experimental research and finite element analysis...
TRANSCRIPT
Research ArticleExperimental Research and Finite Element Analysis onMechanical Property of SFRC T-Beam
Min Sun1 Jiapeng Zhu1 Ning Li1 and C C Fu2
1Department of Civil Engineering Suzhou University of Science and Technology Suzhou Jiangsu 215011 China2University of Maryland at College Park College Park MD 20742 USA
Correspondence should be addressed to Min Sun sunminmailustseducn
Received 23 January 2017 Accepted 14 March 2017 Published 4 May 2017
Academic Editor Peng Zhang
Copyright copy 2017 Min Sun et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Research on mechanical property of SFRC was done through experiments of two SFRC T-beams and one concrete T-beam whilethe influences of different volume fractions of steel fibers on integral rigidity ultimate shear capacity and the crack distributioncharacteristics were analyzed ANSYS finite element software was used to simulate the tests and it was found that there was goodconformation between the results of ANSYS simulation and tests The test results and finite element software simulation bothshowed that the incorporation of steel fibers in the concrete can increase the integral rigidity and ultimate shear capacity whilepartially reducing the propagation of cracks effectively It was also proved that it is reliable to simulate SFRC T-beam by ANSYSsoftware
1 Introduction
T-beam is very commonly used in the Chinese highwaybridges where the crackle status is very serious in T-beamsWith the wide usage of the traditional concrete some obviousshortcomings are exposed gradually such as low strengthpoor ductility and the brittle failure under the impact loadThese shortcomings will limit the application of concrete inthe future structure If some steel fibers are added in concretefiber can not only prevent the development of concrete cracksbut also improve the flexural shear and tensile propertiesof concrete [1ndash4] At the same time steel fibers can improvethe antifatigue anti-impact durability and crack toughnessof concrete [5 6] and make concrete sustain certain plasticproperties
Steel fiber reinforced concrete (SFRC) has a good crackresistance so it is widely used in the fields of airportpavement bridge deck and waterproof roof But now thereare not a lot of researches on the shear performance and crackresistance effect of SFRC T-beam In this paper a concreteT-beam and two SFRC T-beam specimens were designed toinvestigate the effect of steel fiber content on the bearingcapacity of concrete T-beam to understand the characteristicsof SFRC in shear and crack resistance
2 Preparation of Test
21 Description of Specimens In this test three test T-beamswere prepared one three-meter (length) ordinary concreteT-beam and two three-meter (length) SFRC T-beams Theparameters of specimen are shown in Table 1 HRB335 steelbar was used as the tension longitudinal reinforcement whileHPB235 steel bar was used as the compression longitudinalreinforcement the flange plate main bars and the stirrupsThe section size and reinforcement layout are shown inFigure 1
22 Materials Properties In this experiment a tape of wavedsteel fibers produced by Suzhou Longyu Co Ltd with792MPa tensile strength 3018mm fiber length 091mmequivalent diameter and 33-aspect ratio was used Themechanical properties of concrete and the reinforced bar areshown in Tables 2 and 3
23 TestMethod In the test themethod of two-point loadingwas used by the distributive beam The shear span ratio was2 The support of the beam was 225mm far from the beamend and the loading device was a separate type of hydraulic
HindawiAdvances in Civil EngineeringVolume 2017 Article ID 2721356 8 pageshttpsdoiorg10115520172721356
2 Advances in Civil Engineering
Table 1 Test T-beam parameters
Material Beam node Stirrup spacing(mm)
Stirrup ratio Volume fraction ofsteel fiber
Concrete 1 150 048 0SFRC 2 150 048 120588 = 15SFRC 3 150 048 120588 = 20
230 140 230
430
70
500
600
26
3276
192
130
22 230 96 230
1 1
휙8
휙8
휙28
Figure 1 Section size and reinforcement layout (unit mm)
Table 2 Mechanical properties of concrete
Beam nodeCrushing
compressivestrength
Concretecompressivestrength
Youngrsquosmodulus
1 371 282 3192 403 306 3273 405 308 327
Table 3 Mechanical properties of reinforced bar
Steel grade Bardiameter
Yieldstress
Ultimatestress
Youngrsquosmodulus
HPB235 8 342 500 210HRB235 28 389 574 200Note In Tables 2 and 3 length unit is mm the strength unit is Mpa andYoungrsquos modulus unit is Gpa
jack that used a high-precision static servo-hydraulic-controlsystem Gradation loading was acted on the beam and theholding time was 15 minutes In the process of loadingthe crack occurrence and development should be carefullyobserved
Table 4 Summary of shear resistance of beams
Beam node 119881cr (KN) 119881u (KN) 119880max (mm)1 200 830 10772 400 1150 1893 300 gt1200 76
123
0
200
400
600
800
1000
1200
1400Lo
ad (K
N)
5 10 15 200Displacement (mm)
Figure 2 Load-displacement curve of the beams
Displacement gauges were arranged in the support 14points and the mid-span In each loading process thecorresponding load and displacement values were recordedsynchronously
3 Test Results
31 Summary of Load Capacity The crack load (119881cr) ulti-mate load (119881u) and the mid-span displacement (119880max)corresponding to the ultimate load of these three beams areshown in Table 4 The load-displacement curve is shown inFigure 2
32 Summary of Crack Development Status Three test T-beams were carried out under 200KN 500KN 800KN1000KN 1100KN and 1200KN The results are shown inTable 5The crack diagram of each beam is shown in Figure 3
Advances in Civil Engineering 3
EN
ES
WN
WS
(a) Crack diagram of 1 beam
EN
ES
WN
WS
(b) Crack diagram of 2 beam
EN
ES
WN
WS
(c) Crack diagram of 3 beam
Figure 3 Crack diagram of each beam
Table 5The development status of themaximum crack width (unitmm)
NodeLoad
200KN 500KN 800KN 1000KN 1100KN 1200KN
1 0 16 25 mdash mdash mdash
2 mdash 02 15 331 gt4 mdash
3 mdash 01 05 063 15 mdash
4 Finite Element Simulation
41 Element Selection and Finite Element Model WhenANSYS was used for finite element analysis of reinforcedconcrete a separate model was adopted The concrete wassimulated by Solid 65 element and steel bar was simulated byPipe 59 element The bond slip between the steel fiber andconcrete was neglected
This paper established the 12 T-beam model whichcan not only reduce the calculation time but also avoid
4 Advances in Civil Engineering
(a) Finite element solid model (b) Reinforced element model
(c) Finite element mesh
Figure 4 ANSYS model
terminating the calculation during calculation process dueto too many warnings In the finite element simulation thestress concentration was avoided at the support and theloading point by adding an elastic pad The ANSYS model isshown in Figure 4
42 Selection of Constitutive Model of Materials The double-line strong hardening model (BISO) was used in the consti-tutive relation of the steel bar and the formula about uniaxialcompressive stress-strain curve of concrete [7] is (1) and(2) The constitutive relation of SFRC is modified on thebasis of concrete [8ndash10] and the following formula (4) isused
Constitutive relation of concrete is as follows
Ascending stage is
119910 =119873119909 minus 1199092
1 + (119873 minus 2) 119909 (1)
Descending stage is
119910 =119909
120572 (119909 minus 1)2 + 119909 (2)
In the formula
119909 =120576
120576119888
119910 =120590
119891119888
119873 =1198640119864119904
(3)
where 119891119888 is compressive strength of concrete 120576119888 is peak strainassociated with1198911198881198640 is initial elastic modulus of concrete119864119904is secant modulus at the peak strain
Constitutive relation of SFRC is
1198911198881198911015840119888=120573 (1205761205760)
120573 minus 1 + (1205761205760)120573 (4)
In the formula
120573 = 05811 + 193120582minus07406119891
120582119891 =120588119891119897119891119889119891
(5)
where 120588119891 is volume fraction of steel fiber 119897119891 is steel fiberlength and 119889119891 is steel fiber diameter
Advances in Civil Engineering 5
Table 6 Cracking load and ultimate load of three test T-beams
Beam note 119881crexp(KN)
119881crcal(KN) 119881crcal119881crexp 119881uexp
(KN)119881ucal(KN) 119881ucal119881uexp
1 200 213 1065 830 810 09762 400 364 091 1150 1270 11043 300 411 137 gt1200 1420 lt1183Note 119881crexp and119881crcal respectively represent the cracking load of the test and the finite element simulation 119881uexp and119881ucal respectively represent theultimate failure load of the test and the finite element simulation
43 Comparative Analysis of Finite Element Results andTest Results
431 Comparative Analysis of Load-Displacement Curve andLoad Carrying Capacity The comparisons of test data withANSYS simulations are shown in Figure 5
The cracking load and ultimate load of three test T-beamsare shown in Table 6
According to the 1ndash3 beam it can be seen that the load-displacement curve of the finite element is basically consistentwith that of the test and the gap of the failure load is not bigBut the slope of the curve obtained by finite element methodis slightly larger than that of the test chamber The stiffnessof the SFRC beam simulated by the finite element is slightlymore than that of the test result The main reason for thissituation is the simulation of concrete inner and SFRC innerwas ideal andwith no flaw In addition due to the compactingprocess of beams in the actual process the stiffness of thebeam simulated by ANSYS is greater than that of test T-beam
ANSYS simulation results showed that the test T-beamin the process of loading had experienced two stages elasticand inelastic along with the increase of loadThe slope of theload-displacement curve was gradually reduced The load-displacement curve obtained from the test also reflected theprocess of the stiffness degradation
The volume fraction of steel fiber of 1 2 3 test T-beamrespectively was 0 15 and 2 From Figure 5(d) it canbeen seen that the slope of the 2 beam and 3 beam in theelastic stage and the nonelastic stage is significantly greaterthan that of the 1 beam which proves the adding of steelfiber can improve the stiffness and ductility of the concretebeam In the nonelastic stage the higher volume fraction ofsteel fiber is the slower stiffness degradation of the concreteis Figure 5(e) curves obtained from the test also reflect thischaracteristic
FromTable 6 it can be seen that the results of the crackingload and the ultimate failure load simulated by finite elementanalysis are not quite different from the tests result and theratio is close to 1 With the incorporation of steel fiber theultimate bearing capacity has been significantly improvedAnd the higher the volume fraction of steel fiber the higherthe ultimate bearing capacity
44 Crack Distribution and Comparative Analysis of DamageFrom Table 6 the finite element simulation results showedthat in the aspect of cracking loads the cracking load of thetest T-beam increases with the increase of volume fraction of
steel fiber which reflected that the initial cracking of the steelfiber can be suppressed by the addition of steel fiberHoweverthe cracking load of 3 beam is smaller than that of 2 beamwhich could be caused by the uneven mixing of steel fiber
The smeared crack model was used in ANSYS to simulatethe distribution and development of cracks with the lack ofability to simulate single fracture of crack width and crackdevelopment From the crack distribution it can be seen thatthe ordinary concrete beam cracks and SFRC beam cracksalmost distributed in the whole beam section and the resultsgained from half length of the beams were compared inFigure 6 Shown by the comparison the fracture distributionssimulated by finite element are in a good conformation withthe fracture distributions during actual test
From the crack distribution it can be seen that the maincrack spacing of beam 1 is smaller than that of beam 2 andbeam 3 In Figure 6 120579119894 (119894 = 1 2 3) represents the main crackdevelopment angle of each beam ℎ119894 (119894 = 1 2 3) representsthe cross crack length produced by each beam Since maincrack development angle 1205791 of beam 1 is less than 1205792 and 1205793it shows that the incorporation of steel fiber can cause thecrack to be dispersed and avoid the damage caused by thestress concentration In cross crack area the crack length ℎ1produced by beam 1 is smaller than ℎ2 and ℎ3 besides ℎ3 lt ℎ2which reflects that the addition of the steel fiber can increasethe bending crack resistance
The crack width of beam 1 beam 2 and beam 3 iscompared in Table 5 The occurrence of cracking of beam 1was the earliest and the crack development speed was thefastest Beam 2 and beam 3 almost simultaneously crackedbut in the same load conditions the crack width of beam 3was smaller and the crack development speedwas slower thanbeam 2 In the elastic stage of beam 2 the crack developedslowly but after the elastic stage the crack developed quicklywhich showed that the increase of volume fraction of steelfiber can improve the crack resistance of the concrete anddelay the development of cracks Because when volumefraction was greater than 2 it is difficult to blend steel fiberin concrete so the study was not done
5 Conclusions
Through the above test and finite element simulation analysisthe following conclusions can be drawn
(1) The incorporation of steel fiber can improve theintegral rigidity and ductility of concrete T-beam In acertain range the higher the volume fraction of steel
6 Advances in Civil Engineering
TestANSYS
0
100
200
300
400
500
600
700
800
900Lo
ad (K
N)
2 4 6 8 10 120Displacement (mm)
(a) 1 beam comparison diagram
TestANSYS
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(b) 2 beam comparison diagram
TextANSYS
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
5 10 150Displacement (mm)
(c) 3 beam comparison diagram
123
5 10 15 200Displacement (mm)
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
(d) Test results
123
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(e) ANSYS results
Figure 5 Comparison of the results of test with ANSYS simulation
Advances in Civil Engineering 7
WN
h1
z
Crack distribution area
(a) Finite element simulation results and test results of 1 beam cracks
WN
h2
z
Crack distribution area
(b) Finite element simulation results and test results of 2 beam cracks
WN
h3
z
Crack distribution area
(c) Finite element simulation results and test results of 3 beam cracks
Figure 6 Finite element simulation and test results of the cracks of each beam
fiber is the higher the integral rigidity is and theslower the stiffness degradation of T-beam is
(2) With the same reinforcement ratio and shear spanratio the higher volume fraction of steel fiber isthe higher the ultimate shear bearing capacity of theconcrete T-beam is
(3) The increase of volume fraction of steel fiber can delaythe development of cracks and make the distributionof cracks more uniform and also improve crack resis-tance of the concrete T-beam when volume fractionwas less than 2
(4) Finite element analysis of SFRCT-beams by ANSYSis feasible and the results obtained by ANSYS are ingood agreementwith test results ANSYS can simulatethe general trend of the crack and the crack distribu-tion area of the T-beam by using the smeared crackmodel
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
The research described in this paper was financially sup-ported by the Jiangsu Province Key Laboratory of StructureEngineering located in Suzhou University of Science andTechnology
References
[1] X Sun B Diao and Y Ye ldquoFlexural behavior experiments ofultra-high performance concrete beams reinforced with steelbar and hybrid-fiberrdquo Industrial Architecture vol 42 no 11 pp16ndash21 2012
[2] Z Y Sun Y Yang W H Qin S T Ren and G Wu ldquoExperi-mental study on flexural behavior of concrete beams reinforcedby steel-fiber reinforced polymer composite barsrdquo Journal ofReinforced Plastics and Composites vol 31 no 24 pp 1737ndash17452012
[3] H-Z Zhang C-K Huang and R-J Zhang ldquoExperimentalstudy on shear resistance of steel fiber reinforced high strengthconcrete beamsrdquo Journal of Harbin Institute of Technology vol38 no 10 pp 1781ndash1785 2006
[4] J-S ChoTheShear Behavior of Steel Fiber Reinforced PrestressedConcrete Beams without Shear Reinforcement The University ofTexas at Arlington Arlington Tex USA 2011
8 Advances in Civil Engineering
[5] B-X Shi ldquoExperiment study on fatigue characteristic of steelfiber reinforced concreterdquo Journal of Hebei University of Engi-neering (Natural Science Edition) vol 25 no 2 pp 9ndash12 2008
[6] L Wang Study on the Properties of Ultra-Short Ultra-FineSteel Fiber Reinforced Concrete Chongqing Jiaotong UniversityChongqing China 2011
[7] Y Li X Wang and S Chen ldquoComparison of stress-straincurves of concrete under uniaxial compressionrdquo Highway Traf-fic Department vol 10 pp 75ndash78 2005
[8] J Qiu ldquoStudy on nonlinear finite element analysis of steel fiberconcrete structurerdquo Concrete no 3 pp 17ndash20 2011
[9] D A Fanella and A E Naaman ldquoStress-strain properties offiber reinforced mortar in compressionrdquo Journal of the Amer-ican Concrete Institute vol 82 no 4 pp 475ndash483 1985
[10] B Luccioni G Ruano F Isla R Zerbino and G Giaccio ldquoAsimple approach to model SFRCrdquo Construction and BuildingMaterials vol 37 pp 111ndash124 2012
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2 Advances in Civil Engineering
Table 1 Test T-beam parameters
Material Beam node Stirrup spacing(mm)
Stirrup ratio Volume fraction ofsteel fiber
Concrete 1 150 048 0SFRC 2 150 048 120588 = 15SFRC 3 150 048 120588 = 20
230 140 230
430
70
500
600
26
3276
192
130
22 230 96 230
1 1
휙8
휙8
휙28
Figure 1 Section size and reinforcement layout (unit mm)
Table 2 Mechanical properties of concrete
Beam nodeCrushing
compressivestrength
Concretecompressivestrength
Youngrsquosmodulus
1 371 282 3192 403 306 3273 405 308 327
Table 3 Mechanical properties of reinforced bar
Steel grade Bardiameter
Yieldstress
Ultimatestress
Youngrsquosmodulus
HPB235 8 342 500 210HRB235 28 389 574 200Note In Tables 2 and 3 length unit is mm the strength unit is Mpa andYoungrsquos modulus unit is Gpa
jack that used a high-precision static servo-hydraulic-controlsystem Gradation loading was acted on the beam and theholding time was 15 minutes In the process of loadingthe crack occurrence and development should be carefullyobserved
Table 4 Summary of shear resistance of beams
Beam node 119881cr (KN) 119881u (KN) 119880max (mm)1 200 830 10772 400 1150 1893 300 gt1200 76
123
0
200
400
600
800
1000
1200
1400Lo
ad (K
N)
5 10 15 200Displacement (mm)
Figure 2 Load-displacement curve of the beams
Displacement gauges were arranged in the support 14points and the mid-span In each loading process thecorresponding load and displacement values were recordedsynchronously
3 Test Results
31 Summary of Load Capacity The crack load (119881cr) ulti-mate load (119881u) and the mid-span displacement (119880max)corresponding to the ultimate load of these three beams areshown in Table 4 The load-displacement curve is shown inFigure 2
32 Summary of Crack Development Status Three test T-beams were carried out under 200KN 500KN 800KN1000KN 1100KN and 1200KN The results are shown inTable 5The crack diagram of each beam is shown in Figure 3
Advances in Civil Engineering 3
EN
ES
WN
WS
(a) Crack diagram of 1 beam
EN
ES
WN
WS
(b) Crack diagram of 2 beam
EN
ES
WN
WS
(c) Crack diagram of 3 beam
Figure 3 Crack diagram of each beam
Table 5The development status of themaximum crack width (unitmm)
NodeLoad
200KN 500KN 800KN 1000KN 1100KN 1200KN
1 0 16 25 mdash mdash mdash
2 mdash 02 15 331 gt4 mdash
3 mdash 01 05 063 15 mdash
4 Finite Element Simulation
41 Element Selection and Finite Element Model WhenANSYS was used for finite element analysis of reinforcedconcrete a separate model was adopted The concrete wassimulated by Solid 65 element and steel bar was simulated byPipe 59 element The bond slip between the steel fiber andconcrete was neglected
This paper established the 12 T-beam model whichcan not only reduce the calculation time but also avoid
4 Advances in Civil Engineering
(a) Finite element solid model (b) Reinforced element model
(c) Finite element mesh
Figure 4 ANSYS model
terminating the calculation during calculation process dueto too many warnings In the finite element simulation thestress concentration was avoided at the support and theloading point by adding an elastic pad The ANSYS model isshown in Figure 4
42 Selection of Constitutive Model of Materials The double-line strong hardening model (BISO) was used in the consti-tutive relation of the steel bar and the formula about uniaxialcompressive stress-strain curve of concrete [7] is (1) and(2) The constitutive relation of SFRC is modified on thebasis of concrete [8ndash10] and the following formula (4) isused
Constitutive relation of concrete is as follows
Ascending stage is
119910 =119873119909 minus 1199092
1 + (119873 minus 2) 119909 (1)
Descending stage is
119910 =119909
120572 (119909 minus 1)2 + 119909 (2)
In the formula
119909 =120576
120576119888
119910 =120590
119891119888
119873 =1198640119864119904
(3)
where 119891119888 is compressive strength of concrete 120576119888 is peak strainassociated with1198911198881198640 is initial elastic modulus of concrete119864119904is secant modulus at the peak strain
Constitutive relation of SFRC is
1198911198881198911015840119888=120573 (1205761205760)
120573 minus 1 + (1205761205760)120573 (4)
In the formula
120573 = 05811 + 193120582minus07406119891
120582119891 =120588119891119897119891119889119891
(5)
where 120588119891 is volume fraction of steel fiber 119897119891 is steel fiberlength and 119889119891 is steel fiber diameter
Advances in Civil Engineering 5
Table 6 Cracking load and ultimate load of three test T-beams
Beam note 119881crexp(KN)
119881crcal(KN) 119881crcal119881crexp 119881uexp
(KN)119881ucal(KN) 119881ucal119881uexp
1 200 213 1065 830 810 09762 400 364 091 1150 1270 11043 300 411 137 gt1200 1420 lt1183Note 119881crexp and119881crcal respectively represent the cracking load of the test and the finite element simulation 119881uexp and119881ucal respectively represent theultimate failure load of the test and the finite element simulation
43 Comparative Analysis of Finite Element Results andTest Results
431 Comparative Analysis of Load-Displacement Curve andLoad Carrying Capacity The comparisons of test data withANSYS simulations are shown in Figure 5
The cracking load and ultimate load of three test T-beamsare shown in Table 6
According to the 1ndash3 beam it can be seen that the load-displacement curve of the finite element is basically consistentwith that of the test and the gap of the failure load is not bigBut the slope of the curve obtained by finite element methodis slightly larger than that of the test chamber The stiffnessof the SFRC beam simulated by the finite element is slightlymore than that of the test result The main reason for thissituation is the simulation of concrete inner and SFRC innerwas ideal andwith no flaw In addition due to the compactingprocess of beams in the actual process the stiffness of thebeam simulated by ANSYS is greater than that of test T-beam
ANSYS simulation results showed that the test T-beamin the process of loading had experienced two stages elasticand inelastic along with the increase of loadThe slope of theload-displacement curve was gradually reduced The load-displacement curve obtained from the test also reflected theprocess of the stiffness degradation
The volume fraction of steel fiber of 1 2 3 test T-beamrespectively was 0 15 and 2 From Figure 5(d) it canbeen seen that the slope of the 2 beam and 3 beam in theelastic stage and the nonelastic stage is significantly greaterthan that of the 1 beam which proves the adding of steelfiber can improve the stiffness and ductility of the concretebeam In the nonelastic stage the higher volume fraction ofsteel fiber is the slower stiffness degradation of the concreteis Figure 5(e) curves obtained from the test also reflect thischaracteristic
FromTable 6 it can be seen that the results of the crackingload and the ultimate failure load simulated by finite elementanalysis are not quite different from the tests result and theratio is close to 1 With the incorporation of steel fiber theultimate bearing capacity has been significantly improvedAnd the higher the volume fraction of steel fiber the higherthe ultimate bearing capacity
44 Crack Distribution and Comparative Analysis of DamageFrom Table 6 the finite element simulation results showedthat in the aspect of cracking loads the cracking load of thetest T-beam increases with the increase of volume fraction of
steel fiber which reflected that the initial cracking of the steelfiber can be suppressed by the addition of steel fiberHoweverthe cracking load of 3 beam is smaller than that of 2 beamwhich could be caused by the uneven mixing of steel fiber
The smeared crack model was used in ANSYS to simulatethe distribution and development of cracks with the lack ofability to simulate single fracture of crack width and crackdevelopment From the crack distribution it can be seen thatthe ordinary concrete beam cracks and SFRC beam cracksalmost distributed in the whole beam section and the resultsgained from half length of the beams were compared inFigure 6 Shown by the comparison the fracture distributionssimulated by finite element are in a good conformation withthe fracture distributions during actual test
From the crack distribution it can be seen that the maincrack spacing of beam 1 is smaller than that of beam 2 andbeam 3 In Figure 6 120579119894 (119894 = 1 2 3) represents the main crackdevelopment angle of each beam ℎ119894 (119894 = 1 2 3) representsthe cross crack length produced by each beam Since maincrack development angle 1205791 of beam 1 is less than 1205792 and 1205793it shows that the incorporation of steel fiber can cause thecrack to be dispersed and avoid the damage caused by thestress concentration In cross crack area the crack length ℎ1produced by beam 1 is smaller than ℎ2 and ℎ3 besides ℎ3 lt ℎ2which reflects that the addition of the steel fiber can increasethe bending crack resistance
The crack width of beam 1 beam 2 and beam 3 iscompared in Table 5 The occurrence of cracking of beam 1was the earliest and the crack development speed was thefastest Beam 2 and beam 3 almost simultaneously crackedbut in the same load conditions the crack width of beam 3was smaller and the crack development speedwas slower thanbeam 2 In the elastic stage of beam 2 the crack developedslowly but after the elastic stage the crack developed quicklywhich showed that the increase of volume fraction of steelfiber can improve the crack resistance of the concrete anddelay the development of cracks Because when volumefraction was greater than 2 it is difficult to blend steel fiberin concrete so the study was not done
5 Conclusions
Through the above test and finite element simulation analysisthe following conclusions can be drawn
(1) The incorporation of steel fiber can improve theintegral rigidity and ductility of concrete T-beam In acertain range the higher the volume fraction of steel
6 Advances in Civil Engineering
TestANSYS
0
100
200
300
400
500
600
700
800
900Lo
ad (K
N)
2 4 6 8 10 120Displacement (mm)
(a) 1 beam comparison diagram
TestANSYS
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(b) 2 beam comparison diagram
TextANSYS
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
5 10 150Displacement (mm)
(c) 3 beam comparison diagram
123
5 10 15 200Displacement (mm)
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
(d) Test results
123
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(e) ANSYS results
Figure 5 Comparison of the results of test with ANSYS simulation
Advances in Civil Engineering 7
WN
h1
z
Crack distribution area
(a) Finite element simulation results and test results of 1 beam cracks
WN
h2
z
Crack distribution area
(b) Finite element simulation results and test results of 2 beam cracks
WN
h3
z
Crack distribution area
(c) Finite element simulation results and test results of 3 beam cracks
Figure 6 Finite element simulation and test results of the cracks of each beam
fiber is the higher the integral rigidity is and theslower the stiffness degradation of T-beam is
(2) With the same reinforcement ratio and shear spanratio the higher volume fraction of steel fiber isthe higher the ultimate shear bearing capacity of theconcrete T-beam is
(3) The increase of volume fraction of steel fiber can delaythe development of cracks and make the distributionof cracks more uniform and also improve crack resis-tance of the concrete T-beam when volume fractionwas less than 2
(4) Finite element analysis of SFRCT-beams by ANSYSis feasible and the results obtained by ANSYS are ingood agreementwith test results ANSYS can simulatethe general trend of the crack and the crack distribu-tion area of the T-beam by using the smeared crackmodel
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
The research described in this paper was financially sup-ported by the Jiangsu Province Key Laboratory of StructureEngineering located in Suzhou University of Science andTechnology
References
[1] X Sun B Diao and Y Ye ldquoFlexural behavior experiments ofultra-high performance concrete beams reinforced with steelbar and hybrid-fiberrdquo Industrial Architecture vol 42 no 11 pp16ndash21 2012
[2] Z Y Sun Y Yang W H Qin S T Ren and G Wu ldquoExperi-mental study on flexural behavior of concrete beams reinforcedby steel-fiber reinforced polymer composite barsrdquo Journal ofReinforced Plastics and Composites vol 31 no 24 pp 1737ndash17452012
[3] H-Z Zhang C-K Huang and R-J Zhang ldquoExperimentalstudy on shear resistance of steel fiber reinforced high strengthconcrete beamsrdquo Journal of Harbin Institute of Technology vol38 no 10 pp 1781ndash1785 2006
[4] J-S ChoTheShear Behavior of Steel Fiber Reinforced PrestressedConcrete Beams without Shear Reinforcement The University ofTexas at Arlington Arlington Tex USA 2011
8 Advances in Civil Engineering
[5] B-X Shi ldquoExperiment study on fatigue characteristic of steelfiber reinforced concreterdquo Journal of Hebei University of Engi-neering (Natural Science Edition) vol 25 no 2 pp 9ndash12 2008
[6] L Wang Study on the Properties of Ultra-Short Ultra-FineSteel Fiber Reinforced Concrete Chongqing Jiaotong UniversityChongqing China 2011
[7] Y Li X Wang and S Chen ldquoComparison of stress-straincurves of concrete under uniaxial compressionrdquo Highway Traf-fic Department vol 10 pp 75ndash78 2005
[8] J Qiu ldquoStudy on nonlinear finite element analysis of steel fiberconcrete structurerdquo Concrete no 3 pp 17ndash20 2011
[9] D A Fanella and A E Naaman ldquoStress-strain properties offiber reinforced mortar in compressionrdquo Journal of the Amer-ican Concrete Institute vol 82 no 4 pp 475ndash483 1985
[10] B Luccioni G Ruano F Isla R Zerbino and G Giaccio ldquoAsimple approach to model SFRCrdquo Construction and BuildingMaterials vol 37 pp 111ndash124 2012
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Advances in Civil Engineering 3
EN
ES
WN
WS
(a) Crack diagram of 1 beam
EN
ES
WN
WS
(b) Crack diagram of 2 beam
EN
ES
WN
WS
(c) Crack diagram of 3 beam
Figure 3 Crack diagram of each beam
Table 5The development status of themaximum crack width (unitmm)
NodeLoad
200KN 500KN 800KN 1000KN 1100KN 1200KN
1 0 16 25 mdash mdash mdash
2 mdash 02 15 331 gt4 mdash
3 mdash 01 05 063 15 mdash
4 Finite Element Simulation
41 Element Selection and Finite Element Model WhenANSYS was used for finite element analysis of reinforcedconcrete a separate model was adopted The concrete wassimulated by Solid 65 element and steel bar was simulated byPipe 59 element The bond slip between the steel fiber andconcrete was neglected
This paper established the 12 T-beam model whichcan not only reduce the calculation time but also avoid
4 Advances in Civil Engineering
(a) Finite element solid model (b) Reinforced element model
(c) Finite element mesh
Figure 4 ANSYS model
terminating the calculation during calculation process dueto too many warnings In the finite element simulation thestress concentration was avoided at the support and theloading point by adding an elastic pad The ANSYS model isshown in Figure 4
42 Selection of Constitutive Model of Materials The double-line strong hardening model (BISO) was used in the consti-tutive relation of the steel bar and the formula about uniaxialcompressive stress-strain curve of concrete [7] is (1) and(2) The constitutive relation of SFRC is modified on thebasis of concrete [8ndash10] and the following formula (4) isused
Constitutive relation of concrete is as follows
Ascending stage is
119910 =119873119909 minus 1199092
1 + (119873 minus 2) 119909 (1)
Descending stage is
119910 =119909
120572 (119909 minus 1)2 + 119909 (2)
In the formula
119909 =120576
120576119888
119910 =120590
119891119888
119873 =1198640119864119904
(3)
where 119891119888 is compressive strength of concrete 120576119888 is peak strainassociated with1198911198881198640 is initial elastic modulus of concrete119864119904is secant modulus at the peak strain
Constitutive relation of SFRC is
1198911198881198911015840119888=120573 (1205761205760)
120573 minus 1 + (1205761205760)120573 (4)
In the formula
120573 = 05811 + 193120582minus07406119891
120582119891 =120588119891119897119891119889119891
(5)
where 120588119891 is volume fraction of steel fiber 119897119891 is steel fiberlength and 119889119891 is steel fiber diameter
Advances in Civil Engineering 5
Table 6 Cracking load and ultimate load of three test T-beams
Beam note 119881crexp(KN)
119881crcal(KN) 119881crcal119881crexp 119881uexp
(KN)119881ucal(KN) 119881ucal119881uexp
1 200 213 1065 830 810 09762 400 364 091 1150 1270 11043 300 411 137 gt1200 1420 lt1183Note 119881crexp and119881crcal respectively represent the cracking load of the test and the finite element simulation 119881uexp and119881ucal respectively represent theultimate failure load of the test and the finite element simulation
43 Comparative Analysis of Finite Element Results andTest Results
431 Comparative Analysis of Load-Displacement Curve andLoad Carrying Capacity The comparisons of test data withANSYS simulations are shown in Figure 5
The cracking load and ultimate load of three test T-beamsare shown in Table 6
According to the 1ndash3 beam it can be seen that the load-displacement curve of the finite element is basically consistentwith that of the test and the gap of the failure load is not bigBut the slope of the curve obtained by finite element methodis slightly larger than that of the test chamber The stiffnessof the SFRC beam simulated by the finite element is slightlymore than that of the test result The main reason for thissituation is the simulation of concrete inner and SFRC innerwas ideal andwith no flaw In addition due to the compactingprocess of beams in the actual process the stiffness of thebeam simulated by ANSYS is greater than that of test T-beam
ANSYS simulation results showed that the test T-beamin the process of loading had experienced two stages elasticand inelastic along with the increase of loadThe slope of theload-displacement curve was gradually reduced The load-displacement curve obtained from the test also reflected theprocess of the stiffness degradation
The volume fraction of steel fiber of 1 2 3 test T-beamrespectively was 0 15 and 2 From Figure 5(d) it canbeen seen that the slope of the 2 beam and 3 beam in theelastic stage and the nonelastic stage is significantly greaterthan that of the 1 beam which proves the adding of steelfiber can improve the stiffness and ductility of the concretebeam In the nonelastic stage the higher volume fraction ofsteel fiber is the slower stiffness degradation of the concreteis Figure 5(e) curves obtained from the test also reflect thischaracteristic
FromTable 6 it can be seen that the results of the crackingload and the ultimate failure load simulated by finite elementanalysis are not quite different from the tests result and theratio is close to 1 With the incorporation of steel fiber theultimate bearing capacity has been significantly improvedAnd the higher the volume fraction of steel fiber the higherthe ultimate bearing capacity
44 Crack Distribution and Comparative Analysis of DamageFrom Table 6 the finite element simulation results showedthat in the aspect of cracking loads the cracking load of thetest T-beam increases with the increase of volume fraction of
steel fiber which reflected that the initial cracking of the steelfiber can be suppressed by the addition of steel fiberHoweverthe cracking load of 3 beam is smaller than that of 2 beamwhich could be caused by the uneven mixing of steel fiber
The smeared crack model was used in ANSYS to simulatethe distribution and development of cracks with the lack ofability to simulate single fracture of crack width and crackdevelopment From the crack distribution it can be seen thatthe ordinary concrete beam cracks and SFRC beam cracksalmost distributed in the whole beam section and the resultsgained from half length of the beams were compared inFigure 6 Shown by the comparison the fracture distributionssimulated by finite element are in a good conformation withthe fracture distributions during actual test
From the crack distribution it can be seen that the maincrack spacing of beam 1 is smaller than that of beam 2 andbeam 3 In Figure 6 120579119894 (119894 = 1 2 3) represents the main crackdevelopment angle of each beam ℎ119894 (119894 = 1 2 3) representsthe cross crack length produced by each beam Since maincrack development angle 1205791 of beam 1 is less than 1205792 and 1205793it shows that the incorporation of steel fiber can cause thecrack to be dispersed and avoid the damage caused by thestress concentration In cross crack area the crack length ℎ1produced by beam 1 is smaller than ℎ2 and ℎ3 besides ℎ3 lt ℎ2which reflects that the addition of the steel fiber can increasethe bending crack resistance
The crack width of beam 1 beam 2 and beam 3 iscompared in Table 5 The occurrence of cracking of beam 1was the earliest and the crack development speed was thefastest Beam 2 and beam 3 almost simultaneously crackedbut in the same load conditions the crack width of beam 3was smaller and the crack development speedwas slower thanbeam 2 In the elastic stage of beam 2 the crack developedslowly but after the elastic stage the crack developed quicklywhich showed that the increase of volume fraction of steelfiber can improve the crack resistance of the concrete anddelay the development of cracks Because when volumefraction was greater than 2 it is difficult to blend steel fiberin concrete so the study was not done
5 Conclusions
Through the above test and finite element simulation analysisthe following conclusions can be drawn
(1) The incorporation of steel fiber can improve theintegral rigidity and ductility of concrete T-beam In acertain range the higher the volume fraction of steel
6 Advances in Civil Engineering
TestANSYS
0
100
200
300
400
500
600
700
800
900Lo
ad (K
N)
2 4 6 8 10 120Displacement (mm)
(a) 1 beam comparison diagram
TestANSYS
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(b) 2 beam comparison diagram
TextANSYS
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
5 10 150Displacement (mm)
(c) 3 beam comparison diagram
123
5 10 15 200Displacement (mm)
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
(d) Test results
123
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(e) ANSYS results
Figure 5 Comparison of the results of test with ANSYS simulation
Advances in Civil Engineering 7
WN
h1
z
Crack distribution area
(a) Finite element simulation results and test results of 1 beam cracks
WN
h2
z
Crack distribution area
(b) Finite element simulation results and test results of 2 beam cracks
WN
h3
z
Crack distribution area
(c) Finite element simulation results and test results of 3 beam cracks
Figure 6 Finite element simulation and test results of the cracks of each beam
fiber is the higher the integral rigidity is and theslower the stiffness degradation of T-beam is
(2) With the same reinforcement ratio and shear spanratio the higher volume fraction of steel fiber isthe higher the ultimate shear bearing capacity of theconcrete T-beam is
(3) The increase of volume fraction of steel fiber can delaythe development of cracks and make the distributionof cracks more uniform and also improve crack resis-tance of the concrete T-beam when volume fractionwas less than 2
(4) Finite element analysis of SFRCT-beams by ANSYSis feasible and the results obtained by ANSYS are ingood agreementwith test results ANSYS can simulatethe general trend of the crack and the crack distribu-tion area of the T-beam by using the smeared crackmodel
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
The research described in this paper was financially sup-ported by the Jiangsu Province Key Laboratory of StructureEngineering located in Suzhou University of Science andTechnology
References
[1] X Sun B Diao and Y Ye ldquoFlexural behavior experiments ofultra-high performance concrete beams reinforced with steelbar and hybrid-fiberrdquo Industrial Architecture vol 42 no 11 pp16ndash21 2012
[2] Z Y Sun Y Yang W H Qin S T Ren and G Wu ldquoExperi-mental study on flexural behavior of concrete beams reinforcedby steel-fiber reinforced polymer composite barsrdquo Journal ofReinforced Plastics and Composites vol 31 no 24 pp 1737ndash17452012
[3] H-Z Zhang C-K Huang and R-J Zhang ldquoExperimentalstudy on shear resistance of steel fiber reinforced high strengthconcrete beamsrdquo Journal of Harbin Institute of Technology vol38 no 10 pp 1781ndash1785 2006
[4] J-S ChoTheShear Behavior of Steel Fiber Reinforced PrestressedConcrete Beams without Shear Reinforcement The University ofTexas at Arlington Arlington Tex USA 2011
8 Advances in Civil Engineering
[5] B-X Shi ldquoExperiment study on fatigue characteristic of steelfiber reinforced concreterdquo Journal of Hebei University of Engi-neering (Natural Science Edition) vol 25 no 2 pp 9ndash12 2008
[6] L Wang Study on the Properties of Ultra-Short Ultra-FineSteel Fiber Reinforced Concrete Chongqing Jiaotong UniversityChongqing China 2011
[7] Y Li X Wang and S Chen ldquoComparison of stress-straincurves of concrete under uniaxial compressionrdquo Highway Traf-fic Department vol 10 pp 75ndash78 2005
[8] J Qiu ldquoStudy on nonlinear finite element analysis of steel fiberconcrete structurerdquo Concrete no 3 pp 17ndash20 2011
[9] D A Fanella and A E Naaman ldquoStress-strain properties offiber reinforced mortar in compressionrdquo Journal of the Amer-ican Concrete Institute vol 82 no 4 pp 475ndash483 1985
[10] B Luccioni G Ruano F Isla R Zerbino and G Giaccio ldquoAsimple approach to model SFRCrdquo Construction and BuildingMaterials vol 37 pp 111ndash124 2012
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
4 Advances in Civil Engineering
(a) Finite element solid model (b) Reinforced element model
(c) Finite element mesh
Figure 4 ANSYS model
terminating the calculation during calculation process dueto too many warnings In the finite element simulation thestress concentration was avoided at the support and theloading point by adding an elastic pad The ANSYS model isshown in Figure 4
42 Selection of Constitutive Model of Materials The double-line strong hardening model (BISO) was used in the consti-tutive relation of the steel bar and the formula about uniaxialcompressive stress-strain curve of concrete [7] is (1) and(2) The constitutive relation of SFRC is modified on thebasis of concrete [8ndash10] and the following formula (4) isused
Constitutive relation of concrete is as follows
Ascending stage is
119910 =119873119909 minus 1199092
1 + (119873 minus 2) 119909 (1)
Descending stage is
119910 =119909
120572 (119909 minus 1)2 + 119909 (2)
In the formula
119909 =120576
120576119888
119910 =120590
119891119888
119873 =1198640119864119904
(3)
where 119891119888 is compressive strength of concrete 120576119888 is peak strainassociated with1198911198881198640 is initial elastic modulus of concrete119864119904is secant modulus at the peak strain
Constitutive relation of SFRC is
1198911198881198911015840119888=120573 (1205761205760)
120573 minus 1 + (1205761205760)120573 (4)
In the formula
120573 = 05811 + 193120582minus07406119891
120582119891 =120588119891119897119891119889119891
(5)
where 120588119891 is volume fraction of steel fiber 119897119891 is steel fiberlength and 119889119891 is steel fiber diameter
Advances in Civil Engineering 5
Table 6 Cracking load and ultimate load of three test T-beams
Beam note 119881crexp(KN)
119881crcal(KN) 119881crcal119881crexp 119881uexp
(KN)119881ucal(KN) 119881ucal119881uexp
1 200 213 1065 830 810 09762 400 364 091 1150 1270 11043 300 411 137 gt1200 1420 lt1183Note 119881crexp and119881crcal respectively represent the cracking load of the test and the finite element simulation 119881uexp and119881ucal respectively represent theultimate failure load of the test and the finite element simulation
43 Comparative Analysis of Finite Element Results andTest Results
431 Comparative Analysis of Load-Displacement Curve andLoad Carrying Capacity The comparisons of test data withANSYS simulations are shown in Figure 5
The cracking load and ultimate load of three test T-beamsare shown in Table 6
According to the 1ndash3 beam it can be seen that the load-displacement curve of the finite element is basically consistentwith that of the test and the gap of the failure load is not bigBut the slope of the curve obtained by finite element methodis slightly larger than that of the test chamber The stiffnessof the SFRC beam simulated by the finite element is slightlymore than that of the test result The main reason for thissituation is the simulation of concrete inner and SFRC innerwas ideal andwith no flaw In addition due to the compactingprocess of beams in the actual process the stiffness of thebeam simulated by ANSYS is greater than that of test T-beam
ANSYS simulation results showed that the test T-beamin the process of loading had experienced two stages elasticand inelastic along with the increase of loadThe slope of theload-displacement curve was gradually reduced The load-displacement curve obtained from the test also reflected theprocess of the stiffness degradation
The volume fraction of steel fiber of 1 2 3 test T-beamrespectively was 0 15 and 2 From Figure 5(d) it canbeen seen that the slope of the 2 beam and 3 beam in theelastic stage and the nonelastic stage is significantly greaterthan that of the 1 beam which proves the adding of steelfiber can improve the stiffness and ductility of the concretebeam In the nonelastic stage the higher volume fraction ofsteel fiber is the slower stiffness degradation of the concreteis Figure 5(e) curves obtained from the test also reflect thischaracteristic
FromTable 6 it can be seen that the results of the crackingload and the ultimate failure load simulated by finite elementanalysis are not quite different from the tests result and theratio is close to 1 With the incorporation of steel fiber theultimate bearing capacity has been significantly improvedAnd the higher the volume fraction of steel fiber the higherthe ultimate bearing capacity
44 Crack Distribution and Comparative Analysis of DamageFrom Table 6 the finite element simulation results showedthat in the aspect of cracking loads the cracking load of thetest T-beam increases with the increase of volume fraction of
steel fiber which reflected that the initial cracking of the steelfiber can be suppressed by the addition of steel fiberHoweverthe cracking load of 3 beam is smaller than that of 2 beamwhich could be caused by the uneven mixing of steel fiber
The smeared crack model was used in ANSYS to simulatethe distribution and development of cracks with the lack ofability to simulate single fracture of crack width and crackdevelopment From the crack distribution it can be seen thatthe ordinary concrete beam cracks and SFRC beam cracksalmost distributed in the whole beam section and the resultsgained from half length of the beams were compared inFigure 6 Shown by the comparison the fracture distributionssimulated by finite element are in a good conformation withthe fracture distributions during actual test
From the crack distribution it can be seen that the maincrack spacing of beam 1 is smaller than that of beam 2 andbeam 3 In Figure 6 120579119894 (119894 = 1 2 3) represents the main crackdevelopment angle of each beam ℎ119894 (119894 = 1 2 3) representsthe cross crack length produced by each beam Since maincrack development angle 1205791 of beam 1 is less than 1205792 and 1205793it shows that the incorporation of steel fiber can cause thecrack to be dispersed and avoid the damage caused by thestress concentration In cross crack area the crack length ℎ1produced by beam 1 is smaller than ℎ2 and ℎ3 besides ℎ3 lt ℎ2which reflects that the addition of the steel fiber can increasethe bending crack resistance
The crack width of beam 1 beam 2 and beam 3 iscompared in Table 5 The occurrence of cracking of beam 1was the earliest and the crack development speed was thefastest Beam 2 and beam 3 almost simultaneously crackedbut in the same load conditions the crack width of beam 3was smaller and the crack development speedwas slower thanbeam 2 In the elastic stage of beam 2 the crack developedslowly but after the elastic stage the crack developed quicklywhich showed that the increase of volume fraction of steelfiber can improve the crack resistance of the concrete anddelay the development of cracks Because when volumefraction was greater than 2 it is difficult to blend steel fiberin concrete so the study was not done
5 Conclusions
Through the above test and finite element simulation analysisthe following conclusions can be drawn
(1) The incorporation of steel fiber can improve theintegral rigidity and ductility of concrete T-beam In acertain range the higher the volume fraction of steel
6 Advances in Civil Engineering
TestANSYS
0
100
200
300
400
500
600
700
800
900Lo
ad (K
N)
2 4 6 8 10 120Displacement (mm)
(a) 1 beam comparison diagram
TestANSYS
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(b) 2 beam comparison diagram
TextANSYS
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
5 10 150Displacement (mm)
(c) 3 beam comparison diagram
123
5 10 15 200Displacement (mm)
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
(d) Test results
123
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(e) ANSYS results
Figure 5 Comparison of the results of test with ANSYS simulation
Advances in Civil Engineering 7
WN
h1
z
Crack distribution area
(a) Finite element simulation results and test results of 1 beam cracks
WN
h2
z
Crack distribution area
(b) Finite element simulation results and test results of 2 beam cracks
WN
h3
z
Crack distribution area
(c) Finite element simulation results and test results of 3 beam cracks
Figure 6 Finite element simulation and test results of the cracks of each beam
fiber is the higher the integral rigidity is and theslower the stiffness degradation of T-beam is
(2) With the same reinforcement ratio and shear spanratio the higher volume fraction of steel fiber isthe higher the ultimate shear bearing capacity of theconcrete T-beam is
(3) The increase of volume fraction of steel fiber can delaythe development of cracks and make the distributionof cracks more uniform and also improve crack resis-tance of the concrete T-beam when volume fractionwas less than 2
(4) Finite element analysis of SFRCT-beams by ANSYSis feasible and the results obtained by ANSYS are ingood agreementwith test results ANSYS can simulatethe general trend of the crack and the crack distribu-tion area of the T-beam by using the smeared crackmodel
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
The research described in this paper was financially sup-ported by the Jiangsu Province Key Laboratory of StructureEngineering located in Suzhou University of Science andTechnology
References
[1] X Sun B Diao and Y Ye ldquoFlexural behavior experiments ofultra-high performance concrete beams reinforced with steelbar and hybrid-fiberrdquo Industrial Architecture vol 42 no 11 pp16ndash21 2012
[2] Z Y Sun Y Yang W H Qin S T Ren and G Wu ldquoExperi-mental study on flexural behavior of concrete beams reinforcedby steel-fiber reinforced polymer composite barsrdquo Journal ofReinforced Plastics and Composites vol 31 no 24 pp 1737ndash17452012
[3] H-Z Zhang C-K Huang and R-J Zhang ldquoExperimentalstudy on shear resistance of steel fiber reinforced high strengthconcrete beamsrdquo Journal of Harbin Institute of Technology vol38 no 10 pp 1781ndash1785 2006
[4] J-S ChoTheShear Behavior of Steel Fiber Reinforced PrestressedConcrete Beams without Shear Reinforcement The University ofTexas at Arlington Arlington Tex USA 2011
8 Advances in Civil Engineering
[5] B-X Shi ldquoExperiment study on fatigue characteristic of steelfiber reinforced concreterdquo Journal of Hebei University of Engi-neering (Natural Science Edition) vol 25 no 2 pp 9ndash12 2008
[6] L Wang Study on the Properties of Ultra-Short Ultra-FineSteel Fiber Reinforced Concrete Chongqing Jiaotong UniversityChongqing China 2011
[7] Y Li X Wang and S Chen ldquoComparison of stress-straincurves of concrete under uniaxial compressionrdquo Highway Traf-fic Department vol 10 pp 75ndash78 2005
[8] J Qiu ldquoStudy on nonlinear finite element analysis of steel fiberconcrete structurerdquo Concrete no 3 pp 17ndash20 2011
[9] D A Fanella and A E Naaman ldquoStress-strain properties offiber reinforced mortar in compressionrdquo Journal of the Amer-ican Concrete Institute vol 82 no 4 pp 475ndash483 1985
[10] B Luccioni G Ruano F Isla R Zerbino and G Giaccio ldquoAsimple approach to model SFRCrdquo Construction and BuildingMaterials vol 37 pp 111ndash124 2012
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Advances in Civil Engineering 5
Table 6 Cracking load and ultimate load of three test T-beams
Beam note 119881crexp(KN)
119881crcal(KN) 119881crcal119881crexp 119881uexp
(KN)119881ucal(KN) 119881ucal119881uexp
1 200 213 1065 830 810 09762 400 364 091 1150 1270 11043 300 411 137 gt1200 1420 lt1183Note 119881crexp and119881crcal respectively represent the cracking load of the test and the finite element simulation 119881uexp and119881ucal respectively represent theultimate failure load of the test and the finite element simulation
43 Comparative Analysis of Finite Element Results andTest Results
431 Comparative Analysis of Load-Displacement Curve andLoad Carrying Capacity The comparisons of test data withANSYS simulations are shown in Figure 5
The cracking load and ultimate load of three test T-beamsare shown in Table 6
According to the 1ndash3 beam it can be seen that the load-displacement curve of the finite element is basically consistentwith that of the test and the gap of the failure load is not bigBut the slope of the curve obtained by finite element methodis slightly larger than that of the test chamber The stiffnessof the SFRC beam simulated by the finite element is slightlymore than that of the test result The main reason for thissituation is the simulation of concrete inner and SFRC innerwas ideal andwith no flaw In addition due to the compactingprocess of beams in the actual process the stiffness of thebeam simulated by ANSYS is greater than that of test T-beam
ANSYS simulation results showed that the test T-beamin the process of loading had experienced two stages elasticand inelastic along with the increase of loadThe slope of theload-displacement curve was gradually reduced The load-displacement curve obtained from the test also reflected theprocess of the stiffness degradation
The volume fraction of steel fiber of 1 2 3 test T-beamrespectively was 0 15 and 2 From Figure 5(d) it canbeen seen that the slope of the 2 beam and 3 beam in theelastic stage and the nonelastic stage is significantly greaterthan that of the 1 beam which proves the adding of steelfiber can improve the stiffness and ductility of the concretebeam In the nonelastic stage the higher volume fraction ofsteel fiber is the slower stiffness degradation of the concreteis Figure 5(e) curves obtained from the test also reflect thischaracteristic
FromTable 6 it can be seen that the results of the crackingload and the ultimate failure load simulated by finite elementanalysis are not quite different from the tests result and theratio is close to 1 With the incorporation of steel fiber theultimate bearing capacity has been significantly improvedAnd the higher the volume fraction of steel fiber the higherthe ultimate bearing capacity
44 Crack Distribution and Comparative Analysis of DamageFrom Table 6 the finite element simulation results showedthat in the aspect of cracking loads the cracking load of thetest T-beam increases with the increase of volume fraction of
steel fiber which reflected that the initial cracking of the steelfiber can be suppressed by the addition of steel fiberHoweverthe cracking load of 3 beam is smaller than that of 2 beamwhich could be caused by the uneven mixing of steel fiber
The smeared crack model was used in ANSYS to simulatethe distribution and development of cracks with the lack ofability to simulate single fracture of crack width and crackdevelopment From the crack distribution it can be seen thatthe ordinary concrete beam cracks and SFRC beam cracksalmost distributed in the whole beam section and the resultsgained from half length of the beams were compared inFigure 6 Shown by the comparison the fracture distributionssimulated by finite element are in a good conformation withthe fracture distributions during actual test
From the crack distribution it can be seen that the maincrack spacing of beam 1 is smaller than that of beam 2 andbeam 3 In Figure 6 120579119894 (119894 = 1 2 3) represents the main crackdevelopment angle of each beam ℎ119894 (119894 = 1 2 3) representsthe cross crack length produced by each beam Since maincrack development angle 1205791 of beam 1 is less than 1205792 and 1205793it shows that the incorporation of steel fiber can cause thecrack to be dispersed and avoid the damage caused by thestress concentration In cross crack area the crack length ℎ1produced by beam 1 is smaller than ℎ2 and ℎ3 besides ℎ3 lt ℎ2which reflects that the addition of the steel fiber can increasethe bending crack resistance
The crack width of beam 1 beam 2 and beam 3 iscompared in Table 5 The occurrence of cracking of beam 1was the earliest and the crack development speed was thefastest Beam 2 and beam 3 almost simultaneously crackedbut in the same load conditions the crack width of beam 3was smaller and the crack development speedwas slower thanbeam 2 In the elastic stage of beam 2 the crack developedslowly but after the elastic stage the crack developed quicklywhich showed that the increase of volume fraction of steelfiber can improve the crack resistance of the concrete anddelay the development of cracks Because when volumefraction was greater than 2 it is difficult to blend steel fiberin concrete so the study was not done
5 Conclusions
Through the above test and finite element simulation analysisthe following conclusions can be drawn
(1) The incorporation of steel fiber can improve theintegral rigidity and ductility of concrete T-beam In acertain range the higher the volume fraction of steel
6 Advances in Civil Engineering
TestANSYS
0
100
200
300
400
500
600
700
800
900Lo
ad (K
N)
2 4 6 8 10 120Displacement (mm)
(a) 1 beam comparison diagram
TestANSYS
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(b) 2 beam comparison diagram
TextANSYS
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
5 10 150Displacement (mm)
(c) 3 beam comparison diagram
123
5 10 15 200Displacement (mm)
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
(d) Test results
123
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(e) ANSYS results
Figure 5 Comparison of the results of test with ANSYS simulation
Advances in Civil Engineering 7
WN
h1
z
Crack distribution area
(a) Finite element simulation results and test results of 1 beam cracks
WN
h2
z
Crack distribution area
(b) Finite element simulation results and test results of 2 beam cracks
WN
h3
z
Crack distribution area
(c) Finite element simulation results and test results of 3 beam cracks
Figure 6 Finite element simulation and test results of the cracks of each beam
fiber is the higher the integral rigidity is and theslower the stiffness degradation of T-beam is
(2) With the same reinforcement ratio and shear spanratio the higher volume fraction of steel fiber isthe higher the ultimate shear bearing capacity of theconcrete T-beam is
(3) The increase of volume fraction of steel fiber can delaythe development of cracks and make the distributionof cracks more uniform and also improve crack resis-tance of the concrete T-beam when volume fractionwas less than 2
(4) Finite element analysis of SFRCT-beams by ANSYSis feasible and the results obtained by ANSYS are ingood agreementwith test results ANSYS can simulatethe general trend of the crack and the crack distribu-tion area of the T-beam by using the smeared crackmodel
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
The research described in this paper was financially sup-ported by the Jiangsu Province Key Laboratory of StructureEngineering located in Suzhou University of Science andTechnology
References
[1] X Sun B Diao and Y Ye ldquoFlexural behavior experiments ofultra-high performance concrete beams reinforced with steelbar and hybrid-fiberrdquo Industrial Architecture vol 42 no 11 pp16ndash21 2012
[2] Z Y Sun Y Yang W H Qin S T Ren and G Wu ldquoExperi-mental study on flexural behavior of concrete beams reinforcedby steel-fiber reinforced polymer composite barsrdquo Journal ofReinforced Plastics and Composites vol 31 no 24 pp 1737ndash17452012
[3] H-Z Zhang C-K Huang and R-J Zhang ldquoExperimentalstudy on shear resistance of steel fiber reinforced high strengthconcrete beamsrdquo Journal of Harbin Institute of Technology vol38 no 10 pp 1781ndash1785 2006
[4] J-S ChoTheShear Behavior of Steel Fiber Reinforced PrestressedConcrete Beams without Shear Reinforcement The University ofTexas at Arlington Arlington Tex USA 2011
8 Advances in Civil Engineering
[5] B-X Shi ldquoExperiment study on fatigue characteristic of steelfiber reinforced concreterdquo Journal of Hebei University of Engi-neering (Natural Science Edition) vol 25 no 2 pp 9ndash12 2008
[6] L Wang Study on the Properties of Ultra-Short Ultra-FineSteel Fiber Reinforced Concrete Chongqing Jiaotong UniversityChongqing China 2011
[7] Y Li X Wang and S Chen ldquoComparison of stress-straincurves of concrete under uniaxial compressionrdquo Highway Traf-fic Department vol 10 pp 75ndash78 2005
[8] J Qiu ldquoStudy on nonlinear finite element analysis of steel fiberconcrete structurerdquo Concrete no 3 pp 17ndash20 2011
[9] D A Fanella and A E Naaman ldquoStress-strain properties offiber reinforced mortar in compressionrdquo Journal of the Amer-ican Concrete Institute vol 82 no 4 pp 475ndash483 1985
[10] B Luccioni G Ruano F Isla R Zerbino and G Giaccio ldquoAsimple approach to model SFRCrdquo Construction and BuildingMaterials vol 37 pp 111ndash124 2012
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 Advances in Civil Engineering
TestANSYS
0
100
200
300
400
500
600
700
800
900Lo
ad (K
N)
2 4 6 8 10 120Displacement (mm)
(a) 1 beam comparison diagram
TestANSYS
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(b) 2 beam comparison diagram
TextANSYS
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
5 10 150Displacement (mm)
(c) 3 beam comparison diagram
123
5 10 15 200Displacement (mm)
0
200
400
600
800
1000
1200
1400
1600
Load
(KN
)
(d) Test results
123
0
200
400
600
800
1000
1200
1400
Load
(KN
)
5 10 15 200Displacement (mm)
(e) ANSYS results
Figure 5 Comparison of the results of test with ANSYS simulation
Advances in Civil Engineering 7
WN
h1
z
Crack distribution area
(a) Finite element simulation results and test results of 1 beam cracks
WN
h2
z
Crack distribution area
(b) Finite element simulation results and test results of 2 beam cracks
WN
h3
z
Crack distribution area
(c) Finite element simulation results and test results of 3 beam cracks
Figure 6 Finite element simulation and test results of the cracks of each beam
fiber is the higher the integral rigidity is and theslower the stiffness degradation of T-beam is
(2) With the same reinforcement ratio and shear spanratio the higher volume fraction of steel fiber isthe higher the ultimate shear bearing capacity of theconcrete T-beam is
(3) The increase of volume fraction of steel fiber can delaythe development of cracks and make the distributionof cracks more uniform and also improve crack resis-tance of the concrete T-beam when volume fractionwas less than 2
(4) Finite element analysis of SFRCT-beams by ANSYSis feasible and the results obtained by ANSYS are ingood agreementwith test results ANSYS can simulatethe general trend of the crack and the crack distribu-tion area of the T-beam by using the smeared crackmodel
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
The research described in this paper was financially sup-ported by the Jiangsu Province Key Laboratory of StructureEngineering located in Suzhou University of Science andTechnology
References
[1] X Sun B Diao and Y Ye ldquoFlexural behavior experiments ofultra-high performance concrete beams reinforced with steelbar and hybrid-fiberrdquo Industrial Architecture vol 42 no 11 pp16ndash21 2012
[2] Z Y Sun Y Yang W H Qin S T Ren and G Wu ldquoExperi-mental study on flexural behavior of concrete beams reinforcedby steel-fiber reinforced polymer composite barsrdquo Journal ofReinforced Plastics and Composites vol 31 no 24 pp 1737ndash17452012
[3] H-Z Zhang C-K Huang and R-J Zhang ldquoExperimentalstudy on shear resistance of steel fiber reinforced high strengthconcrete beamsrdquo Journal of Harbin Institute of Technology vol38 no 10 pp 1781ndash1785 2006
[4] J-S ChoTheShear Behavior of Steel Fiber Reinforced PrestressedConcrete Beams without Shear Reinforcement The University ofTexas at Arlington Arlington Tex USA 2011
8 Advances in Civil Engineering
[5] B-X Shi ldquoExperiment study on fatigue characteristic of steelfiber reinforced concreterdquo Journal of Hebei University of Engi-neering (Natural Science Edition) vol 25 no 2 pp 9ndash12 2008
[6] L Wang Study on the Properties of Ultra-Short Ultra-FineSteel Fiber Reinforced Concrete Chongqing Jiaotong UniversityChongqing China 2011
[7] Y Li X Wang and S Chen ldquoComparison of stress-straincurves of concrete under uniaxial compressionrdquo Highway Traf-fic Department vol 10 pp 75ndash78 2005
[8] J Qiu ldquoStudy on nonlinear finite element analysis of steel fiberconcrete structurerdquo Concrete no 3 pp 17ndash20 2011
[9] D A Fanella and A E Naaman ldquoStress-strain properties offiber reinforced mortar in compressionrdquo Journal of the Amer-ican Concrete Institute vol 82 no 4 pp 475ndash483 1985
[10] B Luccioni G Ruano F Isla R Zerbino and G Giaccio ldquoAsimple approach to model SFRCrdquo Construction and BuildingMaterials vol 37 pp 111ndash124 2012
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Advances in Civil Engineering 7
WN
h1
z
Crack distribution area
(a) Finite element simulation results and test results of 1 beam cracks
WN
h2
z
Crack distribution area
(b) Finite element simulation results and test results of 2 beam cracks
WN
h3
z
Crack distribution area
(c) Finite element simulation results and test results of 3 beam cracks
Figure 6 Finite element simulation and test results of the cracks of each beam
fiber is the higher the integral rigidity is and theslower the stiffness degradation of T-beam is
(2) With the same reinforcement ratio and shear spanratio the higher volume fraction of steel fiber isthe higher the ultimate shear bearing capacity of theconcrete T-beam is
(3) The increase of volume fraction of steel fiber can delaythe development of cracks and make the distributionof cracks more uniform and also improve crack resis-tance of the concrete T-beam when volume fractionwas less than 2
(4) Finite element analysis of SFRCT-beams by ANSYSis feasible and the results obtained by ANSYS are ingood agreementwith test results ANSYS can simulatethe general trend of the crack and the crack distribu-tion area of the T-beam by using the smeared crackmodel
Conflicts of Interest
The authors declare that they have no conflicts of interest
Acknowledgments
The research described in this paper was financially sup-ported by the Jiangsu Province Key Laboratory of StructureEngineering located in Suzhou University of Science andTechnology
References
[1] X Sun B Diao and Y Ye ldquoFlexural behavior experiments ofultra-high performance concrete beams reinforced with steelbar and hybrid-fiberrdquo Industrial Architecture vol 42 no 11 pp16ndash21 2012
[2] Z Y Sun Y Yang W H Qin S T Ren and G Wu ldquoExperi-mental study on flexural behavior of concrete beams reinforcedby steel-fiber reinforced polymer composite barsrdquo Journal ofReinforced Plastics and Composites vol 31 no 24 pp 1737ndash17452012
[3] H-Z Zhang C-K Huang and R-J Zhang ldquoExperimentalstudy on shear resistance of steel fiber reinforced high strengthconcrete beamsrdquo Journal of Harbin Institute of Technology vol38 no 10 pp 1781ndash1785 2006
[4] J-S ChoTheShear Behavior of Steel Fiber Reinforced PrestressedConcrete Beams without Shear Reinforcement The University ofTexas at Arlington Arlington Tex USA 2011
8 Advances in Civil Engineering
[5] B-X Shi ldquoExperiment study on fatigue characteristic of steelfiber reinforced concreterdquo Journal of Hebei University of Engi-neering (Natural Science Edition) vol 25 no 2 pp 9ndash12 2008
[6] L Wang Study on the Properties of Ultra-Short Ultra-FineSteel Fiber Reinforced Concrete Chongqing Jiaotong UniversityChongqing China 2011
[7] Y Li X Wang and S Chen ldquoComparison of stress-straincurves of concrete under uniaxial compressionrdquo Highway Traf-fic Department vol 10 pp 75ndash78 2005
[8] J Qiu ldquoStudy on nonlinear finite element analysis of steel fiberconcrete structurerdquo Concrete no 3 pp 17ndash20 2011
[9] D A Fanella and A E Naaman ldquoStress-strain properties offiber reinforced mortar in compressionrdquo Journal of the Amer-ican Concrete Institute vol 82 no 4 pp 475ndash483 1985
[10] B Luccioni G Ruano F Isla R Zerbino and G Giaccio ldquoAsimple approach to model SFRCrdquo Construction and BuildingMaterials vol 37 pp 111ndash124 2012
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 Advances in Civil Engineering
[5] B-X Shi ldquoExperiment study on fatigue characteristic of steelfiber reinforced concreterdquo Journal of Hebei University of Engi-neering (Natural Science Edition) vol 25 no 2 pp 9ndash12 2008
[6] L Wang Study on the Properties of Ultra-Short Ultra-FineSteel Fiber Reinforced Concrete Chongqing Jiaotong UniversityChongqing China 2011
[7] Y Li X Wang and S Chen ldquoComparison of stress-straincurves of concrete under uniaxial compressionrdquo Highway Traf-fic Department vol 10 pp 75ndash78 2005
[8] J Qiu ldquoStudy on nonlinear finite element analysis of steel fiberconcrete structurerdquo Concrete no 3 pp 17ndash20 2011
[9] D A Fanella and A E Naaman ldquoStress-strain properties offiber reinforced mortar in compressionrdquo Journal of the Amer-ican Concrete Institute vol 82 no 4 pp 475ndash483 1985
[10] B Luccioni G Ruano F Isla R Zerbino and G Giaccio ldquoAsimple approach to model SFRCrdquo Construction and BuildingMaterials vol 37 pp 111ndash124 2012
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal of
Volume 201
Submit your manuscripts athttpswwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 201
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of