research article experimental and numerical evaluation of...

Research ArticleExperimental and Numerical Evaluation of Direct Tension Testfor Cylindrical Concrete Specimens

Jung J Kim1 and Mahmoud Reda Taha2

1 School of Architecture Kyungnam University Changwon-si 631-701 Republic of Korea2Department of Civil Engineering University of New Mexico Albuquerque NM 87131 USA

Correspondence should be addressed to Mahmoud Reda Taha mrtahaunmedu

Received 14 April 2014 Accepted 22 May 2014 Published 19 June 2014

Academic Editor Serji N Amirkhanian

Copyright copy 2014 J J Kim and M Reda Taha 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

Concrete cracking strength can be defined as the tensile strength of concrete subjected to pure tension stress However as it isdifficult to apply direct tension load to concrete specimens concrete cracking is usually quantified by the modulus of rupture forflexural members In this study a new direct tension test setup for cylindrical specimens (1016mm in diameter and 2032mm inheight) similar to those used in compression test is developed Double steel plates are used to obtain uniform stress distributionsFinite element analysis for the proposed test setup is conducted The uniformity of the stress distribution along the cylindricalspecimen is examined and compared with rectangular cross section Fuzzy image pattern recognition method is used to assessstress uniformity along the specimen Moreover the probability of cracking at different locations along the specimen is evaluatedusing probabilistic finite element analysisThe experimental and numerical results of the cracking location showed that gravity effecton fresh concrete during setting time might affect the distribution of concrete cracking strength along the height of the structuralelements

1 Introduction

Concrete cracking strength is difficult to be quantified andtherefore is a source of considerable uncertainty in ser-viceability prediction The existence of cracks under serviceload in reinforced concrete (RC) structures makes it difficultto predict deflections While cracked concrete is usuallyassumed to be incapable of carrying tensile stresses theconcrete between adjacent cracks can resist tensile force dueto the bond between concrete and steel reinforcementThis isknown as tension stiffening effect Therefore for the consid-eration of the deflections of RC structures concrete crackingstrength affects the structural stiffness of the membersMoreover cracking plays an important role in the durabilityof RC structures When concrete cracks its permeabilityincreases and the processes of concrete deterioration andrebar corrosion get accelerated [1 2]

For flexural elements concrete cracking is usually repre-sented by the modulus of rupture [3] However in research

experiments the modulus of rupture showed a wide vari-ation [4 5] While the modulus of rupture provides agood estimate for cracking strength researchers showedthat accurate serviceability predictions require obtaining thereal tensile strength of concrete [6] Moreover researchershave argued that because of the significance of shrinkageon serviceability of RC structures other cracking criteriasuch as the direct or indirect tensile strength of concreteshould be used as evidence of concrete cracking [7] Threemethods are commonly used to measure concrete crackingstrength flexural splitting and direct tension test While theflexural strength test and splitting tensile strength test canbe conducted in accordance with the American standard testmethod (ASTM) ASTM C 78 [8] and ASTM C 496C 496M[9] respectively ASTM has no recommendations for directtension test for concrete as it is challenging to ensure thatuniaxial stress along the specimen is evenly applied

Several methods have been proposed for direct tensiontest such as using friction grip anchor and epoxy to attach

Hindawi Publishing CorporationAdvances in Civil EngineeringVolume 2014 Article ID 156926 8 pageshttpdxdoiorg1011552014156926

2 Advances in Civil Engineering

the loading machine and concrete specimen However allthese methods induce secondary stresses that result in anuneven stress application to concrete specimens [10] Tomakethe applied point load a more evenly distributed load USBureau of Reclamation [11] proposes the use of a doubleplate system for two sizes of diameters of 1524mm and254mm cylinder specimens The outer plate is connected toa loading machine while the inner plate is bonded with theconcrete specimen with epoxyThe inner and outer plates areconnected to each other by bolts Recently this method wasmodified for the rectangular section of 100mm by 100mmand showed acceptable results [10]

In this study the above method is further developed forcylindrical specimen (1016mm in diameter and 2032mmin height) Moreover the stress uniformity of the proposeddirect tension test method is evaluated using the finiteelement methodThe stress uniformity along the specimen iscompared with the stress uniformity of the direct tension testfor rectangular specimen As experimental results showedthat the cracking location was concentrated at the top half ofthe vertically cured cylindrical specimens the unit weight ofthe two broken parts was measured to examine the effect ofunit weight on cracking strength and cracking location

2 Proposed Test Setup

For the cylinder size of 1016mm diameter and 2032mmheight a double plate system with epoxy adhesive wasadopted for the direct tension test setup as shown inFigure 1 The intention is to use cylinders similar to thoseused to evaluate the compressive strength of concrete in theconcrete industryThe inner and outer plates were connectedto each other by eight high-strength bolts Tension loadwas applied through ball bearings in order to prevent thedeveloping of bending and torsion stresses in the concretespecimen The thickness of the inner plate was determinedto be 381mm according to the US Army Engineer Researchand Development Center (ERDC) CRD-C 164-92 [12] Itwas proposed that the thickness of the end plate should behigher than one third of the diameter of the test specimenThe thickness of the outer plate was chosen as one half ofthat of the inner plate The bolting locations of the inner andouter plates were optimized by finite element analysis to getuniform stress distributionThe direct tension test conductedusing the proposed test setup is shown in Figure 2

3 Finite Element Analyses

Linear elastic finite element analyses were performed toinvestigate the stress distribution along the cylindrical andrectangular specimen as proposed by others [10] ANSYS711 [13] was used for the finite element analyses The testsetups were modeled as 3D solid models The epoxy doubleend plates and concrete were modeled using SOLID 45 [13]which is a solid cubic element with eight nodes having threedegrees of freedom (DOF) for translations about the nodal 119909119910 and 119911 at each node The material properties used for finiteelement analysis are presented in Table 1The bolt connecting

Load

Ball bearing

Outer plateInner plateEpoxy layer

Cylindrical specimen

A

Section A-A

Machine base

Load cell

191A

M8 bolt

191318 318

381191

508 508

45∘

Figure 1 Test setup of the proposed direct tension test for 1016mmdiameter and 2032mm height cylinder (mm)

Ball bearing

Outer plate

Inner plate

M8 bolt

Specimen

Figure 2 Direct tension test conducted by the proposed test setup

the outer and the inner plates was modeled using LINK 8[13] three-dimensional (3D) uniaxial tension-compressionelement with three DOF for translations about the nodal 119909119910 and 119911 at each node

The finite element analyses of the test setups for cylindri-cal and rectangular specimens are conducted It is importantto emphasize that the purpose of numerical modeling isto quantify the uniformity of the stress distribution in thetension specimen and not to examine cracking behavior ofthe concrete specimen Therefore only linear elastic regionof concrete constitutive model is used for finite elementanalyses Considering the symmetry of the test specimen andloading a quarter of the specimenrsquos section and a half of thespecimenrsquos length were modeled The boundary conditions

Advances in Civil Engineering 3

Table 1 Material properties used in finite element analysis

Materials Modulus of elasticity (GPa) Poissonrsquos ratioSteel 200 03Concrete 22 02Epoxy 1 03

of the finite element models were adjusted to simulatesymmetry conditions For the finite element model of thecylindrical specimen 320 solid elements in 8 layers were usedto represent the outer steel plate while 640 solid elementsin 8 layers were used to represent the inner steel plate Forthe finite element model of the rectangular specimen 400solid elements in 4 layers were used to represent the outersteel plate while 800 solid elements in 8 layers were used torepresent the inner steel plate Concrete specimens for thecylindrical and rectangular specimens were modeled with1600 and 2000 solid elements in 20 layers respectively Thebolts were modeled using 3 line elements with compressiveinitial strain of 01 to model the bolting force that was ini-tially appliedwhen the outer and inner plates were connectedUsing these finite element models stress distributions wereobtained to quantify stress uniformity along the concretespecimens

The relative tensile stress is defined as the ratio of the ten-sile stress at any point to the average tensile stress calculatedas the applied load divided by cross section area The relativetensile stress is evaluated both at the top of the specimensand along the specimen This analysis is performed for bothcylindrical and rectangular specimens The results for thecylindrical specimen showed that the relative tensile stressesacross the section vary from 098 to 102 and the variationsof stress distributions at the top of the cylinder were withinplusmn2 of the average tensile stress For the numerical resultsof the whole cylinder the relative tensile stresses varied from096 to 103 and the variation of stress distribution over theentire cylinder was within plusmn4 of the average tensile stressThe numerical results for the rectangular section of 1016mmby 1016mm showed that the relative tensile stresses acrossthe section vary from 094 to 101 while those of the wholespecimen vary from 09 to 103 The results for the tensilestress distribution at the top of the rectangular specimen of100mmby 100mm agreed with the results reported by Zhenget al [10]

31 Stress Uniformity along the Specimens Although thesignificantly low variations of stress for the cylindricalspecimen confirmed the uniformity of stress across andalong the tension specimen a method to quantify stressdistribution similarity at different heights along the specimenwas developed and is presented hereThedegrees of similaritybetween the tensile stress distributions as produced by thefinite element analysis at various cross sections and theapplied tensile stress distribution were quantifiedThe degreeof similarity was determined using principles of fuzzy imagepattern recognition [14] This method is one of the methodsto determine the degree of similarity between two images

The method was applied to two-dimensional (2D) slices Thesimilarity for two images that have the same size and numberof pixels was calculated by comparing pixel values normalizedto the interval [0 255] After the images were converted tothree monochromatic basic color images in red (R) green(G) and blue (B) the similarity between two pixels wasassigned to a pair of pixels in three monochromatic imagesaccording to the difference of pixel values according to Toltand Kalaykov [15] and Su et al [16] such as

120583119901 =

1 minusabs (119898119886 minus 119898119887)

120572 if abs (119898119886 minus 119898119887) le 120572

0 otherwise(1)

where 119898119886 and 119898119887 are the pixel values for the compared twofigures 119886 and 119887 120583119901 is the pixel similarity value that representsthe degree of similarity of two pixel values given a threshold120572The advantage of such similaritymeasure is attributed to itsability to credit a degree of similarity between any two pixelswith absolute difference less than 120572 By taking the arithmeticmean of the similarity values for the monochromatic imagepairs in R G and B three scalar similarity values thatcorrespond to R G and B were obtained The similarity ofthe two images was identified by the arithmeticmean of thosethree similarity values

Forty images representing the stress contours of 20 layersfor each specimen spread at 51mm were generated bythe finite element analysis and were used to calculate thesimilarity of stress distributions along the cylindrical andrectangular specimens The similarity between the tensilestress distributions at various cross sections is presentedin Figure 3 along the specimen By taking the arithmeticmean of the similarity values along the specimen the overallsimilarity of the stress distributionwas calculated as 0933 and0921 for the circular specimen and the rectangular specimenrespectively Given the similarity curves shown in Figure 3and the mean similarity values the stresses produced in thecylindrical specimen were more uniform than those of therectangular specimen

4 Experimental Methods

Three concrete mixtures with target compressive strengthsof 25 40 and 55MPa were considered Three batches ofthe concrete mixes were made for each target compressivestrength case Nine 1016mm in diameter and 2032mm inheight cylinders and three 1016mm times 1016mm times 3556mmprisms were prepared from each batch of concrete mix-ture Ordinary Portland cement and silica fume were usedas cementing materials The maximum size of the coarseaggregate was 10mmThe particle distributions of the coarseand fine aggregates are presented in Figure 4 The slumpof the concrete mixes was maintained between 508 and699mm The mixture proportions of the concrete mixes arepresented in Table 2 The proposed mix was selected to allowcomparison of the experimental results of the new proposedtest with those published by Zheng et al [10]

All 9 cylinders and 3 prisms were demolded after oneday of casting and left to cure in water until the day of


0

20

40

60

80

100

085 090 095 100D

istan

ce fr

om th

e top

of s

peci

men

(mm

)

Similarity

CircularRectangular

Overall similarity for circular section 0931

Overall similarity for rectangular section 0919

Figure 3 Similarity of stress distribution at each layer to the appliedstress distribution for cylindrical and rectangular specimens

0

20

40

60

80

100

01 1 10 100

Pass

ing

()

Sieve size (mm)

Fine aggregateCoarse aggregate

Figure 4 Particle size distributions of the coarse and fine aggregate

the test However 3 cylinders which were used for directtension tests were taken out of the water one day priorto testing After grinding both sides of each specimen thespecimens were dried for 12 hours and adhered to the steelplates with epoxy as shown schematically in Figure 1 Theepoxy was left for 12 hours to dry to improve bond qualitybetween the concrete specimen and the steel plate in thetest setup The compressive strength test flexural strengthtest and splitting tensile strength test were conducted inaccordance with the ASTM C 39C 39M [17] C 78 [8] andC 496C 496M [9] respectively The results are presentedin Table 3 The flexural cracking strength of 1016mm times

0

2

4

6

8

10

10 20 30 40 50 60 70 80

Crac

king

stre

ngth

(MPa

)

Compressive strength (MPa)Direct

SplittingFlexuralSquare root23 power

Figure 5 Correlation of various cracking strengths with compres-sive strength

1016mm times 3556mm prism splitting cracking strength ofcylinder specimens (1016mm in diameter and 2032mmin height) and direct tensile cracking strength of cylinderspecimens (1016mm in diameter and 2032mm in height)were plotted against the corresponding compressive strengthof cylinder specimens (1016mm in diameter and 2032mmin height) in Figure 5

For the tests results the relation between crackingstrengths and the corresponding compressive strength wasdetermined in this study based on the assumption that thecracking strength has linear relation with the two third (23)power of the corresponding compressive strength as reportedby CEB-FIP MC-90 [18] Regression analysis was performedand the following relations ((2) to (4)) were obtained

119891119903 = 21(1198911015840

119888

10)

23

(MPa) (2)

119891119904119901 = 12(1198911015840

119888

10)

23

(MPa) (3)

119891119905 = 08(1198911015840

119888

10)

23

(MPa) (4)

where119891119903119891119904119901119891119905 and1198911015840

119888are the flexural tensile strength split-

ting tensile strength direct tensile strength and compressivestrength respectively Moreover test results of crackingstrengths were also fitted using regression analysis with theassumption that they have linear relation to the square rootof the compressive strength after ACI 318-11 [3] This analysisresults in the following equations

119891119903 = 085radic1198911015840119888(MPa) (5)

119891119904119901 = 049radic1198911015840119888(MPa) (6)

119891119905 = 034radic1198911015840119888(MPa) (7)


Table 2 Concrete mix proportions (kgm3)

Mixture Portland cement(Type I) Silica fume Water Fine

aggregateCoarseaggregate

Admixture(Lm3)

M-1 236 79 192 700 1143 047M-2 289 97 185 587 1192 157M-3 345 115 179 479 1232 363

Table 3 Results for direct tension tests presenting meanstandard deviation (MPa)

Mix Batch Compressive strength Flexural tensile strength Splitting tensile strength Direct tensile strength

M-1B-1 234126 375018 228015 155006B-2 248082 393025 233015 177012B-3 237079 448023 182028 152004

Meanstd 240109 405038 214030 161014

M-2B-4 382144 507040 302024 213015B-5 382035 500021 301016 213007B-6 392018 524016 303029 225006

Meanstd 385090 510026 302021 217011

M-3B-7 540143 607034 384013 244011B-8 592156 673033 380041 253008B-9 567365 678041 384020 250006

Meanstd 566306 653047 383024 249008

The relationship between cracking strengths in this study willbe

119891119903 = 175119891119904119901 = 250119891119905 (8)

It is important to note that the direct tensile strength ofconcrete in (7) is less than half the value proposed by ACI318-11 [3] While ACI 318-11 [3] proposes using the modulusof rupture the use of tensile strength to express crackinghas been recommended by many researchers [6 19] Theproposed tension test should enable a cracking strength limitby ACI 318-11 [3] lower than current limits obtained fromthe modulus of rupture experiments It is also noticeable thatthe regression results for flexural strength test in (2) and (5)lie between the minimum and the average of the regressionresults reported by Legeron and Paultre [20] Moreover thecracking strength models proposed by CEB-FIP MC-90 [18]and ACI 318-11 [3] lie between the regression results ofsplitting and the flexural strengths

5 Cracking Location

Although uniform stress was developed in the concretespecimen subjected to tension by the proposed test setupthe cracking failure location in concrete is difficult to predictdue to the inherent variations in concrete microstructuresThe numerical analysis of the concrete specimen subject totension shows that uniform stress was developed along thespecimen with the assumption that material distribution is

homogeneous and the response is linear elastic If concretehas been properly placed and no variation in the unit weightof concrete along the specimen takes place the crackinglocation in the proposed direct tension test is expected tobe uniformly distributed along the specimen (ie crackingcan take place at any location along the specimen) Howeverdirect tension test results of 27 specimens (results in Table 3)by the proposed test setup showed that the cracking locationwas frequently concentrated in the top one-third of thespecimen as shown in Figure 6 Statistical analysis of crackinglocation proved to be significantly different frommid heightThis observation can be attributed to variation of the unitweight of concrete along the specimen The increase in unitweight towards the bottom is a well-known phenomenon dueto higher consolidation with gravity at the bottom than at thetop of the specimen [21]

To confirm this hypothesis the unit weights of the twobroken parts of all specimens tested by the direct tension testwere measured These measured unit weights were plottedaccording to the distance from the top of the specimen to thecenter of the measured parts as shown in Figure 7 A linearrelationship between the unit weight 119908(119909) and the distancefrom the top of the specimen 119909 in mm is determined as

119908 (119909) = 0789119909 + 23527 (kgm3

) (0 le 119909 le 2032mm)

(9)


0

20

40

60

80

100

Relat

ive f

requ

ency

()

Distance from the top of specimen (mm)0 50 100 150 200

Figure 6 Cracking location measured from the top of specimen

2200

2400

2600

2800

3000

0 50 100 150 200Distance from the top of specimen (mm)

dWdL

dU

w(x) = 07889x + 23527

R2= 02631

Uni

t wei

ght (

kgm

3)

dW

dL

dU

Figure 7 Unit weight distribution along the specimen height

By considering the modulus of elasticity computationalmodel that incorporates the unit weight [3] the modulus ofelasticity variation along the specimen is calculated as

119864 (119909) = 0043119908(119909)15radic1198911015840119888(MPa) (0 le 119909 le 2032mm)

(10)

With the distribution of modulus of elasticity along the spec-imen another set of finite element analyses was conductedHere the cylinder was modeled in full height but a quarterof the section was considered for symmetry conditions Theconcrete cylinder was divided into 40 layers and the modulusof elasticity of each layer was calculated using (9) and (10)From the stress distribution along the cylindrical specimenthe maximum stress distribution along the specimen wasobtained By assuming that the maximum tensile stress ateach layer is normally distributed the probability of crackingat each layer can be calculated As the maximum stress distri-bution at each layer is independent of that at otherrsquos layer theprobability of cracking at each layer can be calculated as

119901119891 (119894) = intint119891119894ge119891119895 119894 = 119895

sdot sdot sdot int 1199011 (1198911) 1199012 (1198912) sdot sdot sdot

11990140 (11989140) 11988911989111198891198912 sdot sdot sdot 11988911989140

(11)

where 119901119894(119894) is the probability density function (PDF) ofthe maximum stress 119891119894 at a layer 119894 However computationof the probability of cracking requires defining the tensilestrength distribution along the specimen Two methodswere considered here First we consider the tensile strengthvariation along the specimen 119891119905(119909) with respect to specimenunit weight119908(119909) according to ACI 209R-92 [22] described as

119891119905 (119909) = 00069radic119908 (119909) 1198911015840119888(MPa) (0 le 119909 le 2032mm)

(12)

Second the tensile strength variation can be derived byconsidering the correlation between cracking strength andmodulus of elasticity which is conventionally accepted to befully correlatedTherefore the tensile strength variation alongthe specimen 119891119905(119909) can be determined by modifying (7) tovary linearly with the modulus of elasticity as

119891119905 (119909) =119864 (119909)

119864 (1016)034radic1198911015840

119888(MPa) (0 le 119909 le 2032mm)

(13)

where119864(1016) is themodulus of elasticity at the center of thespecimen chosen to represent the mean modulus of elasticityof the whole specimen By defining the tensile strengthvariation using (12) or (13) the probability of crackingintegration in (11) can be computed using the Monte Carlosimulation [23] as

119901119891 (119894) =119899 119891119894119891119905 (119894) ge 119891119895119891119905 (119895) 119894 = 119895

119873 (14)

where 119891119905(119894) and 119891119905(119895) are the cracking strength evaluatedat the middle of the 119894th and 119895th layers using (12) or (13)respectivelyThe probabilities of cracking along the specimenwere calculated using (14) by considering 4 times 10

6 samplingiterations for each layer with the coefficient of variation(COV) of the maximum stress taken as 10

For two models of tensile strength variation using (12)or (13) the probabilities of cracking along the specimenare presented in Figures 8(a) and 8(b) respectively Theexperimental observations of the cracking location in directtension tests as shown in Figure 6 met the probabilisticprediction confirming the hypothesis of the significance ofunit weight variation on cracking location The probabilisticprediction using the linear variation of the tensile strengthwith respect to the modulus of elasticity (13) was capableof meeting the experimental observations better than thatusing the variation proposed byACI 209R-92model [22] (12)The experimental and probabilistic prediction results of thecracking location seem to be caused by the effect of gravityon fresh concrete during setting time Therefore this might


0

20

40

60

80

100

Relat

ive f

requ

ency

()

Distance from the top of specimen (mm)

Numerical analysis

Experiments

0 50 100 150 200

(a)

0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(b)

Figure 8 Probability of cracking with the maximum stress COVof 10 when considering the variations of modulus of elasticity andcracking strength along the specimen (a) using (12) and (b) using(13)

be correlated with the properties of fresh concreteThis effectcan be exaggerated for relatively deep beams or slabs In otherwords cracking strengths at the top of a structural elementwould be less than what is predicted by using current designcodes Such variation in concrete properties was observed inbond strength with steel reinforcement [24] and is addressedin development length models by ACI design code [3]Therefore when the negative moment is acting on topregions of concrete structural elements a reduced crackingstrength might be considered for conservative serviceabilitycalculations Further research investigations are needed toconfirm the effect of gravity on cracking strength distributionof concrete while considering the significance of aggregatevolume fraction size and shape

6 Conclusions

A new test setup of direct tension test for cylindrical concretespecimen (1016mm in diameter and 2032mm in height) is

proposed Experimental and numerical methods are used tosupport the proposed test setup The stress uniformity alongthe specimen is examined using the finite element methodaided by a fuzzy image pattern recognition algorithm Theunit weights distribution along cylindrical concrete speci-men (1016mm in diameter and 2032mm in height) wasdetermined Measurements confirmed the increase in unitweight towards the bottom of the specimens Distributionof unit weight is shown to significantly affect the probabilityof cracking along the tension specimens The probabilitiesof cracking along the specimen were also calculated usingMonte Carlo simulation The probabilistic prediction resultsagree with the experimental observations confirming thatcracking location in direct tension tests is a function of unitweight distribution along the specimen

Notations

119886 119887 Images that have the same size andnumber of pixels

119864(119909) Modulus of elasticity at 119909 in concretespecimen

1198911015840

119888 Compressive strength of concrete

119891119894 119891119895 The maximum stress at 119894th and 119895th layer infinite element model

119891119903 Flexural strength of concrete (modulus ofrupture)

119891119904119901 Splitting tensile strength of concrete119891119905 Direct tensile strength of concrete119891119905(119909) Direct tensile strength at 119909 in concrete

specimen119894 119895 119894th and 119895th layer in finite element model119898119886 119898119887 Pixel values for the two figures 119886 and 119887119899 The number of sampling cases that satisfy

the condition in brackets 119873 Total sampling numbers119901119891(119894) Probability of cracking of 119894th layer119901119894(119891119894) Probability density function (PDF) of 119891119894119908(119909) Unit weight at 119909 in concrete specimen119909 Distance from the top of concrete

specimen120572 Threshold of similarity120583119901 Pixel similarity

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The first author would like to acknowledge the NationalResearch Foundation (NRF) Grant funded by the Koreangovernment (MOE) (no 2013R1A1A2062784) The financialsupport to the second author by the Defense Threat Reduc-tion Agency (DTRA) is also acknowledged


References

[1] P K Mehta and P J M Monteiro Concrete MicrostructureProperties and Materials McGraw Hill New York NY USA3rd edition 2006

[2] J GMacGregor and J KWightReinforcedConcreteMechanicsand Design Prentice Hall Upper Saddle River NJ USA 4thedition 2005

[3] ACI Committee 318 Building Code Requirements for StructuralConcrete (318-11) and Commentary (318R-11) American Con-crete Institute Farmington Hills Mich USA 2011

[4] J M Raphael ldquoTensile strength of concreterdquo ACI Journal vol81 no 2 pp 158ndash165 1984

[5] F A Oluokun ldquoPrediction of concrete tensile strength fromits compressive strength Evaluation of existing relations fornormal weight concreterdquo ACI Materials Journal vol 88 no 3pp 302ndash309 1991

[6] A Ghali and R Favre Concrete Structures Stresses and Defor-mations Spon Press London UK 3rd edition 2002

[7] M M Reda Taha and M A Hassanain ldquoEstimating the errorin calculated deflections of HPC slabs a parametric study usingthe theory of error propagationrdquo inControllingDeflection for theFuture vol 210 pp 65ndash92 ACI Special Publication 2003

[8] ASTM C 78-02 Standard Test Method for Flexural Strengthof Concrete (Using Simple Beam with Third-Point Loading)American Standard Test Method West Conshohocken PennUSA 2002

[9] ASTM C 496C 496M-04 Standard Test Method for SplittingTensile Strength of Cylindrical Concrete Specimens AmericanStandard Test Method West Conshohocken Penn USA 2004

[10] WZhengAKHKwan andPKK Lee ldquoDirect tension test ofconcreterdquo ACI Materials Journal vol 98 no 1 pp 63ndash71 2001

[11] US Bureau of Reclamation Procedure for Direct TensileStrength Static Modulus of Elasticity and Poissonrsquos Ratio ofCylindrical Concrete Specimens in Tension (USBR 4914-92)Concrete Manual Part 2 9th edition 1992

[12] CRD-C 164-92 Standard Test Method for Direct Tensile Strengthof Cylindrical Concrete or Mortar Specimens US Army Engi-neering Research and Development Center (ERDC) Vicks-burg Miss USA 1992

[13] SAS ANSYS 71 Finite Element Analysis SYStem SAP IP 2003[14] T J Ross Fuzzy Logic with Engineering Applications JohnWiley

amp Sons Chichester UK 3rd edition 2010[15] G Tolt and I Kalaykov ldquoMeasures based on fuzzy similarity for

stereomatching of color imagesrdquo Soft Computing vol 10 no 12pp 1117ndash1126 2006

[16] M F SuMM Reda Taha C G Christodoulou and I El-KadyldquoFuzzy learning of talbot effect guides optimal mask designfor proximity field nanopatterning lithographyrdquo IEEE PhotonicsTechnology Letters vol 20 no 10 pp 761ndash763 2008

[17] ASTM C 39C 39M-04a Standard Test Method for CompressiveStrength of Cylindrical Concrete Specimens American StandardTest Method West Conshohocken Penn USA 2004

[18] CEP-FIP Model Code 90 Model Code for Concrete StructuresComite Euro-International du Beton (CEB)mdashFederation Inter-nationale de la Precontrainte (FIP) Thomas Telford LondonUK 1993

[19] R I Gilbert ldquoShrinkage cracking and deflectionmdashthe service-ability of concrete structuresrdquo Electronic Journal of StructuralEngineering vol 1 pp 15ndash37 2001

[20] F Legeron and P Paultre ldquoPrediction of modulus of ruptureof concreterdquo ACI Materials Journal vol 97 no 2 pp 193ndash2002000

[21] A M Neville Properties of Concrete Prentice Hall New YorkNY USA 4th edition 1995

[22] ACI Committee 209 Prediction of Creep Shrinkage and Temper-ature Effects in Concrete Structures (209R-92 Reapproved 2008)American Concrete Institute Farmington Hills Mich USA2008

[23] A H-S Ang and W H Tang Probability Concepts in Engi-neering Emphasis on Applications to Civil and EnvironmentalEngineering John Wiley amp Sons 2nd edition 2006

[24] P R Jeanty D Mitchell and M S Mirza ldquoInvestigation of topbar effects in beamsrdquo ACI Structural Journal vol 85 no 3 pp251ndash257 1988

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the loading machine and concrete specimen However allthese methods induce secondary stresses that result in anuneven stress application to concrete specimens [10] Tomakethe applied point load a more evenly distributed load USBureau of Reclamation [11] proposes the use of a doubleplate system for two sizes of diameters of 1524mm and254mm cylinder specimens The outer plate is connected toa loading machine while the inner plate is bonded with theconcrete specimen with epoxyThe inner and outer plates areconnected to each other by bolts Recently this method wasmodified for the rectangular section of 100mm by 100mmand showed acceptable results [10]

In this study the above method is further developed forcylindrical specimen (1016mm in diameter and 2032mmin height) Moreover the stress uniformity of the proposeddirect tension test method is evaluated using the finiteelement methodThe stress uniformity along the specimen iscompared with the stress uniformity of the direct tension testfor rectangular specimen As experimental results showedthat the cracking location was concentrated at the top half ofthe vertically cured cylindrical specimens the unit weight ofthe two broken parts was measured to examine the effect ofunit weight on cracking strength and cracking location

2 Proposed Test Setup

For the cylinder size of 1016mm diameter and 2032mmheight a double plate system with epoxy adhesive wasadopted for the direct tension test setup as shown inFigure 1 The intention is to use cylinders similar to thoseused to evaluate the compressive strength of concrete in theconcrete industryThe inner and outer plates were connectedto each other by eight high-strength bolts Tension loadwas applied through ball bearings in order to prevent thedeveloping of bending and torsion stresses in the concretespecimen The thickness of the inner plate was determinedto be 381mm according to the US Army Engineer Researchand Development Center (ERDC) CRD-C 164-92 [12] Itwas proposed that the thickness of the end plate should behigher than one third of the diameter of the test specimenThe thickness of the outer plate was chosen as one half ofthat of the inner plate The bolting locations of the inner andouter plates were optimized by finite element analysis to getuniform stress distributionThe direct tension test conductedusing the proposed test setup is shown in Figure 2

3 Finite Element Analyses

Linear elastic finite element analyses were performed toinvestigate the stress distribution along the cylindrical andrectangular specimen as proposed by others [10] ANSYS711 [13] was used for the finite element analyses The testsetups were modeled as 3D solid models The epoxy doubleend plates and concrete were modeled using SOLID 45 [13]which is a solid cubic element with eight nodes having threedegrees of freedom (DOF) for translations about the nodal 119909119910 and 119911 at each node The material properties used for finiteelement analysis are presented in Table 1The bolt connecting

Load

Ball bearing

Outer plateInner plateEpoxy layer

Cylindrical specimen

A

Section A-A

Machine base

Load cell

191A

M8 bolt

191318 318

381191

508 508

45∘

Figure 1 Test setup of the proposed direct tension test for 1016mmdiameter and 2032mm height cylinder (mm)

Ball bearing

Outer plate

Inner plate

M8 bolt

Specimen

Figure 2 Direct tension test conducted by the proposed test setup

the outer and the inner plates was modeled using LINK 8[13] three-dimensional (3D) uniaxial tension-compressionelement with three DOF for translations about the nodal 119909119910 and 119911 at each node

The finite element analyses of the test setups for cylindri-cal and rectangular specimens are conducted It is importantto emphasize that the purpose of numerical modeling isto quantify the uniformity of the stress distribution in thetension specimen and not to examine cracking behavior ofthe concrete specimen Therefore only linear elastic regionof concrete constitutive model is used for finite elementanalyses Considering the symmetry of the test specimen andloading a quarter of the specimenrsquos section and a half of thespecimenrsquos length were modeled The boundary conditions








120583119901 =

1 minusabs (119898119886 minus 119898119887)

120572 if abs (119898119886 minus 119898119887) le 120572

0 otherwise(1)







0

20

40

60

80

100

085 090 095 100D

istan

ce fr

om th

e top

of s

peci

men

(mm

)

Similarity

CircularRectangular




0

20

40

60

80

100

01 1 10 100

Pass

ing

()

Sieve size (mm)




0

2

4

6

8

10

10 20 30 40 50 60 70 80

Crac

king

stre

ngth

(MPa

)






119891119903 = 21(1198911015840

119888

10)

23

(MPa) (2)

119891119904119901 = 12(1198911015840

119888

10)

23

(MPa) (3)

119891119905 = 08(1198911015840

119888

10)

23

(MPa) (4)

where119891119903119891119904119901119891119905 and1198911015840



119891119903 = 085radic1198911015840119888(MPa) (5)

119891119904119901 = 049radic1198911015840119888(MPa) (6)

119891119905 = 034radic1198911015840119888(MPa) (7)





Admixture(Lm3)

M-1 236 79 192 700 1143 047M-2 289 97 185 587 1192 157M-3 345 115 179 479 1232 363



M-1B-1 234126 375018 228015 155006B-2 248082 393025 233015 177012B-3 237079 448023 182028 152004

Meanstd 240109 405038 214030 161014

M-2B-4 382144 507040 302024 213015B-5 382035 500021 301016 213007B-6 392018 524016 303029 225006

Meanstd 385090 510026 302021 217011

M-3B-7 540143 607034 384013 244011B-8 592156 673033 380041 253008B-9 567365 678041 384020 250006

Meanstd 566306 653047 383024 249008


119891119903 = 175119891119904119901 = 250119891119905 (8)


5 Cracking Location




119908 (119909) = 0789119909 + 23527 (kgm3

) (0 le 119909 le 2032mm)

(9)


0

20

40

60

80

100

Relat

ive f

requ

ency

()



2200

2400

2600

2800

3000


dWdL

dU

w(x) = 07889x + 23527

R2= 02631

Uni

t wei

ght (

kgm

3)

dW

dL

dU



119864 (119909) = 0043119908(119909)15radic1198911015840119888(MPa) (0 le 119909 le 2032mm)

(10)


119901119891 (119894) = intint119891119894ge119891119895 119894 = 119895


11990140 (11989140) 11988911989111198891198912 sdot sdot sdot 11988911989140

(11)


119891119905 (119909) = 00069radic119908 (119909) 1198911015840119888(MPa) (0 le 119909 le 2032mm)

(12)


119891119905 (119909) =119864 (119909)

119864 (1016)034radic1198911015840

119888(MPa) (0 le 119909 le 2032mm)

(13)


119901119891 (119894) =119899 119891119894119891119905 (119894) ge 119891119895119891119905 (119895) 119894 = 119895

119873 (14)





0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(a)

0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(b)



6 Conclusions



Notations



1198911015840










Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















120583119901 =

1 minusabs (119898119886 minus 119898119887)

120572 if abs (119898119886 minus 119898119887) le 120572

0 otherwise(1)







0

20

40

60

80

100

085 090 095 100D

istan

ce fr

om th

e top

of s

peci

men

(mm

)

Similarity

CircularRectangular




0

20

40

60

80

100

01 1 10 100

Pass

ing

()

Sieve size (mm)




0

2

4

6

8

10

10 20 30 40 50 60 70 80

Crac

king

stre

ngth

(MPa

)






119891119903 = 21(1198911015840

119888

10)

23

(MPa) (2)

119891119904119901 = 12(1198911015840

119888

10)

23

(MPa) (3)

119891119905 = 08(1198911015840

119888

10)

23

(MPa) (4)

where119891119903119891119904119901119891119905 and1198911015840



119891119903 = 085radic1198911015840119888(MPa) (5)

119891119904119901 = 049radic1198911015840119888(MPa) (6)

119891119905 = 034radic1198911015840119888(MPa) (7)





Admixture(Lm3)

M-1 236 79 192 700 1143 047M-2 289 97 185 587 1192 157M-3 345 115 179 479 1232 363



M-1B-1 234126 375018 228015 155006B-2 248082 393025 233015 177012B-3 237079 448023 182028 152004

Meanstd 240109 405038 214030 161014

M-2B-4 382144 507040 302024 213015B-5 382035 500021 301016 213007B-6 392018 524016 303029 225006

Meanstd 385090 510026 302021 217011

M-3B-7 540143 607034 384013 244011B-8 592156 673033 380041 253008B-9 567365 678041 384020 250006

Meanstd 566306 653047 383024 249008


119891119903 = 175119891119904119901 = 250119891119905 (8)


5 Cracking Location




119908 (119909) = 0789119909 + 23527 (kgm3

) (0 le 119909 le 2032mm)

(9)


0

20

40

60

80

100

Relat

ive f

requ

ency

()



2200

2400

2600

2800

3000


dWdL

dU

w(x) = 07889x + 23527

R2= 02631

Uni

t wei

ght (

kgm

3)

dW

dL

dU



119864 (119909) = 0043119908(119909)15radic1198911015840119888(MPa) (0 le 119909 le 2032mm)

(10)


119901119891 (119894) = intint119891119894ge119891119895 119894 = 119895


11990140 (11989140) 11988911989111198891198912 sdot sdot sdot 11988911989140

(11)


119891119905 (119909) = 00069radic119908 (119909) 1198911015840119888(MPa) (0 le 119909 le 2032mm)

(12)


119891119905 (119909) =119864 (119909)

119864 (1016)034radic1198911015840

119888(MPa) (0 le 119909 le 2032mm)

(13)


119901119891 (119894) =119899 119891119894119891119905 (119894) ge 119891119895119891119905 (119895) 119894 = 119895

119873 (14)





0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(a)

0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(b)



6 Conclusions



Notations



1198911015840










Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

20

40

60

80

100

085 090 095 100D

istan

ce fr

om th

e top

of s

peci

men

(mm

)

Similarity

CircularRectangular




0

20

40

60

80

100

01 1 10 100

Pass

ing

()

Sieve size (mm)




0

2

4

6

8

10

10 20 30 40 50 60 70 80

Crac

king

stre

ngth

(MPa

)






119891119903 = 21(1198911015840

119888

10)

23

(MPa) (2)

119891119904119901 = 12(1198911015840

119888

10)

23

(MPa) (3)

119891119905 = 08(1198911015840

119888

10)

23

(MPa) (4)

where119891119903119891119904119901119891119905 and1198911015840



119891119903 = 085radic1198911015840119888(MPa) (5)

119891119904119901 = 049radic1198911015840119888(MPa) (6)

119891119905 = 034radic1198911015840119888(MPa) (7)





Admixture(Lm3)

M-1 236 79 192 700 1143 047M-2 289 97 185 587 1192 157M-3 345 115 179 479 1232 363



M-1B-1 234126 375018 228015 155006B-2 248082 393025 233015 177012B-3 237079 448023 182028 152004

Meanstd 240109 405038 214030 161014

M-2B-4 382144 507040 302024 213015B-5 382035 500021 301016 213007B-6 392018 524016 303029 225006

Meanstd 385090 510026 302021 217011

M-3B-7 540143 607034 384013 244011B-8 592156 673033 380041 253008B-9 567365 678041 384020 250006

Meanstd 566306 653047 383024 249008


119891119903 = 175119891119904119901 = 250119891119905 (8)


5 Cracking Location




119908 (119909) = 0789119909 + 23527 (kgm3

) (0 le 119909 le 2032mm)

(9)


0

20

40

60

80

100

Relat

ive f

requ

ency

()



2200

2400

2600

2800

3000


dWdL

dU

w(x) = 07889x + 23527

R2= 02631

Uni

t wei

ght (

kgm

3)

dW

dL

dU



119864 (119909) = 0043119908(119909)15radic1198911015840119888(MPa) (0 le 119909 le 2032mm)

(10)


119901119891 (119894) = intint119891119894ge119891119895 119894 = 119895


11990140 (11989140) 11988911989111198891198912 sdot sdot sdot 11988911989140

(11)


119891119905 (119909) = 00069radic119908 (119909) 1198911015840119888(MPa) (0 le 119909 le 2032mm)

(12)


119891119905 (119909) =119864 (119909)

119864 (1016)034radic1198911015840

119888(MPa) (0 le 119909 le 2032mm)

(13)


119901119891 (119894) =119899 119891119894119891119905 (119894) ge 119891119895119891119905 (119895) 119894 = 119895

119873 (14)





0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(a)

0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(b)



6 Conclusions



Notations



1198911015840










Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Admixture(Lm3)

M-1 236 79 192 700 1143 047M-2 289 97 185 587 1192 157M-3 345 115 179 479 1232 363



M-1B-1 234126 375018 228015 155006B-2 248082 393025 233015 177012B-3 237079 448023 182028 152004

Meanstd 240109 405038 214030 161014

M-2B-4 382144 507040 302024 213015B-5 382035 500021 301016 213007B-6 392018 524016 303029 225006

Meanstd 385090 510026 302021 217011

M-3B-7 540143 607034 384013 244011B-8 592156 673033 380041 253008B-9 567365 678041 384020 250006

Meanstd 566306 653047 383024 249008


119891119903 = 175119891119904119901 = 250119891119905 (8)


5 Cracking Location




119908 (119909) = 0789119909 + 23527 (kgm3

) (0 le 119909 le 2032mm)

(9)


0

20

40

60

80

100

Relat

ive f

requ

ency

()



2200

2400

2600

2800

3000


dWdL

dU

w(x) = 07889x + 23527

R2= 02631

Uni

t wei

ght (

kgm

3)

dW

dL

dU



119864 (119909) = 0043119908(119909)15radic1198911015840119888(MPa) (0 le 119909 le 2032mm)

(10)


119901119891 (119894) = intint119891119894ge119891119895 119894 = 119895


11990140 (11989140) 11988911989111198891198912 sdot sdot sdot 11988911989140

(11)


119891119905 (119909) = 00069radic119908 (119909) 1198911015840119888(MPa) (0 le 119909 le 2032mm)

(12)


119891119905 (119909) =119864 (119909)

119864 (1016)034radic1198911015840

119888(MPa) (0 le 119909 le 2032mm)

(13)


119901119891 (119894) =119899 119891119894119891119905 (119894) ge 119891119895119891119905 (119895) 119894 = 119895

119873 (14)





0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(a)

0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(b)



6 Conclusions



Notations



1198911015840










Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

20

40

60

80

100

Relat

ive f

requ

ency

()



2200

2400

2600

2800

3000


dWdL

dU

w(x) = 07889x + 23527

R2= 02631

Uni

t wei

ght (

kgm

3)

dW

dL

dU



119864 (119909) = 0043119908(119909)15radic1198911015840119888(MPa) (0 le 119909 le 2032mm)

(10)


119901119891 (119894) = intint119891119894ge119891119895 119894 = 119895


11990140 (11989140) 11988911989111198891198912 sdot sdot sdot 11988911989140

(11)


119891119905 (119909) = 00069radic119908 (119909) 1198911015840119888(MPa) (0 le 119909 le 2032mm)

(12)


119891119905 (119909) =119864 (119909)

119864 (1016)034radic1198911015840

119888(MPa) (0 le 119909 le 2032mm)

(13)


119901119891 (119894) =119899 119891119894119891119905 (119894) ge 119891119895119891119905 (119895) 119894 = 119895

119873 (14)





0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(a)

0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(b)



6 Conclusions



Notations



1198911015840










Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(a)

0

20

40

60

80

100

Relat

ive f

requ

ency

()


Numerical analysis

Experiments

0 50 100 150 200

(b)



6 Conclusions



Notations



1198911015840










Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article experimental and numerical evaluation of...

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