Experimental and Numerical Studies on the Negative ...

Research ArticleExperimental and Numerical Studies on the Negative FlexuralBehavior of Steel-UHPC Composite Beams

Xinhua Liu 12 Jianren Zhang2 Zihan Cheng3 and Meng Ye3

1CCCC Second Highway Consultants Co Ltd Wuhan 430056 China2College of Civil Engineering Changsha University of Science amp Technology Changsha 410114 China3College of Civil Engineering Hunan University Changsha 410082 China

Correspondence should be addressed to Xinhua Liu h2112xh163com

Received 30 June 2020 Revised 4 January 2021 Accepted 21 January 2021 Published 31 January 2021

Academic Editor Filippo Ubertini

Copyright copy 2021 Xinhua Liu et al )is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

)e cracking of concrete in the negative moment region for a composite beam subjected to a negative bending moment reducesthe beamrsquos strength and stiffness To improve the cracking performance of composite beams this paper presents an experimentalinvestigation on applying ultrahigh-performance concrete (UHPC) instead of conventional concrete )ree steel-UHPCcomposite beams with different forms of joints were designed and tested through a unique rotation angle loading method using aspring displacement control testing setup )e crack distribution rotation versus crack width load versus spring displacementand strains in the UHPC slab and steel girders weremeasured and studied Nonlinear finite element analysis using ABAQUS basedon the damaged plasticity model of concrete was carried out for comparison with the test results )e experimental and numericalresults showed that the use of a UHPC slab can enhance the cracking performance of composite beams Considering theconvenience of construction a reasonable joint form was suggested and the appropriate UHPC longitudinal laying length in thenegative moment region was proposed to be 01 L Furthermore a simplified formula for calculating the UHPC crack width wasdeveloped based on bond-slip theory

1 Introduction

Steel-concrete composite bridges have been widely used inhighways and urban construction due to their advantages ofa light weight excellent seismic performance and quickconstruction )e construction method of erecting simplysupported steel girders and then casting a continuousconcrete slab on a multispan structure is often used inconstructing small- and medium-span composite bridgesHowever concrete slabs are liable to crack under serviceloads since the composite beam is subjected to a negativebending moment at the internal supports )e occurrence ofcracks leads to a decrease in the stiffness and durability of acomposite beam )erefore a key aspect of the mechanicalproperties of composite beams is the cracking resistance ofconcrete slabs in the negative moment region

A series of studies have investigated the mechanicalbehavior of composite beams in the negative moment

region Chen [1] performed an experimental study oncomposite beams with external tendons in negative momentregions they found that in hogging moment regions addingprestressing to the composite beams with external tendonscan effectively increase the cracking resistance of the beamsRyu et al [2] conducted an experimental test of two-spancontinuous composite girders with prefabricated slabs undera negative bending moment to study crack control andfound that the initial crack spacing of the slab in a compositegirder with prefabricated slabs can be wider than those ofgeneral reinforced concrete (RC) beam structures

In recent years researchers have tried to apply high-performance materials to improve the cracking behavior ofstructures Alfarabi et al [3] presented an experimentalinvestigation into the use of carbon fibre-reinforced polymer(CFRP) in the negative moment region of continuouscomposite girders and confirmed the effectiveness of CFRPsheets in preventing crack initiation In recent years several

HindawiAdvances in Civil EngineeringVolume 2021 Article ID 8828175 15 pageshttpsdoiorg10115520218828175

studies [4ndash6] have been performed to investigate the be-havior of steel fibre reinforced concrete (SFRC) beams Itwas reported that SFRC has developed as an option tomitigate the unfavorable cracking characteristics of normalconcrete due to the ability of the fibres to increase post-cracking behavior and energy-absorbing capacity In addi-tion the recent development of ultrahigh-performanceconcrete (UHPC) offers an attractive solution for improvingthe mechanical properties of composite beams in the neg-ative moment region Zhang et al [7 8] investigated theflexural behavior of damaged RC bridge deck strengthenedby the UHPC layer

UHPC is an advanced cementitious material that ex-hibits excellent compressive and tensile mechanical be-haviors and great durability properties UHPC has acompressive strength over 150MPa and a tensile strengthover 7MPa and UHPC exhibits strain hardening andmultiple cracking behavior Compared with SFRC UHPC isadvantageous in weight reduction owing to its high strengthIn view of the excellent mechanical properties of UHPC thispaper presented an experimental investigation on applyingUHPC in the negative moment region

In this study the negative flexural behavior of steel-UHPC composite beams with different joints was experi-mentally investigated )e ultimate load the load-dis-placement response and the crack distribution are appliedto evaluate the effect of the joint forms on the crackingperformance of the composite beams Finite element ana-lyses were thus also carried out to model the three compositebeams Based on these tests and simulation results andconsidering the mechanical behavior as well as the con-venience and cost of construction an applicable joint for thenegative moment region and the laying length proportion ofUHPC were proposed to enhance the cracking resistance ofthe concrete slab in the negative moment region for com-posite beams Finally a simplified formula for calculatingUHPC crack width was developed based on bond-sliptheory

2 Experimental Program

21 Test Specimens )ree composite beams CB-1 CB-2and CB-3 were tested in this study Each beam consisted oftwo simply supported welded steel I-girders with a singlespan of 1500mm and a continuous UHPC slab that was caston the steel girders For more enhancement of crackingperformance three different forms of joint at the internalsupport were designed )e details for the beams includingthe span layout the cross section and joint forms are shownin Figure 1 )e composite beams were designed to developfull composite action between the steel girder and the UHPCslab through 10mm diameter 40mm long shear studswelded to the top flange of the steel girder In the UHPCslabs appropriate amounts of 14mm diameter longitudinalreinforcements and 10 mm diameter transverse reinforce-ments with a nominal yielding strength of 400MPa(HRB400) were properly spaced To prevent web distortionvertical stiffeners are welded to the web of the steel beam atthe supports

Figure 1(b) shows the joint forms of steel girders for thethree composite beams In the CB-1 only the top flanges ofthe adjacent steel girders were welded together at the jointCB-2 and CB-3 were similar to CB-1 except that the webs ofCB-2 and CB-3 were also partially welded together at thejoint

22 Material Properties )e mix design of UHPC in thisstudy is given in Table 1 )e UHPC was reinforced by13mm long 02mm diameter hooked-end steel fibres andthe fibre content was 25 by volume of UHPC)ree cubeswith side lengths of 100mm six prisms with dimensions of100mmtimes 100mmtimes300mm and three prisms with di-mensions of 100mmtimes 100mmtimes400mm were prepared forthe material property tests of UHPC )e mechanicalproperties of the steel plates and HRB400 rebar were ob-tained through coupon tests Tables 2 and 3 summarize themechanical properties of these materials

23Test Setupand Instrumentation To simulate the negativemoment region over the internal support two springs wereapplied instead of roller end supports of the compositebeams )e beams were tested by applying two concentratedloads at the spring support ends with two hydraulic jacks asshown in Figure 1 Compared with applying load at themidspan this loading method can achieve larger rotationangle and negative bending moment at the internal supportwhich makes it easier to observe the whole process of crackdevelopment and yield and failure mode of the slabs )eloading process was controlled by the displacement of thesprings with an increment of 05mm per stage )e loadingwas stopped when the displacement of the spring reached30mm

)e beams were instrumented for the purpose ofmeasuring applied load deflections crack formation crackdevelopment and sectional strains across the depth Straingauges were mounted on the UHPC slab steel beams andsteel reinforcements for measuring the longitudinal strainsin the specimens )e deflections at the support locations ineach loading step were measured using four electronic de-flection gauges Moreover four load cells were placed at thesupports to record the load Figure 2 shows the arrangementof the deflection gauges and strain gauges In the tests thecrack width and crack development were also detected andrecorded in each load step with a digital crack-observationdevice

3 Test Results

31 Test Observations According to Rafiee [9] cracks withwidths less than 005mmhave little effect on the durability ofUHPC and thus a crack width of 005mm can be defined asthe critical width )e load corresponding to the appearanceof a 005mm wide crack can be defined as the critical loadand the stress calculated through the load is referred to as thenominal tensile stress In this paper this state is defined asthe critical cracking state

2 Advances in Civil Engineering

)e results of three test beams are summarized in Ta-ble 4 including the load displacement crack width andstrain of the steel beam and UHPC under the criticalcracking state and the final state )e final state is defined asthe state that the spring displacement reached 30mm andthen the loading was stopped Taking CB-1 (Figure 3) as anexample for a detailed description when the total dis-placement of the spring increased to 4mm 2-3 transverse

cracks with widths of 005mm appeared on the top surfaceof the UHPC slab at the joint and the corresponding ro-tation angle at the internal supports was 014deg the tensilestrain of the UHPC slab over the joint was 1453 microε As theload increased the angular displacement at the internalsupports continued to increase and more cracks appearedon the top surface of the UHPC slab When the springdisplacement reached 12mm the rotation angle at the in-ternal supports was 043deg and the maximum crack widthreached 031mm the cracks extended transversely to theedges of the UHPC slab becoming wider and mainly dis-tributed at the joint in the negative moment region (sectionB-B in Figure 1) Finally when the spring displacementreached 30mm the rotation angle at the internal supportswas 107deg the width of the main cracks on the top of theUHPC slab reached 103mm and the tensile strain was5750 microε the angular displacement at the internal supportswas sufficiently large to stop the loading

For CB-2 and CB-3 the test process and crack devel-opment modes were very similar to those of CB-1 In thefinal state the rotation angles at the internal supports of CB-2 and CB-3 were both 107deg and the tensile strains of theUHPC were 5152 microε and 4813 microε respectively

However the stress state of the top flange and web of thesteel girder in these two beams differed from that of CB-1due to the different forms of joints In the final state the topflange of CB-1 was in compression at the joint and thecompressive strain was 1453 microε However the top flanges ofCB-2 and CB-3 were in tension at the joint because the webswere also welded and the tensile strains in the flanges ofthese beams were 1114 microε and 863 microε respectively whichwere still in the elastic state )e bottoms of the welded webs

200

Joint

B

AP P

UHPC slab

Steel girder Steel girder

A

B

1500 1500

K K

Stiffener StiffenerStiffener Stiffener

(a)

120CB-1

70

120

CB-2

120

140 CB-3

Section B-B

tw = 8

6007times75

60

250

190

120

Section A-A

10835

(b)

Figure 1 Details of the beams (a) longitudinal configuration and (b) Section A-A and joints (units mm)

Table 1 Mix design of UHPC

Material Mass ratioCement 1Silica fume 025Quartz sand 11Quartz powder 03Water reducer 0019Water 02

Table 2 Material properties of UHPC (units MPa)

Material fcu ft EcUHPC 1523 82 47300

Table 3 Material properties of steel and reinforcement

Material )ickness ordiameter (mm)

Yield strength(MPa)

Youngrsquosmodulus (MPa)

Steelplate

t 8 3537 206000t 10 3601 206000

HRB400 d 10 4686 200000d 14 4974 200000

Advances in Civil Engineering 3

were in compression at the joint In the final state localbuckling occurred on the welded webs due to their smallcompressive area and the maximum compressive strains ofwebs at the joint were 4264 microε and 3623 microε for CB-2 and CB-3 respectively

32 Crack Distribution and Rotation-Crack WidthRelationship )e final crack distribution and maximumcrack widths in the negative moment region are shown inFigure 4 )e cracks in CB-1 were closely spaced andconcentrated between the internal supports with amaximum width of 103 mm CB-2 exhibited a crackdistribution similar to that of CB-1 with a smallermaximum crack width of 092 mm Compared with theother two beams the cracks in CB-3 had a wider dis-tribution and were more uniformly spaced with thesmallest maximum crack width of 051 mm )ese resultsindicate that CB-3 has greater cracking performance with

smaller crack width chiefly because the cross-sectionalstiffness of CB-3 was larger than those of CB-1 and CB-2at the joint

Figure 5 shows the rotation-crack width relationship ofthe three beams When the crack width reached the criticalvalue of 005mm the angular displacements of CB-1 CB-2and CB-3 were 014deg 023deg and 025deg respectively and thestrains on the top surface of the UHPC slab were 1453 microε1516 microε and 1774 microε respectively Apparently UHPC has amuch higher critical cracking strain than conventionalconcrete which demonstrates that the adoption of UHPC inthe negative moment region can significantly improve thecracking resistance of steel-concrete composite beamsCompared with the other two beams CB-3 had larger an-gular displacement and larger tensile strain demonstratingthat CB-3 has greater cracking performance than the othertwo beams

In the final state the crack widths of CB-1 CB-2 and CB-3were 103mm 092mm and 051mm respectively and the

K K

Load cellElectronic deflection gauge

(a)

1

1

2

2

3

3

4

4 5

5 6 7

6 7

T4-1T4-1

T5-1 T6-1 T7-1

1100 2 times 200 2 times 100 2 times 200 1100

2 times

150

Longitudinal

600

(b)

Figure 2 Layout of the test instruments (a) deflection gauges and (b) strain gauges on the UHPC slab (units mm)

Table 4 Main test results

State Testbeam

Load(kN)

Displacement(mm)

Rotation(deg)

Crack width(mm)

Strain of UHPC topsurface (microε)

Strain of top flange ofsteel girder (microε)

Critical crackingstate

CB-1 90 4 014 005 1453 269CB-2 166 65 023 005 1516 231CB-3 321 7 025 005 1774 206

Final stateCB-1 353 30 107 103 5750 1453CB-2 423 30 107 092 5152 1114CB-3 590 30 107 051 4813 863


strains at the top surface of the UHPC slab were 5750microε5152microε and 4813microε respectively )ese results showed thatjoint forms have a great influence on the strain and cracking ofthe slab in the negative moment region)e joint form in CB-3has greater stiffness and flexural capacity than that in CB-1 andCB-2 and these characteristics can effectively reduce the strain

and crack width in the negative moment region It can beconcluded that the stiffness improvement of the joint haspositive influences on the cracking behavior and the failuremode of steel-UHPC composite beams With the increasementof joint stiffness the cracking strength was improved and thedevelopment of cracks was delayed

Figure 3 Rotation of the composite beam

3 times 200 3 times 2002 times 100

wmax = 103mm

(a)

wmax = 092mm

3 times 2003 times 200 2 times 100

(b)

wmax = 051mm

3 times 200 2 times 100 3 times 200

(c)

Figure 4 Crack distribution in the UHPC slabs (units mm) (a) CB-1 (b) CB-2 and (c) CB-3


33 Load-Spring Displacement Curves Figure 6 shows theload-spring displacement response of the three beams Forthe early stage before the spring displacement reached7mm the load-spring displacement curve of CB-3 has thehighest rate of increase and that of CB-1 has the lowest )esecant slopes of CB-1 CB-2 and CB-3 were 129 211 and414 respectively corresponding to a load equal to 05Pu(ultimate load) the stiffnesses of CB-2 and CB-3 were ap-proximately 60 and 220 greater than that of CB-1 re-spectively )e moment-rotation curves were similar to theload-spring displacement curves and are shown in Figure 7For the early stage before the rotation angle reached 025degthe moment-rotation curve of CB-3 has the highest rate ofincrease and that of CB-1 has the lowest )e results indicatethat the overall stiffness of CB-3 is the greatest while CB-2 isthe greater and CB-1 is the smallest

)e test results showed that welding the web at the jointcontributed to the load-carrying capacity of the compositebeam and that the height of the welded web had a greatinfluence on the load-carrying capacity )e load-carryingcapacities of CB-2 and CB-3 were approximately 40 and140 greater than that of CB-1 respectively

34 UHPC Rotation-Strain Relationship )e rotation-lon-gitudinal strain curves of critical measuring points on thetop surface of the UHPC slab in the negative moment regionare shown in Figure 8 )e strain of the UHPC slab over thejoint increased with increasing angular displacement andthe rotation-strain curves were approximately linear )eresults of three test beams show that the tensile straindistribution along the length of the slab was uneven )estrains of the slab were largest at the joint (measuring pointT4-1) and gradually decreased away from the joint Whenthe rotation angles of the beams were relatively small

corresponding to critical cracking the tensile strains outsidethe range of 500mm from the joint were less than 500 microεwhich greatly reduced the requirements of the crackingperformance Under the same spring displacement for asingle critical point (T4-1) the strain of CB-1 was the highestand that of CB-3 was the lowest indicating that the joint ofCB-1 led to better cracking performance

Under the ultimate state the tensile strains on the UHPCtop surface of the three beams exceeded 4500 microε therebyfully utilizing the tensile performance of UHPC

CB-1CB-2CB-3

Critical width of 005mm

00

02

04

06

08

10

12

Rota

tion

(deg)

02 04 06 08 10 1200Crack width (mm)

Figure 5 Rotation-crack width relationship

7

CB-1CB-2CB-3

0

10

20

30

40

50

60

Load

(kN

)

5 10 15 20 25 300Spring displacement (mm)

Figure 6 Load-spring displacement curves


4 Finite Element Analysis

To verify the reliability of the test results nonlinear analyseswere carried out to simulate the test process and compre-hensively analyse the test beams which laid the foundationfor further structural analysis

41 Modelling )e nonlinear finite element models wereestablished using the commercial software program ABA-QUS as shown in Figure 9 )e steel girder UHPC bearingand shear studs were modelled using eight-node brick el-ements (C3D8R) the steel reinforcements which wereconnected with the UHPC slab by an embedded restraintwere modelled using a two-node linear 3D truss element(T3D2))e shear stud was divided into two parts the upper

part of which was connected with the UHPC slab and thelower part of which was connected with the top flange of thesteel beam by an embedded restraint Surface-to-surface

CB-1CB-2CB-3

025

0

10

20

30

40

50

60

70

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

Figure 7 Moment-rotation curves

T4-1T4-2T5-1

T6-1T7-1

0100020003000400050006000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(a)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

6000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(b)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(c)

Figure 8 Rotation-strain relationships of UHPC slabs (a) CB-1 (b) CB-2 and (c) CB-3

Figure 9 Model of the composite beam


contact was used to define the concrete-steel interaction thetangential direction of the interface adopted a penaltyfunction and the friction coefficient was 03 [10] the normaldirection of the interface adopted hard contact )e inter-action between the support block and the steel beam adopteda tie constraint In addition the influence of mesh size on theaccuracy of the numerical simulation has been investigatedwith different mesh sizes After comparison of the numericalresults the mesh size of 1 cm was used for UHPC slab andsteel beam the mesh size of 5mm was used for steel re-inforcements and the mesh size of 2mmwere used for shearstuds )e loads on the FE model were applied using dis-placement control by two reference points

42 Stress-StrainRelationship )e compressive stress-strainrelationship of UHPC (Figure 10) proposed by Shan [11] wasused herein which is given as follows

σfc

ax +(6 minus 5a)x5

+(4a minus 5)x6 0lexlt 1

x

b(x minus 1)2

+ x xge 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(1)

where the compressive strength fc 1523MPa x εεc0 inwhich εc0 is the strain corresponding to the peak andε0 3500microε a is the ratio of the initial tangent modulus(Ec 473GPa) to the peak secant modulus (Esec fcε0)and b is a test fitting parameter equal to 241

)e tensile stress-strain relationship of UHPC (Fig-ure 10) comprises a two-stage tensile constitutive model[12] and the descending constitutive model [13] is given asfollows

σt

Ecεt 0le εt le εt0

ft εt0 lt εt le εtp

ft

1 + εt minus εtp1113872 1113873lcwp1113872 1113873p εtp lt εt

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)

where the tensile stress ft 82MPa εtp 2000microεwp 07mm lc 40mm and p 10

)e constitutive relationships of the steel beam andreinforcement applied an ideal elastoplastic model)e yieldstrength was obtained through testing as shown in Table 3

)ree constitutive models are available in ABAQUS forconcrete the smeared cracking model the brittle crackingmodel and the damaged plasticity model Since the strainsoftening of concrete under tensile-compressive biaxialstress was considered the damage plasticity model can bettersimulate the mechanical deformation behavior of concretebeams than the other models and the concrete tensileplasticity was simulated through strain hardening and strainsoftening of the descending branch

)e damaged plasticity model of UHPC is composed ofelasticity and plasticity Elastic parameters include elasticmodulus and Poissonrsquos ratio and were obtained throughmaterial tests to be E 473 GPa and ] 02 respectively

)e plastic parameters were set according to the ABAQUSuser manual [14] as shown in Table 5 )e plastic-damageconstitutive relationship of UHPC was determined by theenergy equivalence principle based on the constitutivestress-strain relationship )e damage factor of tensile andcompressive UHPC could be calculated using equation (3)with the stress-strain response obtained from equations (1)and (2) [15]

D 1 minus

σEε

1113970

(3)

43 Finite Element Analysis Results )ree moment-rotationcurves obtained from the nonlinear finite element analysisare compared with the test results in Figure 11 )e momentof the test beams was derived by the values obtained fromload cells )e characteristic points of numerical analysis forCB-1 CB-2 and CB-3 are basically consistent with those inthe test results including the cracking point and the yieldpoint )erefore the comparison shows that the three finiteelement models can accurately simulate the whole bendingprocess of these steel-UHPC composite beams

)e damaged plasticity model in ABAQUS cannotsimulate the cracking of UHPC however the cracks can beidentified through the principal tensile strain contour plotsof UHPC as shown in Figure 12 Comparing these plots withthe measured crack distribution it is found that the straincontour plot calculated by the model is similar to the crackdistribution from the test

5 Cracking Performance of UHPC

Based on the mechanical characteristics of a bridge deck inthe negative moment region one of the following principlescould be chosen when designing the slab for the sake of long-term durability (1) tensile stress is prohibited (2) criticalcracks are prohibited and (3) crack width is limited)e firstprinciple is rarely used due to the strict requirements for slabstress which can only be realized through prestressingtendons and is inconvenient For the second principle tocontrol critical cracks in a UHPC slab the maximum tensilestress of the UHPC slab should be controlled to be less thanthe nominal tensile stress of the UHPC )is paper focuseson the cracking behavior of UHPC in the negative momentregion mainly based on the second design principle

)e second principle is discussed from the followingthree aspects (1) the nominal tensile stress of the test beams(2) the influence of shrinkage on the UHPC cracking per-formance and (3) the calculation of the crack width )enominal tensile stress can be calculated through the testresults as shown in a later section)e shrinkage of UHPC islarger than that of normal concrete due to the low water-to-cementitious material ratio which has a notable effect on thecracking performance of UHPC therefore the influence ofshrinkage on UHPC cracking performance was studied Inaddition to control critical cracks in the slab the crack widthshould be calculated under the given load thus a simple


formula for calculating crack width was proposed based onbond-slip theory

51UHPCNominal Tensile Stress )e nominal tensile stressfcr of a steel-UHPC composite beam was derived as follows

fcr Mcr

αEItimes ht (4)

where Mcr is the cracking moment αE is the ratio ofelasticity modulus of steel and concrete I is the moment ofinertia of the composite section and ht is the distance fromthe section centroid to the UHPC surface )e crackingmoment Mcr was calculated from the critical cracking loadFcr obtained through testing )e slip between the steel plateand the UHPC was not considered Table 6 shows thecalculation results

Note that the nominal tensile stress of the three steel-UHPC composite beams under the negative moment isgreater than 23MPa which is much higher than the tensile

design strength of conventional concrete Apparently theapplication of UHPC can greatly enhance the cracking loadand inhibit the development of cracks in the negativemoment region which may effectively solve the crackingproblem of steel-concrete composite beams in the negativemoment region

52 Shrinkage of UHPC )e total shrinkage of UHPC ishigher than that of normal concrete or high-performanceconcrete due to the ultra-low water-to-cementitious materialratio in UHPC UHPC shrinkagemainly includes drying andautogenous shrinkage Drying shrinkage is caused by thesurface moisture loss in UHPC and autogenous shrinkage isthe consequence of volumetric contraction due to the in-ternal consumption of water during cement hydration

Shrinkage is caused by internal factors and externalfactors )e internal factors affecting UHPC shrinkage arethose related to its constituents (ie aggregates and cements)as follows the water-cementitious material ratio the mixdesign admixtures specimen size and curing conditions

ε

σfc

εc0

(a)

w

Strain hardening Strain soening

σ σ

ft

fp

εpc wpc wp

(b)

Figure 10 Stress-strain model for UHPC (a) compression and (b) tension

Table 5 Parameters for the damaged plasticity model of UHPC

Expansion angle Eccentricity Strength ratio f Kc Viscosity

30deg 01 116 23 00005

FEMTest

0

5

10

15

20

25

30

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(a)

FEMTest

05

10152025303540

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(b)

FEMTest

010203040506070

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(c)

Figure 11 Moment-rotation curves (a) CB-1 (b) CB-2 and (c) CB-3


)e external factors include ambient conditions humidityand restraints To reduce the effect of shrinkage on UHPCcracking performance steam treatment is generally used inthe laboratory (the test beams in this study also adoptedsteam treatment) which can accelerate the shrinkage to suchan extent that the entirety of the shrinkage occurs during a 2-day treatment and the UHPC is then stabilized againstfurther shrinkage [16] However steam curing is difficult toachieve at construction sites due to the limitation of UHPCconstruction conditions )is paper considers the effects ofthe curing conditions constraints steel fibres and admix-tures on the shrinkage and the effect of UHPC shrinkage onthe cracking performance of the composite beams

(1) Curing conditions have a crucial impact on UHPCshrinkage )e shrinkage of UHPC is approximately

zero after steam curing which is beneficial to thestructure but difficult to implement at constructionsites Greybeal concluded that when no steam curingis conducted UHPC tends to exhibit approximately800 microε of shrinkage as measured 1 year after casting[16] According to the French specification [17] inan environment with an average relative humidity of50sim70 the autogenous shrinkage and dryingshrinkage are 500 microε and 150 microε respectively suchthat the total shrinkage reaches a total of 700 microε )eJapanese specification [18] stipulates that the totalshrinkage of UHPC with no steaming should be550 microε )e Swiss specification [19] and the FederalHighway Administration (FHWA) study report [20]suggest that the total shrinkage of UHPC is600ndash800 microε without steam curing )erefore forUHPC under normal moist curing without steamingthe autogenous shrinkage and drying shrinkage areapproximately 550 microε and 150 microε respectively for atotal of approximately 700 microε

(2) Steel bars have a restraint on UHPC shrinkageHuang and Hu investigated the shrinkage charac-teristics of UHPC with different reinforcement ratios

E Max principal(Avg 75)

ndash1091e ndash 04+2334e ndash 03+4776e ndash 03+7219e ndash 03+9661e ndash 03+1210e ndash 02+1455e ndash 02+1699e ndash 02+1943e ndash 02+2187e ndash 02+2432e ndash 02+2676e ndash 02+2920e ndash 02

(a)



(b)



(c)

Figure 12 Principal tensile strain contour plots of UHPC in ultimate states (a) CB-1 (b) CB-2 and (c) CB-3

Table 6 Nominal tensile stress of the model beams

Beam Cracking strain (microε) UHPC nominal tensilestress fcr (MPa)

CB-1 1453 232CB-2 1516 253CB-3 1774 239


under steam curing and concluded that theshrinkage value of unreinforced UHPC is approxi-mately 25 times that of UHPC with a reinforcementratio of 452 [21] Since steam curing only accel-erates autogenous shrinkage but has little effect onthe overall shrinkage value a conclusion is drawnthat steel bars can significantly constrain the UHPCshrinkage under steam curing or normal moistcuring and the autogenous shrinkage of UHPC witha reinforcement ratio of 5 can be reduced by morethan 50

(3) )e presence of steel fibres is able to decrease theshrinkage Wu et al concluded that drying shrinkagecan be reduced by more than 20 by adding a steelfibre content of 2 by volume [22]

In summary the shrinkage strain in UHPC without steamtreatment is approximately 700microε )rough the addition of asteel fibre content of 2 by volume the shrinkage strain ofUHPC can be reduced to less than 400microε An expansive ad-mixture and a shrinkage reducing agent could also be usedduring the setting of UHPC

)e test results of the three specimens show that in thenegative moment region the critical cracking strain of steel-UHPC is greater than 1450microε under steam curing conditionsHowever the shrinkage strain should be taken into account ifthere is no steam curing the value of which is less than 400microεHence if there is no steam curing the cracking strain in the testswill be greater than 1050microε and the corresponding crackingnominal tensile stress is greater than 18sim20MPa which canmeet the engineering requirements

53CalculationofUHPCCrackWidth Based on the classicaltheory of cracks and considering the contribution of thetensioned UHPC between the cracks the crack width at themost tensioned reinforcement ws is given by the followingexpression in the French standard [17]

ws srmax f εsmf minus εcmf1113872 1113873 (5)

where srmax f is the maximum cracking spacing εsmf is theaverage strain in the reinforcement εcmf is the averagestrain in the UHPC between cracks and (εsmf minus εcmf) iscalculated with the following expression

εsmf minus εcmf σs

Es

minusfctfm

Ecm

minuskt fctmel minus fctfm1113872 1113873 1ρeff( 1113857 + EsEcm( 1113857( 1113857

Es

(6)

where σs is the stress in the tensioned reinforcing steel ρeff isthe effective reinforcement ratio Aceff is the effective cross-sectional area of UHPC around the tensioned reinforce-ment and kt is a factor dependent on the duration of theload or its repetition

)emaximum spacing between cracks is calculated fromthe following expressions

srmax f 255 l0 + lt( 1113857 (7)

l0 133c

δ (8)

ltr 03k21 minus fctfmfctmel1113872 1113873

δη⎡⎣ ⎤⎦

ϕρeffge

lf

2 (9)

δ 1 + 05fctfm

fctmel

1113888 1113889 (10)

where l0 is the concrete coating thickness ltr is the loadtransmission length c is the concrete coating for the rein-forcement ϕ is the diameter of the reinforcement η is abond factor (equal to 225 for a steel reinforcement) δ is afactor that expresses the improvement contributed by thefibres in the behavior of the concrete cover area and to thebonding of the reinforcement and k2 is a factor that ac-counts for the distribution of strain in the cracked section

Note that the above formula of the strain differencebetween reinforcing bars and concrete is complicated andhas many parameters To simplify the calculation processthe classical bond-slip theory is used to simplify this formula

)e tests show that when a single crack reached thecritical width of 005 mm the surrounding UHPC wasuncracked In this phase of critical crack formation astrain difference existed only along the load transmissionlength of the reinforcing bars and concrete [23] and thestrain and stress of the reinforcing bars and UHPC can beassumed to be the same as those of the original sectionexcept for the transmission length ltr )erefore for theuncracked section the reinforcing bars and concrete havethe same strain (εse εct) Figure 13 shows the straindistribution of the tensioned members )e stress dif-ference in the steel bars along the load transmissionlength is balanced by the bond force

πdsltrτbm Ar σsr minus σse( 1113857 (11)

where ds is the diameter of the rebar τbm is the bond stressaveraged over the transmission length Ar is the cross-sectional area of the rebar σsr is the rebar stress in thecracking cross section and σse is the rebar stress on bothsides of the crack

σse Esεct αEσct (12)

where αE EsEc in which Es and Ec are the elastic moduliof steel and concrete respectively

)e load transmission length is derived from equations(11) and (12) as follows

ltr σsr minus αE middot σct( 1113857ds

4τbm

(13)

)e strain difference between both ends of the rebar overthe transmission length is Δεsr εsr minus εse )e average rebarand UHPC strains are derived as follows


εsm εsr minus βΔεsr (1 minus β)εsr + βεse (14)

εcm β middot εct β middot εse (15)

)e strain difference between rebars and concrete iscalculated as follows

εsm minus εcm (1 minus β) middot εsr (16)

where β is the average strain distribution factor which isdefined as β middot Δεsr (1ltr) 1113938

ltr

0 εs(x)dx and is suggested tobe 2π [24]

)e calculation for crack width at the most tensionedreinforcement ws is simplified as follows

ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)

Since the UHPC slab and the steel girder are consideredas a composite beam in the simplified calculation it is as-sumed that the UHPC slab has the same curvature as thesteel girder and the crack width wt on the surface of theUHPC slab can be derived from the crack width ws at thelocation of the rebar

wt ws middot1cs

ws middoth1

h1 minus ast

(18)

where cs is the lever arm coefficient of the reinforcing barwhich describes the capacity contribution of rebar and theeffect on inhibiting cracks h1 is the height of the tensionedpart of the cross section and ast is the distance from thecentroid of the rebar to the top surface of the UHPC

)e critical crack width on the top surface of the UHPCslab for the three test beams under the negative bendingmoment is calculated based on the modified crack formula(equations (17) and (18)) and then the calculated results arecompared with the test results as shown in Table 7

)e calculated values of the critical crack width for eachtest beam are in good agreement with the test results and thecalculated values are relatively conservative which cansatisfy the requirements for engineering calculations

6 Steel-UHPC Composite Beam Joint Forms

)e test and analysis results above verified the feasibility ofapplying UHPC to steel-concrete composite beams in the

negative moment region Considering the cracking behaviorload-carrying capacity web yield strength and convenientconstruction the applicability of different joint forms wasevaluated

)e nominal tensile stresses of the three test beams are allabove 23MPa and close to each other )e load-carryingcapacity of CB-3 is higher than those of the other twoConsidering that the web stiffness of the joints is small inCB-2 and CB-3 which are prone to web distortion and thejoint of CB-1 is easier to construct than those of CB-2 andCB-3 the joint form in CB-1 is more applicable toconstruction

At construction sites the top flange of the steel beam canbe welded or bolted at the joint as shown in Figure 14(a)Compared with a welded connection a bolted connection ismore convenient to construct and is of higher qualityMoreover if the joint form of CB-3 is chosen to be used fromthe perspective of load-carrying capacity the webs undercompression should be stiffened to avoid local buckling asshown in Figure 14(b)

7 Longitudinal Laying Length of UHPC

At present UHPC materials are much more expensive andmore complicated to construct than normal concrete)erefore the amount of UHPC should be minimized tomeet the economic requirements under the premise ofmeeting the structural mechanical requirements )e lon-gitudinal laying length of UHPC for the steel-UHPCcomposite beam is determined herein

A two-span steel-concrete composite bridge is taken asan example which is simply supported with a continuouslink slab and has a clear span of 30m )e width of a singlecomposite girder is 168m Figure 15 shows the longitudinaland cross-sectional configurations

A finite element model was established to determine themaximum tensile stress of the top surface of the UHPC slabin the negative moment region the value of which is170MPa From the perspective of cracking behavior allthree test beams can satisfy the demands of principle (2)which stipulates that the tensile stress is less than the normalstress given in 41

Figure 16 shows the stress distribution in the top surfaceof the deck slab along the bridge Apparently UHPC can belaid at the place where the tensile stress in the top surface of

Rebar

UHPC εsm = βεct

εse

Cracking cross section

Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct

εsm = εsr ndash β∆εsr

ltr

Figure 13 Strain distribution in the UHPC steel fibre and rebar


NC UHPC(008~015) L

Tensile stress of deck slab

Allowable tensile stress (or ftd)

0 31 2ndash1ndash2ndash3Distance (m)

0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)

Figure 16 Longitudinal laying length of UHPC

Table 7 Calculation of the critical crack width for the test beams

Beam Rebar stress (MPa) Calculation result ① (mm) Test result ② (mm) (①minus②)② ()CB-1 13451 00571 005 142CB-2 15139 00548 005 96CB-3 19357 00512 005 24

UHPC

Bolted (or welded)Bolted connection

Welded connection

(a) (b)

Figure 14 Joint form in the construction site (a) bolted connection and welded connection and (b) web stiffener for CB-3

2 times 30000

Bearing Bearing Bearing

A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)

Figure 15 Details of the steel-concrete composite bridge (a) span layout and (b) cross section (units mm)


the deck slab exceeds the allowable tensile stress or ftd thedesign tensile strength of deck concrete Normal concretecan be used in other parts In the range of approximately 3min the negative moment region the tensile stress is largerthan the tensile strength of normal concrete Hence therecommended laying length of UHPC is 3m (01L) whichgreatly reduces the amount of UHPC under the premise ofmeeting the structural mechanical requirements

8 Conclusion

)is paper presented a method for applying UHPC insteadof conventional concrete and new forms of joints in thenegative moment region to solve the slab cracking problemof composite beams )ree composite beams were testedand FE models were analysed to study the mechanical be-havior of steel-UHPC composite beams under a negativebending moment )e following conclusions were drawn

(1) )e spring loading method can be applied to sim-ulate the angular displacement and mechanical be-havior of the structure in the negative momentregion

(2) )e cracking strength of UHPC in composite beamsunder a negative bending moment is greater than20MPa which is much higher than that of steel-concrete composite beams )is finding demon-strates that UHPC can increase the cracking load ofcomposite beams subjected to a negative bendingmoment moreover the cracks in the UHPC areclosely spaced and the development of cracks isgreatly inhibited )us the cracking performance ofcomposite beams in the negative moment regiongreatly improved through the use of UHPC )en asimple formula for calculating the crack width isproposed

(3) )e joint form of welding or bolting the top flange ofadjacent steel girders in the negative moment regioncan satisfy the functional requirements and facilitateon-site construction Since steam curing of UHPC isdifficult to achieve on-site it is recommended to usenormal moist curing )e shrinkage strain of UHPCcan be reduced by adding steel fibres introducingexpansive agents to the concrete mix and increasingthe reinforcement ratio Considering the economy ofengineering applications the suggested laying lengthof UHPC in the negative moment region is 01L

Data Availability

)e data models or code generated or used during the studyare included within the submitted article

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)is research was sponsored by the Science and TechnologyProgram of Shaanxi and Yunnan Provincial Department of

Transportation (grant no HMDDGC-D-03) )e authorsare grateful for the financial support

References

[1] S Chen ldquoExperimental study of prestressed steel-concretecomposite beams with external tendons for negative mo-mentsrdquo Journal of Constructional Steel Research vol 61no 12 pp 1613ndash1630 2005

[2] H-K Ryu S-P Chang Y-J Kim and B-S Kim ldquoCrackcontrol of a steel and concrete composite plate girder withprefabricated slabs under hogging momentsrdquo EngineeringStructures vol 27 no 11 pp 1613ndash1624 2005

[3] M S Alfarabi A S Mohammad K A Abul andH B Mohammed ldquoUse of CFRP to maintain compositeaction for continuous steelndashconcrete composite girdersrdquoJournal of Composites for Construction vol 20 no 4 ArticleID 4015088 2016

[4] C E Chalioris and P A )omas ldquoFlexural analysis of steelfibre-reinforced concrete membersrdquo Computers and Concretevol 22 pp 11ndash25 2018

[5] C E Chalioris P K Kosmidou and C G Karayannis ldquoCyclicresponse of steel fiber reinforced concrete slender beams anexperimental studyrdquo Materials vol 12 no 9 p 1398 2019

[6] V K Kytinou C E Chalioris and C G KarayannisldquoAnalysis of residual flexural stiffness of steel fiber-reinforcedconcrete beams with steel reinforcementrdquo Materials vol 13no 12 p 2698 2020

[7] Y Zhang Y Zhu M Yeseta et al ldquoFlexural behaviors andcapacity prediction on damaged reinforcement concrete (RC)bridge deck strengthened by ultra-high performance concrete(UHPC) layerrdquo Construction and Building Materials vol 215pp 347ndash359 2019

[8] Y Zhu Y Zhang H H Hussein and G Chen ldquoNumericalmodeling for damaged reinforced concrete slab strengthenedby ultra-high performance concrete (UHPC) layerrdquo Engi-neering Structures vol 209 Article ID 110031 2020

[9] A Rafiee Computer Modeling and Investigation on the SteelCorrosion in Cracked Ultra High Performance ConcreteUniversity of Kassel Kassel Germany 2012

[10] P Baltay and A Gjelsvik ldquoCoefficient of friction for steel onconcrete at high normal stressrdquo Journal of Materials in CivilEngineering vol 2 no 1 pp 46ndash49 1990

[11] B Shan ldquoExperimental study on basic mechanical propertiesof reactive power concreterdquo Master thesis Hunan UniversityChangsha China 2002 in Chinese

[12] Z Zhang X D Shao W G Li P Zhu and H Chen ldquoAnxialtensile behavior test of ultra high performance concreterdquoChina Journal of Highway and Transport vol 28 no 8pp 50ndash58 2015 in Chinese

[13] L F Li X Fan X W Shi and X D Shao ldquoExperimentalstudy on flexural behavior of large-scale prestressed UHPCT-shaped beamrdquo China Civil Engineering Journal vol 51no 5 pp 84ndash94 2018 in Chinese

[14] ABAQUS Inc ABAQUS Beory Manual Version 613ABAQUS Inc Palo Alto CA USA 2014

[15] J H Cao ldquoResearch on basic performance of steel-thin UHPClightweight composite deckrdquo PhD thesis Hunan UniversityChangsha China 2016 in Chinese

[16] B Graybeal Material Property Characterization of Ultra-highPerformance concrete FHWA-HRT-06ndash103 Mclean FederalHighway Administration Washington DC USA 2006

[17] AFNOR NF P 18-710 National Addition to Eurocode2-Designof Concrete Structures Specific Rules for Ultrahigh


Performance Fibre-Reinforced Concrete UHPFRC ParisFrance 2016

[18] JSCE Recommendations for Design and Construction of Ultra-high Strength Fiber Reinforced Concrete Structures JapanSociety of Civil Engineers Tokyo Japan 2006

[19] MCS-EPFL Ultra-high Performance Fibre Reinforced CementBased composites(UHPFRC) Construction Material Dimen-sioning and application Switzerland Swiss Federal Insitute ofTechnology Zurich Switzerland 2016

[20] FHWA Material Property Characterization of Ultra-highPerformance Concrete US Department of TransportationFederal Highway Administration Washington DC USA2006

[21] Z Y Huang and G Q Hu ldquoResearch on the shrinkageperformance of ultra high performance concrete during heatcuringrdquoMaterials Review vol 30 no 2 pp 115ndash120 2016 inChinese

[22] L M Wu C J Wu Z H Zhang and H Wang ldquoEffects ofsteel fiber on drying shrinkage of ultra high performanceconcreterdquoMaterials Review vol 31 no 12 pp 58ndash65 2017 inChinese

[23] T Leutbecher and E Fehling ldquoTensile behavior of ultra-high-performance concrete reinforced with reinforcing bars andfibers minimizing fiber contentrdquo ACI Structural Journalvol 109 no 2 pp 253ndash264 2012

[24] B Chen ldquoResearch and experiment on bending behavior ofwet joints in lightweight composite deck system composed oforthotropic steel and UHPC layerrdquo PhD thesis HunanUniversity Changsha China 2018 in Chinese


studies [4ndash6] have been performed to investigate the be-havior of steel fibre reinforced concrete (SFRC) beams Itwas reported that SFRC has developed as an option tomitigate the unfavorable cracking characteristics of normalconcrete due to the ability of the fibres to increase post-cracking behavior and energy-absorbing capacity In addi-tion the recent development of ultrahigh-performanceconcrete (UHPC) offers an attractive solution for improvingthe mechanical properties of composite beams in the neg-ative moment region Zhang et al [7 8] investigated theflexural behavior of damaged RC bridge deck strengthenedby the UHPC layer

UHPC is an advanced cementitious material that ex-hibits excellent compressive and tensile mechanical be-haviors and great durability properties UHPC has acompressive strength over 150MPa and a tensile strengthover 7MPa and UHPC exhibits strain hardening andmultiple cracking behavior Compared with SFRC UHPC isadvantageous in weight reduction owing to its high strengthIn view of the excellent mechanical properties of UHPC thispaper presented an experimental investigation on applyingUHPC in the negative moment region

In this study the negative flexural behavior of steel-UHPC composite beams with different joints was experi-mentally investigated )e ultimate load the load-dis-placement response and the crack distribution are appliedto evaluate the effect of the joint forms on the crackingperformance of the composite beams Finite element ana-lyses were thus also carried out to model the three compositebeams Based on these tests and simulation results andconsidering the mechanical behavior as well as the con-venience and cost of construction an applicable joint for thenegative moment region and the laying length proportion ofUHPC were proposed to enhance the cracking resistance ofthe concrete slab in the negative moment region for com-posite beams Finally a simplified formula for calculatingUHPC crack width was developed based on bond-sliptheory

2 Experimental Program

21 Test Specimens )ree composite beams CB-1 CB-2and CB-3 were tested in this study Each beam consisted oftwo simply supported welded steel I-girders with a singlespan of 1500mm and a continuous UHPC slab that was caston the steel girders For more enhancement of crackingperformance three different forms of joint at the internalsupport were designed )e details for the beams includingthe span layout the cross section and joint forms are shownin Figure 1 )e composite beams were designed to developfull composite action between the steel girder and the UHPCslab through 10mm diameter 40mm long shear studswelded to the top flange of the steel girder In the UHPCslabs appropriate amounts of 14mm diameter longitudinalreinforcements and 10 mm diameter transverse reinforce-ments with a nominal yielding strength of 400MPa(HRB400) were properly spaced To prevent web distortionvertical stiffeners are welded to the web of the steel beam atthe supports

Figure 1(b) shows the joint forms of steel girders for thethree composite beams In the CB-1 only the top flanges ofthe adjacent steel girders were welded together at the jointCB-2 and CB-3 were similar to CB-1 except that the webs ofCB-2 and CB-3 were also partially welded together at thejoint

22 Material Properties )e mix design of UHPC in thisstudy is given in Table 1 )e UHPC was reinforced by13mm long 02mm diameter hooked-end steel fibres andthe fibre content was 25 by volume of UHPC)ree cubeswith side lengths of 100mm six prisms with dimensions of100mmtimes 100mmtimes300mm and three prisms with di-mensions of 100mmtimes 100mmtimes400mm were prepared forthe material property tests of UHPC )e mechanicalproperties of the steel plates and HRB400 rebar were ob-tained through coupon tests Tables 2 and 3 summarize themechanical properties of these materials

23Test Setupand Instrumentation To simulate the negativemoment region over the internal support two springs wereapplied instead of roller end supports of the compositebeams )e beams were tested by applying two concentratedloads at the spring support ends with two hydraulic jacks asshown in Figure 1 Compared with applying load at themidspan this loading method can achieve larger rotationangle and negative bending moment at the internal supportwhich makes it easier to observe the whole process of crackdevelopment and yield and failure mode of the slabs )eloading process was controlled by the displacement of thesprings with an increment of 05mm per stage )e loadingwas stopped when the displacement of the spring reached30mm

)e beams were instrumented for the purpose ofmeasuring applied load deflections crack formation crackdevelopment and sectional strains across the depth Straingauges were mounted on the UHPC slab steel beams andsteel reinforcements for measuring the longitudinal strainsin the specimens )e deflections at the support locations ineach loading step were measured using four electronic de-flection gauges Moreover four load cells were placed at thesupports to record the load Figure 2 shows the arrangementof the deflection gauges and strain gauges In the tests thecrack width and crack development were also detected andrecorded in each load step with a digital crack-observationdevice

3 Test Results

31 Test Observations According to Rafiee [9] cracks withwidths less than 005mmhave little effect on the durability ofUHPC and thus a crack width of 005mm can be defined asthe critical width )e load corresponding to the appearanceof a 005mm wide crack can be defined as the critical loadand the stress calculated through the load is referred to as thenominal tensile stress In this paper this state is defined asthe critical cracking state






200

Joint

B

AP P

UHPC slab


A

B

1500 1500

K K


(a)

120CB-1

70

120

CB-2

120

140 CB-3

Section B-B

tw = 8

6007times75

60

250

190

120

Section A-A

10835

(b)








Yield strength(MPa)


Steelplate

t 8 3537 206000t 10 3601 206000

HRB400 d 10 4686 200000d 14 4974 200000







K K


(a)

1

1

2

2

3

3

4

4 5

5 6 7

6 7

T4-1T4-1

T5-1 T6-1 T7-1


2 times

150

Longitudinal

600

(b)



State Testbeam

Load(kN)

Displacement(mm)

Rotation(deg)

Crack width(mm)




CB-1 90 4 014 005 1453 269CB-2 166 65 023 005 1516 231CB-3 321 7 025 005 1774 206







wmax = 103mm

(a)

wmax = 092mm


(b)

wmax = 051mm


(c)








CB-1CB-2CB-3


00

02

04

06

08

10

12

Rota

tion

(deg)

02 04 06 08 10 1200Crack width (mm)


7

CB-1CB-2CB-3

0

10

20

30

40

50

60

Load

(kN

)








CB-1CB-2CB-3

025

0

10

20

30

40

50

60

70

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)


T4-1T4-2T5-1

T6-1T7-1

0100020003000400050006000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(a)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

6000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(b)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(c)






σfc

ax +(6 minus 5a)x5


x

b(x minus 1)2

+ x xge 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(1)



σt



ft


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)






D 1 minus

σEε

1113970

(3)









fcr Mcr

αEItimes ht (4)






ε

σfc

εc0

(a)

w


σ σ

ft

fp

εpc wpc wp

(b)




30deg 01 116 23 00005

FEMTest

0

5

10

15

20

25

30

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(a)

FEMTest

05

10152025303540

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(b)

FEMTest

010203040506070

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(c)









(a)



(b)



(c)




CB-1 1453 232CB-2 1516 253CB-3 1774 239










Es

minusfctfm

Ecm


Es

(6)



srmax f 255 l0 + lt( 1113857 (7)

l0 133c

δ (8)


δη⎡⎣ ⎤⎦

ϕρeffge

lf

2 (9)

δ 1 + 05fctfm

fctmel

1113888 1113889 (10)










4τbm

(13)








ltr



ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)


wt ws middot1cs

ws middoth1

h1 minus ast

(18)














Rebar

UHPC εsm = βεct

εse


Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct


ltr



NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References
































200

Joint

B

AP P

UHPC slab


A

B

1500 1500

K K


(a)

120CB-1

70

120

CB-2

120

140 CB-3

Section B-B

tw = 8

6007times75

60

250

190

120

Section A-A

10835

(b)








Yield strength(MPa)


Steelplate

t 8 3537 206000t 10 3601 206000

HRB400 d 10 4686 200000d 14 4974 200000







K K


(a)

1

1

2

2

3

3

4

4 5

5 6 7

6 7

T4-1T4-1

T5-1 T6-1 T7-1


2 times

150

Longitudinal

600

(b)



State Testbeam

Load(kN)

Displacement(mm)

Rotation(deg)

Crack width(mm)




CB-1 90 4 014 005 1453 269CB-2 166 65 023 005 1516 231CB-3 321 7 025 005 1774 206







wmax = 103mm

(a)

wmax = 092mm


(b)

wmax = 051mm


(c)








CB-1CB-2CB-3


00

02

04

06

08

10

12

Rota

tion

(deg)

02 04 06 08 10 1200Crack width (mm)


7

CB-1CB-2CB-3

0

10

20

30

40

50

60

Load

(kN

)








CB-1CB-2CB-3

025

0

10

20

30

40

50

60

70

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)


T4-1T4-2T5-1

T6-1T7-1

0100020003000400050006000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(a)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

6000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(b)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(c)






σfc

ax +(6 minus 5a)x5


x

b(x minus 1)2

+ x xge 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(1)



σt



ft


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)






D 1 minus

σEε

1113970

(3)









fcr Mcr

αEItimes ht (4)






ε

σfc

εc0

(a)

w


σ σ

ft

fp

εpc wpc wp

(b)




30deg 01 116 23 00005

FEMTest

0

5

10

15

20

25

30

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(a)

FEMTest

05

10152025303540

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(b)

FEMTest

010203040506070

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(c)









(a)



(b)



(c)




CB-1 1453 232CB-2 1516 253CB-3 1774 239










Es

minusfctfm

Ecm


Es

(6)



srmax f 255 l0 + lt( 1113857 (7)

l0 133c

δ (8)


δη⎡⎣ ⎤⎦

ϕρeffge

lf

2 (9)

δ 1 + 05fctfm

fctmel

1113888 1113889 (10)










4τbm

(13)








ltr



ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)


wt ws middot1cs

ws middoth1

h1 minus ast

(18)














Rebar

UHPC εsm = βεct

εse


Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct


ltr



NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References

































K K


(a)

1

1

2

2

3

3

4

4 5

5 6 7

6 7

T4-1T4-1

T5-1 T6-1 T7-1


2 times

150

Longitudinal

600

(b)



State Testbeam

Load(kN)

Displacement(mm)

Rotation(deg)

Crack width(mm)




CB-1 90 4 014 005 1453 269CB-2 166 65 023 005 1516 231CB-3 321 7 025 005 1774 206







wmax = 103mm

(a)

wmax = 092mm


(b)

wmax = 051mm


(c)








CB-1CB-2CB-3


00

02

04

06

08

10

12

Rota

tion

(deg)

02 04 06 08 10 1200Crack width (mm)


7

CB-1CB-2CB-3

0

10

20

30

40

50

60

Load

(kN

)








CB-1CB-2CB-3

025

0

10

20

30

40

50

60

70

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)


T4-1T4-2T5-1

T6-1T7-1

0100020003000400050006000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(a)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

6000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(b)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(c)






σfc

ax +(6 minus 5a)x5


x

b(x minus 1)2

+ x xge 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(1)



σt



ft


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)






D 1 minus

σEε

1113970

(3)









fcr Mcr

αEItimes ht (4)






ε

σfc

εc0

(a)

w


σ σ

ft

fp

εpc wpc wp

(b)




30deg 01 116 23 00005

FEMTest

0

5

10

15

20

25

30

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(a)

FEMTest

05

10152025303540

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(b)

FEMTest

010203040506070

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(c)









(a)



(b)



(c)




CB-1 1453 232CB-2 1516 253CB-3 1774 239










Es

minusfctfm

Ecm


Es

(6)



srmax f 255 l0 + lt( 1113857 (7)

l0 133c

δ (8)


δη⎡⎣ ⎤⎦

ϕρeffge

lf

2 (9)

δ 1 + 05fctfm

fctmel

1113888 1113889 (10)










4τbm

(13)








ltr



ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)


wt ws middot1cs

ws middoth1

h1 minus ast

(18)














Rebar

UHPC εsm = βεct

εse


Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct


ltr



NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References
































wmax = 103mm

(a)

wmax = 092mm


(b)

wmax = 051mm


(c)








CB-1CB-2CB-3


00

02

04

06

08

10

12

Rota

tion

(deg)

02 04 06 08 10 1200Crack width (mm)


7

CB-1CB-2CB-3

0

10

20

30

40

50

60

Load

(kN

)








CB-1CB-2CB-3

025

0

10

20

30

40

50

60

70

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)


T4-1T4-2T5-1

T6-1T7-1

0100020003000400050006000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(a)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

6000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(b)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(c)






σfc

ax +(6 minus 5a)x5


x

b(x minus 1)2

+ x xge 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(1)



σt



ft


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)






D 1 minus

σEε

1113970

(3)









fcr Mcr

αEItimes ht (4)






ε

σfc

εc0

(a)

w


σ σ

ft

fp

εpc wpc wp

(b)




30deg 01 116 23 00005

FEMTest

0

5

10

15

20

25

30

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(a)

FEMTest

05

10152025303540

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(b)

FEMTest

010203040506070

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(c)









(a)



(b)



(c)




CB-1 1453 232CB-2 1516 253CB-3 1774 239










Es

minusfctfm

Ecm


Es

(6)



srmax f 255 l0 + lt( 1113857 (7)

l0 133c

δ (8)


δη⎡⎣ ⎤⎦

ϕρeffge

lf

2 (9)

δ 1 + 05fctfm

fctmel

1113888 1113889 (10)










4τbm

(13)








ltr



ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)


wt ws middot1cs

ws middoth1

h1 minus ast

(18)














Rebar

UHPC εsm = βεct

εse


Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct


ltr



NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References

































CB-1CB-2CB-3


00

02

04

06

08

10

12

Rota

tion

(deg)

02 04 06 08 10 1200Crack width (mm)


7

CB-1CB-2CB-3

0

10

20

30

40

50

60

Load

(kN

)








CB-1CB-2CB-3

025

0

10

20

30

40

50

60

70

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)


T4-1T4-2T5-1

T6-1T7-1

0100020003000400050006000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(a)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

6000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(b)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(c)






σfc

ax +(6 minus 5a)x5


x

b(x minus 1)2

+ x xge 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(1)



σt



ft


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)






D 1 minus

σEε

1113970

(3)









fcr Mcr

αEItimes ht (4)






ε

σfc

εc0

(a)

w


σ σ

ft

fp

εpc wpc wp

(b)




30deg 01 116 23 00005

FEMTest

0

5

10

15

20

25

30

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(a)

FEMTest

05

10152025303540

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(b)

FEMTest

010203040506070

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(c)









(a)



(b)



(c)




CB-1 1453 232CB-2 1516 253CB-3 1774 239










Es

minusfctfm

Ecm


Es

(6)



srmax f 255 l0 + lt( 1113857 (7)

l0 133c

δ (8)


δη⎡⎣ ⎤⎦

ϕρeffge

lf

2 (9)

δ 1 + 05fctfm

fctmel

1113888 1113889 (10)










4τbm

(13)








ltr



ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)


wt ws middot1cs

ws middoth1

h1 minus ast

(18)














Rebar

UHPC εsm = βεct

εse


Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct


ltr



NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References
































CB-1CB-2CB-3

025

0

10

20

30

40

50

60

70

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)


T4-1T4-2T5-1

T6-1T7-1

0100020003000400050006000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(a)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

6000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(b)

T4-1T4-2T5-1

T6-1T7-1

0

1000

2000

3000

4000

5000

Stra

in (μ

ε)

02 04 06 08 10 1200Rotation (deg)

(c)






σfc

ax +(6 minus 5a)x5


x

b(x minus 1)2

+ x xge 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(1)



σt



ft


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)






D 1 minus

σEε

1113970

(3)









fcr Mcr

αEItimes ht (4)






ε

σfc

εc0

(a)

w


σ σ

ft

fp

εpc wpc wp

(b)




30deg 01 116 23 00005

FEMTest

0

5

10

15

20

25

30

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(a)

FEMTest

05

10152025303540

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(b)

FEMTest

010203040506070

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(c)









(a)



(b)



(c)




CB-1 1453 232CB-2 1516 253CB-3 1774 239










Es

minusfctfm

Ecm


Es

(6)



srmax f 255 l0 + lt( 1113857 (7)

l0 133c

δ (8)


δη⎡⎣ ⎤⎦

ϕρeffge

lf

2 (9)

δ 1 + 05fctfm

fctmel

1113888 1113889 (10)










4τbm

(13)








ltr



ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)


wt ws middot1cs

ws middoth1

h1 minus ast

(18)














Rebar

UHPC εsm = βεct

εse


Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct


ltr



NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References






























σfc

ax +(6 minus 5a)x5


x

b(x minus 1)2

+ x xge 1

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(1)



σt



ft


⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(2)






D 1 minus

σEε

1113970

(3)









fcr Mcr

αEItimes ht (4)






ε

σfc

εc0

(a)

w


σ σ

ft

fp

εpc wpc wp

(b)




30deg 01 116 23 00005

FEMTest

0

5

10

15

20

25

30

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(a)

FEMTest

05

10152025303540

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(b)

FEMTest

010203040506070

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(c)









(a)



(b)



(c)




CB-1 1453 232CB-2 1516 253CB-3 1774 239










Es

minusfctfm

Ecm


Es

(6)



srmax f 255 l0 + lt( 1113857 (7)

l0 133c

δ (8)


δη⎡⎣ ⎤⎦

ϕρeffge

lf

2 (9)

δ 1 + 05fctfm

fctmel

1113888 1113889 (10)










4τbm

(13)








ltr



ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)


wt ws middot1cs

ws middoth1

h1 minus ast

(18)














Rebar

UHPC εsm = βεct

εse


Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct


ltr



NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References






























fcr Mcr

αEItimes ht (4)






ε

σfc

εc0

(a)

w


σ σ

ft

fp

εpc wpc wp

(b)




30deg 01 116 23 00005

FEMTest

0

5

10

15

20

25

30

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(a)

FEMTest

05

10152025303540

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(b)

FEMTest

010203040506070

Mom

ent (

kNmiddotm

)

02 04 06 08 10 1200Rotation (deg)

(c)









(a)



(b)



(c)




CB-1 1453 232CB-2 1516 253CB-3 1774 239










Es

minusfctfm

Ecm


Es

(6)



srmax f 255 l0 + lt( 1113857 (7)

l0 133c

δ (8)


δη⎡⎣ ⎤⎦

ϕρeffge

lf

2 (9)

δ 1 + 05fctfm

fctmel

1113888 1113889 (10)










4τbm

(13)








ltr



ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)


wt ws middot1cs

ws middoth1

h1 minus ast

(18)














Rebar

UHPC εsm = βεct

εse


Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct


ltr



NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References


































(a)



(b)



(c)




CB-1 1453 232CB-2 1516 253CB-3 1774 239










Es

minusfctfm

Ecm


Es

(6)



srmax f 255 l0 + lt( 1113857 (7)

l0 133c

δ (8)


δη⎡⎣ ⎤⎦

ϕρeffge

lf

2 (9)

δ 1 + 05fctfm

fctmel

1113888 1113889 (10)










4τbm

(13)








ltr



ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)


wt ws middot1cs

ws middoth1

h1 minus ast

(18)














Rebar

UHPC εsm = βεct

εse


Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct


ltr



NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References




































Es

minusfctfm

Ecm


Es

(6)



srmax f 255 l0 + lt( 1113857 (7)

l0 133c

δ (8)


δη⎡⎣ ⎤⎦

ϕρeffge

lf

2 (9)

δ 1 + 05fctfm

fctmel

1113888 1113889 (10)










4τbm

(13)








ltr



ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)


wt ws middot1cs

ws middoth1

h1 minus ast

(18)














Rebar

UHPC εsm = βεct

εse


Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct


ltr



NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References

































ltr



ws 255 l0 + lt( 1113857(1 minus β)σsr

Es

(17)


wt ws middot1cs

ws middoth1

h1 minus ast

(18)














Rebar

UHPC εsm = βεct

εse


Steel fibre

ε

εfr

εsr

x

εfm = 05εfr

εse = εsct


ltr



NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References




























NC UHPC(008~015) L




0

2

4

6

8

10

12

14

16

18

Stre

ss (M

Pa)




UHPC


Welded connection

(a) (b)


2 times 30000


A

A

(a)

3 times 2800

1352

400tw = 16

3216

650

(b)




8 Conclusion





Data Availability




Acknowledgments



References





























8 Conclusion





Data Availability




Acknowledgments



References




























Experimental and Numerical Studies on the Negative ...

Documents

Transcript of Experimental and Numerical Studies on the Negative ...