N Dancygier and Z Savir ldquoFlexural behavior ofHSFRCwithlow reinforcement ratiosrdquo Engineering Structures vol 28 no 11pp 1503ndash1512 2006
[8] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010
[9] RILEM and Final recommendations of TC 162-TDF ldquoTest anddesign methods for steel fibre reinforced concrete 120590-120576 designmethodrdquoMaterials and Structures vol 36 pp 560ndash565 2003
[10] European Committee for Standardization Eurocode 2 (EC2)Design of Concrete Structures 2004
[11] AFGCGroupe de Travail BFUP SETRA-AFGCUltra High Per-formance Fiber-Reinforced Concretes Interim Recommendation2002
[12] B I Bae C S Choi and H K Choi ldquoEvaluation of rectangularstress block parameters of reactive powder concrete membersrdquoJournal of the Architectural Institute of Korea vol 28 no 7 pp3ndash11 2012
[13] R N Swamy and S A Al-Tarsquoan ldquoDeformation and ultimatestrength in flexure of reinforced concrete beamsmadewith steelfibre concreterdquo Journal of the American Concrete Institute vol78 no 5 pp 395ndash405 1981
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
10 Advances in Materials Science and Engineering
on the flexural behavior of fibrous concrete beamsrdquo EngineeringStructures vol 22 no 9 pp 1145ndash1158 2000
[7] A N Dancygier and Z Savir ldquoFlexural behavior ofHSFRCwithlow reinforcement ratiosrdquo Engineering Structures vol 28 no 11pp 1503ndash1512 2006
[8] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010
[9] RILEM and Final recommendations of TC 162-TDF ldquoTest anddesign methods for steel fibre reinforced concrete 120590-120576 designmethodrdquoMaterials and Structures vol 36 pp 560ndash565 2003
[10] European Committee for Standardization Eurocode 2 (EC2)Design of Concrete Structures 2004
[11] AFGCGroupe de Travail BFUP SETRA-AFGCUltra High Per-formance Fiber-Reinforced Concretes Interim Recommendation2002
[12] B I Bae C S Choi and H K Choi ldquoEvaluation of rectangularstress block parameters of reactive powder concrete membersrdquoJournal of the Architectural Institute of Korea vol 28 no 7 pp3ndash11 2012
[13] R N Swamy and S A Al-Tarsquoan ldquoDeformation and ultimatestrength in flexure of reinforced concrete beamsmadewith steelfibre concreterdquo Journal of the American Concrete Institute vol78 no 5 pp 395ndash405 1981
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials