Mechanical Model for Shear Friction Capacity of Concrete ...downloads.hindawi.com/journals/amse/2018/9264503.pdf · ResearchArticle Mechanical Model for Shear Friction Capacity of

Research ArticleMechanical Model for Shear Friction Capacity of Concrete atConstruction Joints

Seung-Jun Kwon 1 Keun-Hyeok Yang 2 and Ju-Hyun Mun2

1Civil and Environment Engineering Hannam University Daejeon Republic of Korea2Architectural Engineering Kyonggi University Suwon Republic of Korea

Correspondence should be addressed to Keun-Hyeok Yang yangkhkguackr

Received 16 January 2018 Revised 31 May 2018 Accepted 2 July 2018 Published 24 July 2018

Academic Editor Charles C Sorrell

Copyright copy 2018 Seung-Jun Kwon et al is 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 isproperly cited

is study examined the reliability and limitations of code equations for determining the shear friction strength of a concreteinterface with construction joints is was achieved by examining the code equations (ACI 318-14 AASHTO and fib 2010) andcomparing the results predicted by equations with experimental data compiled from 207 push-off specimens (133 rough and 74smooth construction joints) e integrated mechanical model for the monolithic interface derived from the upper-bound theoremof concrete plasticity was also modified to estimate the shear friction strength of the construction joints e upper limit for shearfriction strength was formulated from a concrete crushing failure limit on the strut-and-tie action along the interfacial plane to avoidoverestimating the shear transfer capacity of transverse reinforcement with a high clamping force Code equations are highlyconservative and dispersive in predicting the shear friction strength of rough construction joints and yield large scattering in the datafor the ratios between themeasured and predicted shear friction strengthse predictions obtained using the proposedmodel agreedwell with test results indicating correlating trends with the test results for evaluating the effects of various parameters on the shearfriction strength of rough construction joints According to the proposed model the values of cohesion and coefficient of friction forconcrete could be determined as 011 (fcprime )065 and 064 respectively for smooth construction joints and 027 (fcprime )065 and 095respectively for rough construction joints where fcprime is the compressive strength of concrete

1 Introduction

Shear friction is generally accepted as a major mechanism ofload transfer along a concrete-to-concrete interface which issubjected to simultaneous shear and normal stresses ecrack propagation and failure plane of a member governedby shear friction are concentrated on the interfacial shearplane [1ndash3] Despite the fact that the mechanism of shearfriction is considerably more complex than that of con-ventional friction [4 5] the ACI 318-14 provision [6] simplyconsiders that applied shear is mostly transferred by theresistance generated from the friction between the twosliding faces and a clamping force e clamping force isinduced by the transverse reinforcement crossing the in-terfaces To calculate the clamping force the stress of thetransverse reinforcement is assumed to have reached its yieldpoint erefore the shear friction strength of concrete

interfaces calculated using the equations of the code pro-visions [6 7] increases in proportion to the clamping forcewhich is commonly expressed as ρvffy where ρvf and fy arethe ratio and yield strength of the interface reinforcing barsrespectively However Harries et al [4] revealed that thestress in a high-strength steel reinforcement (with a yieldstrength of approximately 700MPa) is lower than its yieldstrength at the ultimate state of concrete interfaces Kwonet al [8] examined code safety through comparisons withtest results taken from 103 push-off specimens withmonolithic interfaces ey concluded that the ACI 318-14and AASHTO equations yield significant underestimationswhereas the overestimations of AASHTO equation are alsofrequently observed as ρvffy is less than 8MPa In particularthe underestimation and disagreement owing to the use ofthe AASHTO equation are increased for the interface withsmooth construction joints [9] Overall code equations that

HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 9264503 12 pageshttpsdoiorg10115520189264503

are empirically formulated using test data collected undera narrow range of influencing parameters do not sufficientlycapture the mechanical diversity of the shear friction ca-pacity of concrete interfaces with different concrete castingtimes

Concrete interfaces frequently have a construction jointbetween the precast element and the cast-in-place concreteor at the surface formed by placing one layer of concrete onan existing layer of hardened concrete When shear is ap-plied to construction joints the aggregate interlocking ac-tion and tensile resistance of concrete are insignificant alongthe interfacial plane Hence a lower shear friction resistanceis inevitable along the construction joints than along themonolithic interfaces with or without initial cracks How-ever many of the empirical equations [4 5 10ndash13] used toestimate shear friction strength have been proposed formonolithic interface based on different experimental pro-grams and the shear friction action associated with the trussmodel us test data and analytical approaches for con-struction joints are relatively insufficient Code provisions[6 7] specify that compared with that of monolithic in-terfaces the coefficient of friction (μ) must be approximately30 lower for smooth construction joints and approxi-mately 60 lower for rough construction joints Howeverthere is no explicit experimental or analytical validation ofthis requirement

e fib 2010 [14] provision specifies a 167 higher valueof μ for rough construction joints than for smooth con-struction joints Mattock [15] reported that the sheartransfer due to concrete cohesion is considerably reduced inconstruction joints compared with the shear transfer thatdevelops along monolithic interfaces in concrete Santos andJulio [16] pointed out that the roughness of the concretesubstrate should be considered in the design expressions inthe form of the coefficients of cohesion andor frictionbecause the bond strength of concrete-to-to interfaces issignificantly affected by their substrate state However thecohesion and frictional coefficient of concrete in con-struction joints are still insufficiently interpreted particu-larly for high-strength concrete with smooth surfacesMoreover the shear friction strength at overreinforcedconstruction joints needs to be appropriately limited toavoid concrete crushing failure before the transverse re-inforcement yield is reached Most of the code equations donot provide an explicit validation for the upper limit orsafety evaluationus the safety and rationality evaluationsof the code equations are quite unsatisfactory for rough andsmooth construction joints although such evaluations formonolithic interfaces have been extensively performed inprevious studies [3 11 15]

is study determines the cohesion and frictionalcoefficients of concrete at smooth and rough constructionjoints using a mechanical approach derived from theupper-bound theorem of concrete plasticity e upperlimits of the shear friction strength are derived from thestate of concrete crushing failure limit on the strut-and-tie action along the construction joints to avoid over-estimating the shear transfer capacity of a transversereinforcement with a high clamping force e reliability

and limitation of the code equations [6 7 14] used todetermine the shear friction strength of constructionjoints are also examined through comparisons with theexperimental data compiled from different sources ena parametric study is conducted using the proposedmodel the AASHTO equation and the results from thecollected database to evaluate the effect of different pa-rameters on the shear friction capacity of constructionjoints

2 Database of Push-Off Specimens withConstruction Joints

A total of 207 push-off specimens (including 133 roughconstruction joints and 74 smooth construction joints)compiled from different sources in the literature[4 5 11 17ndash25] were used to examine the reliability andsafety of the code equations and mechanical equations withregard to the effect of the different parameters on the shearfriction strength of the construction jointse distributionof the different parameters in the database is shown inFigure 1 Although the roughness parameters such asmaximum peak-to-valley height total roughness heightand maximum valley depth influence the cohesion alongthe concrete interface [26] most of the literature does notprovide the details on the substrate state of the interfaceus in the database an interface with only a steel-brushing treatment is classified as a smooth constructionjoint whereas an interface intentionally treated withsand blast with the full amplitude above approximately15mm is classified as a rough construction joint withreference to the surface roughness classification specified infib 2010 [14]

e test data available for smooth construction joints arerelatively limited All the specimens included in the databasewere reported to have failed in shear friction owing toa major crack along the interfacial plane Only a fewspecimens had no transverse reinforcement crossing theinterface Most of the specimens with smooth constructionjoints were made of concrete with a high compressivestrength (exceeding 55MPa) whereas the compressivestrength (fcprime) of the concrete specimens with rough con-struction joints ranged between 12MPa and 100MPa eclamping stress induced by the transverse reinforcementwhich can be expressed as ρvffy varied between 151MPaand 637MPa for smooth construction joints and between140MPa and 1229MPa for rough construction jointswhere ρvf and fy are the ratio and yield strength of thetransverse reinforcement respectively e inclination (θs)of the transverse reinforcement to the interfacial planevaried between 45deg and 90deg Most specimens with roughconstruction joints were tested with no normal stresses(σx) externally applied to the interface Six rough con-struction joints were tested under additional appliedtensile stresses ranging between minus004 fcprime and minus01 fcprimeFor the smooth construction joints subjected to an ad-ditional normal compressive stress σxfcprimewas fixed at 015Compressive and tensile stresses are denoted by thesymbols (+) and (minus) respectively

2 Advances in Materials Science and Engineering

3 Shear Friction Strength Models

Most empirical equations [4 5 10ndash13] for shear frictionstrength were tted to a monolithic interface Mattock [15]derived an experimental constant to determine the sheartransfer of concrete in his empirical shear friction modelfor a monolithic normal-weight concrete interface isconstant was 01fcprime However the constant was xed at276MPa for a rough construction joint No tting data orexplanation for smooth construction joints is available inthe empirical model developed by Mattock erefore thisexamination of the shear friction design for constructionjoints focuses on the code equations and mechanicalmodels

31 ACI 318-14 Equation e ACI 318-14 [6] provisionspecies that the shear friction strength (τn VnAc) ofnormal-weight concrete interfaces based on the shearfriction theory is

τn VnAc

ρvffy μ sin θs + cos θs( ) (1)

τn lemin 02fcprime 33 + 008fcprime 11( ) (in MPa)for rough construction joints

(2a)

τn lemin 02fcprime 55( ) (in MPa)for smooth construction joints

(2b)

where Vn is the shear friction capacity Ac is the section areaof the interfacial plane μ ( tanϕprime) is the coecient offriction and ϕprime is the friction angle of the concrete along theconstruction joint e value of fy is limited to 420MPa toavoid the overestimation of the shear transfer capacity foroverreinforcement or high-strength steel reinforcement Anupper limit for τn is imposed as a function of the concreteshear resistance although the shear transfer capacity ofconcrete is ignored in calculating the shear friction strengthof the interfacial plane e increase in the shear friction

3

4037

27 26

1

2428

21

0

10

20

30

40

50

60

12~20 20~40 40~60 60~80 80~100

Freq

uenc

y

(MPa)fcprime

Rough construction jointSmooth construction joint

(a)

0

17

2632

37

74 3

19

1

43

8

0

10

20

30

40

50

60

0 0~2 2~4 4~6 6~8 8~10 10~12 12~14

Freq

uenc

y

ρvf fy (MPa)


(b)

1 4 1

127

36 38

0

30

60

90

120

150

ndash01 ndash010~ndash005 ndash004 0 015

Freq

uenc

y

σx

Applied normalstress in tension

Applied normalstress in

compression


fcprime

(c)

Figure 1 Distribution of dierent parameters in the 207 push-o specimens with construction joints (a) compressive strength of concrete(fcprime) (b) clamping stress provided by transverse reinforcement (ρvffy) (c) ratio of applied normal stresses (σx) to fcprime

Advances in Materials Science and Engineering 3

resistance due to the applied compressive stresses is notconsidered in (1) whereas the applied tensile stresses requirean additional transverse reinforcement at the interfacialplane e amount of transverse reinforcement can be de-termined by the equilibrium condition of force e value ofμ was set to be 10 and 06 for rough and smooth con-struction joints respectively as listed in Table 1 For thesmooth construction joints a reduced shear friction wasaccepted under the assumption that the shear force is pri-marily resisted by the dowel action of the transverse re-inforcement According to ((2a) and (2b)) the upper limit[(τn)max] is governed by 02fcprime when fcprime is less than 28MParegardless of concrete joint type whereas it is governed by(33 + 008fcprime) for the rough construction joints and 55MPafor the smooth construction joints when fcprime is between28MPa and 100MPaMoreover (1) and ((2a) and (2b)) implythat the clamping force induced by the transverse rein-forcement becomes insignificant when ρvffy exceeds a certainlimit For example for interfaces made using concrete with fcprimeranging between 28MPa and 100MPa the ratio of the re-inforcement arranged perpendicular to the interfacial planedoes not have to be greater than (33 + 008fcprime)fy for roughconstruction joints and 5506fy for smooth constructionjoints is also implies that the ultimate frictional resistanceprovided by the transverse reinforcement depends on theroughness of the interfacial shear plane

32 AASHTO Equation e AASHTO equations [7] as-sume that interface shear resistance is directly proportionalto the net normal clamping stress based on a modified shearfriction model that accounts for a contribution from co-hesion andor aggregate interlock e AASHTO provisionspecifies the nominal τn of the interfacial plane as follows

τn cprime + μ ρvffy + σx1113872 1113873 cprime + μσeq

τn lemin K1fcprime K2( 1113857(3)

where cprime is the concrete cohesion along the constructionjoint for which the values are taken to be 052MPa and166MPa for smooth and rough construction joints re-spectively e compressive stresses at the interfaces thatdevelop from the transverse reinforcement and the exter-nally applied normal compressive stresses are commonlyequivalent to the summation of ρvffy + σx which is thendefined as the equivalent normal stress (σeq inMPa) [27]e experimental constants at the upper limits of τn K1 andK2 are taken as 02 and 552MPa respectively for smoothconstruction joints and 025 and 1035MPa respectively forrough construction joints For smooth construction joints

the value of (τn)max specified in the AASHTO provision isidentical to that in the ACI 318-14 equation For roughconstruction joints (τn)max is governed by 025fcprimewhen fcprime isless than 40MPa beyond which the upper limit increases to1035MPa is indicates that the AASHTO equation allowsfor a higher upper limit than the ACI 318-14 equation erestriction for fy is identical to ACI 318-14 All transversereinforcing bars are assumed to be arranged perpendicularto the interface

33 fib 2010 Equation e fib 2010 model [14] has a similarstructure to the AASHTO equation but it considers in-teraction factor and dowel action of the transverse re-inforcement It is presented as follows

τn c1 fcprime( 111385713

+ k1ρvffyd μ sin θs + cos θs( 1113857 + μσx

+ k2ρvffydfcd

1113969

τn le βc]fcd

] 05530fcprime

1113888 1113889

13

lt 055

(4)

where c1 is the factor to account for the aggregate inter-lock effect in concrete cohesion k1 and k2 are the inter-action factors for tensile force and flexural resistancegenerated in the transverse reinforcement fcd(fprime15)

and fyd(fy115) are the design compressive strength ofconcrete and design yield strength of reinforcement βc is thefactor for the strength of the compression strut and ] is thestrength reduction factor of concretee values of c1 k1 k2and βc are taken to be 0 05 11 and 04 respectively forsmooth construction joints e corresponding values forrough construction joints are 01 05 09 and 05respectively

e fib 2010 considers that the main contributions to thesear resistance along the construction joints result frommechanical interlocking and adhesive bonding of concretefriction due to external compression forces normal to theinterface and clamping forces by reinforcement and dowelaction of reinforcement crossing the interface e inter-locking and adhesive bonding capacities of concrete dependon the surface roughness of the construction joints as-suming that the interlock effects at smooth constructionjoints are negligible Compared with the cohesion capacity ofthe AASHTO equation (4) yields a lower value indicatingthat the interlocking and adhesive bonding capacities ofconcrete disappear compared to the other mechanisms of

Table 1 Comparison of cohesion and frictional coefficients of concrete in each model

ModelCohesion Coefficient of friction

Rough joint Smooth joint Rough joint Smooth jointACI 318-14 Ignored 10 06AASHTO 166MPa 052MPa 10 06fib 2010 010 (fcprime)

13 0 07 06is study 027 (fcprime)

065 011 (fcprime)065 095 064


shear friction and dowel action e upper limit of τn in-creases linearly with respect to fcprime For example the upperlimit of τn for construction joints is calculated to be 367MPawhen fcprime is 20MPa and 123MPa when fcprime is 100MPaCompared with the value of μ in the ACI 318-14 andAASHTO provisions the b 2010 species the same valuefor smooth surfaces but a 30 lower value for rough sur-faces as listed in Table 1

34 Mechanical Equations Derived Using Concrete PlasticityNielsen and Hoang [28] and Kwon et al [8] showed thatmechanism analysis based on the upper-bound theorem ofconcrete plasticity is a very promising method for describingthe concrete cohesion and shear friction response of con-crete monolithic interfaces or construction joints eyreported that concrete interfaces under direct shear and axialloads are usually separated into two rigid blocks at failure asshown in Figure 2 One rigid block has two translational androtational displacement components relative to the otherrigid block us one rigid block can be assumed to rotateabout an instantaneous center (IC) Similar to the failuremechanism of monolithic interfaces the shear plane atfailure along a construction joint can be regarded as a planestrain problem Nielsen and Hoang [28] demonstrated thatthe angle between the relative displacement (δ) about an ICand the failure plane can be assumed to be equal to thefrictional angle (ϕprime) of concrete along construction jointis angle can also be considered to be a constant valueFurthermore tensile resistance in the concrete at con-struction joints is not usually expected implying that theshear transfer of concrete along construction joints is en-tirely resisted by concrete cohesion Concrete is regarded asa rigid perfectly plastic material that obeys a modiedCoulomb failure criteria with eective compressive andtensile strengthserefore if the tensile strength of concreteis ignored the integrated model [8] for the shear frictionstrength of monolithic concrete interfaces can be modiedfor construction joints in the following form

τn cprime + ρvffycos θs minus ϕprime( )

cos ϕprime+ σx tanϕprime (5)

For construction joints with transverse reinforcement ofθs 90deg (5) can be written as follows

τn cprime + ρvffy + σx( )tanϕprime cprime + σeq tanϕprime (6)

Overall the mechanical approach derived from theupper-bound theorem for the construction joints has thesame format as shear friction theory Equations (5) and (6)imply that the shear friction strength of nonreinforcedconstruction joints without additional axial stresses isresisted only by the concrete cohesion along the interfacialfailure plane e AASHTO provision assumes the value ofcprime to be a constant whereas b 2010 [14] considers it to bea function of fcprime as listed in Table 1 Nielsen and Hoang [28]reported that the value of cprime depends on fcprime and theroughness along the interfacial plane Dahl [29] conducteda regression analysis using a small set of test data obtained

from four push-o specimens with smooth constructionjoints and showed that cprime could be expressed as a function of(fcprime)

05 Experimental programs for determining the value ofcprime of nonreinforced construction joints are very scarce Ifpush-o specimens analysed by Choi et al [30] and Hwang[18] are plotted to show cprime for smooth and rough con-struction joints as a function of fcprime the approximate re-lationship obtained is expressed as follows (Figure 3)

cprime 011 fcprime( )065 for smooth construction joints (7a)

cprime 027 fc( )065 for rough construction joints (7b)

According to the code provisions the enhanced cohesionon the rough surface due tomechanical treatment is estimatedto be 320 for the AASHTO equation whereas the b 2010neglects the cohesion capacity of smooth surface Equation((7a) and (7b)) shows that the rough surface has approxi-mately 245 higher cohesion than the smooth surface eseequations yield a higher value for cprime than the code equationsincluding b 2010 but a lower value than the calculation ofNielsen and Hoangrsquos equation [28] Equation ((7a) and (7b))would need to be further veried using the test data con-ducted under extensive range of fcprime values and for con-struction joints with the other surface impact treatments

To determine the value of ϕprime using the test data (5) isrearranged as follows

ϕprime tanminus1τn minus cprime minus ρvffy cos θsρvffy sin θs + σx

( ) (8)

e calculated ϕprime values for the test data in the databasecommonly range between 294deg and 445deg for smooth con-struction joints and between 333deg and 544deg for roughconstruction joints e average value of 328deg (μ 064) forsmooth construction joints and 435deg (μ 095) for roughconstruction joints are within the typical ranges specied inb model code 2010 [14]

Figure 4 plots the relationship between ρvffy and thenormalized shear friction strength (τnfcprime) for rough con-struction joints e normalized shear friction strength in-creases in proportion to ρvffy up to a certain limit beyond

Rigidblock I

Rigidblock II

Failure plane alongconstruction joint

Transversereinforcing bar

τ (=VAc)

τ (=VAc)

σx(=NxAc)

σx (=NxAc)

IC(XIC YIC)

ω

δα = ϕprime

θs

Y

X

cos αX IC

r =

Figure 2 Idealized failure mechanism of the concrete interfacewith construction joints


which the rate of increase gradually slows is implies thatthe τn at the overreinforced construction joints is governed bythe crushing of the concrete before the transverse re-inforcement reaches its yield strength Hence τn needs to belimited to certain value in order to avoid the overestimation ofthe shear transfer of transverse reinforcement due to theprecrushing failure of concrete Figure 5 shows the idealizedstrut-and-tie action needed to transfer the applied shear alongthe construction joints [28] based on the concrete plasticitye combined action of the shear force and clamping forces inthe transverse reinforcement yields an inclined compressiveforce across the interfacial plane e equilibrium conditionof the forces yields the following relationship

τn( )max middot Ac ]cf2maxAc sin θ cos θ (9)

where ]c is the eectiveness factor of the concrete incompression to account for the assumed rigid plasticityf2max is the compressive strength of a cracked concrete strutunder biaxial state of stresses and θ((π2)minusϕprime) is theinclination of the concrete struts appearing perpendicfularto the frictional angle [31] Kwon et al [8] calculated thevalue of ]c using the actual stress-strain curve of concreteand formulated it as follows

]c 079 exp minus003fcprime

fco( )

09 ρoρc( )

16 (10)

where fco (10MPa) and ρo (2300 kgm3) are the reference

values for the compressive strength and the unit weight ofconcrete respectively Belarbi and Hsu [32] tested concretepanels loaded under in-plane shear and proposed the fol-lowing relationship between f2max and fcprime

f2max 09

1 + 400ε1radic fcprime (11)

where ε1 is the transverse tensile strain For the crackedconcrete along the interfacial plane the value of ε1 depends onthe magnitude of fcprime and ρvffy However it is not easy task toestablish the relationship of ε1 and the incurrenuencing parametersin the concrete interface subjected to direct shear For sim-plicity of the equation for (τn)max the present study assumesthat ε1 would be approximately equivalent to the yield strain

(asymp0002) of the mild transverse reinforcement Overall theupper limit of the shear friction strength at the constructionjoints can be simply expressed as follows

τn( )max 067]cfcprime sinϕprime cos ϕprime (12)

Figure 6 shows the variation of (τn)maxfcprime calculatedusing the code and the proposed equations according to fcprimeAll the equations yield the same trend that is (τn)maxfcprimedecreases with the increase of fcprime implying that the in-creasing rate of the crushing strength of concrete undera biaxial stress state is not linearly proportional to fcprime Rahal[33] empirically proposed the upper limit based on exper-imental results using normal- and high-strength concreteindicating that (τn)maxfcprime varies linearly from 031 to 022whenfcprime increases from 20MPa to 100MPa regardless of theroughness of the concrete substrate along the interface Forsmooth construction joints (Figure 6(a)) the ACI 318-14and AASHTO equations have the same values of (τn)maxfcprimeproducing lower values than rough construction joints whenfcprime is greater than 28MPaat is a higher rate of decrease in(τn)maxfcprime is observed in the smooth construction jointsthan in the rough construction joints e developedequation has higher (τn)maxfcprime values than the AASHTOand b 2010 equations For rough construction joints(Figure 6(b)) the ACI 318-14 equation exhibits a lower(τn)max than the other equations when fcprime is lower than

00

01

02

03

0 2 4 6 8 10 12

τ n

ρvf fy

Rough construction joint

f cprime

Figure 4 Relationship between τnfcprime and ρvffy for the con-struction joints

(τn)max

Nx

Avfmiddotf yρvf f y + σx


θ

Interficalplane(Ac)

vc f2max

Figure 5 Idealized strut-and-tie action at the construction joints

0

05

1

15

2

25

3

35

4

45

10 20 30 40 50 60 70

cprime (M

Pa)

Best-fit curve for smoothconstruction joint

y = 011x065

Best-fit curve for roughconstruction joint

y = 027x065

(MPa)fcprime

Figure 3 Relationship between cprime and fcprime for the nonreinforcedconstruction joints


90MPa e value of (τn)maxfcprime calculated using theAASHTO equation remains constant at 025 up to an fcprime of50MPa beyond which the value decreases rapidlye valueof (τn)maxfcprime calculated using the b 2010 equation alsoshows similar trend to the AASHTO equation but yieldshigher level than the other models when fcprime is less than40MPa e developed equation has a higher (τn)maxfcprimevalue for rough construction joints than for smooth con-struction joints resulting in lower values than the b 2010equation when fcprime is lower than 50MPa

4 Comparison of Prediction Models andTest Results

41 Statistical Comparisons Figure 7 shows comparisonsbetween the measured shear friction strength of the push-ospecimens with construction joints in the database and thepredictions made by the code and developed equations Notethat any strength reduction factors are not considered incalculating shear friction strength using code equations andproposed model Table 2 lists the statistical values for themean (cm) standard deviation (cs) and coecient of var-iation (cv) of the ratios [c (τn)Exp(τn)Pre] between theexperimental and predicted shear friction strengths If cgt 1the prediction model is conservative Considering thatvarious sources of test data may have dierent geometricaldimensions material properties and test arrangements the5 (c5) and 95 (c95) fractiles in all the tests areemployed for evaluating the reliability of the predictionequations e 5 and 95 fractiles are calculated fromstatistics as follows [34]

c5 cm minusR0cs

c95 cm + R0cs(13)

e coecient R0 depends on the number (n) of testdata samples used to compute the average and standarddeviation Because the values of R0 range from 1645 for nmore than 120 to 2010 for n of 40 and to 2568 for n of 10

R0 can be calculated from the interpolation of these valuese specimens without transverse reinforcement were ex-cluded from the comparisons made using the ACI 318-14equation because the code equation neglects concrete co-hesion e signicant ndings derived from the compar-isons are discussed below

e ACI 318-14 equation (Figure 7(a)) considerablyunderestimates the shear friction strength of reinforcedsmooth construction joints which results in very high valuesof cm and c95 e values exceed 315 and 729 respectivelyis is because the predictions do not consider concrete sheartransfer by cohesion and are governed by the upper limit of τnwhen σvffy is greater than approximately 87MPa For roughconstruction joints the ACI 318-14 equation is still veryconservative yielding a high value of c95 exceeding 395although a few unsafe data points are observed and cm de-creases to 216 Large scattering of the data for the c value isobserved in the ACI 318-14 equations resulting in consid-erably high cs values of 223 and 113 for smooth and roughconstruction joints respectively e AASHTO equation alsoprovides underestimated results (Figure 7(b)) for smoothconstruction joints although a few overestimated data pointsare observed when σeq is greater than approximately 11MPae values of cm and cs obtained using the AASHTOequation are far smaller than those obtained using the ACI318-14 equation However large scattering of the c values isstill observed in the AASHTO equationerefore signicantamounts of overestimated data points are observed for roughconstruction joints e predictions obtained from the b2010 equation are frequently lower than the test results(Figure 7(c)) regardless of the roughness of the interfacialsurface e predictions yield lower values of cm and cs forsmooth construction joints than the previous code equationse unconservative trend of the b 2010 equation for smoothconstruction joints is magnied when σeq is greater thanapproximately 11MPa e b 2010 equation for roughconstruction joints has higher cm and cs values than theAASHTO equation e predictions of the proposed modelagree more closely with the test results (Figure 7(d))

0

005

01

015

02

025

20 40 60 80 100

(τn)

max

Concrete compressive strength (MPa)

ACI 318-14AASHTO

fib 2010This study

f cprime

fcprime

(a)

(τn)

max

0

005

01

015

02

025

03

20 40 60 80 100

ACI 318-14AASHTO

fib 2010This study

f cprime

Concrete compressive strength (MPa) fcprime

(b)

Figure 6 Comparisons of (τn)max in the code and proposed models (a) smooth construction joints (b) rough construction joints


0

1

2

3

4

5

0 3 6 9 12 15 18

(τn)

Exp

(τn)

Pre

σeq (=ρvf fy + σx)


(a)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(b)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(c)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(d)

Figure 7 Comparisons of the measured and predicted shear friction strengths (a) ACI 318-14 equation (b) AASHTO equation (c) b 2010equation (d) this study

Table 2 Statistical comparison of measured and predicted shear friction strengths

Interface type Statistical valueProposer

ACI 318-14 AASHTO b 2010 is study

Smooth construction joint

cm 315 180 173 099cs 223 087 076 039cv 071 048 044 039c5 NA 018 031 027c95 729 342 314 172


cm 216 141 299 100cs 113 049 135 028cv 052 035 045 028c5 036 063 084 055c95 395 220 514 144

Total

cm 246 156 256 101cs 164 068 133 032cv 067 044 052 032c5 NA 043 038 048c95 515 268 475 155


exhibiting the lowest scatter value of c according to thevariation of ρeq e values for cm and cs are 099 and 039respectively for smooth construction joints and 100 and 028respectively for rough construction joints e overall valuesof cm cs and cv for the complete dataset are 101 032 and032 respectively indicating smaller deviation in the pro-posed model than in the code equations when the shearfriction strength of construction joints is predicted Mean-while the proposed model exhibits more unconservativeresults than code equations especially for construction jointswith σeq exceeding 11MPa us the proposed model needsto be further adjusted to incorporate the strength reductionfactor considering the values of c95 and c5 to reduce theunconservative estimation of shear friction strength

42 Verication of Primary Inuencing Parameters eincurrenuence of the primary parameters on the shear frictionstrength of the rough construction joints is studied using the

proposed model and the AASHTO equation as well asappropriate experimental results available in the databaseTo examine whether the code provisions reasonably considerthe incurrenuencing parameters the AASHTO equation withlower cs and cv values than the ACI 318-14 and b 2010equations is selected In the parametric study one parameteris incrementally changed while the others are kept constantHowever because the test results in the database werecollected from dierent sources it would not be possible tostrictly achieve this so average values of the concrete andsteel reinforcement properties are used

Figure 8(a) shows the eect of fcprime on τn for roughconstruction joints without additionally applied normalstresses e prediction obtained using the AASHTOequation increases in proportion to fcprime up to a certain limitbeyond which it remains constant e AASHTO equationtends to underestimate the shear friction strength of roughconstruction joints for fcprime gt 50MPa e proposed modelshows a similar trend to the AASHTO equation yet it has

0

4

8

12

16

20

0 10 20 30 40 50 60 70 80

τ n (M

Pa)

f primec (MPa)

Exp (70 le ρvf fy (MPa) le 80)AASHTOThis study

(a)

τ n (M

Pa)

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10ρvf fy (MPa)

Exp (25 le (MPa) le 30)AASHTOThis study

fcprime

(b)

τ n (M

Pa)

0

4

8

12

16

20

ndash014 ndash009 ndash004 001 006 011

Exp (f primec = 27 MPa ρvf fy = 372 MPa)AASHTOThis study

σxf primec

(c)

Figure 8 Eects of dierent parameters on the shear friction strength of construction joints (a) compressive strength of concrete (fcprime)(b) clamping stress provided by transverse reinforcement (ρvffy) (c) ratio of applied normal stresses (σx) to fcprime


a higher threshold pointe threshold point of τn against fcprimevaries according to σeq e predictions of the proposedmodel exhibit a good correlation with the test results

A similar trend for the effect of ρvffy on τn forrough construction joints is observed in both equations(Figure 8(b)) indicating a bilinear relationship with athreshold point at a certain ρvffy is trend is also verifiedby the test data e proposed model exhibits slightly betteraccuracy than the AASHTO equation with respect to theexperimental data with ρvffy exceeding approximately6MPa

e effect of σxfcprime on τn for rough construction jointswith fcprime of 27MPa and ρvffy of 372MPa is shown inFigure 8(c) ere are no available data for rough con-struction joints subjected to an externally applied normalstress in compression as shown in Figure 1 Both equationsexhibit a very close relationship between σxfcprime and τnindicating that a further increase in τn is not expected whenσxfcprime is greater than a certain value For the rough con-struction joints subjected to an additional tensile stress thepredictions obtained using both equations agree well withthe test results

5 Conclusions

is study develops rational approach and model for shearfriction design of concrete interface with smooth and roughconstruction joints on the basis of the upper-bound theoremof concrete plasticity e reliability and limitations of codeequations and proposed models for determining the shearfriction strength (τn) of construction joints are examinedthrough comparisons with test data compiled from 207push-off specimens with interfaces between concrete thatwas cast at different times However this study classified thesurface roughness into two categories of smooth and roughconstruction joints Hence the code and proposed equationsneed to be further verified for construction joints treatedwith other impact methods e effects of various param-eters on the shear friction strength of construction joints arealso investigated using test results and prediction modelsincluding the AASHTO equation and a proposed one efollowing conclusions may be drawn according to the resultsobtained using the code equations and the proposed model

(1) e developed equation has a higher upper limit forτn than the other equations but yields a lower upperlimit for rough construction joints than the fib 2010equation for fcprime lt 50MPa e ACI 318-14 equationgives a lower upper limit for τn for rough con-struction joints than the other equations when fcprime islower than 90MPa

(2) e ACI 318-14 equation significantly un-derestimates the shear friction strength of reinforcedconstruction joints In addition larger scattering ofthe c value is obtained with the ACI 318-14 equationthan with the other equations resulting in very highstandard deviation (cs) values of 223 and 113 for theratios (c) in the cases of smooth and rough con-struction joints respectively

(3) Large scattering of the c value is also observed in theAASHTO equation although the determined valuesof the mean (cm) and cs are considerably lower thanthose obtained using the ACI 318-14 equation

(4) e predictions obtained using the fib 2010 equationfrequently underestimate the test results regardlessof the roughness of the interfacial surface epredictions yield lower values of cm and cs forsmooth construction joints than the previous codeequations e unconservative trend of the fib 2010equation for smooth construction joints is magnifiedwhen σeq is greater than approximately 11MPa

(5) e predictions of the proposed model agree wellwith the test results indicating the lowest scattervalue for c e values of cm and cs are 099 and 039respectively for smooth construction joints and 100and 028 respectively for rough construction jointsis results in overall values for cm and cs of 101 and032 respectively for the complete dataset

(6) According to the proposed model the values of thecohesion and coefficient of friction of concrete aredetermined as 011 (fcprime)

065 and 064 respectively forsmooth construction joints and 027 (fcprime)

065 and095 respectively for rough construction joints

Notation

Ac Section area of interfacial failure planeAvf Area of transverse reinforcement crossing

interfacial failure planecprime Cohesion of concrete along construction jointsc1 Factor to account for roughness of interfacial plane

in concrete cohesionf2max Compressive strength of cracked concrete under

biaxial stressfcprime Compressive strength of concretefco Reference value of the compressive strength of

concrete (10MPa)fte 5 fractile for tensile strength of concretefy Yield strength of transverse reinforcementfcd Design compressive strength of concretefyd Design tensile strength of reinforcementk1 Interaction factors for tensile force activated in the

reinforcement or the dowelsk2 Interaction factors for flexural resistance activated

in the reinforcement or the dowelsn Number of test dataVn Direct shear force at interfacial failure planeβc Factor for the strength of the compression strutc Ratio between test results and predictionsc5 5 fractile of c valuesc95 95 fractile of c valuescm Mean of c valuescs Standard deviation of c valuescv Coefficient of variation of c valuesδ Relative displacement about an instantaneous

centerε1 Transverse tensile strain along interfacial plane


θ Inclination of concrete strut relative to interfacialfailure plane

θs Inclination of transverse reinforcement relative tointerfacial failure plane

μ Coefficient of friction] Strength reduction factor]c Effectiveness factor for concrete compressive

strengthρc Unit weight of concreteρo Reference value for unit weight of concrete

(2300 kgm3)ρvf Transverse reinforcement ratioσx Axial stress normally applied to interfacial failure

planeσeq Equivalent normal compressive stress

( ρvffy + σx)τn Shear friction strength(τn)max Upper limit for shear friction strengthϕprime Friction angle of concrete along construction joint

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e author declares that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is work was supported by the National Research Foun-dation of Korea (NRF) grant funded by the Korea Gov-ernment (MSIP) (no NRF-2014R1A2A2A09054557)

References

[1] L Ahmed and A Ansell ldquoDirect shear strength of high-strength fibre concreterdquo Magazine of Concrete Researchvol 62 no 5 pp 379ndash390 2010

[2] P M D Santoa and E N B S Julio ldquoA state-of-the-art reviewon shear frictionrdquo Engineering Structures vol 45 no 1pp 435ndash448 2012

[3] K H Yang J I Sim J H Kang and A F Ashour ldquoShearcapacity of monolithic concrete joints without transversereinforcementrdquoMagazine of Concrete Research vol 64 no 9pp 767ndash779 2012

[4] K A Harries G Zeno and B Shahrooz ldquoToward an im-proved understanding of shear-friction behaviourrdquo ACIStructural Journal vol 109 no 6 pp 835ndash844 2012

[5] N Randl ldquoDesign recommendations for interface sheartransfer in fib model code 2010rdquo Structural Concrete vol 14no 3 pp 230ndash241 2013

[6] ACI Committee 318 Building Code Requirements for Struc-tural Concrete (ACI 318-14) and Commentary AmericanConcrete Institute Farmington Hills MI USA 2014

[7] AASHTO AASHTO LRFD Bridge Design SpecificationsAmerican Association of State Highway and TransportationOfficial Washington DC USA 7th edition 2014

[8] S J Kwon K H Yang Y H Hwang and A F Ashour ldquoShearfriction strength of monolithic concrete interfacesrdquoMagazineof Concrete Research vol 69 no 5 pp 230ndash244 2017

[9] Y H Hwang and K H Yang ldquoEffect of transverse re-inforcement on the shear friction capacity of concrete in-terfaces with construction jointrdquo Journal of Korea ConcreteInstitute vol 28 no 5 pp 555ndash562 2016

[10] R E Loov and A K Patnaik ldquoHorizontal shear strength ofcomposite concrete beams with a rough interfacerdquo PCIJournal vol 39 no 1 pp 48ndash69 1994

[11] M A Mansur T Vinayagam and K H Tan ldquoShear transferacross a crack in reinforced high-strength concreterdquo Journal ofMaterials Civil Engineering vol 20 no 4 pp 294ndash302 2008

[12] A F Shaikh ldquoProposed revisions to shear-friction pro-visionsrdquo PCI Journal vol 23 no 2 pp 12ndash21 1978

[13] J C Walraven J Frenay and A Pruijssers ldquoInfluence ofconcrete strength and load history on the shear friction ca-pacity of concrete membersrdquo PCI Journal vol 32 no 1pp 66ndash84 1987

[14] fib Model Code for Concrete Structures 2010 Special ActivityGroup 5 Federation Internationale de Beton LausanneSwitzerland 2013

[15] A H Mattock ldquoShear friction and high-strength concreterdquoACI Structural Journal vol 98 no 1 pp 50ndash59 2001

[16] P M D Santos and E N B S Julio ldquoA state-of-the-art reviewon shear-frictionrdquo Engineering Structures vol 45 pp 435ndash448 2012

[17] J Frenay ldquoShear transfer across a single crack in reinforcedconcrete under sustained loadingrdquo Report No 5-85-5 StevinLaboratory Department of Civil Engineering Delft Univer-sity of Technology Delft Netherlands 1985

[18] Y H Hwang ldquoEvaluation of concrete shear friction strengthconsidering its unit weightrdquo MS thesis Department ofArchitectural Engineering Kyonggi University Suwon SouthKorea 2016

[19] L F Kahn and A D Mitchell ldquoShear friction tests with high-strength concreterdquo ACI Structural Journal vol 99 no 1pp 98ndash103 2002

[20] A H Mattock ldquoShear transfer under monotonic loadinga cross an interface between concrete cast at different timesrdquoReport No SM76-3 University of Washington WashingtonDC USA 1976

[21] A H Mattock L Johal and H C Chow ldquoShear transfer inreinforced concrete with moment or tension acting across theshear planerdquo PCI Journal vol 20 no 4 pp 76ndash93 1975

[22] A Pruijssers and L G Liqui ldquoShear transfer across a crack inconcrete subjected to repeated loadingrdquo Report No 5-85-12Stevin Laboratory Department of Civil Engineering DelftUniversity of Technology Delft Netherlands 1985

[23] J C Walraven and J Stroband ldquoShear friction in high-strength concreterdquo ACI Structural Journal vol 149 no 17pp 311ndash330 1994

[24] E N B S Julio D Dias-da-Costa F A B Branco andJ M V Alfaiate ldquoAccuracy of design code expressions forestimating longitudinal shear strength of strengthening concreteoverlaysrdquo Engineering Structures vol 32 pp 2387ndash2393 2010

[25] J Xiao C Sun and D A Lange ldquoEffect of joint interfaceconditions on shear transfer behaviour of recycled aggregateconcreterdquo Construction and Building Materials vol 105pp 343ndash355 2016

[26] P M D Santos E N B S Julio and V D Silva ldquoCorrelationbetween concrete-to-concrete bond strength and the rough-ness of the substrate surfacerdquo Construction and BuildingMaterials vol 21 pp 1688ndash1695 2007


[27] K H Yang ldquoShear stressndashrelative slip relationship at concreteinterfacesrdquo Advances in Materials Science and Engineeringvol 2016 pp 1ndash9 2016

[28] M P Nielsen and L C Hoang Limit Analysis and ConcretePlasticity Prentice-Hall London UK 2011

[29] K K B Dahl ldquoConstruction joints in normal and highstrength concreterdquo Report No R-314 Department ofStructural Engineering Technical University of DenmarkKongens Lyngby Denmark 1994

[30] O C Choi S S Cho G S Hong I Y Chung and Y S ShinldquoInterfacial shear transfer characteristics of concrete jointsrdquoJournal of the Architectural Institute of Korea vol 10 no 8pp 89ndash96 1994

[31] fib ldquoStructural connections for precast concrete buildingsguide to good practicerdquo Federation Internationale de BetonLausanne Switzerland 2008

[32] A Belarbi and T T C Hsu ldquoConstitutive laws of softenedconcrete in biaxial tension-compressionrdquo ACI StructuralJournal vol 92 no 5 pp 562ndash573 1995

[33] K N Rahal ldquoShear-transfer strength of reinforced concreterdquoACI Structural Journal vol 107 no 4 pp 419ndash426 2010

[34] G H Givens and J A Hoeting Computational statisticsWiley New York NY USA 2005


CorrosionInternational Journal of

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High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in



ChemistryAdvances in


Advances inPhysical Chemistry


BioMed Research InternationalMaterials

Journal of


Na

nom

ate

ria

ls


Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

are empirically formulated using test data collected undera narrow range of influencing parameters do not sufficientlycapture the mechanical diversity of the shear friction ca-pacity of concrete interfaces with different concrete castingtimes

Concrete interfaces frequently have a construction jointbetween the precast element and the cast-in-place concreteor at the surface formed by placing one layer of concrete onan existing layer of hardened concrete When shear is ap-plied to construction joints the aggregate interlocking ac-tion and tensile resistance of concrete are insignificant alongthe interfacial plane Hence a lower shear friction resistanceis inevitable along the construction joints than along themonolithic interfaces with or without initial cracks How-ever many of the empirical equations [4 5 10ndash13] used toestimate shear friction strength have been proposed formonolithic interface based on different experimental pro-grams and the shear friction action associated with the trussmodel us test data and analytical approaches for con-struction joints are relatively insufficient Code provisions[6 7] specify that compared with that of monolithic in-terfaces the coefficient of friction (μ) must be approximately30 lower for smooth construction joints and approxi-mately 60 lower for rough construction joints Howeverthere is no explicit experimental or analytical validation ofthis requirement

e fib 2010 [14] provision specifies a 167 higher valueof μ for rough construction joints than for smooth con-struction joints Mattock [15] reported that the sheartransfer due to concrete cohesion is considerably reduced inconstruction joints compared with the shear transfer thatdevelops along monolithic interfaces in concrete Santos andJulio [16] pointed out that the roughness of the concretesubstrate should be considered in the design expressions inthe form of the coefficients of cohesion andor frictionbecause the bond strength of concrete-to-to interfaces issignificantly affected by their substrate state However thecohesion and frictional coefficient of concrete in con-struction joints are still insufficiently interpreted particu-larly for high-strength concrete with smooth surfacesMoreover the shear friction strength at overreinforcedconstruction joints needs to be appropriately limited toavoid concrete crushing failure before the transverse re-inforcement yield is reached Most of the code equations donot provide an explicit validation for the upper limit orsafety evaluationus the safety and rationality evaluationsof the code equations are quite unsatisfactory for rough andsmooth construction joints although such evaluations formonolithic interfaces have been extensively performed inprevious studies [3 11 15]

is study determines the cohesion and frictionalcoefficients of concrete at smooth and rough constructionjoints using a mechanical approach derived from theupper-bound theorem of concrete plasticity e upperlimits of the shear friction strength are derived from thestate of concrete crushing failure limit on the strut-and-tie action along the construction joints to avoid over-estimating the shear transfer capacity of a transversereinforcement with a high clamping force e reliability

and limitation of the code equations [6 7 14] used todetermine the shear friction strength of constructionjoints are also examined through comparisons with theexperimental data compiled from different sources ena parametric study is conducted using the proposedmodel the AASHTO equation and the results from thecollected database to evaluate the effect of different pa-rameters on the shear friction capacity of constructionjoints

2 Database of Push-Off Specimens withConstruction Joints

A total of 207 push-off specimens (including 133 roughconstruction joints and 74 smooth construction joints)compiled from different sources in the literature[4 5 11 17ndash25] were used to examine the reliability andsafety of the code equations and mechanical equations withregard to the effect of the different parameters on the shearfriction strength of the construction jointse distributionof the different parameters in the database is shown inFigure 1 Although the roughness parameters such asmaximum peak-to-valley height total roughness heightand maximum valley depth influence the cohesion alongthe concrete interface [26] most of the literature does notprovide the details on the substrate state of the interfaceus in the database an interface with only a steel-brushing treatment is classified as a smooth constructionjoint whereas an interface intentionally treated withsand blast with the full amplitude above approximately15mm is classified as a rough construction joint withreference to the surface roughness classification specified infib 2010 [14]

e test data available for smooth construction joints arerelatively limited All the specimens included in the databasewere reported to have failed in shear friction owing toa major crack along the interfacial plane Only a fewspecimens had no transverse reinforcement crossing theinterface Most of the specimens with smooth constructionjoints were made of concrete with a high compressivestrength (exceeding 55MPa) whereas the compressivestrength (fcprime) of the concrete specimens with rough con-struction joints ranged between 12MPa and 100MPa eclamping stress induced by the transverse reinforcementwhich can be expressed as ρvffy varied between 151MPaand 637MPa for smooth construction joints and between140MPa and 1229MPa for rough construction jointswhere ρvf and fy are the ratio and yield strength of thetransverse reinforcement respectively e inclination (θs)of the transverse reinforcement to the interfacial planevaried between 45deg and 90deg Most specimens with roughconstruction joints were tested with no normal stresses(σx) externally applied to the interface Six rough con-struction joints were tested under additional appliedtensile stresses ranging between minus004 fcprime and minus01 fcprimeFor the smooth construction joints subjected to an ad-ditional normal compressive stress σxfcprimewas fixed at 015Compressive and tensile stresses are denoted by thesymbols (+) and (minus) respectively





τn VnAc



(2a)


(2b)


3

4037

27 26

1

2428

21

0

10

20

30

40

50

60

12~20 20~40 40~60 60~80 80~100

Freq

uenc

y

(MPa)fcprime


(a)

0

17

2632

37

74 3

19

1

43

8

0

10

20

30

40

50

60

0 0~2 2~4 4~6 6~8 8~10 10~12 12~14

Freq

uenc

y

ρvf fy (MPa)


(b)

1 4 1

127

36 38

0

30

60

90

120

150


Freq

uenc

y

σx



compression


fcprime

(c)












+ k2ρvffydfcd

1113969

τn le βc]fcd

] 05530fcprime

1113888 1113889

13

lt 055

(4)








065 011 (fcprime)065 095 064
















( ) (8)



Rigidblock I

Rigidblock II



τ (=VAc)

τ (=VAc)

σx(=NxAc)

σx (=NxAc)

IC(XIC YIC)

ω

δα = ϕprime

θs

Y

X

cos αX IC

r =







fco( )

09 ρoρc( )

16 (10)



f2max 09






00

01

02

03

0 2 4 6 8 10 12

τ n

ρvf fy


f cprime


(τn)max

Nx



θ

Interficalplane(Ac)

vc f2max


0

05

1

15

2

25

3

35

4

45

10 20 30 40 50 60 70

cprime (M

Pa)


y = 011x065


y = 027x065

(MPa)fcprime






c5 cm minusR0cs

c95 cm + R0cs(13)




0

005

01

015

02

025

20 40 60 80 100

(τn)

max


ACI 318-14AASHTO

fib 2010This study

f cprime

fcprime

(a)

(τn)

max

0

005

01

015

02

025

03

20 40 60 80 100

ACI 318-14AASHTO

fib 2010This study

f cprime


(b)



0

1

2

3

4

5

0 3 6 9 12 15 18

(τn)

Exp

(τn)

Pre



(a)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(b)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(c)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(d)






cm 315 180 173 099cs 223 087 076 039cv 071 048 044 039c5 NA 018 031 027c95 729 342 314 172


cm 216 141 299 100cs 113 049 135 028cv 052 035 045 028c5 036 063 084 055c95 395 220 514 144

Total

cm 246 156 256 101cs 164 068 133 032cv 067 044 052 032c5 NA 043 038 048c95 515 268 475 155






0

4

8

12

16

20

0 10 20 30 40 50 60 70 80

τ n (M

Pa)

f primec (MPa)


(a)

τ n (M

Pa)

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10ρvf fy (MPa)


fcprime

(b)

τ n (M

Pa)

0

4

8

12

16

20



σxf primec

(c)






5 Conclusions










Notation

















Data Availability




Acknowledgments


References







































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







τn VnAc



(2a)


(2b)


3

4037

27 26

1

2428

21

0

10

20

30

40

50

60

12~20 20~40 40~60 60~80 80~100

Freq

uenc

y

(MPa)fcprime


(a)

0

17

2632

37

74 3

19

1

43

8

0

10

20

30

40

50

60

0 0~2 2~4 4~6 6~8 8~10 10~12 12~14

Freq

uenc

y

ρvf fy (MPa)


(b)

1 4 1

127

36 38

0

30

60

90

120

150


Freq

uenc

y

σx



compression


fcprime

(c)












+ k2ρvffydfcd

1113969

τn le βc]fcd

] 05530fcprime

1113888 1113889

13

lt 055

(4)








065 011 (fcprime)065 095 064
















( ) (8)



Rigidblock I

Rigidblock II



τ (=VAc)

τ (=VAc)

σx(=NxAc)

σx (=NxAc)

IC(XIC YIC)

ω

δα = ϕprime

θs

Y

X

cos αX IC

r =







fco( )

09 ρoρc( )

16 (10)



f2max 09






00

01

02

03

0 2 4 6 8 10 12

τ n

ρvf fy


f cprime


(τn)max

Nx



θ

Interficalplane(Ac)

vc f2max


0

05

1

15

2

25

3

35

4

45

10 20 30 40 50 60 70

cprime (M

Pa)


y = 011x065


y = 027x065

(MPa)fcprime






c5 cm minusR0cs

c95 cm + R0cs(13)




0

005

01

015

02

025

20 40 60 80 100

(τn)

max


ACI 318-14AASHTO

fib 2010This study

f cprime

fcprime

(a)

(τn)

max

0

005

01

015

02

025

03

20 40 60 80 100

ACI 318-14AASHTO

fib 2010This study

f cprime


(b)



0

1

2

3

4

5

0 3 6 9 12 15 18

(τn)

Exp

(τn)

Pre



(a)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(b)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(c)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(d)






cm 315 180 173 099cs 223 087 076 039cv 071 048 044 039c5 NA 018 031 027c95 729 342 314 172


cm 216 141 299 100cs 113 049 135 028cv 052 035 045 028c5 036 063 084 055c95 395 220 514 144

Total

cm 246 156 256 101cs 164 068 133 032cv 067 044 052 032c5 NA 043 038 048c95 515 268 475 155






0

4

8

12

16

20

0 10 20 30 40 50 60 70 80

τ n (M

Pa)

f primec (MPa)


(a)

τ n (M

Pa)

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10ρvf fy (MPa)


fcprime

(b)

τ n (M

Pa)

0

4

8

12

16

20



σxf primec

(c)






5 Conclusions










Notation

















Data Availability




Acknowledgments


References







































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls













+ k2ρvffydfcd

1113969

τn le βc]fcd

] 05530fcprime

1113888 1113889

13

lt 055

(4)








065 011 (fcprime)065 095 064
















( ) (8)



Rigidblock I

Rigidblock II



τ (=VAc)

τ (=VAc)

σx(=NxAc)

σx (=NxAc)

IC(XIC YIC)

ω

δα = ϕprime

θs

Y

X

cos αX IC

r =







fco( )

09 ρoρc( )

16 (10)



f2max 09






00

01

02

03

0 2 4 6 8 10 12

τ n

ρvf fy


f cprime


(τn)max

Nx



θ

Interficalplane(Ac)

vc f2max


0

05

1

15

2

25

3

35

4

45

10 20 30 40 50 60 70

cprime (M

Pa)


y = 011x065


y = 027x065

(MPa)fcprime






c5 cm minusR0cs

c95 cm + R0cs(13)




0

005

01

015

02

025

20 40 60 80 100

(τn)

max


ACI 318-14AASHTO

fib 2010This study

f cprime

fcprime

(a)

(τn)

max

0

005

01

015

02

025

03

20 40 60 80 100

ACI 318-14AASHTO

fib 2010This study

f cprime


(b)



0

1

2

3

4

5

0 3 6 9 12 15 18

(τn)

Exp

(τn)

Pre



(a)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(b)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(c)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(d)






cm 315 180 173 099cs 223 087 076 039cv 071 048 044 039c5 NA 018 031 027c95 729 342 314 172


cm 216 141 299 100cs 113 049 135 028cv 052 035 045 028c5 036 063 084 055c95 395 220 514 144

Total

cm 246 156 256 101cs 164 068 133 032cv 067 044 052 032c5 NA 043 038 048c95 515 268 475 155






0

4

8

12

16

20

0 10 20 30 40 50 60 70 80

τ n (M

Pa)

f primec (MPa)


(a)

τ n (M

Pa)

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10ρvf fy (MPa)


fcprime

(b)

τ n (M

Pa)

0

4

8

12

16

20



σxf primec

(c)






5 Conclusions










Notation

















Data Availability




Acknowledgments


References







































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls


















( ) (8)



Rigidblock I

Rigidblock II



τ (=VAc)

τ (=VAc)

σx(=NxAc)

σx (=NxAc)

IC(XIC YIC)

ω

δα = ϕprime

θs

Y

X

cos αX IC

r =







fco( )

09 ρoρc( )

16 (10)



f2max 09






00

01

02

03

0 2 4 6 8 10 12

τ n

ρvf fy


f cprime


(τn)max

Nx



θ

Interficalplane(Ac)

vc f2max


0

05

1

15

2

25

3

35

4

45

10 20 30 40 50 60 70

cprime (M

Pa)


y = 011x065


y = 027x065

(MPa)fcprime






c5 cm minusR0cs

c95 cm + R0cs(13)




0

005

01

015

02

025

20 40 60 80 100

(τn)

max


ACI 318-14AASHTO

fib 2010This study

f cprime

fcprime

(a)

(τn)

max

0

005

01

015

02

025

03

20 40 60 80 100

ACI 318-14AASHTO

fib 2010This study

f cprime


(b)



0

1

2

3

4

5

0 3 6 9 12 15 18

(τn)

Exp

(τn)

Pre



(a)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(b)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(c)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(d)






cm 315 180 173 099cs 223 087 076 039cv 071 048 044 039c5 NA 018 031 027c95 729 342 314 172


cm 216 141 299 100cs 113 049 135 028cv 052 035 045 028c5 036 063 084 055c95 395 220 514 144

Total

cm 246 156 256 101cs 164 068 133 032cv 067 044 052 032c5 NA 043 038 048c95 515 268 475 155






0

4

8

12

16

20

0 10 20 30 40 50 60 70 80

τ n (M

Pa)

f primec (MPa)


(a)

τ n (M

Pa)

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10ρvf fy (MPa)


fcprime

(b)

τ n (M

Pa)

0

4

8

12

16

20



σxf primec

(c)






5 Conclusions










Notation

















Data Availability




Acknowledgments


References







































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








fco( )

09 ρoρc( )

16 (10)



f2max 09






00

01

02

03

0 2 4 6 8 10 12

τ n

ρvf fy


f cprime


(τn)max

Nx



θ

Interficalplane(Ac)

vc f2max


0

05

1

15

2

25

3

35

4

45

10 20 30 40 50 60 70

cprime (M

Pa)


y = 011x065


y = 027x065

(MPa)fcprime






c5 cm minusR0cs

c95 cm + R0cs(13)




0

005

01

015

02

025

20 40 60 80 100

(τn)

max


ACI 318-14AASHTO

fib 2010This study

f cprime

fcprime

(a)

(τn)

max

0

005

01

015

02

025

03

20 40 60 80 100

ACI 318-14AASHTO

fib 2010This study

f cprime


(b)



0

1

2

3

4

5

0 3 6 9 12 15 18

(τn)

Exp

(τn)

Pre



(a)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(b)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(c)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(d)






cm 315 180 173 099cs 223 087 076 039cv 071 048 044 039c5 NA 018 031 027c95 729 342 314 172


cm 216 141 299 100cs 113 049 135 028cv 052 035 045 028c5 036 063 084 055c95 395 220 514 144

Total

cm 246 156 256 101cs 164 068 133 032cv 067 044 052 032c5 NA 043 038 048c95 515 268 475 155






0

4

8

12

16

20

0 10 20 30 40 50 60 70 80

τ n (M

Pa)

f primec (MPa)


(a)

τ n (M

Pa)

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10ρvf fy (MPa)


fcprime

(b)

τ n (M

Pa)

0

4

8

12

16

20



σxf primec

(c)






5 Conclusions










Notation

















Data Availability




Acknowledgments


References







































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







c5 cm minusR0cs

c95 cm + R0cs(13)




0

005

01

015

02

025

20 40 60 80 100

(τn)

max


ACI 318-14AASHTO

fib 2010This study

f cprime

fcprime

(a)

(τn)

max

0

005

01

015

02

025

03

20 40 60 80 100

ACI 318-14AASHTO

fib 2010This study

f cprime


(b)



0

1

2

3

4

5

0 3 6 9 12 15 18

(τn)

Exp

(τn)

Pre



(a)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(b)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(c)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(d)






cm 315 180 173 099cs 223 087 076 039cv 071 048 044 039c5 NA 018 031 027c95 729 342 314 172


cm 216 141 299 100cs 113 049 135 028cv 052 035 045 028c5 036 063 084 055c95 395 220 514 144

Total

cm 246 156 256 101cs 164 068 133 032cv 067 044 052 032c5 NA 043 038 048c95 515 268 475 155






0

4

8

12

16

20

0 10 20 30 40 50 60 70 80

τ n (M

Pa)

f primec (MPa)


(a)

τ n (M

Pa)

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10ρvf fy (MPa)


fcprime

(b)

τ n (M

Pa)

0

4

8

12

16

20



σxf primec

(c)






5 Conclusions










Notation

















Data Availability




Acknowledgments


References







































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




0

1

2

3

4

5

0 3 6 9 12 15 18

(τn)

Exp

(τn)

Pre



(a)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(b)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(c)

(τn)

Exp

(τn)

Pre


0

1

2

3

4

5

0 3 6 9 12 15 18


(d)






cm 315 180 173 099cs 223 087 076 039cv 071 048 044 039c5 NA 018 031 027c95 729 342 314 172


cm 216 141 299 100cs 113 049 135 028cv 052 035 045 028c5 036 063 084 055c95 395 220 514 144

Total

cm 246 156 256 101cs 164 068 133 032cv 067 044 052 032c5 NA 043 038 048c95 515 268 475 155






0

4

8

12

16

20

0 10 20 30 40 50 60 70 80

τ n (M

Pa)

f primec (MPa)


(a)

τ n (M

Pa)

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10ρvf fy (MPa)


fcprime

(b)

τ n (M

Pa)

0

4

8

12

16

20



σxf primec

(c)






5 Conclusions










Notation

















Data Availability




Acknowledgments


References







































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








0

4

8

12

16

20

0 10 20 30 40 50 60 70 80

τ n (M

Pa)

f primec (MPa)


(a)

τ n (M

Pa)

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10ρvf fy (MPa)


fcprime

(b)

τ n (M

Pa)

0

4

8

12

16

20



σxf primec

(c)






5 Conclusions










Notation

















Data Availability




Acknowledgments


References







































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







5 Conclusions










Notation

















Data Availability




Acknowledgments


References







































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls











Data Availability




Acknowledgments


References







































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls















Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




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