Research Article Flexural Behavior of Posttensioned Flat

Research ArticleFlexural Behavior of Posttensioned Flat PlatesDepending on Tendon Layout

Min Sook Kim and Young Hak Lee

Department of Architectural Engineering Kyung Hee University 1732 Deogyeong-daero Yongin 17104 Republic of Korea

Correspondence should be addressed to Young Hak Lee leeyhkhuackr

Received 27 April 2016 Accepted 4 July 2016

Academic Editor Ana S Guimaraes

Copyright copy 2016 M S Kim and Y H Lee This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper discusses the experimental results on the flexural behavior and deflections of posttensioned concrete flat platesdepending on tendon layout One reinforced concrete flat plate and two posttensioned concrete flat plates were manufacturedand tested One-way posttensioning layout and two-way posttensioning layout were considered in this paper The load-deflectionbehavior and modes of crack are presented from the test results Posttension systems effectively controlled crack and deflectionOne-way and two-way posttensioning layouts both showed similarmaximum load However serviceability improvedwith two-wayposttensioning layout compared to one-way posttensioning layout Also the yield-line theory was applied to predict the ultimateload for the posttensioned flat platesThe comparison between the test results and estimation by yield-line analysis generally showedgood agreement

1 Introduction

Posttensioned concrete flat plate structure has many advan-tages such as reduction of overall member thickness andsimpler construction Also these systems have exhibitedgood performance in terms of ductility and flexural capacity

The critical failure mode for flat plates is punching shearTherefore researchers have studied the way to improve thestructural performance of the flat plate through an appropri-ate tendon layout Burns and Hemakom [1] performed thetest to observe the strength and behavior of posttensionedflat plate The banded tendon layout was applied in columnstrip of 119909-direction and single tendons were distributed in 119910-direction of slab It was found from the experiment that thebanded and distributed tendon layout can improve the flex-ural and shear capacities The flexural failure demonstratedthat the banded tendon layout of column strip resisted thepunching shear effectively Kosut et al [2] experimentallyevaluated the behavior of posttensioned flat plates with dis-tributed and banded tendon arrangement in each directionThey presented that the banded tendon on the column stripcan resist the punching shear failure and distributed tendoncan improve flexural capacity Ramos et al [3] presented

the experimental results of flat plates with tendon underpunching shear They showed the results that load capacitydecreased as the distance between the tendons and thecolumn increased For analytical studies Gilbert et al [4]proposed automatic yield-line analysis to predict ultimatestrength of two-way slabs Harajli [5] proposed an equationusing plastic analysis to calculate the stress in unbonded ten-dons at ultimate load They verified the accuracy of the pro-posed equation in comparison with test data and ACI designcode

Recently Functionally Graded Materials (FGMs) weredeveloped to improve strength ductility and chemical resis-tance of structural materials FGMs are a new kind ofinhomogeneous composite materials which have low densityexcellent chemical resistance and high stiffness to weightratioThe application of FGM has been extended to slabs andbridges due to its many advantages In order to apply FGMsto structural member such as beams and slabs it is necessaryto build a new theory for the beam and the plate Mahi et al[6] developed hyperbolic shear deformation theory to predictfree vibration frequencies of FGM plates They showed theaccuracy and efficiency of the proposed theory Belabed et al[7] presented higher order shear and normal deformation

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2016 Article ID 2651435 11 pageshttpdxdoiorg10115520162651435

2 Advances in Materials Science and Engineering

Column

Banded

Min two strands over column

tendons

(a) Banded-distributed (b) Banded-banded

Min two strands over column(c) Distributed-distributed (d) Mixed

Figure 1 Principal options of tendon layout [4]

theory for FGM platesThey verified that the theory can con-sider both shear deformation and thickness stretching effectsHebali et al [8] proposed a new quasi-three-dimensionalhyperbolic shear deformation theory to analyze the bendingand free vibration for FGMS plates

There are several possible arrangements for the tendonlayout in two-way slab system supported by columns [9]Thetendons in each direction can be arranged in combination ofbanded and distributed layouts as shown in Figure 1 Sincethe four options provide equal strength capacity the choice oftendon layout is usually determined by constructability [3]

Posttensioned slabs are used for long spans and heavylive loads where flexural strength and ductility assume asignificant role It is known that the flexural behaviors usuallygovern the behavior of interior panel in the flat plates Inotherwords the distribution of tendons can affect the flexuralstrength and ductility in the interior panel of the flat platesThough many researchers have researched into the effect of

punching shear to the posttensioned flat plates with varioustendon layouts in column strips most of these researchespointed out that the tendon layouts designs are only presentedto prevent punching shear failure Little information isavailable on the flexural behavior of posttensioned flat plateThis study aims to recommend the concerning tendon layoutdesign to improve flexural strength and ductility for postten-sioned flat plates

In this study flexural tests on three concrete flat platespecimens were performed in order to evaluate the flexuralbehavior and deflection according to the tendon layoutFor the comparison purpose one of three specimens wastypical concrete flat plate and the tendons were distributedin one way and in two ways for the other two specimensCracking pattern failure modes strain and maximum loadwere obtained and analyzed from the tests The test resultswere also compared to examine the validity of the yield-linetheory

Advances in Materials Science and Engineering 3

Table 1 Material properties of tendon

Type Diameter(mm)

Area(mm2)

Unitweight(kgkm)

Elongation()

SWPC 7B 127 987 774 35

2 Experimental Program

21 Materials The design compressive strength of the con-crete used for the fabrication of the specimens was 35MPaThe average compressive strength measured at 28 days was367MPa Deformed steel bars with a diameter of 13mmand 10mm were used as longitudinal reinforcement andstirrups respectively And their tensile strength andmodulusof elasticity were 400MPa and 200GPa respectively Seven-wire steel strand tendons with 127mm diameter were usedThe nominal ultimate tensile strength of the tendon was1860MPaMaterial properties of the tendons are summarizedin Table 1

22 Specimen Details One concrete flat plate (FR-control)and two posttensioned flat plates were manufactured forthe test For two posttensioned flat plates one specimenhad tendons distributed in only 119909-direction (FR-PT-119909) andthe other distributed in both 119909- and 119910-directions (FR-PT-119909119910) Details of the specimens are illustrated in Figure 2 andsummarized in Table 2 The size of the test specimens was3000mm times 3000mm and 250mm thickness A minimumconcrete cover of 40mm was designed for all specimensat compression and tension sides Two specimens wereposttensioned with a constant eccentricity of 43mm SinceACI code recommended that the tendon spacing not begreater than eight times the slab thickness [5] the tendonswere placed in the middle of the slab at a spacing of350mm Prestressing force of 1488MPa corresponding toapproximately 80 of the tensile strength of the tendon wasapplied A load cell was used to measure the applied jackingload to the tendons during the posttensioning Minimumbonded deformed longitudinal reinforcement is required indesign of prestressed slabs to limit crack width at service loadwhen concrete tensile stresses exceed the modulus of ruptureand for flat plate with unbonded tendons to ensure flexuralperformance at ultimate strength [10 11] The minimumamount of bonded deformed longitudinal reinforcement wascalculated for the specimens using (1) in positive moment assuggested by ACI 318

119860119904min =

119873119888

05119891119910

017radic1198911015840

119888lt 119891119905le 05radic119891

1015840

119888

(1)

where 119860119904min is a minimum area of bonded deformed longi-

tudinal reinforcement119873119888is the resultant tensile force acting

on the portion of the concrete cross section that is subjectedto tensile stresses due to the combined effects of service loadsand effective prestress 119891

119910is a tensile strength of longitudinal

reinforcement 1198911015840119888is compressive strength of concrete 119891

119905is

extreme fiber stress in tension in the precompressed tensilezone calculated at service load using gross section properties

Also two-way slabs with reinforcement ratios of 10 ormore are likely to fail due to a punching shear [12] For thistest flexural reinforcement ratio of 019 was determinedEach specimen had the same flexural reinforcement ratioin order to secure the equivalent flexural stiffness providedby the longitudinal reinforcement bars All specimens werereinforced in loading point zone with steel stirrups to preventpunching shear failure that might occur prior to the flexuralfailure

23 Test Setup Load was applied to each specimen using ahydraulic jack with maximum capacity of 5000 kN In orderto induce the specimens to typical flexural behavior as shownFigure 3 the test specimens were simply supported alongthe four sides The force generated by the hydraulic jack wastransmitted to a 500mm times 500mm loading plate which wasplaced at the middle of the specimen as shown in Figure 4The distance from support to loading point was 125m togive a shear span to depth ratio of 6 The magnitude ofthe loading was measured by a load cell attached to thebottom of the jack All specimens were loaded until failureto observe the ultimate load-carrying capacity Nine linearvariable displacement transducers (LVDTs) were installedat the bottom of the specimen to measure the verticaldisplacement and the strain gauges were attached to thelongitudinal reinforcing bars as shown in Figure 4 A datalogger was used to collect load displacement and strain data

3 Test Results

31 Crack Pattern and Deflection Figure 5 shows the cracksand failure of the specimens The solid lines represent theexperimental crack patterns and the dashed lines representthe theoretical yield-line patterns in the figure For allspecimens cracks appeared similar to the theoretical yield-line patterns for simply supported four sides of two-way slabsIn the case of the FP specimen the reinforced concrete flatplate initial flexural cracks occurred on the bottom surfaceAnd the flexural cracks occurred intensively near the centerof the specimen afterward but did not extend outward Afterreaching the maximum load the flexural cracks becamewider and some cracks appeared around the edge of theloading plateThe failure occurred at the center of the bottomof the specimen

In the case of FP-PT-119909 and FP-PT-119909119910 specimens theflexural cracks occurred at the center of the specimenHowever unlike the FP specimen the cracks diagonallypropagated towards near the edges of the specimen FP-PT-119909 and FP-PT-119909119910 specimens showed well distributed flexuralcracks compared to FP specimen As the load increasedsome cracks appeared around the edge of the loading plateUpon reaching the maximum load flexural cracks becamewider and finally failed However less number of cracks andsmaller crack width were observed in FP-PT-119909119910 than FP-PT-119909 specimen


D13280D10 reinforcement

(a) FP-control specimen

D13280Tendon350

25016882

D10

rei

nfor

cem

ent

(b) FP-PT-119909 specimen

D13280

25016882

Tendon350

Tend

on35

0

D10

rei

nfor

cem

ent

(c) FP-PT-119909119910 specimen

Figure 2 Details of the specimens


Table 2 Details of specimens

Specimen 119860119904119909(mm2) 119860

119904119910(mm2) 119891

119901119890(MPa) 119891

119901119890119891119901119906120588119901119909

() 120588119901119910

() 120588119904119909

() 120588119904119910

() 119889119901(mm) 1198911015840

119888(MPa)

FP-control mdash mdash mdash mdash mdash mdash 0185 0185 mdash367FP-PT-119909 4935 mdash 1488 08 0198 mdash 0185 0185 168

FP-PT-119909119910 4935 4935 1488 08 0198 0198 0185 0185 168

250 2502500

250

D10 shear reinforcement

D13280

D13280

Loading plate

(a)

3000

3000

4040 450 450 450 450 560560

LVDTStrain gauge

Load

ing

plat

e(500

times500

)

(b)

Figure 3 Test setup


SupportsDeflected shape

(a) Plan of plate

(b) Deflection

(d) Deflection

(f) Bending stresses at centerTension

P

(c) Moment Mx

(e) Moment My

x

y

Figure 4 Simply supported flat plate under vertical point loading

The deflection profiles for the specimens are shown inFigure 6 The deflections obtained at nine locations wereanalyzed at different loading stages As shown in the figurelarge curvatures before the failure confirm that the failuremechanism of the slabs was governed by flexure rather thanshear In the case of the FP specimen it was observed thatthe deflection curve kept almost straight line at a load of150 kN and the deflection of the center began to increaseafterwardThe deflection slope became sharper from a load of450 kN For both FP-PT-119909 and FP-PT-119909119910 specimens similardeflection curves were observed which showed less deflec-tions than the FP specimen This is because posttensioningcontributed to the effective stress distribution

32 Load-Carrying Capacity The test results for maximumload and deflection are summarized inTable 3Themaximumload of the FP-control specimen was approximately 520 kNwhile the maximum loads of FP-PT-119909 test specimen a slabin which the tendons were placed in one-way direction andFP-PT-119909119910 test specimen a slab in which the tendons wereplaced in two-way directions were approximately 718 kN and757 kN respectively For FP-PT-119909 specimen the maximumload was increased by 38 compared to the control speci-menrsquos while 45 increase was observed for FP-PT-119909119910 speci-men The load-displacement relations are shown in Figure 7The stiffness of all specimens was similar for a load up to120 kN where the initial flexural cracks occurred Howeverthe posttensioned specimen showed greater stiffness afterthe initial cracks Remarkable differences were not observedin terms of initial stiffness maximum load and ductilitybehavior between FP-PT-119909 and FP-PT-119909119910 The maximumload of FP-PT-119909119910 specimen comparing with FP-PT-119909 wasincreased by approximately 5 while the displacement was

Table 3 Test results

Specimen 119875 (kN) 120575 (mm) 119875PT119875control 120575PT120575controlFP-control 52022 3224 mdash mdashFP-PT-119909 71881 4031 138 125FP-PT-119909119910 75672 4271 145 132

reduced by approximately 6 Although the case of whichtendons were placed in two-way directions showed moreeffective behavior in regard to the crack patterns the one-wayand two-way layouts of tendons did not affect significantly themaximum load capacity and deflection

The strains were measured at nine points of tensionrebars as shown in Figure 3 The load-strain relations arepresented in Figure 8 As shown in the figure from theapplied load of 120 kN the strain of rebars of FP-controlspecimen increased rapidly while the strain of rebars startedincreasing dramatically from the applied load of 300 kN forFP-PT-119909 and from 500 kN for FP-PT-119909119910 because the tensionrebar controlled the tensile cracks after the occurrence ofthe flexural cracks on the concrete for FP-control specimenwhile the tensile forces applied to the tendons controlled theconcretersquos tensile cracks for FP-PT specimens

33 Load Capacity Prediction Yield-line theory is an upperbound solution which depends on pattern of yield lines[13] It is based on the failure mechanisms in reinforcedconcrete slabs The slab is idealized as a rigid body whichis connected together by yield lines At the ultimate loadthe total plastic strain energy in the yield lines equated tothe external work done by the loads In this paper yield-line analysis was performed to predict the ultimate flexural


C

B C D E F G H I J K L M N O PA

ME LJI OA KGFDB PH N16151413121110

987654321

(a) FP-control (top)

C



987654321

(b) FP-control (bottom)

C



987654321

(c) FP-PT-119909 (top)

C



987654321

(d) FP-PT-119909 (bottom)

C



987654321

(e) FP-PT-119909119910 (top)

C



987654321

(f) FP-PT-119909119910 (bottom)

Figure 5 Continued


(g) Failure in FP-PT-119909119910 specimen

Figure 5 Crack patterns of the specimens

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)

450minus1350 0 1350minus900 900minus450150kN300kN

450kN

500kN

(a) FP-controlminus35

minus30

minus25

minus20

minus15

minus10

minus5

0minus1350 minus900 minus450 0 450 900 1350

Defl

ectio

n (m

m)

150kN300kN450kN

600kN

700kN

(b) FP-PT-119909

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)

minus450 450 900 1350minus1350 minus900 0150kN300kN450kN

600kN

700kN

(c) FP-PT-119909119910

Figure 6 Deflection profiles of the specimens

capacity of posttensioned flat plates [2 14] Figure 9 presentsthe failuremechanism and the yield-lines pattern adopted forthis study External work (119864) and internal work (119868) can becomputed from (2) and (3) respectively

119864 = sum119875120575 +sum120596119889119860119889120575119888 (2)

119868 = sum119872119901119909120579119909119897119910+sum119872

119901119910120579119910119897119910 (3)

where 119875 is failure load 120575 is vertical displacement 120596119889is self-

weight of the specimen 119860119889is area of the failure mechanism

120579 is rotation of the crack line and 119897 is length of the crack lineFailure load can be found based on assumption 119864 = 119868

The internal work done by flexure and the external workdone by the failure load and self-weight of the slab havebeen calculated Table 4 summarizes the result of the failureload analysis using yield-line theory From the table it can


FP-controlFP-PT-FP-PT-

Appl

ied

load

(kN

)

0 20 3010 5040Displacement (mm)

0

100

200

300

400

500

600

700

800

x

xy

Figure 7 Load-displacement relations

0 3000 4000minus1000 50001000 2000Strain (120583)

800

FP-PT-FP-controlFP-PT-

0

100

200

300

400

500

600

700

Appl

ied

load

(kN

)

x

xy

Figure 8 Load-strain relations

Table 4 Results of failure load

Specimen 119875exp (kN) 119875cal (kN) 119875exp119875calFP-control 52022 504 103FP-PT-119909 71881 661 109FP-PT-119909119910 75672 688 110

be seen that the calculated failure load of 504 kN is in goodagreement with the experimental failure load 520 kN in FP-control specimen However the yield-line theory tends torelatively underestimate the failure loads for posttensionedspecimens The difference between the experimental resultsand calculated results is attributed to load carried by mem-brane action of the slabs

4 Conclusions

In this paper the behavior of posttensioned concrete flatplates has been investigated experimentally Flexural testson three concrete flat plate specimens were performed toexamine the effect of the tendon layout type The crackingpatterns failure modes strain and maximum load wereanalyzed Test results were compared with the estimationscalculated by the yield-line theoryThe following conclusionswere drawn from this study

(1) For the posttensioned specimens the cracks diago-nally propagated towards near the edges of the flatplates while the flexural cracks occurred intensivelynear the center of the typical concrete flat plateAnd for the test specimen where the posttension


x

y

F

(a) Yield-line pattern120579

120572

120572

(b) Flexural hinge

Figure 9 Analysis of the slabs

was not applied failure occurred at relatively lowerload compared with the other two posttensionedspecimensrsquo results The maximum loads for one-wayposttensioned and two-way posttensioned specimensincreased 38 and 45 respectively Based on theseresults the flexural behavior of the flat plate canbe improved by the application of posttensioningregardless of the layouts of tendons

(2) It was found that the increase of the maximum loadcapacity was not affected by tendon layouts eventhough the tendons were placed in two directionssince the maximum load and deflection of the spec-imens in which the tendons were placed in two-waydirections were greater by 5 and 6 respectivelythan the one placed in one-way direction Howeverthe flexural cracks were observed evenly all overthe slabs where the tendons were placed in twodirections and several deep cracks were observed inthe case of which the tendons were placed in one-waydirection compared to those in two-way directionswhen the crack growth was compared on the surfaceConsequently the placement of tendons in two-waydirections is more effective in terms of crack control

(3) The yield-line theory was applied in order to pre-dict the maximum load of posttensioned flat platesComparing with the test results the calculations bythe yield-line theory estimated the maximum loadson average of 93 However it tended to relativelyunderestimate the prediction for the posttensionedslabs because themembrane action resulting from theposttensioning was not considered sufficiently

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korean government(MSIP) (NRF-2013R1A2A2A01067754)

References

[1] N H Burns and R Hemakom ldquoTest of post-tensioned flat platewith banded tendonsrdquo Journal of Structural Engineering vol 111no 9 pp 1899ndash1915 1985

[2] G M Kosut N H Burns and C V Winter ldquoTest of four-panelpost-tensioned flat platerdquo Journal of Structural Engineering vol111 no 9 pp 1916ndash1929 1985

[3] A P Ramos V J G Lucio and D M V Faria ldquoThe effect of thevertical component of prestress forces on the punching strengthof flat slabsrdquo Engineering Structures vol 76 pp 90ndash98 2014

[4] M Gilbert L He C C Smith and C V Le ldquoAutomatic yield-line analysis of slabs using discontinuity layout optimizationrdquoProceedings of the Royal Society of London A MathematicalPhysical and Engineering Sciences vol 470 no 2168 Article ID20140071 2014

[5] M H Harajli ldquoTendon stress at ultimate in continuousunbonded post-tensioned members proposed modification ofACI 318 Eq (18-4) and (18-5)rdquo ACI Structural Journal vol 109no 2 pp 183ndash192 2012

[6] A Mahi E A Adda Bedia and A Tounsi ldquoA new hyperbolicshear deformation theory for bending and free vibration anal-ysis of isotropic functionally graded sandwich and laminated


composite platesrdquo Applied Mathematical Modelling Simulationand Computation for Engineering and Environmental Systemsvol 39 no 9 pp 2489ndash2508 2015

[7] Z Belabed M S Ahmed Houari A Tounsi S R Mahmoudand O Anwar Beg ldquoAn efficient and simple higher order shearand normal deformation theory for functionally graded mate-rial (FGM) platesrdquo Composites Part B Engineering vol 60 pp274ndash283 2014

[8] H Hebali A Tounsi M S A Houari A Bessaim and E AA Bedia ldquoNew quasi-3D hyperbolic shear deformation theoryfor the static and free vibration analysis of functionally gradedplatesrdquo Journal of EngineeringMechanics vol 140 no 2 pp 374ndash383 2014

[9] B O Aalami ldquoLayout of post-tensioning and passive reinforce-ment in floor slabsrdquo PTI Technical Note 8 Post-TensioningInstitute Phoenix Ariz USA 1999

[10] ACI Committee 318-14 Building Code Requirements for Rein-forced Concrete and Commentary American Concrete InstituteFarmington Hills Mich USA 2014

[11] K B Bondy ldquoTwo-way post-tensioned slabs with bondedtendonsrdquo PTI Journal vol 8 no 2 pp 43ndash48 2012

[12] H Marzouk and A Hussein ldquoExperimental investigation onthe behavior of high-strength concrete slabsrdquo ACI StructuralJournal vol 88 no 6 pp 701ndash713 1991

[13] KW JohansenYield Line Formulae for Slabs Cement andCon-crete Association London UK 1972

[14] A C Scordelis T Y Lin and H R May ldquoShearing strength ofprestressed lift slabsrdquo ACI Structural Journal vol 55 no 10 pp485ndash506 1958

Submit your manuscripts athttpwwwhindawicom

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CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


Column

Banded

Min two strands over column

tendons

(a) Banded-distributed (b) Banded-banded

Min two strands over column(c) Distributed-distributed (d) Mixed

Figure 1 Principal options of tendon layout [4]

theory for FGM platesThey verified that the theory can con-sider both shear deformation and thickness stretching effectsHebali et al [8] proposed a new quasi-three-dimensionalhyperbolic shear deformation theory to analyze the bendingand free vibration for FGMS plates

There are several possible arrangements for the tendonlayout in two-way slab system supported by columns [9]Thetendons in each direction can be arranged in combination ofbanded and distributed layouts as shown in Figure 1 Sincethe four options provide equal strength capacity the choice oftendon layout is usually determined by constructability [3]

Posttensioned slabs are used for long spans and heavylive loads where flexural strength and ductility assume asignificant role It is known that the flexural behaviors usuallygovern the behavior of interior panel in the flat plates Inotherwords the distribution of tendons can affect the flexuralstrength and ductility in the interior panel of the flat platesThough many researchers have researched into the effect of

punching shear to the posttensioned flat plates with varioustendon layouts in column strips most of these researchespointed out that the tendon layouts designs are only presentedto prevent punching shear failure Little information isavailable on the flexural behavior of posttensioned flat plateThis study aims to recommend the concerning tendon layoutdesign to improve flexural strength and ductility for postten-sioned flat plates

In this study flexural tests on three concrete flat platespecimens were performed in order to evaluate the flexuralbehavior and deflection according to the tendon layoutFor the comparison purpose one of three specimens wastypical concrete flat plate and the tendons were distributedin one way and in two ways for the other two specimensCracking pattern failure modes strain and maximum loadwere obtained and analyzed from the tests The test resultswere also compared to examine the validity of the yield-linetheory



Type Diameter(mm)

Area(mm2)

Unitweight(kgkm)

Elongation()

SWPC 7B 127 987 774 35




119860119904min =

119873119888

05119891119910

017radic1198911015840

119888lt 119891119905le 05radic119891

1015840

119888

(1)






119905is




3 Test Results






D13280Tendon350

25016882

D10

rei

nfor

cem

ent


D13280

25016882

Tendon350

Tend

on35

0

D10

rei

nfor

cem

ent





Specimen 119860119904119909(mm2) 119860

119904119910(mm2) 119891

119901119890(MPa) 119891

119901119890119891119901119906120588119901119909

() 120588119901119910

() 120588119904119909

() 120588119904119910

() 119889119901(mm) 1198911015840

119888(MPa)


FP-PT-119909119910 4935 4935 1488 08 0198 0198 0185 0185 168

250 2502500

250


D13280

D13280

Loading plate

(a)

3000

3000

4040 450 450 450 450 560560

LVDTStrain gauge

Load

ing

plat

e(500

times500

)

(b)

Figure 3 Test setup



(a) Plan of plate

(b) Deflection

(d) Deflection


P

(c) Moment Mx

(e) Moment My

x

y










C



987654321


C



987654321


C



987654321

(c) FP-PT-119909 (top)

C



987654321


C



987654321

(e) FP-PT-119909119910 (top)

C



987654321

(f) FP-PT-119909119910 (bottom)

Figure 5 Continued




minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


450kN

500kN


minus30

minus25

minus20

minus15

minus10

minus5


Defl

ectio

n (m

m)

150kN300kN450kN

600kN

700kN

(b) FP-PT-119909

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


600kN

700kN

(c) FP-PT-119909119910



119864 = sum119875120575 +sum120596119889119860119889120575119888 (2)

119868 = sum119872119901119909120579119909119897119910+sum119872

119901119910120579119910119897119910 (3)







Appl

ied

load

(kN

)


0

100

200

300

400

500

600

700

800

x

xy


0 3000 4000minus1000 50001000 2000Strain (120583)

800


0

100

200

300

400

500

600

700

Appl

ied

load

(kN

)

x

xy





4 Conclusions




x

y

F


120572

120572

(b) Flexural hinge





Competing Interests


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Type Diameter(mm)

Area(mm2)

Unitweight(kgkm)

Elongation()

SWPC 7B 127 987 774 35




119860119904min =

119873119888

05119891119910

017radic1198911015840

119888lt 119891119905le 05radic119891

1015840

119888

(1)






119905is




3 Test Results






D13280Tendon350

25016882

D10

rei

nfor

cem

ent


D13280

25016882

Tendon350

Tend

on35

0

D10

rei

nfor

cem

ent





Specimen 119860119904119909(mm2) 119860

119904119910(mm2) 119891

119901119890(MPa) 119891

119901119890119891119901119906120588119901119909

() 120588119901119910

() 120588119904119909

() 120588119904119910

() 119889119901(mm) 1198911015840

119888(MPa)


FP-PT-119909119910 4935 4935 1488 08 0198 0198 0185 0185 168

250 2502500

250


D13280

D13280

Loading plate

(a)

3000

3000

4040 450 450 450 450 560560

LVDTStrain gauge

Load

ing

plat

e(500

times500

)

(b)

Figure 3 Test setup



(a) Plan of plate

(b) Deflection

(d) Deflection


P

(c) Moment Mx

(e) Moment My

x

y










C



987654321


C



987654321


C



987654321

(c) FP-PT-119909 (top)

C



987654321


C



987654321

(e) FP-PT-119909119910 (top)

C



987654321

(f) FP-PT-119909119910 (bottom)

Figure 5 Continued




minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


450kN

500kN


minus30

minus25

minus20

minus15

minus10

minus5


Defl

ectio

n (m

m)

150kN300kN450kN

600kN

700kN

(b) FP-PT-119909

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


600kN

700kN

(c) FP-PT-119909119910



119864 = sum119875120575 +sum120596119889119860119889120575119888 (2)

119868 = sum119872119901119909120579119909119897119910+sum119872

119901119910120579119910119897119910 (3)







Appl

ied

load

(kN

)


0

100

200

300

400

500

600

700

800

x

xy


0 3000 4000minus1000 50001000 2000Strain (120583)

800


0

100

200

300

400

500

600

700

Appl

ied

load

(kN

)

x

xy





4 Conclusions




x

y

F


120572

120572

(b) Flexural hinge





Competing Interests


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






D13280Tendon350

25016882

D10

rei

nfor

cem

ent


D13280

25016882

Tendon350

Tend

on35

0

D10

rei

nfor

cem

ent





Specimen 119860119904119909(mm2) 119860

119904119910(mm2) 119891

119901119890(MPa) 119891

119901119890119891119901119906120588119901119909

() 120588119901119910

() 120588119904119909

() 120588119904119910

() 119889119901(mm) 1198911015840

119888(MPa)


FP-PT-119909119910 4935 4935 1488 08 0198 0198 0185 0185 168

250 2502500

250


D13280

D13280

Loading plate

(a)

3000

3000

4040 450 450 450 450 560560

LVDTStrain gauge

Load

ing

plat

e(500

times500

)

(b)

Figure 3 Test setup



(a) Plan of plate

(b) Deflection

(d) Deflection


P

(c) Moment Mx

(e) Moment My

x

y










C



987654321


C



987654321


C



987654321

(c) FP-PT-119909 (top)

C



987654321


C



987654321

(e) FP-PT-119909119910 (top)

C



987654321

(f) FP-PT-119909119910 (bottom)

Figure 5 Continued




minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


450kN

500kN


minus30

minus25

minus20

minus15

minus10

minus5


Defl

ectio

n (m

m)

150kN300kN450kN

600kN

700kN

(b) FP-PT-119909

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


600kN

700kN

(c) FP-PT-119909119910



119864 = sum119875120575 +sum120596119889119860119889120575119888 (2)

119868 = sum119872119901119909120579119909119897119910+sum119872

119901119910120579119910119897119910 (3)







Appl

ied

load

(kN

)


0

100

200

300

400

500

600

700

800

x

xy


0 3000 4000minus1000 50001000 2000Strain (120583)

800


0

100

200

300

400

500

600

700

Appl

ied

load

(kN

)

x

xy





4 Conclusions




x

y

F


120572

120572

(b) Flexural hinge





Competing Interests


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Specimen 119860119904119909(mm2) 119860

119904119910(mm2) 119891

119901119890(MPa) 119891

119901119890119891119901119906120588119901119909

() 120588119901119910

() 120588119904119909

() 120588119904119910

() 119889119901(mm) 1198911015840

119888(MPa)


FP-PT-119909119910 4935 4935 1488 08 0198 0198 0185 0185 168

250 2502500

250


D13280

D13280

Loading plate

(a)

3000

3000

4040 450 450 450 450 560560

LVDTStrain gauge

Load

ing

plat

e(500

times500

)

(b)

Figure 3 Test setup



(a) Plan of plate

(b) Deflection

(d) Deflection


P

(c) Moment Mx

(e) Moment My

x

y










C



987654321


C



987654321


C



987654321

(c) FP-PT-119909 (top)

C



987654321


C



987654321

(e) FP-PT-119909119910 (top)

C



987654321

(f) FP-PT-119909119910 (bottom)

Figure 5 Continued




minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


450kN

500kN


minus30

minus25

minus20

minus15

minus10

minus5


Defl

ectio

n (m

m)

150kN300kN450kN

600kN

700kN

(b) FP-PT-119909

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


600kN

700kN

(c) FP-PT-119909119910



119864 = sum119875120575 +sum120596119889119860119889120575119888 (2)

119868 = sum119872119901119909120579119909119897119910+sum119872

119901119910120579119910119897119910 (3)







Appl

ied

load

(kN

)


0

100

200

300

400

500

600

700

800

x

xy


0 3000 4000minus1000 50001000 2000Strain (120583)

800


0

100

200

300

400

500

600

700

Appl

ied

load

(kN

)

x

xy





4 Conclusions




x

y

F


120572

120572

(b) Flexural hinge





Competing Interests


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





(a) Plan of plate

(b) Deflection

(d) Deflection


P

(c) Moment Mx

(e) Moment My

x

y










C



987654321


C



987654321


C



987654321

(c) FP-PT-119909 (top)

C



987654321


C



987654321

(e) FP-PT-119909119910 (top)

C



987654321

(f) FP-PT-119909119910 (bottom)

Figure 5 Continued




minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


450kN

500kN


minus30

minus25

minus20

minus15

minus10

minus5


Defl

ectio

n (m

m)

150kN300kN450kN

600kN

700kN

(b) FP-PT-119909

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


600kN

700kN

(c) FP-PT-119909119910



119864 = sum119875120575 +sum120596119889119860119889120575119888 (2)

119868 = sum119872119901119909120579119909119897119910+sum119872

119901119910120579119910119897119910 (3)







Appl

ied

load

(kN

)


0

100

200

300

400

500

600

700

800

x

xy


0 3000 4000minus1000 50001000 2000Strain (120583)

800


0

100

200

300

400

500

600

700

Appl

ied

load

(kN

)

x

xy





4 Conclusions




x

y

F


120572

120572

(b) Flexural hinge





Competing Interests


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




C



987654321


C



987654321


C



987654321

(c) FP-PT-119909 (top)

C



987654321


C



987654321

(e) FP-PT-119909119910 (top)

C



987654321

(f) FP-PT-119909119910 (bottom)

Figure 5 Continued




minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


450kN

500kN


minus30

minus25

minus20

minus15

minus10

minus5


Defl

ectio

n (m

m)

150kN300kN450kN

600kN

700kN

(b) FP-PT-119909

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


600kN

700kN

(c) FP-PT-119909119910



119864 = sum119875120575 +sum120596119889119860119889120575119888 (2)

119868 = sum119872119901119909120579119909119897119910+sum119872

119901119910120579119910119897119910 (3)







Appl

ied

load

(kN

)


0

100

200

300

400

500

600

700

800

x

xy


0 3000 4000minus1000 50001000 2000Strain (120583)

800


0

100

200

300

400

500

600

700

Appl

ied

load

(kN

)

x

xy





4 Conclusions




x

y

F


120572

120572

(b) Flexural hinge





Competing Interests


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


450kN

500kN


minus30

minus25

minus20

minus15

minus10

minus5


Defl

ectio

n (m

m)

150kN300kN450kN

600kN

700kN

(b) FP-PT-119909

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

Defl

ectio

n (m

m)


600kN

700kN

(c) FP-PT-119909119910



119864 = sum119875120575 +sum120596119889119860119889120575119888 (2)

119868 = sum119872119901119909120579119909119897119910+sum119872

119901119910120579119910119897119910 (3)







Appl

ied

load

(kN

)


0

100

200

300

400

500

600

700

800

x

xy


0 3000 4000minus1000 50001000 2000Strain (120583)

800


0

100

200

300

400

500

600

700

Appl

ied

load

(kN

)

x

xy





4 Conclusions




x

y

F


120572

120572

(b) Flexural hinge





Competing Interests


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Appl

ied

load

(kN

)


0

100

200

300

400

500

600

700

800

x

xy


0 3000 4000minus1000 50001000 2000Strain (120583)

800


0

100

200

300

400

500

600

700

Appl

ied

load

(kN

)

x

xy





4 Conclusions




x

y

F


120572

120572

(b) Flexural hinge





Competing Interests


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




x

y

F


120572

120572

(b) Flexural hinge





Competing Interests


Acknowledgments


References
























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Documents

Research Article Flexural Behavior of Posttensioned Flat