Research Article Shear Failure of RC Dapped-End Beams · 2019. 7. 31. · Reinforced concrete dapped-end beams (RC-DEBs) are mainly used for precast element construction. RC-DEBs

Research ArticleShear Failure of RC Dapped-End Beams

Muhammad Aswin1 Bashar S Mohammed1 M S Liew1 and Zubair Imam Syed2

1Department of Civil and Environmental Engineering Universiti Teknologi PETRONAS 32610 Bandar Seri IskandarPerak Darul Ridzuan Malaysia2Department of Civil Engineering Abu Dhabi University PO Box 59911 Abu Dhabi UAE

Correspondence should be addressed to Muhammad Aswin aswin tekniksipilyahoocom

Received 2 May 2015 Revised 6 August 2015 Accepted 6 August 2015

Academic Editor Joao M P Q Delgado

Copyright copy 2015 Muhammad Aswin et al 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

Reinforced concrete dapped-end beams (RC-DEBs) are mainly used for precast element construction RC-DEBs generally arerecessed at their end parts and supported by columns cantilevers inverted T-beams or corbels The geometric discontinuity ofdapped-end beams evokes a severe stress concentration at reentrant corners that may lead to shear failureTherefore stress analysisis required at the reentrant vicinity for design requirement of these beams Four large-scale RC-DEBs specimens were preparedcast and tested up to failureThree parameters were investigated amount of nib reinforcements main flexural reinforcements andconcrete type at the dapped-end area Finite element analysis using Vec2 was also conducted to predict the behavior of RC-DEBsIt has been found that highest stresses concentration factors occur at the reentrant corners and its vicinity By using engineeredcementitious composite (ECC) in the dapped-end area the failure load has increased by 519 while the increment in the failureload was 622 and 467 as the amount of nib reinforcement andmain flexural reinforcement increased respectively In additionVec2 analysis has been found to provide better accuracy for predicting the failure load of RC-DEBs compared to other analysisapproaches

1 Introduction

The reinforced concrete dapped-end beams (RC-DEBs) areusually used for precast elements construction of bridgegirders [1] RC-DEBs are recessed at end parts and supportedby columns cantilevers inverted T-beams or corbels Theadvantages of using these beams are firstly to increase thelateral stability of the structure elements at the support andsecondly to decrease the overall height of the precast concretefloor [2 3] However due to recessing of RC beam at endparts there are two main problems related to designing RC-DEBs Firstly if the nib section height is less than 045 timestotal height of the beam (undapped section) then the beamsexhibit a very small shear strength capacity According toWang et al [4] it was recommended that the nib heightshould not be less than 045 times total beam height whichis in agreement with the suggestion by Mattock and Chan[5] Secondly the geometric discontinuity leads to highstress concentrations at the reentrant corners If appropriatereinforcements are not prepared close to reentrant corner

diagonal cracks can appear rapidly and failure can occurimmediately or without early warning [6] Strut-and-TieModels are widely used in analysis of RC-DEBs and manymodels available in the codes of practice (such as ACIcode FIP Eurocode2 Canadian code) which can providesignificantly different results for the same specimen Thiscondition can be attributed to the use of different truss modelto capture the stress flow at the dapped-end area

Based on available experimental results the failure of RC-DEBs commonly occurs at the reentrant corners or dapped-end area The applied load is usually positioned at a distancein which shear span-depth ratio (119886V119889) is less than 2 where 119886Vis the shear span (distance from the load point to the support)and 119889 is the effective depth of RC-DEB However limitedresearch works have been carried out to determine the struc-tural behavior of the RC-DEBs Yang et al [7] investigatedthe shear strength of RC-DEBs using failure mechanism oryield line theorem and found that their proposed analysisprovides adequate predicted shear strength Lu et al [3]have experimentally investigated the shear strength capacity

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2015 Article ID 309135 11 pageshttpdxdoiorg1011552015309135

2 Advances in Materials Science and Engineering

of the RC-DEBs and they reported that the shear strengthof dapped-end beams increases with increase of concretecompressive strength and nib flexural reinforcement areaThe shear strength capacity of RC-DEBs also increases withdecrease of nominal shear span-depth ratio Mattock [8]demonstrated that dapped-end beams exhibit different shearcapacity with variation of the nib height and nominal shearspan-depth ratio while Peng [9] suggested that by usinga proper anchorage and adequate hanger reinforcementsRC-DEBs exhibit higher shear strength capacity and goodductility even after yielding of hanger reinforcements Wanget al [4] have showed that the shear strength capacity of RC-DEBs is enhanced by increasing the nib height nominal shearspan or amount of hanger reinforcements It was also notedthat by using diagonal reinforcement through the reentrantcorners shear strength capacity can be increased

Different strengthening techniques have been employedto enhance the shear strength capacity of RC-DEBs suchas the use of external steel angle unbounded inclined steelbolts steel plate jacketing and CFRP [1] It has been reportedthat all the strengthening methods are enhancing the shearstrength capacity of RC-DEBs however the unboundedinclined steel bolts method has yielded better results Inaddition experimental results reported by Huang and Nanni[6] andNagy-Gyorgy et al [10] showed that the shear strengthcapacity of the RC-DEBs can be significantly increased byusing CFRP strengthening Other approaches by focusingon different types of concrete to enhance the shear strengthcapacity of RC-DEBs have been investigated by Mohamedand Elliot [11] They investigated the shear capacity of RC-DEBs made of self-compacting steel fiber concrete andreported that the shear capacity has been enhanced whichcan lead to reduction in the amount of dapped-end reinforce-ments

Fukuyama et al [12] reported that a new ductile engi-neered cementitious composite (ECC) has been developedbased on themicromechanical principles byVC LiTheECCmixtures exhibit wide range of strain hardeningwith up to 7strain capacity and show steel-like behavior Further detailson ECC properties and behavior have been reported by otherresearchers [13ndash18]

Therefore the main objective of the research workreported in this paper is to predict the failure load and load-deformation response of RC-DEBs as well as to investi-gate the stress concentration at the dapped-end area Threeparameters were considered concrete type at the nib areaamount of nib reinforcement and amount of main flexuralreinforcement In this study the steel reinforcements require-ment of RC-DEBs were designed using the PCI DesignHandbook [19] whereas the failure load of RC-DEBs waspredicted using available codes Strut-and-Tie Model (STM)and finite element modeling (FEM) All these analysis resultswere compared to experimental results to gain the accurateanalysis

2 Experimental Works

For this study four large-scale RC-DEBs were prepared andcast in accordance with the requirements of PCI code Allbeams were tested up to failure

Table 1 Mix proportions

Ingredients NSC ECCCement (OPC) 100 100Fly ash mdash 120Water 057 032Fine aggregate 164 080Coarse aggregate 200 mdashSuperplasticizer mdash 1PVA fiber mdash 2

Ah = 21206018A = 21206018

Strain gage for steel reinforcement

21206018

Welded by usinga cross rebar

P

= 312060110BMFR

100-= 1206018St= 312060110NFR

= 31206018Ash

Figure 1 Reinforcement details

21 Test Specimens The overall length of each RC-DEBwas 1800mm The nib dimensions were 110mm length140mm height and 120mm width The undapped portiondimensions were 120mm width and 250mm height Thebeams were labeled as DEB-1 DEB-2 DEB-3 and DEB-4Normal strength concrete (NSC) was used in DEB-1 DEB-3 and DEB-4 While ECC mixture was used only in thedapped-end area of DEB-2 Only longitudinal reinforcementwas used (without shear reinforcement) for DEB-1 andDEB-2 Steel reinforcement for DEB-3 and DEB-4 was inaccordance with the requirements of PCI code Howevermain flexural reinforcement for DEB-4 was decreased by36 The mix proportions for normal concrete and ECC areshown in Table 1 Concrete cover of 15mm is provided for allreinforcement bars NSC and ECC compressive strength andthe reinforcement details are shown in Table 2 and Figure 1All main longitudinal reinforcements either in extended endor undepth portion of beams were welded at the ends of thebeams using cross steel bars to provide sufficient anchorage inaccordance with the requirements of ACI code [22] as shownin Figure 1

22 Instrumentations All beams were tested with nominalshear span (119886) of 102mm and nib depth (119889) of 112mm Theselected nominal shear span-depth ratio (119886119889) was 091 (lessthan 1) to fulfill the PCI requirements Four rosette straingages were attached to the surface of each beam to studythe principal stresses and stress concentration at points AB C and D as shown in Figure 2 Uniaxial strain gageswere attached to main flexural reinforcement nib flexuralreinforcement and hanger reinforcement as well as nib

Advances in Materials Science and Engineering 3

Table 2 The compressive strength and reinforcement details

Specimen 1198911015840

119888 Concrete type 119860ℎ

119860V HR 119891119910119904

NFR BMFR 119891119910

MPa mm mm mm MPa mm mm MPaDEB-1 27 NSC mdash mdash mdash 312060110 312060110 470DEB-2 27 79 NSC ECC mdash mdash mdash 312060110 312060110DEB-3 27 NSC 21206018 (U) 21206018 (St) 31206018 (St) 387 312060110 312060110DEB-4 27 NSC 21206018 (U) 21206018 (St) 31206018 (St) 312060110 31206018U = U bar (2 legs) St = stirrup (2 legs) 119860

ℎ= nib horizontal reinforcement 119860V = nib vertical reinforcement HR = 119860

119904ℎ= hanger reinforcement NFR = nib

flexure reinforcement BMFR = beam main flexure reinforcement 1198911015840119888= concrete compressive strength and 119891

119910= yield stress of reinforcement

Table 3 Experimental and analysis results

NumberFailure load (kN) Failure load ratio (analysis-experimental)

Test PC STM Vec2119875119906

119864119875119906

PC119875119906

STM119875119906

Vec2119875119906

PC119875119906

119864119875119906

STM119875119906

119864119875119906

Vec2119875119906

119864

DEB-1 6487 5625 9634 5800 087 149 089DEB-2 9856 8327 9634 9580 084 098 097DEB-3 10526 9667 9634 10780 092 092 102DEB-4 9516 9667 5071 10700 102 053 112

Mean (M) 091 098 100Standard deviation (S) 005 034 009

Coefficient of variation (CoV) 006 035 008

Figure 2 Layout of the rosette strain gages

vertical and horizontal reinforcement to evaluate the strainsvalues in these reinforcements as shown in Figure 1 LinearVariable Differential Transducer (LVDT) was positioned atthe soffit of the beam below the loading point to measure thevertical deflection The test setup of the beams is shown inFigures 3(a) and 3(b) To study the localized effect of shearfailure of the RC-DEBs the shear span-depth ratio (119886V119889) wastaken as 143 (less than 2)

3 Results and Discussion

31 Failure Load Thefailure loads for all RC-DEBs are shownin Table 3 Different analytical methods were used to predictthe failure load of RC-DEBs To explore the accuracy ofanalytical methods the analytical results were compared tothe experimental results Analytical results based on available

codes are labeled as 119875119862 Results from Strut-and-Tie Modelwere labeled as 119875STM and lastly results from finite elementmodeling by package Vector2 were grouped and labeled as119875Vec2 In first group (119875119862) DEB-1 was analyzed according to

ACI code [22] for singly reinforced concrete without stirrupsDEB-2 was analyzed according to RILEM provision for fiberreinforced concrete [20 21] and DEB-3 and DEB-4 wasanalyzed according to Section 563 of PCI code It is worthnoting that no single code is suitable for analyzing all thebeams therefore three codes were used in the analysis

Stress-strain relationship of steel fiber reinforced concretewith ordinary reinforcing bars based on RILEM provision isshown in Figure 4

According to Figure 4

119872119899= 119860119904119891119910(119889 minus

119886

2

) + 119891119891119905(ℎ minus 119909) 119887119911 (1)

where 119860119904and 119891

119910are area and yield strength of steel rein-

forcements respectively 119865119891119888119905

= 119891119891119905(ℎ minus 119909)119887 is tensile force of

fiber reinforced concrete 119891119891119905

= 033radic1198911015840

119888119905is tensile strength

of concrete [23] 1198911015840119888119905is compressive strength of concrete 119911 =

05(ℎ minus 119909) + 119909(1 minus 12057312) is internal lever arm ℎ is total

height of beam 119889 is effective depth 119909 is neutral axis positionmeasured from the top of beam 119888 is distance between centerof flexure rebar and bottom side of beam 120573

1is coefficient of

compressive stress block 119886 = 1205731119909 and 119887 is width of beam

Five potential failure modes of RC dapped-end beam aresuggested by PCI code as shown in Figure 5 These failure


(a)

55mm160mm

140mm

110mm

55mm55

Vu

LVDT1620mm1800mm

70mm

Pu

(b)

Figure 3 Experimental setup

w

x

dh

c

z

Ffcmax120576fc

Ffcth minus x

Fst120576fct

Figure 4 The stress-strain relationship RILEM [20 21]

120001d

120001d

2 4 3 5

hVu + Nu(h minus d)

Nu

1 A

Vu

120001p

a

Ah

120001d

As

23dmaxd

DH

15998400998400max

Hminus d

Hminus D

A998400sh

Ash

Figure 5 Potential failure modes [19]

modes are (1) flexure and axial tension in extended end(2) direct vertical shear between nib and undapped portion(3) diagonal tension initiating from reentrant corner (4)diagonal tension in the nib area and (5) diagonal tensionin undapped portion According to the empirical methodspecified in the PCI code the smallest value of strengthcapacity which was calculated is taken as the predicted failureload of RC dapped-end beams

(1) the flexure and axial tension in the nib

119860119904=

[119881119906(119886119889) + 119873

119906(ℎ119889)]

120593119891119910

(2)

where 119881119906= reaction force 120593 = strength reduction

factor = 075 and119873119906= 0 (no bearing pad)

(2) direct shear

119860119904=

(2119881119906)

(3120593119891119910120583119890)

+

119873119906

(120593119891119910)

120583119890=

(1000120593120582119887ℎ120583)

119881119906

(3)

where 120583119890le 34 120582 = concrete coefficient = 1 for normal

weight 120583 = shear-friction coefficient = 14 lowast 120582(3) hanger reinforcement for diagonal tension at reen-

trant corner

119860119904ℎ=

119881119906

(120593119891119910119901)

(4)

where 119891119910119901

= the yield stress of hanger reinforcement


P

30mm

80mm

30mm

110mm

55mm55mm

160mm

RA

B

AE

CAB

CAB

120572

(a) Single node of truss model for DEB-1 and DEB-2

Pu

Vu

30mm

80mm30mm

80mm30mm

55mm55mm

80mm30mm

410mm 400mm 700mm 70mm

(b) STM for DEB-3 and DEB-4 (based on FIP model)

Figure 6 Truss model

(4) diagonal tension in the nib

119860V =(119881119906120593 minus 2120582119887119889radic119891

1015840

119888)

(2119891119910V)

119891119910V

= the yield stress of vertical reinforcement in the nib

(5)

The analysis results for the group of 119875119862 using ACI codeRILEM provision and PCI code are compared as shown inTable 3 According to failure load comparison analysis usingPCI code were found to be more accurate than ACI code andRILEM provision in predicting the failure load of RC-DEBs

The common beams theory based on Bernoullirsquos theoremcan not be applied to nonlinear condition and nonprismaticmembers in RC structures such as pile caps deep beamscorbels and dapped-end beams STM provides an acceptableanalysis and design solution for the nonlinear conditionand disturbed regions subjected to high stress flow in RCstructures [24 25] Many codes facilitate analysis usingSTM provisions However for STM analysis in this studyEurocode2 [26] has been utilized

As suggested by Mattock trial and error has been con-ducted to select themost appropriate STMThe selected STMis consistent with the observed behavior of dapped-ends [8]For DEB-1 andDEB-2 single node trussmodel has been usedwhich consisted of one node-one strut-one tie at the support(CCT) as shown in Figure 6 For DEB-3 and DEB-4 trussmodel based on FIP provision has been used [27 28]

For DEB-1 and DEB-2 node119860 is CCT According to EC2obtained

120590119877119889max = 119896

2120592119891119888119889 (6)

where120590119877119889max ismaximumdesign stress of RCbeam 119896

2=085

for CCT 120592 = 1 minus 119891119888119896250 119891

119888119889= 0567119891

119888119896 119891119888119896is characteristic

concrete compressive strength and 119891119888119889

is design concretecompressive strength

The analysis procedure is in accordance with the require-ments of EC2 For DEB-1 and DEB-2 the single node trussmodel can accommodate their condition in which each DEBhas no stirrup but only available nib flexure reinforcements(NFR) For DEB-3 and DEB-4 truss model established byFIP provision was used Structure analysis of this truss modelshowed that internal force of hanger reinforcement is almostequal to the reaction force This condition is in agreementwith Mattock [8] suggestion Results of analysis using STMare shown in Table 3

For DEB-1 by using STM the strength of strut is higherthan tie so the failure load is determined by strength oftie (9634 kN) Nib flexure reinforcements (tie) fail first Bycomparing to experimental result it can be seen that ACIcode yields better result than STM for DEB-1 (5625 kN) ForDEB-2 by using STM the failure load was also determinedby strength of tie (9634 kN) Meanwhile by using RILEMprovision the failure load was 8357 kN so STM analysisprovides better result than RILEM provision For DEB-3 andDEB-4 as shown in Table 3 it can be seen that analysis resultsby using PCI code provide better results compared to STManalysis ACI code and RILEM provision

Based on experimental results and by comparing tocontrol beam (DEB-1) it had been found that the failureload increased by 5193 by using engineered cementitiouscomposite (ECC) in the dapped-end area and the failureload increased by 6226 and 4669 as the amount of nibreinforcement and main flexural reinforcement increasedrespectively

The FEM analysis in this study was carried out by usingVec2 Each model uses a total of 687 elements which consistof rectangular element of 220 triangular element of 343 andtruss element of 124 with total nodes of 452 For the analysisrequirement Vec2 uses elastic modulus of 286 KNmm2 and22KNmm2 for NSC and ECC respectively Poissonrsquos ratiovalue of 015 and other parameters were used in accordancewith the test specimen data Analysis results are presented inTable 3


Failure load comparison

PCSTM

Vec2Linear (LINEAR)

0

20

40

60

80

100

120

140

Failu

re lo

ad a

naly

sis (k

N)

20 40 60 80 100 120 1400Test result (kN)

Figure 7 Dissemination of failure load values for experimental andanalysis results

As shown in Table 3 and Figure 7 Vector2 analysis yieldsmore accurate results than other methods as the finiteelement model in Vec2 can simulate the behavior of theRC-DEBs more realistically All parameters related to thetest specimen used were facilitated in Vec2 which involvesconcrete steel reinforcements the steel reinforcement con-figuration section size of the test specimen applied load andsupport position and so forth Based on input data Vec2 hadsimulated all actual condition of the test specimens

32 Stress Concentration The intensity of a stress concentra-tion is usually expressed by the ratio of the maximum stressto the nominal stress called the stress concentration factor 119896

119896 =

1205901

120590nom (7)

where 120590nom = 80 119875119906119860119888119904and 119860

119888119904is vertical shear plane

area of dapped-end (same direction with reaction force)Figure 8 shows Mohrrsquos circle 120590

1denotes maximum principal

stress and 1205902represents the minimum principal stress The

procedure on calculation of principal stresses is referred toGere and Timoshenko [29]

Themaximum principal stresses and stress concentrationfactor are shown in Table 4 and Figure 9 It is worth notingthat the calculation is based on strain readings at 80 ofthe failure load to avoid any missing data due to damage ofstrain gage suggested byMohammed et al [30] FromTable 4and Figure 9 it can be observed that stress concentrationfactor for DEB-1 is higher than other beams and also stressconcentration at point C is higher than other points of allbeams DEB-1 has the lowest failure load compared to otherbeams Meantime stress concentration factor for DEB-3 issmaller than other beams and its stress concentration atpoint C is lower than other points of all beams DEB-3 hasthe highest failure load compared to other beams Theseobservations presented that the value of stress concentration

1205901120590y

S2

D998400

1205902

120590x1

120590x1

120590x120591x1y1

120591x1y1P2

minus120591xy

S1

P1

120591xy

120590ave = (120590x + 120590y)2 (120590x minus 120590y)2

O

120579 = 90∘)B(

120579 = 120579)D(

120579 = 0∘)A(

Figure 8 Mohrrsquos circle

DEB-1 DEB-2 DEB-3 DEB-4Rosette strain gage

A

B

C

D

020406080

100120140160

Stre

ss co

ncen

trat

ion

fact

or

087

043

022

048

138

31

855

5

796

2 916

6

59 139

07 157

668

6

285

6

222

4

334

2

Figure 9 Stress concentration factor of RC-DEBs

factor can indicate the failure load capacity of RC-DEBsThe highest stress concentration was found to occur at thereentrant corners

33 The Failure Mode and Crack Pattern The existence ofrecess (geometric discontinuity) in the end part of RC-DEBevokes the load path flow and raises the stress concentrationat the vicinity of the reentrant corners leading to initiatecracks According to experimental result it showed that thefirst crack appears at the reentrant corner for all RC-DEBs Asthe applied load increased the principal tensile (maximum)stresses increased and the crack width also increased untilfinal failure It clearly indicates that the reentrant corner isthe most susceptible to fail due to the applied load comparedto another location of dapped-end area Reentrant corner isthe weakest point of RC-DEBs This failure basically causedby the first crack initially propagates faster from the cornerof the recess As shown in (8) the strength capacity (momentcapacity) of the nib is reduced due to the recessing in whichthe nib height is reduced and also the rigiditymodulus (119864119868) of


Table 4 The principal stresses and stress concentration factor at each RC-DEB (for all types of strain gages)

DEB Strain gage 80 of 119875119906

119860119888119904

120590nom 1205902

1205901(120590max) 119896

119894=

KN mm2 MPa MPa MPa 1205901120590nom

DEB-1

A 5178 16800 308 (582) 267 087B 5178 16800 308 (14762) 20608 6686C 5178 16800 308 (19367) 42629 13831D 5178 16800 308 (1288) 1817 590

DEB-2

A 7947 16800 473 (526) 203 043B 7947 16800 473 (9822) 13511 2856C 7947 16800 473 (17114) 40470 8555D 7947 16800 473 (468) 657 139

DEB-3

A 8407 16800 500 (267) 112 022B 8407 16800 500 (7930) 11129 2224C 8407 16800 500 (19708) 39842 7962D 8407 16800 500 (064) 352 070

DEB-4

A 7617 16800 453 (517) 217 048B 7617 16800 453 (9586) 15154 3342C 7617 16800 453 (16055) 41556 9166D 7617 16800 453 (214) 712 157

DEB-1

(a)

DEB-2

(b)

DEB-3

(c)

DEB-4

(d)

Figure 10 Failure mode and crack pattern of test specimens


Table 5 The deformation ratio between experimental and Vec2 analysis results

SpecimenExperimental Vector2 Vec2Exp

120575119864

max 120575119864

rupt 120575119881

max 120575119881

rupt 120575119881

max120575119864

max 120575119881

rupt120575119864

rupt

mm mm mm mm mdash mdashDEB-1 154 183 149 228 10 12DEB-2 187 326 167 329 09 10DEB-3 182 296 181 344 10 12DEB-4 176 265 208 351 12 13

Mean 10 12120575max = deflection of RC-DEB at maximum load condition 120575rupt = deflection of RC-DEB at rupture condition

DEB-1 DEB-2

DEB-3 DEB-4

(a) Stress flow

(b) Shear failure mode and crack pattern (b) Shear failure mode and crack pattern

(a) Stress flow

(b) Shear failure mode and crack pattern

(a) Stress flow (a) Stress flow


Figure 11 The high stress flow and crack pattern based on Vec2 analysis

the nib between the reentrant corner and support is reducedas well [29]

119872 = minus119864119868

1198892

119910

1198892

119909

(8)

where119872 = nominal moment capacity 119864 = elastic modulus 119868= inertia moment and 119889

2

1199101198892

119909= the second-order differential

of deflectionExperimental results by Mohammed et al [31] also

demonstrated that presence of discontinuity leads to highstress concentrations at the corners of the opening which


Load-deflection curve

DEB-1 (Vector2)DEB-1 (Exp)

0

20

40

60

80

100

120

Load

(kN

)

10 20 30 40 500Deflection (mm)

(a) DEB-1



0

20

40

60

80

100

120

Load

(kN

)


(b) DEB-2

0

20

40

60

80

100

120

Load

(kN

)




(c) DEB-3

0

20

40

60

80

100

120Lo

ad (k

N)




(d) DEB-4

Figure 12 The load-deformation relationship

initiates the cracks and leads to final failure Mansur and Tan[32] stated that plastic hinges (yielding) also can occur at theregion near the geometric discontinuity and it may cause thefailure at this area

Figure 10 shows the crack patterns of the tested beamsUnlike DEB-2 the bonding between concrete and steel rein-forcements was weaker so that the shear crack propagatingalong the nib flexure reinforcement for DEB-1 ECC hasthe strong bonding with the steel reinforcement so thecrack propagation was not along the side of nib flexurereinforcements but the cracks were propagating toward theloading point as shown in Figure 10 The tailoring of ECC(mechanical interactions between the fibers matrix andinterface) can provide high performance of ECC even if thecracks width was wider Therefore ECC enhances strengthcapacity and ductility of RC-DEBs For comparison FEMVec2 analysis which includes high stress flow and crack

pattern ofDEBmodels can be seen in Figure 11 Generally thehigh stress flow and failure of RC-DEBs occur at the reentrantcorners

34 Load-Deformation Relationship Comparison of load-deformation relationship between experimental and Vec2analysis results was shown in Figure 12 and Table 5The Vec2analysis results are in good agreement with experimentalresults for all RC-DEBs The mean value of the deformationratio at maximum and rupture condition also present a goodaccuracy where the ratio is close to 1 To obtain similarstructural behavior of test specimen Vec2 facilitates theappropriate model which involves concrete models rein-forcement models and bond models The concrete modelscover compression prepeak and postpeak response com-pression softening tension stiffening and softening tensionsplitting confined strength crack and so forth whereas


the reinforcement models cover hysteretic response dowelaction and buckling All these conditions had supportedVec2 for providing better accuracy of results than otheranalyses

For requirement of tension stiffening model in this Vec2analysis uses modified Bentz 2003 [23] Modified Bentzmodel proposes a tension stiffening formulation that involvesthe bond characteristics of the steel reinforcement providedthat the effect of tension stiffening relies upon dowel actionafter concrete crackedThe Vec2 models basically formulatedfor sectional analysis of reinforced concrete elements havebeen adapted by Vecchio andWong [23] to consider for two-dimensional stress conditions and disposition of smearedand discrete reinforcement All these conditions had sup-ported Vec2 to provide better accuracy in predicting load-deformation than other analyses

According to experimental results and by comparing tocontrol beam (DEB-1) it had been also found that the failuredeflection enhanced by 7814 by using ECC in the dapped-end area and the failure deflection enhanced by 6175and 4481 as the amount of nib reinforcement and mainflexural reinforcement increased respectively DEB-2 (thebeam that uses ECC at the nib area) yields larger deflectioncapacity (326mm) than other beams Moreover the failureload capacity of DEB-2 increased by 5193 compared toDEB-1 So ECC provides better enhancement for strengthcapacity and ductility of RC-DEBs

4 Conclusion

The following conclusions can be made from this study(1) Vec2 analysis provides better accuracy for predicting

the failure load of RC-DEBs compared to otheranalysis approaches

(2) The largest principal stress and the highest stress con-centration factor of RC-DEBs occur at the reentrantcorner and its vicinity which potentially may indicatethat the dominant cracks and failure occur at thereentrant corner of dapped-end

(3) RC-DEBs which have the largest value of princi-pal stress and stress concentration factor were theweakest as well as providing the lowest failure loadcapacity RC-DEBs which have the smallest value ofprincipal stress and stress concentration factor werethe strongest as well as providing the highest failureload capacity

(4) Vec2 analysis results are in good agreement withthe experimental results in predicting the load-deformation response of the RC-DEBs

(5) Using ductile engineered cementitious composite(ECC) at the dapped-end area of the beams willincrease the strength capacity and plastic deforma-tion

(6) Reinforced dapped-end beams made of normal con-crete usually fail in shear at the nib area Howeverincreasing the reinforcement ratio will enhance thestrength capacity of these beams

Conflict of Interests

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

Acknowledgments

The authors would like to thank the Ministry of Education(MOE) ofMalaysia and Universiti Teknologi PETRONAS forgranting the project under codes FRGS 2013-2 and STIRF382012 respectively

References

[1] S E-D F Taher ldquoStrengthening of critically designed girderswith dapped-endsrdquo Structures and Buildings vol 158 no 2 pp141ndash152 2005

[2] R Herzinger Stud reinforcements in dapped-ends of concretebeams [PhD thesis] University of Calgary Calgary Canada2008

[3] W-Y Lu I-J Lin S-J Hwang and Y-H Lin ldquoShear strengthof high-strength concrete dapped-end beamsrdquo Journal of theChinese Institute of Engineers vol 26 no 5 pp 671ndash680 2003

[4] Q Wang Z Guo and P C J Hoogenboom ldquoExperimentalinvestigation on the shear capacity of RCdapped end beams anddesign recommendationsrdquo Structural Engineering and Mechan-ics vol 21 no 2 pp 221ndash235 2005

[5] A H Mattock and T C Chan ldquoDesign and behavior of dappedend beamsrdquo PCI Journal vol 24 no 6 pp 28ndash45 1979

[6] P-C Huang and A Nanni ldquoDapped-end strengthening offull-scale prestressed double tee beams with FRP compositesrdquoAdvances in Structural Engineering vol 9 no 2 pp 293ndash3082006

[7] K-H Yang A F Ashour and J-K Lee ldquoShear strength ofRC dapped-end beams using mechanism analysisrdquoMagazine ofConcrete Research vol 63 no 2 pp 81ndash97 2010

[8] A H Mattock Strut-and-Tie Models for Dapped-End BeamsConcrete International 2012

[9] T Peng Influence of detailing on response of dapped-end beams[MS thesis] McGill University Montreal Canada 2009

[10] T Nagy-Gyorgy G Sas A C Daescu J A O Barros and VStoian ldquoExperimental and numerical assessment of the effec-tiveness of FRP-based strengthening configurations for dapped-end RC beamsrdquo Engineering Structures vol 44 pp 291ndash3032012

[11] R N Mohamed and K S Elliot Shear Strength of Short RecessPrecast Dapped-End Beams Made of Steel Fiber Self CompactingConcrete Singapore Concrete Institute Singapore 2008

[12] H Fukuyama Y Sato V C Li Y Matsuzaki and H MihashildquoDuctile engineered cementitious composite elements for seis-mic structural applicationrdquo in Proceedings of the World Confer-ence on Earthquake Engineering (WCEE rsquo00) 2000

[13] V C Li and T Kanda ldquoEngineered cementitious composites forstructural applicationsrdquo Journal of Materials in Civil Engineer-ing vol 10 no 2 pp 66ndash69 1998

[14] M D Lepech and V C Li ldquoLarge-scale processing of engi-neered cementitious compositesrdquo ACI Materials Journal vol105 no 4 pp 358ndash366 2008

[15] E-H Yang and V C Li ldquoTailoring engineered cementi-tious composites for impact resistancerdquo Cement and ConcreteResearch vol 42 no 8 pp 1066ndash1071 2012


[16] H M E-D Afefy and M H Mahmoud ldquoStructural perfor-mance of RC slabs provided by pre-cast ECC strips in tensioncover zonerdquo Construction and Building Materials vol 65 pp103ndash113 2014

[17] J Zhang Z Wang X Ju and Z Shi ldquoSimulation of flexuralperformance of layered ECC-concrete composite beam withfracturemechanicsmodelrdquoEngineering FractureMechanics vol131 pp 419ndash438 2014

[18] S Qudah and M Maalej ldquoApplication of Engineered Cementi-tious Composites (ECC) in interior beamndashcolumn connectionsfor enhanced seismic resistancerdquo Engineering Structures vol 69pp 235ndash245 2014

[19] PCI Design Handbook PrecastPrestressed Concrete Institute7th edition 2010

[20] A Abid and K B Franzen Design of fiber reinforced concretebeams and slabs [MS thesis] Chalmers University of Technol-ogy Gothenburg Sweden 2011

[21] RILEM TC 162-TDF ldquoTest and design methods for steel fibrereinforced concreterdquo Materials and Structures vol 36 no 262pp 560ndash567 2000

[22] ACI ldquoBuilding code requirements for structural concrete andcommentaryrdquo ACI 318-08 2008

[23] F J Vecchio and P S Wong Vector2 amp Formworks UserrsquosManual University of Toronto Toronto Canada 2002

[24] A Shah E Haq and S Khan ldquoAnalysis and design of disturbedregions in concrete structuresrdquo Procedia Engineering vol 14 pp3317ndash3324 2011

[25] J Schlaich and K Schafer ldquoDesign and detailing of structuralconcrete using strut and tie modelsrdquo The Structural Engineervol 69 no 6 pp 113ndash125 1991

[26] Eurocode 2 Design of Concrete Structures Part 1-1 General Rulesand Rules for Buildings 2004

[27] J Y Moreno-Martınez and R Meli ldquoExperimental study on thestructural behavior of concrete dapped-end beamsrdquoEngineeringStructures vol 75 pp 152ndash163 2014

[28] FIP Recommendations Practical Design of Structural ConcreteCEB FIP 1999

[29] J M Gere and S P Timoshenko Mechanics of MaterialsStanley Thornes (Publishers) 4th edition 1999

[30] B S Mohammed L W Ean and M A Malek ldquoOne way RCwall panels with openings strengthened with CFRPrdquo Construc-tion and Building Materials vol 40 pp 575ndash583 2013

[31] B SMohammed B H A Bakar andK K Choong ldquoBehaviourof axially loaded fired-claymasonry panels with openingsrdquoTheIndian Concrete Journal vol 83 no 4 pp 9ndash16 2009

[32] M A Mansur and K H Tan Concrete Beams with OpeningsmdashAnalysis and Design CRC Press Boca Raton Fla USA 1999

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


of the RC-DEBs and they reported that the shear strengthof dapped-end beams increases with increase of concretecompressive strength and nib flexural reinforcement areaThe shear strength capacity of RC-DEBs also increases withdecrease of nominal shear span-depth ratio Mattock [8]demonstrated that dapped-end beams exhibit different shearcapacity with variation of the nib height and nominal shearspan-depth ratio while Peng [9] suggested that by usinga proper anchorage and adequate hanger reinforcementsRC-DEBs exhibit higher shear strength capacity and goodductility even after yielding of hanger reinforcements Wanget al [4] have showed that the shear strength capacity of RC-DEBs is enhanced by increasing the nib height nominal shearspan or amount of hanger reinforcements It was also notedthat by using diagonal reinforcement through the reentrantcorners shear strength capacity can be increased

Different strengthening techniques have been employedto enhance the shear strength capacity of RC-DEBs suchas the use of external steel angle unbounded inclined steelbolts steel plate jacketing and CFRP [1] It has been reportedthat all the strengthening methods are enhancing the shearstrength capacity of RC-DEBs however the unboundedinclined steel bolts method has yielded better results Inaddition experimental results reported by Huang and Nanni[6] andNagy-Gyorgy et al [10] showed that the shear strengthcapacity of the RC-DEBs can be significantly increased byusing CFRP strengthening Other approaches by focusingon different types of concrete to enhance the shear strengthcapacity of RC-DEBs have been investigated by Mohamedand Elliot [11] They investigated the shear capacity of RC-DEBs made of self-compacting steel fiber concrete andreported that the shear capacity has been enhanced whichcan lead to reduction in the amount of dapped-end reinforce-ments

Fukuyama et al [12] reported that a new ductile engi-neered cementitious composite (ECC) has been developedbased on themicromechanical principles byVC LiTheECCmixtures exhibit wide range of strain hardeningwith up to 7strain capacity and show steel-like behavior Further detailson ECC properties and behavior have been reported by otherresearchers [13ndash18]

Therefore the main objective of the research workreported in this paper is to predict the failure load and load-deformation response of RC-DEBs as well as to investi-gate the stress concentration at the dapped-end area Threeparameters were considered concrete type at the nib areaamount of nib reinforcement and amount of main flexuralreinforcement In this study the steel reinforcements require-ment of RC-DEBs were designed using the PCI DesignHandbook [19] whereas the failure load of RC-DEBs waspredicted using available codes Strut-and-Tie Model (STM)and finite element modeling (FEM) All these analysis resultswere compared to experimental results to gain the accurateanalysis

2 Experimental Works

For this study four large-scale RC-DEBs were prepared andcast in accordance with the requirements of PCI code Allbeams were tested up to failure

Table 1 Mix proportions

Ingredients NSC ECCCement (OPC) 100 100Fly ash mdash 120Water 057 032Fine aggregate 164 080Coarse aggregate 200 mdashSuperplasticizer mdash 1PVA fiber mdash 2

Ah = 21206018A = 21206018

Strain gage for steel reinforcement

21206018

Welded by usinga cross rebar

P

= 312060110BMFR

100-= 1206018St= 312060110NFR

= 31206018Ash

Figure 1 Reinforcement details

21 Test Specimens The overall length of each RC-DEBwas 1800mm The nib dimensions were 110mm length140mm height and 120mm width The undapped portiondimensions were 120mm width and 250mm height Thebeams were labeled as DEB-1 DEB-2 DEB-3 and DEB-4Normal strength concrete (NSC) was used in DEB-1 DEB-3 and DEB-4 While ECC mixture was used only in thedapped-end area of DEB-2 Only longitudinal reinforcementwas used (without shear reinforcement) for DEB-1 andDEB-2 Steel reinforcement for DEB-3 and DEB-4 was inaccordance with the requirements of PCI code Howevermain flexural reinforcement for DEB-4 was decreased by36 The mix proportions for normal concrete and ECC areshown in Table 1 Concrete cover of 15mm is provided for allreinforcement bars NSC and ECC compressive strength andthe reinforcement details are shown in Table 2 and Figure 1All main longitudinal reinforcements either in extended endor undepth portion of beams were welded at the ends of thebeams using cross steel bars to provide sufficient anchorage inaccordance with the requirements of ACI code [22] as shownin Figure 1

22 Instrumentations All beams were tested with nominalshear span (119886) of 102mm and nib depth (119889) of 112mm Theselected nominal shear span-depth ratio (119886119889) was 091 (lessthan 1) to fulfill the PCI requirements Four rosette straingages were attached to the surface of each beam to studythe principal stresses and stress concentration at points AB C and D as shown in Figure 2 Uniaxial strain gageswere attached to main flexural reinforcement nib flexuralreinforcement and hanger reinforcement as well as nib



Specimen 1198911015840


119860V HR 119891119910119904

NFR BMFR 119891119910









119864119875119906

PC119875119906

STM119875119906

Vec2119875119906

PC119875119906

119864119875119906

STM119875119906

119864119875119906

Vec2119875119906

119864

DEB-1 6487 5625 9634 5800 087 149 089DEB-2 9856 8327 9634 9580 084 098 097DEB-3 10526 9667 9634 10780 092 092 102DEB-4 9516 9667 5071 10700 102 053 112











119872119899= 119860119904119891119910(119889 minus

119886

2

) + 119891119891119905(ℎ minus 119909) 119887119911 (1)

where 119860119904and 119891





= 033radic1198911015840





1is coefficient of




(a)

55mm160mm

140mm

110mm

55mm55

Vu

LVDT1620mm1800mm

70mm

Pu

(b)


w

x

dh

c

z

Ffcmax120576fc

Ffcth minus x

Fst120576fct


120001d

120001d

2 4 3 5

hVu + Nu(h minus d)

Nu

1 A

Vu

120001p

a

Ah

120001d

As

23dmaxd

DH

15998400998400max

Hminus d

Hminus D

A998400sh

Ash




119860119904=

[119881119906(119886119889) + 119873

119906(ℎ119889)]

120593119891119910

(2)



(2) direct shear

119860119904=

(2119881119906)

(3120593119891119910120583119890)

+

119873119906

(120593119891119910)

120583119890=

(1000120593120582119887ℎ120583)

119881119906

(3)



trant corner

119860119904ℎ=

119881119906

(120593119891119910119901)

(4)

where 119891119910119901



P

30mm

80mm

30mm

110mm

55mm55mm

160mm

RA

B

AE

CAB

CAB

120572


Pu

Vu

30mm

80mm30mm

80mm30mm

55mm55mm

80mm30mm

410mm 400mm 700mm 70mm




119860V =(119881119906120593 minus 2120582119887119889radic119891

1015840

119888)

(2119891119910V)

119891119910V


(5)





120590119877119889max = 119896

2120592119891119888119889 (6)


2=085

for CCT 120592 = 1 minus 119891119888119896250 119891

119888119889= 0567119891










PCSTM

Vec2Linear (LINEAR)

0

20

40

60

80

100

120

140

Failu

re lo

ad a

naly

sis (k

N)

20 40 60 80 100 120 1400Test result (kN)




119896 =

1205901

120590nom (7)

where 120590nom = 80 119875119906119860119888119904and 119860







1205901120590y

S2

D998400

1205902

120590x1

120590x1

120590x120591x1y1

120591x1y1P2

minus120591xy

S1

P1

120591xy

120590ave = (120590x + 120590y)2 (120590x minus 120590y)2

O

120579 = 90∘)B(

120579 = 120579)D(

120579 = 0∘)A(



A

B

C

D

020406080

100120140160

Stre

ss co

ncen

trat

ion

fact

or

087

043

022

048

138

31

855

5

796

2 916

6

59 139

07 157

668

6

285

6

222

4

334

2







119860119888119904

120590nom 1205902

1205901(120590max) 119896

119894=


DEB-1

A 5178 16800 308 (582) 267 087B 5178 16800 308 (14762) 20608 6686C 5178 16800 308 (19367) 42629 13831D 5178 16800 308 (1288) 1817 590

DEB-2

A 7947 16800 473 (526) 203 043B 7947 16800 473 (9822) 13511 2856C 7947 16800 473 (17114) 40470 8555D 7947 16800 473 (468) 657 139

DEB-3

A 8407 16800 500 (267) 112 022B 8407 16800 500 (7930) 11129 2224C 8407 16800 500 (19708) 39842 7962D 8407 16800 500 (064) 352 070

DEB-4

A 7617 16800 453 (517) 217 048B 7617 16800 453 (9586) 15154 3342C 7617 16800 453 (16055) 41556 9166D 7617 16800 453 (214) 712 157

DEB-1

(a)

DEB-2

(b)

DEB-3

(c)

DEB-4

(d)





120575119864

max 120575119864

rupt 120575119881

max 120575119881

rupt 120575119881

max120575119864

max 120575119881

rupt120575119864

rupt



DEB-1 DEB-2

DEB-3 DEB-4

(a) Stress flow


(a) Stress flow






119872 = minus119864119868

1198892

119910

1198892

119909

(8)


2

1199101198892







0

20

40

60

80

100

120

Load

(kN

)


(a) DEB-1



0

20

40

60

80

100

120

Load

(kN

)


(b) DEB-2

0

20

40

60

80

100

120

Load

(kN

)




(c) DEB-3

0

20

40

60

80

100

120Lo

ad (k

N)




(d) DEB-4










4 Conclusion










Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Specimen 1198911015840


119860V HR 119891119910119904

NFR BMFR 119891119910









119864119875119906

PC119875119906

STM119875119906

Vec2119875119906

PC119875119906

119864119875119906

STM119875119906

119864119875119906

Vec2119875119906

119864

DEB-1 6487 5625 9634 5800 087 149 089DEB-2 9856 8327 9634 9580 084 098 097DEB-3 10526 9667 9634 10780 092 092 102DEB-4 9516 9667 5071 10700 102 053 112











119872119899= 119860119904119891119910(119889 minus

119886

2

) + 119891119891119905(ℎ minus 119909) 119887119911 (1)

where 119860119904and 119891





= 033radic1198911015840





1is coefficient of




(a)

55mm160mm

140mm

110mm

55mm55

Vu

LVDT1620mm1800mm

70mm

Pu

(b)


w

x

dh

c

z

Ffcmax120576fc

Ffcth minus x

Fst120576fct


120001d

120001d

2 4 3 5

hVu + Nu(h minus d)

Nu

1 A

Vu

120001p

a

Ah

120001d

As

23dmaxd

DH

15998400998400max

Hminus d

Hminus D

A998400sh

Ash




119860119904=

[119881119906(119886119889) + 119873

119906(ℎ119889)]

120593119891119910

(2)



(2) direct shear

119860119904=

(2119881119906)

(3120593119891119910120583119890)

+

119873119906

(120593119891119910)

120583119890=

(1000120593120582119887ℎ120583)

119881119906

(3)



trant corner

119860119904ℎ=

119881119906

(120593119891119910119901)

(4)

where 119891119910119901



P

30mm

80mm

30mm

110mm

55mm55mm

160mm

RA

B

AE

CAB

CAB

120572


Pu

Vu

30mm

80mm30mm

80mm30mm

55mm55mm

80mm30mm

410mm 400mm 700mm 70mm




119860V =(119881119906120593 minus 2120582119887119889radic119891

1015840

119888)

(2119891119910V)

119891119910V


(5)





120590119877119889max = 119896

2120592119891119888119889 (6)


2=085

for CCT 120592 = 1 minus 119891119888119896250 119891

119888119889= 0567119891










PCSTM

Vec2Linear (LINEAR)

0

20

40

60

80

100

120

140

Failu

re lo

ad a

naly

sis (k

N)

20 40 60 80 100 120 1400Test result (kN)




119896 =

1205901

120590nom (7)

where 120590nom = 80 119875119906119860119888119904and 119860







1205901120590y

S2

D998400

1205902

120590x1

120590x1

120590x120591x1y1

120591x1y1P2

minus120591xy

S1

P1

120591xy

120590ave = (120590x + 120590y)2 (120590x minus 120590y)2

O

120579 = 90∘)B(

120579 = 120579)D(

120579 = 0∘)A(



A

B

C

D

020406080

100120140160

Stre

ss co

ncen

trat

ion

fact

or

087

043

022

048

138

31

855

5

796

2 916

6

59 139

07 157

668

6

285

6

222

4

334

2







119860119888119904

120590nom 1205902

1205901(120590max) 119896

119894=


DEB-1

A 5178 16800 308 (582) 267 087B 5178 16800 308 (14762) 20608 6686C 5178 16800 308 (19367) 42629 13831D 5178 16800 308 (1288) 1817 590

DEB-2

A 7947 16800 473 (526) 203 043B 7947 16800 473 (9822) 13511 2856C 7947 16800 473 (17114) 40470 8555D 7947 16800 473 (468) 657 139

DEB-3

A 8407 16800 500 (267) 112 022B 8407 16800 500 (7930) 11129 2224C 8407 16800 500 (19708) 39842 7962D 8407 16800 500 (064) 352 070

DEB-4

A 7617 16800 453 (517) 217 048B 7617 16800 453 (9586) 15154 3342C 7617 16800 453 (16055) 41556 9166D 7617 16800 453 (214) 712 157

DEB-1

(a)

DEB-2

(b)

DEB-3

(c)

DEB-4

(d)





120575119864

max 120575119864

rupt 120575119881

max 120575119881

rupt 120575119881

max120575119864

max 120575119881

rupt120575119864

rupt



DEB-1 DEB-2

DEB-3 DEB-4

(a) Stress flow


(a) Stress flow






119872 = minus119864119868

1198892

119910

1198892

119909

(8)


2

1199101198892







0

20

40

60

80

100

120

Load

(kN

)


(a) DEB-1



0

20

40

60

80

100

120

Load

(kN

)


(b) DEB-2

0

20

40

60

80

100

120

Load

(kN

)




(c) DEB-3

0

20

40

60

80

100

120Lo

ad (k

N)




(d) DEB-4










4 Conclusion










Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




(a)

55mm160mm

140mm

110mm

55mm55

Vu

LVDT1620mm1800mm

70mm

Pu

(b)


w

x

dh

c

z

Ffcmax120576fc

Ffcth minus x

Fst120576fct


120001d

120001d

2 4 3 5

hVu + Nu(h minus d)

Nu

1 A

Vu

120001p

a

Ah

120001d

As

23dmaxd

DH

15998400998400max

Hminus d

Hminus D

A998400sh

Ash




119860119904=

[119881119906(119886119889) + 119873

119906(ℎ119889)]

120593119891119910

(2)



(2) direct shear

119860119904=

(2119881119906)

(3120593119891119910120583119890)

+

119873119906

(120593119891119910)

120583119890=

(1000120593120582119887ℎ120583)

119881119906

(3)



trant corner

119860119904ℎ=

119881119906

(120593119891119910119901)

(4)

where 119891119910119901



P

30mm

80mm

30mm

110mm

55mm55mm

160mm

RA

B

AE

CAB

CAB

120572


Pu

Vu

30mm

80mm30mm

80mm30mm

55mm55mm

80mm30mm

410mm 400mm 700mm 70mm




119860V =(119881119906120593 minus 2120582119887119889radic119891

1015840

119888)

(2119891119910V)

119891119910V


(5)





120590119877119889max = 119896

2120592119891119888119889 (6)


2=085

for CCT 120592 = 1 minus 119891119888119896250 119891

119888119889= 0567119891










PCSTM

Vec2Linear (LINEAR)

0

20

40

60

80

100

120

140

Failu

re lo

ad a

naly

sis (k

N)

20 40 60 80 100 120 1400Test result (kN)




119896 =

1205901

120590nom (7)

where 120590nom = 80 119875119906119860119888119904and 119860







1205901120590y

S2

D998400

1205902

120590x1

120590x1

120590x120591x1y1

120591x1y1P2

minus120591xy

S1

P1

120591xy

120590ave = (120590x + 120590y)2 (120590x minus 120590y)2

O

120579 = 90∘)B(

120579 = 120579)D(

120579 = 0∘)A(



A

B

C

D

020406080

100120140160

Stre

ss co

ncen

trat

ion

fact

or

087

043

022

048

138

31

855

5

796

2 916

6

59 139

07 157

668

6

285

6

222

4

334

2







119860119888119904

120590nom 1205902

1205901(120590max) 119896

119894=


DEB-1

A 5178 16800 308 (582) 267 087B 5178 16800 308 (14762) 20608 6686C 5178 16800 308 (19367) 42629 13831D 5178 16800 308 (1288) 1817 590

DEB-2

A 7947 16800 473 (526) 203 043B 7947 16800 473 (9822) 13511 2856C 7947 16800 473 (17114) 40470 8555D 7947 16800 473 (468) 657 139

DEB-3

A 8407 16800 500 (267) 112 022B 8407 16800 500 (7930) 11129 2224C 8407 16800 500 (19708) 39842 7962D 8407 16800 500 (064) 352 070

DEB-4

A 7617 16800 453 (517) 217 048B 7617 16800 453 (9586) 15154 3342C 7617 16800 453 (16055) 41556 9166D 7617 16800 453 (214) 712 157

DEB-1

(a)

DEB-2

(b)

DEB-3

(c)

DEB-4

(d)





120575119864

max 120575119864

rupt 120575119881

max 120575119881

rupt 120575119881

max120575119864

max 120575119881

rupt120575119864

rupt



DEB-1 DEB-2

DEB-3 DEB-4

(a) Stress flow


(a) Stress flow






119872 = minus119864119868

1198892

119910

1198892

119909

(8)


2

1199101198892







0

20

40

60

80

100

120

Load

(kN

)


(a) DEB-1



0

20

40

60

80

100

120

Load

(kN

)


(b) DEB-2

0

20

40

60

80

100

120

Load

(kN

)




(c) DEB-3

0

20

40

60

80

100

120Lo

ad (k

N)




(d) DEB-4










4 Conclusion










Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




P

30mm

80mm

30mm

110mm

55mm55mm

160mm

RA

B

AE

CAB

CAB

120572


Pu

Vu

30mm

80mm30mm

80mm30mm

55mm55mm

80mm30mm

410mm 400mm 700mm 70mm




119860V =(119881119906120593 minus 2120582119887119889radic119891

1015840

119888)

(2119891119910V)

119891119910V


(5)





120590119877119889max = 119896

2120592119891119888119889 (6)


2=085

for CCT 120592 = 1 minus 119891119888119896250 119891

119888119889= 0567119891










PCSTM

Vec2Linear (LINEAR)

0

20

40

60

80

100

120

140

Failu

re lo

ad a

naly

sis (k

N)

20 40 60 80 100 120 1400Test result (kN)




119896 =

1205901

120590nom (7)

where 120590nom = 80 119875119906119860119888119904and 119860







1205901120590y

S2

D998400

1205902

120590x1

120590x1

120590x120591x1y1

120591x1y1P2

minus120591xy

S1

P1

120591xy

120590ave = (120590x + 120590y)2 (120590x minus 120590y)2

O

120579 = 90∘)B(

120579 = 120579)D(

120579 = 0∘)A(



A

B

C

D

020406080

100120140160

Stre

ss co

ncen

trat

ion

fact

or

087

043

022

048

138

31

855

5

796

2 916

6

59 139

07 157

668

6

285

6

222

4

334

2







119860119888119904

120590nom 1205902

1205901(120590max) 119896

119894=


DEB-1

A 5178 16800 308 (582) 267 087B 5178 16800 308 (14762) 20608 6686C 5178 16800 308 (19367) 42629 13831D 5178 16800 308 (1288) 1817 590

DEB-2

A 7947 16800 473 (526) 203 043B 7947 16800 473 (9822) 13511 2856C 7947 16800 473 (17114) 40470 8555D 7947 16800 473 (468) 657 139

DEB-3

A 8407 16800 500 (267) 112 022B 8407 16800 500 (7930) 11129 2224C 8407 16800 500 (19708) 39842 7962D 8407 16800 500 (064) 352 070

DEB-4

A 7617 16800 453 (517) 217 048B 7617 16800 453 (9586) 15154 3342C 7617 16800 453 (16055) 41556 9166D 7617 16800 453 (214) 712 157

DEB-1

(a)

DEB-2

(b)

DEB-3

(c)

DEB-4

(d)





120575119864

max 120575119864

rupt 120575119881

max 120575119881

rupt 120575119881

max120575119864

max 120575119881

rupt120575119864

rupt



DEB-1 DEB-2

DEB-3 DEB-4

(a) Stress flow


(a) Stress flow






119872 = minus119864119868

1198892

119910

1198892

119909

(8)


2

1199101198892







0

20

40

60

80

100

120

Load

(kN

)


(a) DEB-1



0

20

40

60

80

100

120

Load

(kN

)


(b) DEB-2

0

20

40

60

80

100

120

Load

(kN

)




(c) DEB-3

0

20

40

60

80

100

120Lo

ad (k

N)




(d) DEB-4










4 Conclusion










Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





PCSTM

Vec2Linear (LINEAR)

0

20

40

60

80

100

120

140

Failu

re lo

ad a

naly

sis (k

N)

20 40 60 80 100 120 1400Test result (kN)




119896 =

1205901

120590nom (7)

where 120590nom = 80 119875119906119860119888119904and 119860







1205901120590y

S2

D998400

1205902

120590x1

120590x1

120590x120591x1y1

120591x1y1P2

minus120591xy

S1

P1

120591xy

120590ave = (120590x + 120590y)2 (120590x minus 120590y)2

O

120579 = 90∘)B(

120579 = 120579)D(

120579 = 0∘)A(



A

B

C

D

020406080

100120140160

Stre

ss co

ncen

trat

ion

fact

or

087

043

022

048

138

31

855

5

796

2 916

6

59 139

07 157

668

6

285

6

222

4

334

2







119860119888119904

120590nom 1205902

1205901(120590max) 119896

119894=


DEB-1

A 5178 16800 308 (582) 267 087B 5178 16800 308 (14762) 20608 6686C 5178 16800 308 (19367) 42629 13831D 5178 16800 308 (1288) 1817 590

DEB-2

A 7947 16800 473 (526) 203 043B 7947 16800 473 (9822) 13511 2856C 7947 16800 473 (17114) 40470 8555D 7947 16800 473 (468) 657 139

DEB-3

A 8407 16800 500 (267) 112 022B 8407 16800 500 (7930) 11129 2224C 8407 16800 500 (19708) 39842 7962D 8407 16800 500 (064) 352 070

DEB-4

A 7617 16800 453 (517) 217 048B 7617 16800 453 (9586) 15154 3342C 7617 16800 453 (16055) 41556 9166D 7617 16800 453 (214) 712 157

DEB-1

(a)

DEB-2

(b)

DEB-3

(c)

DEB-4

(d)





120575119864

max 120575119864

rupt 120575119881

max 120575119881

rupt 120575119881

max120575119864

max 120575119881

rupt120575119864

rupt



DEB-1 DEB-2

DEB-3 DEB-4

(a) Stress flow


(a) Stress flow






119872 = minus119864119868

1198892

119910

1198892

119909

(8)


2

1199101198892







0

20

40

60

80

100

120

Load

(kN

)


(a) DEB-1



0

20

40

60

80

100

120

Load

(kN

)


(b) DEB-2

0

20

40

60

80

100

120

Load

(kN

)




(c) DEB-3

0

20

40

60

80

100

120Lo

ad (k

N)




(d) DEB-4










4 Conclusion










Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






119860119888119904

120590nom 1205902

1205901(120590max) 119896

119894=


DEB-1

A 5178 16800 308 (582) 267 087B 5178 16800 308 (14762) 20608 6686C 5178 16800 308 (19367) 42629 13831D 5178 16800 308 (1288) 1817 590

DEB-2

A 7947 16800 473 (526) 203 043B 7947 16800 473 (9822) 13511 2856C 7947 16800 473 (17114) 40470 8555D 7947 16800 473 (468) 657 139

DEB-3

A 8407 16800 500 (267) 112 022B 8407 16800 500 (7930) 11129 2224C 8407 16800 500 (19708) 39842 7962D 8407 16800 500 (064) 352 070

DEB-4

A 7617 16800 453 (517) 217 048B 7617 16800 453 (9586) 15154 3342C 7617 16800 453 (16055) 41556 9166D 7617 16800 453 (214) 712 157

DEB-1

(a)

DEB-2

(b)

DEB-3

(c)

DEB-4

(d)





120575119864

max 120575119864

rupt 120575119881

max 120575119881

rupt 120575119881

max120575119864

max 120575119881

rupt120575119864

rupt



DEB-1 DEB-2

DEB-3 DEB-4

(a) Stress flow


(a) Stress flow






119872 = minus119864119868

1198892

119910

1198892

119909

(8)


2

1199101198892







0

20

40

60

80

100

120

Load

(kN

)


(a) DEB-1



0

20

40

60

80

100

120

Load

(kN

)


(b) DEB-2

0

20

40

60

80

100

120

Load

(kN

)




(c) DEB-3

0

20

40

60

80

100

120Lo

ad (k

N)




(d) DEB-4










4 Conclusion










Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






120575119864

max 120575119864

rupt 120575119881

max 120575119881

rupt 120575119881

max120575119864

max 120575119881

rupt120575119864

rupt



DEB-1 DEB-2

DEB-3 DEB-4

(a) Stress flow


(a) Stress flow






119872 = minus119864119868

1198892

119910

1198892

119909

(8)


2

1199101198892







0

20

40

60

80

100

120

Load

(kN

)


(a) DEB-1



0

20

40

60

80

100

120

Load

(kN

)


(b) DEB-2

0

20

40

60

80

100

120

Load

(kN

)




(c) DEB-3

0

20

40

60

80

100

120Lo

ad (k

N)




(d) DEB-4










4 Conclusion










Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






0

20

40

60

80

100

120

Load

(kN

)


(a) DEB-1



0

20

40

60

80

100

120

Load

(kN

)


(b) DEB-2

0

20

40

60

80

100

120

Load

(kN

)




(c) DEB-3

0

20

40

60

80

100

120Lo

ad (k

N)




(d) DEB-4










4 Conclusion










Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials







4 Conclusion










Acknowledgments


References









































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Documents

Research Article Shear Failure of RC Dapped-End Beams · 2019. 7. 31. · Reinforced concrete dapped-end beams (RC-DEBs) are mainly used for precast element construction. RC-DEBs