performanceofreinforcedreactivepowderconcrete beam...

Research ArticlePerformance of Reinforced Reactive Powder ConcreteBeam-Column Joints under Cyclic Loads

Wenzhong Zheng 1 Dehong Wang 12 and Yanzhong Ju2

1Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education Harbin Institute of TechnologyHarbin 150090 China2School of Civil Engineering and Architecture Northeast Electric Power University Jilin 132012 China

Correspondence should be addressed to Dehong Wang hitwdh126com

Received 3 August 2017 Revised 14 October 2017 Accepted 20 November 2017 Published 14 March 2018

Academic Editor Peng Zhang

Copyright copy 2018 Wenzhong Zheng 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

An experimental research was carried out to investigate the seismic performance and shear strength of reactive powder concreteinterior beam-column joints subjected to reverse cyclic loads Four beam-column joint specimens were cast and tested in theinvestigation -e failure characteristics deformational properties ductility and energy dissipation of reinforced reactive powderconcrete interior beam-column joints were analyzed in this paper -e shear strength of joints was calculated according to theGB5001-2010 and ACI 318-14 -e results shows that reactive powder concrete beam-column joints have a higher shear-crackingstrength and shear carrying capacity and strength degradation and rigidity degradation are not notable Additionally the use ofRPC for beam-column joints can reduce the congestion of stirrups in joints core-e shear force in the RPC joint is mainly carriedby the diagonal strut mechanism the design expression of ACI 318-14 can be used for calculating the shear strength of RPC jointswhich has a safety margin of 22sim38 in this test

1 Introduction

Since the 1960s the performance of reinforced concrete beam-column joints has been an active subject in the earthquakeresistance of engineering structures and the field has seennumerous achievements [1ndash4] Normal concrete and high-strength concrete have low tension strength and poortoughness so the ductility of the concrete joints primarilydepends on the stirrups this causes congestion of reinforcingbars in joint and poses difficulty in the placement of concrete[5 6] Besides due to the brittleness of concrete and theuncoordinated deformation between concrete and bars thebonding properties of steel and concrete in the joint region willdeteriorate under seismic loading Furthermore splittingtensile failure and concrete cover spalling failure occur at theinterface between concrete and bars For these reasons somenew design approaches were developed Ibrahim [6] pro-posed studs with a head at each end in lieu of conventionalclosed stirrups in reinforced concrete beam-column joints

Kotsovou and Harris [7] proposed a method for the seismicdesign of beam-column joints and proved its validity Re-searches have demonstrated that the spacing of stirrups inthe joint area can be decreased by using steel fiber-reinforcedconcrete instead of normal concrete [8ndash10] In other wordsusing fiber concrete or new design approaches can reducethe amount of stirrups which is convenient for constructionOn the other hand the durability of reinforced concretestructures has become increasingly important Concretecarbonation and the corrosion of steel bars in reinforcedconcrete structures can cause premature failure Reactivepowder concrete can be a feasible solution to overcome theseproblems in reinforced concrete frame joint

Reactive powder concrete (RPC) is a new cement-basedcomposite with ultrahigh strength and performance -ecompressive strength can be as high as 200sim800MPa theflexural strength can reach 30sim60MPa [11 12] -e frost-resistance level of RPC can exceed 690 cycles of freezingand thawing with a low mass-loss rate below 3 RPCrsquos

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 3914815 12 pageshttpsdoiorg10115520183914815

resistance to carbonation and chloride ion permeability ismuch higher than other concrete [13 14] erefore themechanical properties and durability of frame structures canbe improved by using reactive powder concrete with highstrength and durability Additionally the section size of themember and the number of stirrups can be reduced

In recent years there has been extensive researchconducted on RPC in terms of the mix preparation andmechanical properties and the results indicate that themechanical properties of RPC are better than NC and HSC[15 16] in addition studies on the mechanical behavior ofthe beams and columns has been carried out by Hung andChueh [17] Malik and Foster [18] and Deng et al [19]Wang et al [20] presented the reported study on theseismic behavior of RPC exterior joints with high-strengthbars Studies have demonstrated that RPC structures diersignicantly from normal and high-strength concretestructures because of the dierence of performances ofRPC materials [21 22] is paper based on the RPCbeam-column joints quasistatic test studies the seismicperformance of RPC beam-column joints investigates theinuence of the stirrup ratio and axial compression ratioon the seismic performance of RPC beam-column jointsstudies the RPC joint forced destruction mechanism andprovides reference for the seismic design of RPC framestructure

2 Experimental Programs

21 Test Specimens In order to obtain the performance andthe shear strength of RPC joint under cyclic loads the testspecimens need to ensure that shear failure in the joint coreoccurs before beam and column exural failure Accordingto the concept ldquoweak connection-strong member weakbeam-strong columnrdquo four joint specimens were designede specimen design parameters are shown in Table 1 especimen number consists of the initial letter of joint thenumber of stirrups in the core area and the axial com-pression ratio For example ldquoJ-1-03rdquo indicates that the jointspecimen has one stirrup in the core and an axial com-pression ratio of 03 e column section size of the spec-imens is 200mmtimes 200mm and the beam cross-section sizeis 150mmtimes 250mm Specimen size and reinforcementdetails are shown in Figure 1

22 Material Properties Table 2 summarizes mixtureproportions of RPC produced e RPC were made usingGrade 425 ordinary Portland cement Table 3 shows thechemical compositions and physical properties of thecement Silica fume has a particle size of less than 2 μma density of 2214 kgm3 and an SiO2 content of 822eaggregate is quartz sand with diameter range of 0ndash25mm

Table 1 Specimen parameters

Specimens number Compressive strength of RPC (MPa) Stirrups in joint core Axial compression ratioJ-0-03 1123 0 03J-0-05 1041 0 05J-1-03 1058 One 2-leg loop 6mmφ 03J-1-05 985 One 2-leg loop 6mmφ 05

B

B4

2

AA

1

3

1

1

3

4

Section A-A

Section B-B

P

P 314 mm φ bars

214 mm φ bars

214 mm φ bars

314 mm φ bars

2L 6 mm φ 100cc

2L 6 mm φ 100cc

6mm φ 100cc

6 mm φ 100cc2

2150

2300

2001050 1050200980

450

250

650

1350

575

575

250

980

200

200

250

Figure 1 Details of reinforcement

2 Advances in Civil Engineering

Figure 2 shows the particle size distribution curve of quartzsand e steel ber volume content is 13 e compressivestrength of RPC is shown in Table 1 e longitudinal re-inforcement bars of the specimens are HRB400 hot rolledribbed steel bars (diameter of 14mm) e stirrups areHPB300 reinforced (diameter of 6mm) Table 4 shows themeasured mechanical properties of the reinforcing bars

23 Test Apparatus and Loading Procedure Figure 3 showsthe test setup and instrumentation For all specimens anaxial load was applied to the column and was maintainedconstant throughout the test An antisymmetric concen-trated force (or displacement) was applied to the free end ofthe beam e column end axial force was applied bya hydraulic jack and a 2000 kN load sensor was used tomeasure the value e beam tip cyclic load was applied byMTS electrohydraulic servo actuator e force and dis-placement of beam tips were recorded by MTS actuator

e shear deformation of the joints was measured by twodisplacement sensors placed in themain diagonal directions asshown in Figure 3(b) e shear deformation of the joints wasobtained by converting the displacement measured by dis-placement sensors e rotating plastic hinge region is rep-resented by the average cross-sectional curvature eapparatus used for measuring the curvature of the beams isshown in Figure 3(b)e strains in longitudinal reinforcement

bar and stirrups in joint core were monitored by electricalresistance strain gauges

To eliminate unevenness of axial load 30 of the axialforce is applied initially then it is unloaded to 0 and nallythe load is applied to the design value and is maintainedconstant throughout the test e axial loading history isshown in Figure 4(a) e cyclic loading procedure of thebeam tip for all specimens consists of two phases It beginswith a load-controlled phase followed by a displacement-controlled one During the force-controlled phase a load of5 kN is applied with dierential loading step by step andevery load cycle occurs once When the specimen reachescracking or at steel bar yield the process is switched todisplacement control and at this time the displacement isdenoted as Δy e displacement is incremented by Δy andeach displacement level cycle occurs three times e teststops when the load reduces to 85 of the peak load eloading history of the beam tip is shown in Figure 4(b) andthe left and right tips of the beam simultaneously load inreverse

3 Test Results and Discussion

31 Failure Characteristics of RPC Beam-Column Joints efailure model of all four of the specimens was shear failure andall of the specimens had a similar failure process which can bedivided into three stages the initial crack penetrating crackand failure In the initial-crack stage when the load reachedabout 55 of the peak load the rst diagonal crack wasobserved in a diagonal direction of the joint area At this timethe stirrup strain was small (about 600times10minus6sim800times10minus6) Inthe reverse loading phase the rst diagonal crack was observedin another diagonal direction For the moment the shear inthe joint was mainly aorded by the RPC For the specimensthe crack load of the joint core area was very close the crackload of specimen J-0-03 and J-0-05 were 25 kN whereas theother two specimens had crack loads of 30 kN e sheardeformation of four specimens at crack load was less than0001 rad

With an increased load and number of cycles theinitial crack along the diagonal direction continued toextend and the specimens gradually entered into thepenetrating crack stage At the rst 2Δy cycle the originaldiagonal cracks along the diagonal direction extended tothe corner forming the main perforation cracks In thevicinity of the diagonal there were three or four small

Table 2 Mixture proportions of RPC

Material Cement Silica fume Quartz sand Steel ber Superplasticizer Water from SP WaterQuantity (kgm3) 7567 2270 12781 1058 204 475 1689

Table 3 e chemical compositions and physical properties and of the cement

Chemical compositions () Physical propertiesSiO2 Fe2O3 Al2O3 CaO MgO SO3 R2O LOI Density (gcm3) fctf3 (MPa) fctf28 (MPa) fctf3 (MPa) fctf28 (MPa)2104 293 466 6597 182 252 090 211 318 517 962 292 615LOI loss on ignition

015 03 06 118 2360

20

40

60

80

100

Cum

ulat

ive p

assin

g (

)

Particle size (mm)

Figure 2 e particle size distribution curve of quartz sand

Advances in Civil Engineering 3

diagonal cracks that paralleled the diagonal direction Atthis time the maximum crack width of the joint area wasapproximately 03mm and the joint core still had goodshear resistance the average shear deformation of the jointwas 264 times10minus3 rad When the 2Δy cycle continued for thesecond and third cycles the widening of the main crackaccelerated and a larger number of diagonal cracks withsmall widths appeared around the main crack When therst 3Δy cycle ended the width of the main diagonal crackin the joint core area signicantly increased and themaximumwidth was about 15mm

At the failure stage the width of the main diagonalcrack in the joint continued to increase the stirrup strainin joint core rapidly increased and eventually reachedyield and the average shear deformation of the joint

multiplied Parts of steel bers were pulled out from thematrix and part of the RPC near the main crack started topeel At the loading ends large cracks might appear butspecimens remained as an integral e specimen failuremode is shown in Figure 5 RPC has a high tensile strengthand tension strain which can delay joint core cracking aswell as delay the tensile yield of stirrups in the joint core Inaddition the high tensile strength of RPC can reduce thespeed at which cracks develop thus the compressivestrength can be sucopycient to play and improve the carryingcapacity of joints

32 Load-Deformation Hysteresis Curve e load-displacement(P-Δ) curve of beam tip is a comprehensive reection ofjoint specimens under cyclic loading which can reect

Table 4 Mechanical properties of reinforcing bars

Type of reinforcement Application Diameter (mm) Yield strength (MPa) Ultimate strength (MPa) Modulus of elastic (GPa)HRB400 Longitudinal bars 14 42340 63240 200HPB300 Transverse stirrup 6 35356 39830 210

345 6

1

62

8

9

7

(a)

10

10

1010

1010

10

10

10

10

(b)

Figure 3 Loading device of the test (a) Schematic diagram of load test (b) Displacement sensor arrangement (1) Rigid frame (2) reacting-force wall (3) hydraulic jack (4) load sensor (5) hinge (6) MTS actuators (7) spreader beam (8) specimen (9) hinge base (10) dis-placement sensor

0

Axi

al lo

ad N

03 N

Time

(a)

0Cycles

Force control Displacement control

Disp

lace

men

t (Δ

Δ y)

Load

(kN

)

0

minus3minus2

minus4minus5

minus1

1 2 3 4 5 6 7 8 9 10 11 12 13 17161514

12345

(b)

Figure 4 e schematic view of loading history (a) Loading procedure of column end (b) Loading procedure of beam tip


jointsrsquo seismic performance indicators such as bearingcapacity ductility energy dissipation the strength re-duction rigidity degradation and so on Figure 6 shows theload-displacement hysteretic loop of four test specimenswhere L represents the left beam and R represents the rightbeam -e hysteresis curve of reinforced RPC beam-column joint has the following characteristics

(1) In the early stage the hysteresis loops were narrowstrips and the area surrounded by hysteresis loopswas smaller-e slope decline of hysteresis curve wasnot obvious

(2) In the stage of displacement control during 1Δydisplacement stage strength of joints almost did notreduce When the loading displacement increased to2Δy the load of beam end continued to increase andspecimens J-0-03 J-1-03 and J-1-05 reached theirmaximum carrying capacity respectively at the firstcycle of 2Δy During the second and third cycles of2Δy the strength declined slightly the decline wereno more than 5 During the first cycle of 3Δy thestrength of specimen J-0-05 reached its maximumwhile the strength of other specimens were close tothe strength at 2Δy first cycle With the increase ofthe cycles the capacity of specimens began to declinesignificantly In this case the load-displacementhysteresis curve became ldquoSrdquo shape and the areasurrounded by the hysteresis loop also increasedrapidly it indicated that the energy dissipation ofspecimen increased

33 Shear Force-Deformation Angle Hysteresis Loops -ejoint shear deformation angle of joint can be calculated by

c

a2 + b2

radic

2abΔ1 + Δ2 + Δ3 + Δ4( 1113857 (1)

where c represents the average value of joint sheardeformation angle a and b represent the horizontal andvertical distances between the end points of the diagonaland (Δ1 + Δ2) and (Δ3 + Δ4) are the changes in length ofdiagonals (Figure 7)

According to the China code the shear strength (Vj) ofreinforced RPC joints can be calculated by the equation[23]

Vj sumMb

hb0 minus asprime

1minushb0 minus as

prime

Hc minus hb

1113888 1113889 (2)

where sumMb represents the total bending moment of beamadjoining joint core sumMb P1L1 + P2L2 Hc is total depthof column hb0 is effective depth of beam hb0 hb minus as hb isdepth of beam and as and as

prime are the distance from theresultant force center of tensile and compressive re-inforcement to corresponding edge

Figure 8 shows the shear force-deformation angle (Vj-c)hysteretic curves of the four specimens It can be observedfrom Figure 8 that the slope rates of the loading curve werebasically consistent with unloading curve during loadcontrol stage this indicates that the joint is about in elasticstate before cracking in joint core During the 1Δy

(a) (b)

(c) (d)

Figure 5 Failure mode of joints (a) Specimen J-0-03 (b) Specimen J-0-05 (c) Specimen J-1-03 (d) Specimen J-1-05


minus75 minus60 minus45 minus30 minus15 00 15 30 45 60 75

minus60 minus30 0 30 60 90minus90Beam tip displacement (mm)

minus80

minus40

0

40

80

Beam

tip

load

(kN

)

J-0-03-R



minus80

minus40

0

40

80Be

am ti

p lo

ad (k

N)

J-0-03-L

(a)

minus90 minus60 minus30 0 30 60 90minus80

minus40

0

40

80

Beam tip displacement (mm)

J-0-05-L

minus75 minus60 minus45 minus30 minus15 00 15 30 45 60 75Story drift ratio ()

Beam

tip

load

(kN

)


minus40

0

40

80


J-0-05-R


Beam

tip

load

(kN

)

(b)


minus40

0

40

80


J-1-03-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-03-R


Beam

tip

load

(kN

)

(c)

Figure 6 Continued


displacement stage the shear deformation value of jointswas very small During the 2Δy displacement stage four jointspecimens all reached the maximum shear carrying ca-pacities at the first 2Δy cycle then the strength reduction andstiffness degradation began to appear at the second and thirdcycles of 2Δy displacement At the first 3Δy cycle the sheardeformation angles significantly increase but the shear loadof specimens is close to the value at the first 2Δy cycle -isindicates that RPC beam-column joint has a good ability ofdeformation and toughness At the second and third cyclesof 3Δy displacement the shear deformation angles ofspecimens continue to increase and strengths drop tillfailure

34 Strength Degradation -e strength of the joint speci-mens decreased at the same displacement level with an

increasing number of cycles -e strength degradation co-efficient (λj) presented in the Chinese code [24] is used toillustrate the degradation λj can be calculated by

λj Pj

i

P1j

(3)

where P1j is the peak force of the first cycle at the dis-

placement level of j (j∆∆y) and Pji is the peak force of the

second or third cycle (i 2 or 3) at the same displacementlevel of j (j∆∆y)

-e λj versus ∆∆y curve for the reinforced RPC beam-column joints is shown in Figure 9 It can be seen that thecoefficient λj of the specimens decreases as the level ofdisplacement increases λj decreases as cycles increases at thesame displacement level λj increases as the axial com-pression ratio increases

35 Rigidity Degradation -e rigidity coefficient Kj is de-fined as the slope of the line joining the upward anddownward peak loads of one loop of the load-displacementhysteresis loops Figure 10 shows the looped rigidity co-efficient (Kj) versus displacement (∆∆y) relationship of RPCconcrete beam-column joints For each displacement levelthe rigidity coefficient was calculated using the peak loadvalues of the first cycle

According to Figure 10 rigidity degradation can befound in all specimens and the rigidity coefficient ofspecimen changes marginally from 1Δy to 2Δy but rigiditycoefficient decreased significantly when the displacement ofbeam tip exceeds 2Δy-is can be contributed to the fact thatcracks were developing quickly and failures started to occurat 3Δy

36 Ductility of Joints Ductility is an important index for theseismic design of structures and is characterized by a ductilityfactor According to different deformation types the ductility


minus40

0

40

80


J-1-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-05-R


Beam

tip

load

(kN

)

(d)

Figure 6 Hysteresis curve of joints (a) Specimen J-0-03 (b) Specimen J-0-05 (c) Specimen J-1-03 (d) Specimen J-1-05

a

b

Δ 1

Δ 2

Δ3

Δ4

Figure 7 Calculation of the joint shear deformation angle c


factor can be divided into three types a curvature ductilityfactor displacement ductility factor and rotation ductility factorIn this paper the displacement ductility factor μ is used tomeasure the ductility of the specimens It is dened asμΔuΔye where Δu is the ultimate displacement when thespecimen destructs which is the beam tip corresponding tothe displacement when the load reaches 85 of the maxi-mum loade corresponding load to Δu is the ultimate loadPu Yield displacement Δye can be calculated by the Parkmethod [25] and the corresponding load to Δye is the yieldload Pye

Table 5 shows the main feature pointsrsquo test results anddisplacement ductility factors of each specimen e rstcrack load increased with increase of stirrup in joint andaxial load of column which may be due to the increase inconned eect from stirrup and compression from columne ductility factors of four specimens are small rangingfrom about 163 to 229 is is because the failure mode ofall four specimens is shear failure in joint core Specimen J-1-03 and specimen J-1-05 which congure only a stirrup inthe joint core do not manifest a higher ductility thanspecimens without stirrup in the joint core is phenom-enon can contribute to fewer stirrups being congured by

specimens e stirrups yielded before the specimensreached their maximum carrying capacity so fewer stirrupsin the joint area have no eect on the ductility of thespecimens Furthermore this also indicates that RPC hasa good shear ductility which shows an excellent ductilitycharacteristic under shear load and the feature has lessdependence upon the restraint of the stirrups It can reducethe consumption of stirrup to use RPC instead of normalconcrete in the joint area and it is easy for construction

37 Energy Dissipation Energy dissipation is an importantindicator of seismic performance e enclosed area formedby the load-displacement hysteresis loops can be used tocharacterize the size of the energy dissipation

Figure 11 shows the hysteretic energy dissipation curveof dierent RPC beam-column joints under dierent loadinggrades As can be seen from the gure specimens in thesmall deformation stage have less energy dissipationWhen theload displacement was 1Δy (about 21 drift) the energydissipation capacities of the four specimens were 5162 kNmiddotmm5546 kNmiddotmm 5516 kNmiddotmm and 5289 kNmiddotmm When theload displacement was 2Δy (about 43 drift) the energy

0

minus25 minus20 minus15 minus10 minus5 0 5 10 15 20 25minus500minus400minus300minus200minus100

100200300400500

J-0-03

γ (times10minus3 rad)

V j (k

N)

(a)


1000

200300400500

J-0-05


V j (k

N)

(b)

minus25 minus20 minus15 minus10 minus5 5 10 15 20 25minus500minus400minus300minus200

1000

200300400500

J-1-03

0γ (times10minus3 rad)

minus100V j (k

N)

(c)


1000

200300400500

J-1-05


V j (k

N)

(d)

Figure 8 Shear force versus shear deformation angle of joints core (a) Specimen J-0-03 (b) Specimen J-0-05 (c) Specimen J-1-03(d) Specimen J-1-05


dissipation capacities of the four specimens were 23745kNmiddotmm28371kNmiddotmm 26401kNmiddotmm and 27905 kNmiddotmm When theload displacement was 3Δy (about 64 drift) the energy

dissipation capacities of the four specimens were 50582kNmiddotmm59566 kNmiddotmm 50716kNmiddotmm and 54135kNmiddotmm

e energy dissipation of joints increases with increasingaxial compression Under the same axial compression ratiothe stirrup of the joint core can improve the energy con-sumption slightly An increase in RPC shear strength canimprove the energy dissipation capacity to a certain degreeAfter stirrups yield energy dissipations of the four speci-mens are close e reason could be the axial compressionand the existence of stirrups can suppress diagonal crack ofjoint core developing In addition the axial compression alsoimproves the friction resistance between longitudinal re-inforcements and RPC in the joint core

4 Shear Strength of RPC Beam-Column Joints

Based on test results the shear strength of reinforced RPCjoints can be calculated by (2) Table 6 shows the shearstrength of four specimens in order to study the inuenceof axial compression ratio and stirrup ratio in joints coreon shear strength Considering the dierences in RPCstrength of dierent specimens shear-compression ratio(Vjfcbjhj) was dened to analyze shear strength of unit

ndash3 ndash2 ndash1 0 1 2 306

07

08

09

10

11

ΔΔy

J-0-03-L i = 2 J-0-03-R i = 2J-0-03-L i = 3 J-0-03-R i = 3

jλ

(a)

06

07

08

09

10

11

minus3 minus2 minus1 0 1 2 3∆∆y

J-0-05-L i = 2J-0-05-L i = 3

J-0-05-R i = 2J-0-05-R i = 3

jλ

(b)

06

07

08

09

10

11


J-1-03-L i = 2J-1-03-L i = 3

J-1-03-R i = 2J-1-03-R i = 3

jλ

(c)

06

07

08

09

10

11


J-1-05-L i = 2J-1-05-L i = 3

J-1-05-R i = 2J-1-05-R i = 3

jλ

(d)

Figure 9 λj versus ΔΔy relationship (a) Specimen J-0-03 (b) Specimen J-0-05 (c) Specimen J-1-03 (d) Specimen J-1-05

1 2 3 40

500

1000

1500

2000

J-0-03-LJ-0-03-RJ-0-05-LJ-0-05-R

K j (k

Nm

m)

∆∆y

J-1-03-LJ-1-03-RJ-1-05-LJ-1-05-R

Figure 10 Kj versus ΔΔy relations


area of RPC Vj is the shear carrying capacity of RPCjoint which can be calculated by (2) fc is the compressivestrength of RPC bj is the width of joint and hj is theheight of joint

e inuence of axial compression ratio and stirrup ratio toshear-compression ratio is shown in Figure 12 e shear-compression ratio of specimen J-1-03 increased by 79 ascompared to J-0-03 and the shear-compression ratio ofspecimen J-1-05 decreased by 23 as compared to J-0-05is could be explained by the fact that yield of stirrup in jointcore was found before peak load For specimens J-1-03 and

J-1-05 there was only a double-leg loop with a 6mm diameterin the joints so the restriction eect on RPC was weaker andthe enhance eect of the shear strength was not obvious Underthe same axial compression ratioe stirrups in the joints playa role in constraining the concrete of joint core which canimprove the compressive and shear strength of concrete be-sides stirrups in the joint core can bear directly part of theshear force of joint thus it can eectively improve theshear strength of the joint by conguring a number ofstirrups [5] It is necessary to use a certain amount stirrupsin RPC joint core even though RPC joint has high strengthand ductility Under the same reinforcement condition theshear-compression ratio of specimen J-0-05 increased by181 as compared to J-0-03 and the shear-compressionratio of J-1-05 increased by 69 as compared to J-1-03e cracking resistance of concrete can be improved by in-creasing the axial compression ratio e microcracks inconcrete can reclose under the axial compressive force and itis benecial for improving the shear strength of concrete byproperly increasing the axial compressive force withina certain range A similar behavior was reported by otherresearchers [8 26 27] in which the joint shear strengthmoderately increases as the axial load level increases withina certain range On the other hand the increase in the axialcompressive force can reduce ductility of beam-column jointLi and Leong [27] reported that any increase in the columnaxial compressive load beyond 03fprime

cAg did not improve theshear strength and the application of column axial com-pression ratios above 03 causes a decrease in shear strengthand a degradation of rigidity Kim and Lafave [28] reported

Table 5 Main feature pointsrsquo test results and displacement ductility factor

Specimennumbers Direction

Firstcrackload(kN)

DisplacementΔye at yield load

(mm)

Yieldload Pye(kN)

DisplacementΔmax at peakload (mm)

PeakloadPmax(kN)

Displacement Δuat ultimate load

(mm)

Ultimateload Pu(kN)

Displacementductilityfactor μ

J-0-03-LDownward 25 3473 4469 4046 505 6475 4293 186Upward 30 3576 4843 4046 533 6907 4531 193Average 275 35245 4656 4046 519 6691 4412 190

J-0-03-RDownward 30 2838 4116 4046 454 6326 3859 223Upward 25 3393 6064 6069 667 7951 567 234Average 275 31155 509 50575 5605 71385 47645 229







0 10 20 30 40 50 60 70 80 900

1500

3000

4500

6000

7500

9000

Ener

gy (k

Nmiddotm

m)


J-0-03J-0-05

J-1-03J-1-05

Figure 11 Energy dissipation of joint specimens


that the column axial compression ratio had little influence onthe joint shear behavior

Based on the test results of the mechanical properties ofreinforced bars and RPC the shear strength of joint spec-imens were calculated according to the China code forseismic design of buildings (GB50011-2010) [23]and ACI318-14 (in accordance with ACI R352-02 committee report)[29] respectively-e calculated results of the shear strengthwere lower than those of the test result -e calculated valueusing GB50011-2010 was lower than that using ACI 318-14and the test value was about 151 times larger than the valuecalculated by GB50011-2010 and was about 130 times largerthan the value calculated by ACI 318-14 -e comparison isnot satisfactory this may be due to the following reasonsRPC has higher compressive strength however the tension-compression ratio of the RPC is smaller than that of ordinaryconcrete -e tensile strength ft of concrete is used asrepresentative value of shear strength in the China code andthe compressive strengthrsquos square root 1113874

fprimec

11139691113875 of concrete is

used as the representative value of shear strength in ACI318-14 -us the value calculated by the China code issmaller than the value calculated by ACI 318-14 -e testresult indicates that the shear force in the RPC joint is mainlycarried by the diagonal strut mechanism which is consistentwith design expression of ACI 318-14 the shear strength testresults were found to be 22sim38 more than thevalue calculated by ACI 318-14 So the design expressionsVj αacijλacij

fprimec

1113969

Aj can be used for calculating the shearstrength of RPC joints

5 Conclusions

(1) Reinforced RPC beam-column joints have a highershear-cracking strength and shear bearing capacityand strength reduction and rigidity degradation areslow -e use of RPC for beam-column joints canreduce the congestion of stirrups in joints core

(2) Within the range of the axial compression ratio inthis test the energy dissipation capacities of thebeam-column joints increase with the axial com-pression ratio increases

(3) -e shear force in the RPC joint is mainly carried bythe diagonal strut mechanism -e stirrup in thejoint core can improve strength of diagonal strut andthe energy dissipation of joints

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-e work described in this paper was fully supported bythe National Natural Science Foundation of China(Project no 51378095) -e authors would like to thankthe staff in the Structural engineering lab of NortheastElectric Power University for their kind assistance duringthe tests

Table 6 Test results and analysis

Specimen number Stirrup Axial compression ratio Test value (ExpkN)Calculation value of shear strength (kN)

GB 50010-2010 ExpGB ACI 318-14 ExpACIJ-0-03 0 03 37482 250116 150 308192 122J-0-05 0 05 41021 251841 163 296727 138J-1-03 1 03 38091 259118 147 29914 127J-1-05 1 05 37921 261665 145 288636 131

minus02 00 02 04 06 08 10 12 14 160090

0095

0100

0105

0110

0115

0120

J-03J-05

sv()

V jf cb jh j

(a)

03 04 050090

0095

0100

0105

0110

0115

0120

Axial compression ratio

J-0J-1Φ6

V jf cb jh j

(b)

Figure 12 Influence of axial compression ratio and stirrup ratio to shear-compression ratio (a) Stirrup ratio of joint core (b) Axialcompression ratio


References

[1] N W Hanson and H W Conner ldquoSeismic resistance ofreinforced concrete beam-column jointsrdquo Journal of theStructural Division American Society of Civil Engineersvol 93 no 5 pp 533ndash559 1967

[2] T Paulay and M J N Priestley Seismic Design of ReinforcedConcrete and Masonry Buildings Wiley New York NY USA1992

[3] S A Attaalla ldquoGeneral analytical model for nominal shearstress of type 2 normal- and high-strength concrete beam-column jointsrdquo ACI Materials Journal vol 101 no 6pp 65ndash75 2004

[4] S J Hwang and H J Lee ldquoStrength prediction for discon-tinuity regions by softened strut-and-tie modelrdquo Journal ofStructural Engineering vol 128 no 12 pp 1519ndash1526 2002

[5] J R Tang C B Hu K J Yang and Y Yongcheng ldquoSeismicbehaviour and shear strength of framed joint using steel-fiberreinforced concreterdquo Journal of Structural Engineeringvol 118 no 2 pp 341ndash358 1992

[6] H Ibrahim Stud Reinforcement in Beam-Column Joints underSeismic Loads University of Calgary Calgary AB Canada2011

[7] G Kotsovou and M Harris ldquoExterior RC beamndashcolumnjoints new design approachrdquo Engineering Structures vol 41pp 307ndash319 2012

[8] X Liang Y Wang Y Tao and M K Deng ldquoSeismic per-formance of fiber-reinforced concrete interior beam-columnjointsrdquo Engineering Structures vol 126 pp 432ndash445 2016

[9] A Filiatrault K Ladicani and B Massicotte ldquoSeismic per-formance of code-designed fiber reinforced concrete jointsrdquoACI Materials Journal vol 91 no 5 pp 564ndash571 1994

[10] Z Bayasi and M Gebman ldquoReduction of lateral re-inforcement in seismic beam-column connection via appli-cation of steel fibersrdquo ACI Structural Journal vol 99 no 6pp 772ndash780 2002

[11] P Richard and M Cheyrezy ldquoComposition of reactivepowder concretesrdquo Cement amp Concrete Research vol 25no 7 pp 1501ndash1511 1995

[12] R Yu P Spiesz and H J H Brouwers ldquoDevelopment of aneco-friendly Ultra-High Performance Concrete (UHPC) withefficient cement and mineral admixtures usesrdquo Cement ampConcrete Composites vol 55 no 1 pp 383ndash394 2015

[13] N Roux C Andrade andM A Sanjuan ldquoExperimental studyof durability of reactive powder concretesrdquo Journal of Ma-terials in Civil Engineering vol 8 no 1 pp 1ndash6 1996

[14] B Graybeal and J Tanesi ldquoDurability of an ultrahigh-performance concreterdquo Journal of Materials in Civil Engi-neering vol 19 no 10 pp 848ndash854 2007

[15] H Yigiter S Aydın H Yazıcı and M Y Yardımcı ldquoMe-chanical performance of low cement reactive powder concrete(LCRPC)rdquo Composites Part B Engineering vol 43 no 8pp 2907ndash2914 2012

[16] S Ahmad A Zubair and M Maslehuddin ldquoEffect of keymixture parameters on flow and mechanical properties ofreactive powder concreterdquo Construction amp BuildingMaterialsvol 99 no 11 pp 73ndash81 2015

[17] C C Hung and C Y Chueh ldquoCyclic behavior of UHPFRCflexural members reinforced with high-strength steel rebarrdquoEngineering Structures vol 122 no 9 pp 108ndash120 2016

[18] A R Malik and S J Foster ldquoCarbon fiber-reinforced polymerconfined reactive powder concrete columns-experimentalinvestigationrdquo ACI Structural Journal vol 107 no 3pp 263ndash271 2010

[19] Z Deng C Chen and X Chen ldquoExperimental research on theshear behaviors of hybrid fiber reinforced RPC beamsrdquo ChinaCivil Engineering Journal vol 48 no 5 pp 51ndash60 2015

[20] D H Wang Y Z Ju and W Z Zheng ldquoStrength of reactivepowder concrete beam-column joints reinforced with high-strength (HRB600) bars under seismic loadingrdquo Strength ofMaterials vol 49 no 1 pp 139ndash151 2017

[21] Y Z Ju D H Wang and J Bai ldquoSeismic performance ofreactive powder concrete columnsrdquo Journal of Harbin In-stitute of Technology vol 45 no 8 pp 111ndash116 2013

[22] W Zhou H Hu and W Zheng ldquoBearing capacity of reactivepowder concrete reinforced by steel fibersrdquo Construction ampBuilding Materials vol 48 no 19 pp 1179ndash1186 2013

[23] GB 50011-2010 Code for Seismic Design of Buildings ChinaBuilding Industry Press Beijing China 2010

[24] JGJ 101-96 Specificating of Testing Methods for EarthquakeResistant Building China Building Industry Press BeijingChina 1997

[25] B Zhu Structure Seismic Test Seismological Press BeijingChina 1989

[26] P Alaee and B Li ldquoHigh-strength concrete interior beam-column joints with high-yield-strength steel reinforcementsrdquoJournal of Structural Engineering vol 143 no 7 p 040170382017

[27] B Li and C L Leong ldquoExperimental and numerical in-vestigations of the seismic behavior of high-strength concretebeam-column joints with column axial loadrdquo Journal ofStructural Engineering vol 141 no 9 p 04014220 2015

[28] J Kim and J M Lafave ldquoKey influence parameters for thejoint shear behaviour of reinforced concrete (RC) beamndashcolumn connectionsrdquo Steel Construction vol 29 no 10pp 2523ndash2539 2007

[29] ACI 318-14 Building Code Requirements for StructuralConcrete and Commentary American Concrete InstituteFarmington Hills MI USA 2014


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

resistance to carbonation and chloride ion permeability ismuch higher than other concrete [13 14] erefore themechanical properties and durability of frame structures canbe improved by using reactive powder concrete with highstrength and durability Additionally the section size of themember and the number of stirrups can be reduced

In recent years there has been extensive researchconducted on RPC in terms of the mix preparation andmechanical properties and the results indicate that themechanical properties of RPC are better than NC and HSC[15 16] in addition studies on the mechanical behavior ofthe beams and columns has been carried out by Hung andChueh [17] Malik and Foster [18] and Deng et al [19]Wang et al [20] presented the reported study on theseismic behavior of RPC exterior joints with high-strengthbars Studies have demonstrated that RPC structures diersignicantly from normal and high-strength concretestructures because of the dierence of performances ofRPC materials [21 22] is paper based on the RPCbeam-column joints quasistatic test studies the seismicperformance of RPC beam-column joints investigates theinuence of the stirrup ratio and axial compression ratioon the seismic performance of RPC beam-column jointsstudies the RPC joint forced destruction mechanism andprovides reference for the seismic design of RPC framestructure

2 Experimental Programs

21 Test Specimens In order to obtain the performance andthe shear strength of RPC joint under cyclic loads the testspecimens need to ensure that shear failure in the joint coreoccurs before beam and column exural failure Accordingto the concept ldquoweak connection-strong member weakbeam-strong columnrdquo four joint specimens were designede specimen design parameters are shown in Table 1 especimen number consists of the initial letter of joint thenumber of stirrups in the core area and the axial com-pression ratio For example ldquoJ-1-03rdquo indicates that the jointspecimen has one stirrup in the core and an axial com-pression ratio of 03 e column section size of the spec-imens is 200mmtimes 200mm and the beam cross-section sizeis 150mmtimes 250mm Specimen size and reinforcementdetails are shown in Figure 1

22 Material Properties Table 2 summarizes mixtureproportions of RPC produced e RPC were made usingGrade 425 ordinary Portland cement Table 3 shows thechemical compositions and physical properties of thecement Silica fume has a particle size of less than 2 μma density of 2214 kgm3 and an SiO2 content of 822eaggregate is quartz sand with diameter range of 0ndash25mm

Table 1 Specimen parameters

Specimens number Compressive strength of RPC (MPa) Stirrups in joint core Axial compression ratioJ-0-03 1123 0 03J-0-05 1041 0 05J-1-03 1058 One 2-leg loop 6mmφ 03J-1-05 985 One 2-leg loop 6mmφ 05

B

B4

2

AA

1

3

1

1

3

4

Section A-A

Section B-B

P

P 314 mm φ bars

214 mm φ bars

214 mm φ bars

314 mm φ bars

2L 6 mm φ 100cc

2L 6 mm φ 100cc

6mm φ 100cc

6 mm φ 100cc2

2150

2300

2001050 1050200980

450

250

650

1350

575

575

250

980

200

200

250

Figure 1 Details of reinforcement














015 03 06 118 2360

20

40

60

80

100

Cum

ulat

ive p

assin

g (

)

Particle size (mm)









345 6

1

62

8

9

7

(a)

10

10

1010

1010

10

10

10

10

(b)


0

Axi

al lo

ad N

03 N

Time

(a)

0Cycles


Disp

lace

men

t (Δ

Δ y)

Load

(kN

)

0

minus3minus2

minus4minus5

minus1

1 2 3 4 5 6 7 8 9 10 11 12 13 17161514

12345

(b)







c

a2 + b2

radic

2abΔ1 + Δ2 + Δ3 + Δ4( 1113857 (1)



Vj sumMb

hb0 minus asprime

1minushb0 minus as

prime

Hc minus hb

1113888 1113889 (2)




(a) (b)

(c) (d)





minus80

minus40

0

40

80

Beam

tip

load

(kN

)

J-0-03-R



minus80

minus40

0

40

80Be

am ti

p lo

ad (k

N)

J-0-03-L

(a)


minus40

0

40

80


J-0-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-0-05-R


Beam

tip

load

(kN

)

(b)


minus40

0

40

80


J-1-03-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-03-R


Beam

tip

load

(kN

)

(c)

Figure 6 Continued





λj Pj

i

P1j

(3)









minus40

0

40

80


J-1-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-05-R


Beam

tip

load

(kN

)

(d)


a

b

Δ 1

Δ 2

Δ3

Δ4








0


100200300400500

J-0-03


V j (k

N)

(a)


1000

200300400500

J-0-05


V j (k

N)

(b)


1000

200300400500

J-1-03


minus100V j (k

N)

(c)


1000

200300400500

J-1-05


V j (k

N)

(d)









07

08

09

10

11

ΔΔy

J-0-03-L i = 2 J-0-03-R i = 2J-0-03-L i = 3 J-0-03-R i = 3

jλ

(a)

06

07

08

09

10

11


J-0-05-L i = 2J-0-05-L i = 3

J-0-05-R i = 2J-0-05-R i = 3

jλ

(b)

06

07

08

09

10

11


J-1-03-L i = 2J-1-03-L i = 3

J-1-03-R i = 2J-1-03-R i = 3

jλ

(c)

06

07

08

09

10

11


J-1-05-L i = 2J-1-05-L i = 3

J-1-05-R i = 2J-1-05-R i = 3

jλ

(d)


1 2 3 40

500

1000

1500

2000

J-0-03-LJ-0-03-RJ-0-05-LJ-0-05-R

K j (k

Nm

m)

∆∆y

J-1-03-LJ-1-03-RJ-1-05-LJ-1-05-R









Firstcrackload(kN)


(mm)

Yieldload Pye(kN)


PeakloadPmax(kN)


(mm)

Ultimateload Pu(kN)










0 10 20 30 40 50 60 70 80 900

1500

3000

4500

6000

7500

9000

Ener

gy (k

Nmiddotm

m)


J-0-03J-0-05

J-1-03J-1-05





fprimec



fprimec

1113969


5 Conclusions






Acknowledgments





minus02 00 02 04 06 08 10 12 14 160090

0095

0100

0105

0110

0115

0120

J-03J-05

sv()

V jf cb jh j

(a)

03 04 050090

0095

0100

0105

0110

0115

0120


J-0J-1Φ6

V jf cb jh j

(b)



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














015 03 06 118 2360

20

40

60

80

100

Cum

ulat

ive p

assin

g (

)

Particle size (mm)









345 6

1

62

8

9

7

(a)

10

10

1010

1010

10

10

10

10

(b)


0

Axi

al lo

ad N

03 N

Time

(a)

0Cycles


Disp

lace

men

t (Δ

Δ y)

Load

(kN

)

0

minus3minus2

minus4minus5

minus1

1 2 3 4 5 6 7 8 9 10 11 12 13 17161514

12345

(b)







c

a2 + b2

radic

2abΔ1 + Δ2 + Δ3 + Δ4( 1113857 (1)



Vj sumMb

hb0 minus asprime

1minushb0 minus as

prime

Hc minus hb

1113888 1113889 (2)




(a) (b)

(c) (d)





minus80

minus40

0

40

80

Beam

tip

load

(kN

)

J-0-03-R



minus80

minus40

0

40

80Be

am ti

p lo

ad (k

N)

J-0-03-L

(a)


minus40

0

40

80


J-0-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-0-05-R


Beam

tip

load

(kN

)

(b)


minus40

0

40

80


J-1-03-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-03-R


Beam

tip

load

(kN

)

(c)

Figure 6 Continued





λj Pj

i

P1j

(3)









minus40

0

40

80


J-1-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-05-R


Beam

tip

load

(kN

)

(d)


a

b

Δ 1

Δ 2

Δ3

Δ4








0


100200300400500

J-0-03


V j (k

N)

(a)


1000

200300400500

J-0-05


V j (k

N)

(b)


1000

200300400500

J-1-03


minus100V j (k

N)

(c)


1000

200300400500

J-1-05


V j (k

N)

(d)









07

08

09

10

11

ΔΔy

J-0-03-L i = 2 J-0-03-R i = 2J-0-03-L i = 3 J-0-03-R i = 3

jλ

(a)

06

07

08

09

10

11


J-0-05-L i = 2J-0-05-L i = 3

J-0-05-R i = 2J-0-05-R i = 3

jλ

(b)

06

07

08

09

10

11


J-1-03-L i = 2J-1-03-L i = 3

J-1-03-R i = 2J-1-03-R i = 3

jλ

(c)

06

07

08

09

10

11


J-1-05-L i = 2J-1-05-L i = 3

J-1-05-R i = 2J-1-05-R i = 3

jλ

(d)


1 2 3 40

500

1000

1500

2000

J-0-03-LJ-0-03-RJ-0-05-LJ-0-05-R

K j (k

Nm

m)

∆∆y

J-1-03-LJ-1-03-RJ-1-05-LJ-1-05-R









Firstcrackload(kN)


(mm)

Yieldload Pye(kN)


PeakloadPmax(kN)


(mm)

Ultimateload Pu(kN)










0 10 20 30 40 50 60 70 80 900

1500

3000

4500

6000

7500

9000

Ener

gy (k

Nmiddotm

m)


J-0-03J-0-05

J-1-03J-1-05





fprimec



fprimec

1113969


5 Conclusions






Acknowledgments





minus02 00 02 04 06 08 10 12 14 160090

0095

0100

0105

0110

0115

0120

J-03J-05

sv()

V jf cb jh j

(a)

03 04 050090

0095

0100

0105

0110

0115

0120


J-0J-1Φ6

V jf cb jh j

(b)



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








345 6

1

62

8

9

7

(a)

10

10

1010

1010

10

10

10

10

(b)


0

Axi

al lo

ad N

03 N

Time

(a)

0Cycles


Disp

lace

men

t (Δ

Δ y)

Load

(kN

)

0

minus3minus2

minus4minus5

minus1

1 2 3 4 5 6 7 8 9 10 11 12 13 17161514

12345

(b)







c

a2 + b2

radic

2abΔ1 + Δ2 + Δ3 + Δ4( 1113857 (1)



Vj sumMb

hb0 minus asprime

1minushb0 minus as

prime

Hc minus hb

1113888 1113889 (2)




(a) (b)

(c) (d)





minus80

minus40

0

40

80

Beam

tip

load

(kN

)

J-0-03-R



minus80

minus40

0

40

80Be

am ti

p lo

ad (k

N)

J-0-03-L

(a)


minus40

0

40

80


J-0-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-0-05-R


Beam

tip

load

(kN

)

(b)


minus40

0

40

80


J-1-03-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-03-R


Beam

tip

load

(kN

)

(c)

Figure 6 Continued





λj Pj

i

P1j

(3)









minus40

0

40

80


J-1-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-05-R


Beam

tip

load

(kN

)

(d)


a

b

Δ 1

Δ 2

Δ3

Δ4








0


100200300400500

J-0-03


V j (k

N)

(a)


1000

200300400500

J-0-05


V j (k

N)

(b)


1000

200300400500

J-1-03


minus100V j (k

N)

(c)


1000

200300400500

J-1-05


V j (k

N)

(d)









07

08

09

10

11

ΔΔy

J-0-03-L i = 2 J-0-03-R i = 2J-0-03-L i = 3 J-0-03-R i = 3

jλ

(a)

06

07

08

09

10

11


J-0-05-L i = 2J-0-05-L i = 3

J-0-05-R i = 2J-0-05-R i = 3

jλ

(b)

06

07

08

09

10

11


J-1-03-L i = 2J-1-03-L i = 3

J-1-03-R i = 2J-1-03-R i = 3

jλ

(c)

06

07

08

09

10

11


J-1-05-L i = 2J-1-05-L i = 3

J-1-05-R i = 2J-1-05-R i = 3

jλ

(d)


1 2 3 40

500

1000

1500

2000

J-0-03-LJ-0-03-RJ-0-05-LJ-0-05-R

K j (k

Nm

m)

∆∆y

J-1-03-LJ-1-03-RJ-1-05-LJ-1-05-R









Firstcrackload(kN)


(mm)

Yieldload Pye(kN)


PeakloadPmax(kN)


(mm)

Ultimateload Pu(kN)










0 10 20 30 40 50 60 70 80 900

1500

3000

4500

6000

7500

9000

Ener

gy (k

Nmiddotm

m)


J-0-03J-0-05

J-1-03J-1-05





fprimec



fprimec

1113969


5 Conclusions






Acknowledgments





minus02 00 02 04 06 08 10 12 14 160090

0095

0100

0105

0110

0115

0120

J-03J-05

sv()

V jf cb jh j

(a)

03 04 050090

0095

0100

0105

0110

0115

0120


J-0J-1Φ6

V jf cb jh j

(b)



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






c

a2 + b2

radic

2abΔ1 + Δ2 + Δ3 + Δ4( 1113857 (1)



Vj sumMb

hb0 minus asprime

1minushb0 minus as

prime

Hc minus hb

1113888 1113889 (2)




(a) (b)

(c) (d)





minus80

minus40

0

40

80

Beam

tip

load

(kN

)

J-0-03-R



minus80

minus40

0

40

80Be

am ti

p lo

ad (k

N)

J-0-03-L

(a)


minus40

0

40

80


J-0-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-0-05-R


Beam

tip

load

(kN

)

(b)


minus40

0

40

80


J-1-03-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-03-R


Beam

tip

load

(kN

)

(c)

Figure 6 Continued





λj Pj

i

P1j

(3)









minus40

0

40

80


J-1-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-05-R


Beam

tip

load

(kN

)

(d)


a

b

Δ 1

Δ 2

Δ3

Δ4








0


100200300400500

J-0-03


V j (k

N)

(a)


1000

200300400500

J-0-05


V j (k

N)

(b)


1000

200300400500

J-1-03


minus100V j (k

N)

(c)


1000

200300400500

J-1-05


V j (k

N)

(d)









07

08

09

10

11

ΔΔy

J-0-03-L i = 2 J-0-03-R i = 2J-0-03-L i = 3 J-0-03-R i = 3

jλ

(a)

06

07

08

09

10

11


J-0-05-L i = 2J-0-05-L i = 3

J-0-05-R i = 2J-0-05-R i = 3

jλ

(b)

06

07

08

09

10

11


J-1-03-L i = 2J-1-03-L i = 3

J-1-03-R i = 2J-1-03-R i = 3

jλ

(c)

06

07

08

09

10

11


J-1-05-L i = 2J-1-05-L i = 3

J-1-05-R i = 2J-1-05-R i = 3

jλ

(d)


1 2 3 40

500

1000

1500

2000

J-0-03-LJ-0-03-RJ-0-05-LJ-0-05-R

K j (k

Nm

m)

∆∆y

J-1-03-LJ-1-03-RJ-1-05-LJ-1-05-R









Firstcrackload(kN)


(mm)

Yieldload Pye(kN)


PeakloadPmax(kN)


(mm)

Ultimateload Pu(kN)










0 10 20 30 40 50 60 70 80 900

1500

3000

4500

6000

7500

9000

Ener

gy (k

Nmiddotm

m)


J-0-03J-0-05

J-1-03J-1-05





fprimec



fprimec

1113969


5 Conclusions






Acknowledgments





minus02 00 02 04 06 08 10 12 14 160090

0095

0100

0105

0110

0115

0120

J-03J-05

sv()

V jf cb jh j

(a)

03 04 050090

0095

0100

0105

0110

0115

0120


J-0J-1Φ6

V jf cb jh j

(b)



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




minus80

minus40

0

40

80

Beam

tip

load

(kN

)

J-0-03-R



minus80

minus40

0

40

80Be

am ti

p lo

ad (k

N)

J-0-03-L

(a)


minus40

0

40

80


J-0-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-0-05-R


Beam

tip

load

(kN

)

(b)


minus40

0

40

80


J-1-03-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-03-R


Beam

tip

load

(kN

)

(c)

Figure 6 Continued





λj Pj

i

P1j

(3)









minus40

0

40

80


J-1-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-05-R


Beam

tip

load

(kN

)

(d)


a

b

Δ 1

Δ 2

Δ3

Δ4








0


100200300400500

J-0-03


V j (k

N)

(a)


1000

200300400500

J-0-05


V j (k

N)

(b)


1000

200300400500

J-1-03


minus100V j (k

N)

(c)


1000

200300400500

J-1-05


V j (k

N)

(d)









07

08

09

10

11

ΔΔy

J-0-03-L i = 2 J-0-03-R i = 2J-0-03-L i = 3 J-0-03-R i = 3

jλ

(a)

06

07

08

09

10

11


J-0-05-L i = 2J-0-05-L i = 3

J-0-05-R i = 2J-0-05-R i = 3

jλ

(b)

06

07

08

09

10

11


J-1-03-L i = 2J-1-03-L i = 3

J-1-03-R i = 2J-1-03-R i = 3

jλ

(c)

06

07

08

09

10

11


J-1-05-L i = 2J-1-05-L i = 3

J-1-05-R i = 2J-1-05-R i = 3

jλ

(d)


1 2 3 40

500

1000

1500

2000

J-0-03-LJ-0-03-RJ-0-05-LJ-0-05-R

K j (k

Nm

m)

∆∆y

J-1-03-LJ-1-03-RJ-1-05-LJ-1-05-R









Firstcrackload(kN)


(mm)

Yieldload Pye(kN)


PeakloadPmax(kN)


(mm)

Ultimateload Pu(kN)










0 10 20 30 40 50 60 70 80 900

1500

3000

4500

6000

7500

9000

Ener

gy (k

Nmiddotm

m)


J-0-03J-0-05

J-1-03J-1-05





fprimec



fprimec

1113969


5 Conclusions






Acknowledgments





minus02 00 02 04 06 08 10 12 14 160090

0095

0100

0105

0110

0115

0120

J-03J-05

sv()

V jf cb jh j

(a)

03 04 050090

0095

0100

0105

0110

0115

0120


J-0J-1Φ6

V jf cb jh j

(b)



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





λj Pj

i

P1j

(3)









minus40

0

40

80


J-1-05-L


Beam

tip

load

(kN

)


minus40

0

40

80


J-1-05-R


Beam

tip

load

(kN

)

(d)


a

b

Δ 1

Δ 2

Δ3

Δ4








0


100200300400500

J-0-03


V j (k

N)

(a)


1000

200300400500

J-0-05


V j (k

N)

(b)


1000

200300400500

J-1-03


minus100V j (k

N)

(c)


1000

200300400500

J-1-05


V j (k

N)

(d)









07

08

09

10

11

ΔΔy

J-0-03-L i = 2 J-0-03-R i = 2J-0-03-L i = 3 J-0-03-R i = 3

jλ

(a)

06

07

08

09

10

11


J-0-05-L i = 2J-0-05-L i = 3

J-0-05-R i = 2J-0-05-R i = 3

jλ

(b)

06

07

08

09

10

11


J-1-03-L i = 2J-1-03-L i = 3

J-1-03-R i = 2J-1-03-R i = 3

jλ

(c)

06

07

08

09

10

11


J-1-05-L i = 2J-1-05-L i = 3

J-1-05-R i = 2J-1-05-R i = 3

jλ

(d)


1 2 3 40

500

1000

1500

2000

J-0-03-LJ-0-03-RJ-0-05-LJ-0-05-R

K j (k

Nm

m)

∆∆y

J-1-03-LJ-1-03-RJ-1-05-LJ-1-05-R









Firstcrackload(kN)


(mm)

Yieldload Pye(kN)


PeakloadPmax(kN)


(mm)

Ultimateload Pu(kN)










0 10 20 30 40 50 60 70 80 900

1500

3000

4500

6000

7500

9000

Ener

gy (k

Nmiddotm

m)


J-0-03J-0-05

J-1-03J-1-05





fprimec



fprimec

1113969


5 Conclusions






Acknowledgments





minus02 00 02 04 06 08 10 12 14 160090

0095

0100

0105

0110

0115

0120

J-03J-05

sv()

V jf cb jh j

(a)

03 04 050090

0095

0100

0105

0110

0115

0120


J-0J-1Φ6

V jf cb jh j

(b)



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







0


100200300400500

J-0-03


V j (k

N)

(a)


1000

200300400500

J-0-05


V j (k

N)

(b)


1000

200300400500

J-1-03


minus100V j (k

N)

(c)


1000

200300400500

J-1-05


V j (k

N)

(d)









07

08

09

10

11

ΔΔy

J-0-03-L i = 2 J-0-03-R i = 2J-0-03-L i = 3 J-0-03-R i = 3

jλ

(a)

06

07

08

09

10

11


J-0-05-L i = 2J-0-05-L i = 3

J-0-05-R i = 2J-0-05-R i = 3

jλ

(b)

06

07

08

09

10

11


J-1-03-L i = 2J-1-03-L i = 3

J-1-03-R i = 2J-1-03-R i = 3

jλ

(c)

06

07

08

09

10

11


J-1-05-L i = 2J-1-05-L i = 3

J-1-05-R i = 2J-1-05-R i = 3

jλ

(d)


1 2 3 40

500

1000

1500

2000

J-0-03-LJ-0-03-RJ-0-05-LJ-0-05-R

K j (k

Nm

m)

∆∆y

J-1-03-LJ-1-03-RJ-1-05-LJ-1-05-R









Firstcrackload(kN)


(mm)

Yieldload Pye(kN)


PeakloadPmax(kN)


(mm)

Ultimateload Pu(kN)










0 10 20 30 40 50 60 70 80 900

1500

3000

4500

6000

7500

9000

Ener

gy (k

Nmiddotm

m)


J-0-03J-0-05

J-1-03J-1-05





fprimec



fprimec

1113969


5 Conclusions






Acknowledgments





minus02 00 02 04 06 08 10 12 14 160090

0095

0100

0105

0110

0115

0120

J-03J-05

sv()

V jf cb jh j

(a)

03 04 050090

0095

0100

0105

0110

0115

0120


J-0J-1Φ6

V jf cb jh j

(b)



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








07

08

09

10

11

ΔΔy

J-0-03-L i = 2 J-0-03-R i = 2J-0-03-L i = 3 J-0-03-R i = 3

jλ

(a)

06

07

08

09

10

11


J-0-05-L i = 2J-0-05-L i = 3

J-0-05-R i = 2J-0-05-R i = 3

jλ

(b)

06

07

08

09

10

11


J-1-03-L i = 2J-1-03-L i = 3

J-1-03-R i = 2J-1-03-R i = 3

jλ

(c)

06

07

08

09

10

11


J-1-05-L i = 2J-1-05-L i = 3

J-1-05-R i = 2J-1-05-R i = 3

jλ

(d)


1 2 3 40

500

1000

1500

2000

J-0-03-LJ-0-03-RJ-0-05-LJ-0-05-R

K j (k

Nm

m)

∆∆y

J-1-03-LJ-1-03-RJ-1-05-LJ-1-05-R









Firstcrackload(kN)


(mm)

Yieldload Pye(kN)


PeakloadPmax(kN)


(mm)

Ultimateload Pu(kN)










0 10 20 30 40 50 60 70 80 900

1500

3000

4500

6000

7500

9000

Ener

gy (k

Nmiddotm

m)


J-0-03J-0-05

J-1-03J-1-05





fprimec



fprimec

1113969


5 Conclusions






Acknowledgments





minus02 00 02 04 06 08 10 12 14 160090

0095

0100

0105

0110

0115

0120

J-03J-05

sv()

V jf cb jh j

(a)

03 04 050090

0095

0100

0105

0110

0115

0120


J-0J-1Φ6

V jf cb jh j

(b)



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








Firstcrackload(kN)


(mm)

Yieldload Pye(kN)


PeakloadPmax(kN)


(mm)

Ultimateload Pu(kN)










0 10 20 30 40 50 60 70 80 900

1500

3000

4500

6000

7500

9000

Ener

gy (k

Nmiddotm

m)


J-0-03J-0-05

J-1-03J-1-05





fprimec



fprimec

1113969


5 Conclusions






Acknowledgments





minus02 00 02 04 06 08 10 12 14 160090

0095

0100

0105

0110

0115

0120

J-03J-05

sv()

V jf cb jh j

(a)

03 04 050090

0095

0100

0105

0110

0115

0120


J-0J-1Φ6

V jf cb jh j

(b)



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




fprimec



fprimec

1113969


5 Conclusions






Acknowledgments





minus02 00 02 04 06 08 10 12 14 160090

0095

0100

0105

0110

0115

0120

J-03J-05

sv()

V jf cb jh j

(a)

03 04 050090

0095

0100

0105

0110

0115

0120


J-0J-1Φ6

V jf cb jh j

(b)



References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


References

































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


performanceofreinforcedreactivepowderconcrete beam...

Documents