Journal of Constructional Steel Research 94 (2014) 1–10

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Journal of Constructional Steel Research

Study on fatigue property of steel–concrete composite beams and studs

Wang Yu-Hang a,⁎, Nie Jian-Guo b, Li Jian-Jun b

a Railway Engineering Research Institute, China Academy of Railway Sciences, Beijing 100081, Chinab Department of Civil Engineering, Tsinghua University, Beijing 100084, China

⁎ Corresponding author.E-mail address: wangyuhang1985@gmail.com (W. Yu

0143-974X/$ – see front matter © 2013 Elsevier Ltd. All rhttp://dx.doi.org/10.1016/j.jcsr.2013.11.004

a b s t r a c t

a r t i c l e i n f o

Article history:Received 19 November 2012Accepted 1 November 2013Available online 7 December 2013

Keywords:Steel–concrete composite beamsStudFatigueDeflection

The fatigue problemof steel–concrete composite beams has beenpaid attention to in recent years, and the reviewof available literatures about the fatigue behavior of studs, including fatigue life and slip, was firstly made. Inorder to study the fatigue behavior of studs in steel–concrete composite beams, the fatigue test on seven speci-mens was carried out. The shear fatigue failure of studs was the fatigue failure mode of specimens, with goodductility. The fatigue life was significantly affected by the shear stress amplitude of studs. Then the calculationmethod for the deflection of steel–concrete composite beams was proposed, and the good agreement with testresults indicated that the proposed method was effective. Furthermore, the influences of various parameterson the deflection of steel–concrete composite beams subjected to fatigue load were also analyzed. Based on alarge number of fatigue test data of studs, the provisions in various Codeswere summarized and evaluated, show-ing that the equation in AASHTO (American Association of State Highway and Transportation Officials) was thesafest equation for predicting the fatigue life of studs in practical design.

© 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Currently, steel–concrete composite beams arewidely used in build-ing structures and bridge structures. Compared with conventional rein-forced concrete beams, steel–concrete composite beams have majoradvantages in their bending resistance and stiffness by fully utilizingthe material strength of both steel and concrete, and taking advantageof the light weight and rapid construction features. Besides the staticload, the cyclic load caused by the vehicles always exists in the bridgestructures, so the fatigue behavior of steel–concrete composite beamsneeds to be studied. From 1950s, the steel–concrete composite beamsstarted to be used in actual engineering, and the fatigue problemshave already been observed. Therefore, a series of studies has been com-pleted by researchers. In this paper, firstly, the literatures werereviewed in detail, and then the experimental study was carried out inorder to investigate the fatigue life of the studs in the steel–concretecomposite beam, instead of the traditional push-out test. Based on thetest results, the calculationmethodwas also proposed in order to obtainthe more reasonable predicted deformation of steel–concrete compos-ite beams subjected to fatigue load. At last, combined with the provi-sions in various codes, the investigation on the fatigue life of studsbased on the data from literatures was made.

The shear connectors were the key member in steel–concrete com-posite beams, and the studs were commonly used. Therefore, in earlierstudies on the fatigue behavior of steel–concrete composite beams, themechanical behavior of studs subjected to fatigue load was the main

-Hang).

ights reserved.

research objective, including the fatigue life, interface slip and fatiguefailure modes. The standard push-out test device shown in Fig. 1 wasfrequently used for tests.

In 1966 and 1967, Slutter and Fisher have carried out the fatigue teston studs [1], indicating that the fatigue failure of studs occurred in thewelding zone between the steel plate and studs, and the relationsbetween the shear stress amplitude Δτ and loading cycles n were alsogiven:

Δτ ¼ 1020n−0:186: ð1Þ

This test was the first study on the fatigue problem of steel–concretecomposite structures, finding one kind of the fatigue failure modes ofstuds, and the calculation equation for the fatigue life of studs was pro-posed based on the “S–N”method. The studies completed by Slutter andFisher have great significance on the research on the fatigue behavior ofsteel–concrete composite structures.

In 1990, Hiragi, Matsui and Y. Fukumoto proposed the detailedcalculation equations for the fatigue life of studs based on the regressionmethods from 179 static test data and 145 fatigue test data [2]. In theproposed equations, the fatigue life of studs was not only related tothe shear stress amplitude of studs, but also to the geometrical dimen-sions of studs and the concrete compressive strength. In this study,more influencing factors were considered, and the higher precision ofthe predicting results could be obtained.

In 1997, N. Gattesco and E. Giuriani have studied the mechanicalbehavior of eight specimens subjected to low-cycle fatigue load [3],and they thought that the traditional “S–N” method was only suitablefor describing the fatigue property of structural members in elastic

Steel beam

Concrete slab

Studs

Fig. 1. Standard push-out test device.

2 W. Yu-Hang et al. / Journal of Constructional Steel Research 94 (2014) 1–10

state. For the long-span steel–concrete composite bridges, the concretenear the stud would crush due to the relative large slip on the interfacebetween the concrete and steel, so the inelastic deformation of studsexisted. Based on the test results shown in Fig. 2, the “ε-N” relationwas proposed for predicting the fatigue life of studs. From the curveand data in Fig. 2, the linear relationship between the slip on the inter-face and the fatigue life of studs could be observed. This study presenteda completely newmethod for calculating the fatigue life of studs in long-span steel–concrete composite beams, andmore tests should be carriedout for verifying the precision of the new method.

R.P. Johnson, themost famous expert in theworld has given a simpli-fied equation for predicting the fatigue life of studs based on plenty ofexperimental data [4], and this equation has been already adopted inEuro code 4:

lgN þ 8 lgΔτ ¼ 22:123: ð2Þ

The equation mentioned above was still based on the traditional“S–N”method, somore influencing factors could not be included. How-ever, the equationwas obtained from the regressionmethod based on alarge number of test data and the guarantee ratewas also considered, soit was very suitable for practical design.

In 2005, Pil-Goo Lee et al. have studied the fatigue property of large-diameter stud [5]. The test on twelve specimens, with diameter rangingfrom 27 mm to 30 mm, subjected to low cycle fatigue load was carriedout. The results indicated that the fatigue life of large-diameter stud inthe test was lower than that predicted by the equation in Euro code 4.Therefore, it could be seen that the fatigue life of large-diameter studpredicted by using the equation in Euro coed 4 was not safe. This was

1

23

4

5

67

8

Load

Slip

Max

imal

slip

(m

m)

Fatigue life

SminSmax

102 103 104 1050.5

1.0

5.0

Fig. 2. Fatigue life versus slip relations of studs subjected to low-cycle fatigue load.

mainly because the more initial imperfection and stress concentrationexisted in the weld between the steel plate and large-diameter stud.Therefore, in practical design, the safety degree of the fatigue life oflarge-diameter stud should be greatly improved.

In 2006, GerhardHanswille, Markus Porsch and CenkUstundag havecarried out the standard fatigue push-out test on 71 studs fabricatedaccording to the provisions in Euro code 4 [6,7]. The test results weresystematically analyzed and a new equation for calculating the fatiguelife of studs considering the influence of various factors was proposed:

lgN ¼ Pu;0−Pmax

K1Pu;0−K2Pmeanð3Þ

where Pmax, Pmean, and Pu,0 were themaximum load,minimum load andstatic shear bearing capacity of studs respectively. K1 and K2 were theconstant parameters which could be determined as: (1) K1 = 0.1267and K 2 = 0.1344 for the confined concrete; (2) K1 = 0.1483 andK2 = 0.1680 for the common concrete. From Eq. (3), it can be seenthat the comprehensive factors were included, and the boundary condi-tions were also satisfied.

In the study on the fatigue behavior of studs, the fatigue life has beenmainly paid attention to by the researchers. However, the slip on theinterface between steel and concrete was also an important factor,affecting the rigidity and deformation of steel–concrete compositebeams subjected to fatigue load, and some literatures could be alreadyavailable now.

In 1985, D.J. Oehlers and C.G. Coughlan have carried on the push-outtest on 116 specimens [8], and the monotonic cyclic fatigue load andreversed cyclic fatigue load were both applied. Based on the famous“Paris” equation in fracture mechanics and test results, the equationfor calculating the relation between the loading cycles n and the slip δon the interface of steel and concrete was derived:

dδ=dn ¼ c R=Rshð Þm ð4Þ

where c andmwere constant parameters, Rwas the shear force ampli-tude of studs, and Rsh was the static shear bearing capacity of studs. Theresearch results showed that the maximum slip on the interface wasapproximately equal to the one third of the diameter of studs, and theconcrete compressive strengthen was an important influencing factor.

In 1997, Geoff Taplin and Paul Geundy have studied the cumulativeslip on the interface between steel and concrete subjected to monotoniccyclic fatigue load and reversed cyclic fatigue load [9], indicating thatthe growth rate of slip under monotonic cyclic fatigue load was muchslower than that under reversed cyclic fatigue load. Ten years later,G. Hanswille, M. Porsch and C. Ustundag proposed the equations forcalculating the residual slip δr on the interface between steel and concretewith loading cycles n [7]. Based on this equation, the develop trend of theresidual slip on the interface with the loading cycles was shown in Fig. 3.In Fig. 3, the three steps can be observed: (1) at the initial loading stage,the residual slip increased fast with increment of loading cycles; (2) thegrowth rate of the residual slip gradually became slow and stable; and(3) after the loading cycles exceeded 80% of the fatigue life, the residualslip increased fast again until the fatigue failure occurred.

In 2010, Dai and Liew have investigated the static and fatigue strengthbehavior of a composite sandwich system [10]. Itwas found thatmaximumapplied load and load range affect fatigue performance independently. Themaximum applied load had a significant effect on fatigue performancewhen the difference between it and the load range was large.

In 2012, Dogan and Roberts have carried out a series of fatigue testson six nominally identical push-shear specimens [11], and the testresults revealed that the lifetime of steel–concrete–steel sandwichsystems under cycling loads could be predicted beforehand throughthe evaluation of the stiffness reduction in shear connections. In 2013,Lin et al. have studied the fatigue behavior of composite steel andconcrete beams subjected to negative bendingmoment [12]. The results

0 50 100 150 2000.0

0.5

1.0

1.5

2.0R

esid

ual s

lip (

mm

)

Loading cycles (104)

Fig. 3. Relations between fatigue load and residual slip.

3W. Yu-Hang et al. / Journal of Constructional Steel Research 94 (2014) 1–10

indicated that when the repeated load was equivalent to the initialcracking load, the fatigue test had only limited influence on beam stiff-ness or crack patterns.

In this paper, seven specimens were tested under fatigue load, inorder to obtain the fatigue failure modes, fatigue life and fatigue rigidityof composite beams. The deformation of all specimens was measuredduring the whole fatigue loading history, in order to provide thedetailed test data for verifying the proposed theoretical model Then anew method for predicting the deflection of steel–concrete compositebeams was proposed, and the parametric analysis was also made. Atlast, based on a large number of fatigue test data of studs, the provisionsin various Codes were summarized and evaluated, in order to investi-gate the prediction effect of different S–N equations.

2. Test on fatigue behavior of steel–concrete composite beams

The mechanical state of studs in composite beams, shown in Fig. 4,was different from that in the push-out test. The tensile stress or com-pressive stress exists in the concrete slab and the top flange of thesteel beam, and the fatigue behavior of studs was significantly affectedby the stress state of the steel plate and concrete nearby. The resultsof the standard push-out test cannot precisely describe the mechanicalstate of studs in steel–concrete composite beams. Therefore, the beammodel test was carried out in this study, in order to find the fatigue fail-ure process, failure modes and fatigue life of studs in steel–concretecomposite beams.

2.1. Test specimens

In order to investigate the fatigue life and fatigue rigidity of steel–concrete composite beams subjected to constant fatigue load, the teston seven specimens, numbered from FSCB-1 to FSCB-7 was carried

Fig. 4. Mechanical state of the studs in composite beams.

out. The specimens were 4500 mm long and the tested span lengthwas 4000 mm. The detailed geometrical dimensions were identical, asshown in Fig. 5. The magnitude of the fatigue load applied on the spec-imenswas themain research objective in this paper. The tensile stress ofthe bottom flange of the steel beams was strictly controlled in order toavoid the fatigue failure of the steel in tension, which had been alreadyfully studied in the past.

The concrete of the specimens was designed for compressive cubestrength (fcu) of approximately 35 MPa at 28 days. The strips of thesteel material were tested in tension. Four coupons taken from thesteel tube were tested in tension. The material strength of the steeland concrete of all the specimens were illustrated in Table 1. To avoidlongitudinal shear failures, all the beams were provided with 10 mmdiameter stirrups having a 70 mm spacing along the whole beamspan. Shear connections were achieved by using headed studs of a16 mm diameter. The ultimate tensile strength of studs is 509 N/mm2.

2.2. Test devices and procedure and measurement

All the specimens were simply supported beams, and subjected totwo-point symmetrical load. The load was applied by a 500 kN hydrau-lic jack. A roller support was placed at one end of the beam for horizon-tal movement. The loading set-up is shown in Fig. 6(a).

As shown in Fig. 6(b), the loading procedures were divided into twostages:

Stage1: Fatigue loading—The cyclic loads were sinusoidal, with aconstant amplitude, and had a frequency of 4.1 Hz (250 times perminute) which was much different from the natural vibrationfrequency of beams. Hiragi et al. indicated that resonant vibrationswould happen when the loading frequency was approached to thenatural vibration frequency of beams [2]. Therefore, sympatheticresonant vibrations would not occur in this fatigue experiment.Stage 2: Residual static loading—After the specimens failed infatigue, they were reloaded with a static loading to obtain theirresidual static bearing capacity.

In the tests, the beams were instrumented to measure the deflec-tions, concrete strains, and strains of the bottom flange of steel beams.All the strain gages were placed along the longitudinal direction. Thestrain data was collected by dynamic strain gages and the deflectiondata was collected by electric eddy dynamic displacement meters. Allthe data was recorded automatically by a computer through a DHDASsignal system.

Fatigue failure modes

Fatigue failure modes of all the specimens were similar, and thefatigue failure process of typical specimen FSCB-3 was described as anexample.

At the beginning of the fatigue loading, no cracks of concrete couldbe observed, because the neutral axis of the composite section existedin the section of steel beam. When loading cycles were up to 300,000,the minor slip appeared on the interface between the steel beam andconcrete slab. As the loading cycles reached 600,000, the slip on theinterface became more obvious. Then a “bang” sound was heard, indi-cating that some studs had failed under the cyclic shear force, and thefriction sound could be heard for a long time until the fatigue failuresurface of studs was worn smooth. The vertical crack with maximalwidth 2.3 mm appeared in the concrete slab due to the local failure ofthe composite action between the concrete slab and steel beam. Whenloading cycles reached 685,000, due to the fatigue failure of the speci-men, the fatigue load could not be retained, and the deformation rapidlybecame larger. Then the fatigue loading was stopped. The detailed fail-ure modes of specimen FSCB-3 was shown in Fig. 7.

(a) Side view

(b) Beam section

Fig. 5. Geometrical dimensions of specimens.

4 W. Yu-Hang et al. / Journal of Constructional Steel Research 94 (2014) 1–10

2.3. Fatigue failure modes of studs

In this test, the fatiguemodes of all the specimenswere shear fatiguefailure of studs. Combining with the existing literatures about thefatigue behavior of studs, it can be concluded that there were totallythree kinds of fatigue failure modes of studs: (1) Fatigue shear failureoccurred at the bottom section of studs (Fig. 8a). (2) Fatigue crackappeared on the steel plate near the stud (Fig. 8b). (3) The weldbetween the stud and steel plate failed (Fig. 8c).

From the microscopic level, all the three fatigue failure modes ofstuds were due to the fatigue crack expansion caused by the materialinitial imperfection and stress concentration. The third failure mode ofstuds shown in Fig. 8(c) mainly resulted from the bad welding qualitywith more initial imperfection. Therefore, the stiffness of the weld isrelatively low, leading to the large cyclic deformation between thestud and the steel plate, then the weld subjected to fatigue stress failedin a short time. When the ratio of the diameter of studs to the thicknessof steel plates was relatively large, the initial fatigue crackwould appearon the steel plate near the studs due to the influence of welding residualstress and the stress concentration caused by the shear force of studs, sothe steel plate failed and the stud was in good condition, as shown inFig. 8(b). In order to avoid the second fatigue failure mode in Fig. 8(b),the ratio of the diameter of studs to the thickness of steel plates shouldbe strictly controlled in practical design.

For the reasonable designed and constructed steel–concrete com-posite beam, the first fatigue failure mode of studs was the commonmode, as observed in this test. Under cyclic fatigue shear load, the initial

Table 1Concrete material properties.

Concrete material

Specimen no. FSCB-1 FSCB-2 FSCB-3 FSCB-4 FSCB-5 FSCB-6 FSCB-7

Compressivestrength (MPa)

37.3 38.85 38.45 44.15 47.85 36.3 36.35

Steel material

Strip no. 1 2 3 4 Average value

Yield strength (MPa) 355.21 369.95 365.27 361.12 362.89Ultimatestrength (MPa)

452.92 473.13 449.7 456.36 458.03

fatigue crack at the bottom section of studs appeared and graduallyexpanded, and the area of the net section of studs gradually decreased.When the net section of studs could not resist themaximum load of thefatigue shear load, the studs would be sheared with large shear defor-mation of the section due to the good ductility of the steel material.Fig. 9 showed the section of studs when the first fatigue failure modeoccurred. It can be obviously observed that the section could be dividedinto two parts: the fatigue crack expansion area and the static shear fail-ure area, corresponding well to the fatigue failure process of the studs.Furthermore,when the single stud subjected to fatigue shear load failed,the redistribution of the shear force on the interface of steel beam andconcrete slab could be achieved, so the steel–concrete beam couldcontinue to bear the fatigue load. In one word, the first fatigue failuremode of studs shown in Fig. 8(a) had good ductility, and should bedesigned as the controlled fatigue failure mode of steel–concrete com-posite beams.

2.4. Fatigue Life

Test results of the present study indicated that the fatigue failuremode of steel–concrete composite beams was essentially the fatiguefailure of the stud. Therefore, Table 2 listed the fatigue life of all the spec-imens in the test, and the shear stress amplitudes of studs calculatedfrom the fatigue load were also given. From the results it can be seenthat the shear stress amplitude of studs had an important influence onthe fatigue life of specimens. Then the shear stress amplitude versusfatigue life relation of the studs was plotted in Fig. 10. Fig. 10 andTable 2 indicated that the fatigue life of the specimens increased withthe decrease of the shear stress amplitude of studs. However, comparedwith the regression equation shown in Fig. 10 for the relation betweenlgΔτ and lgN, the obvious discreteness still existed. Thematerial fatigueproblem was a discrete and random problem, which was affected bymany factors such as initial imperfection and stress concentration, sothere was an obvious exception in Fig. 10.

2.5. Residual static test results

After the fatigue failure of specimens, the monotonic static load wasapplied, in order to obtain the residual static mechanical behavior ofsteel–concrete composite beams. The load versus displacement curvesof all the specimens were shown in Fig. 11. From Fig. 11 we can seethat all the specimens had good ductility although the fatigue failure

Specimen

hydraulic Jack

Force sensor Rigid girder

SupportSupport

t

Pmax

Pmin

P

Stage 1

-

Stage 2

(a) Test set-up (b) Loading procedures

Fig. 6. Fatigue load in the test.

5W. Yu-Hang et al. / Journal of Constructional Steel Research 94 (2014) 1–10

had already occurred, and the unloading rigidity of the beamwas nearlyequal to the initial tangential rigidity. In addition, the rigidity and bear-ing capacity of the specimens with low fatigue load amplitude weregenerally much higher than those with high fatigue load amplitude.

3. Method for calculating deflection of composite beam subjected tofatigue load

3.1. Calculation method

According to the conclusions in reference [7], the steel–concretecomposite beam subjected to high-cycle fatigue loadwasmainly in elas-tic state, so the deflection f of the beam can be regarded as the superpo-sition of the elastic deflection and the residual deflection:

f ¼ F n;…ð Þ ¼ f e þ f r: ð5Þ

where fr was the residual deflection of the composite beamatmid-span,related to the number of loading cycles n. fe was the elastic deflection ofthe beam caused by themaximum fatigue load, which can be calculatedby the reduced rigiditymethod proposed in reference [13]. According to

(a) Concrete cracks

(c) Shear fail

Fig. 7. Detailed failure mod

the literatures available, when structures subjected to fatigue load, thedegradation of the modulus of the material existed, and the results inreference showed that the modulus of the steel material was nearlythe same with the initial elastic modulus, but the modulus of concretematerial decreased obviously as the loading cycles increased, whichcan be calculated as [15]:

E fc ¼ 0:6515−0:0646 ln n=N fð Þ½ �Ec; 0bn≤N fð Þ ð6Þ

where Ec was the initial elastic modulus of the concrete.In order to calculate the residual deflection of the composite beamat

mid-span, the residual slip on the interface of the steel and concreteshould be determined firstly. Based on a large number of fatigue testresults on studs in reference [7], the equations for calculating the resid-ual slip on the interface of the steel and concrete can be obtained as:

0bn=N fb0:9; δpl;n ¼ C1−C2 lnN f−n

n

� �≥0 ; ð7Þ

n=N f ¼ 0; δpl;n ¼ 0 ð8Þ

(b) Lift between the concrete slab and steel beam

ure of studs

es of specimen FSCB-3.

(c)(a) (b)

Stud

WeldSteel plate Steel plate

Stud

WeldSteel plate

Stud

Weld

Fig. 8. Fatigue failure modes of studs.

Table 2Main results of fatigue test.

Specimen No. Fatigue load (kN) Fatigue life(104)

Shear stressamplitude of studs(MPa)

Upperlimit

Lowerlimit

Amplitude

FSCB-1 120 20 100 38 140.85FSCB-2 114 30 84.0 206 118.31FSCB-3 128.7 30 98.7 68.5 139.02FSCB-4 118 30 88.0 170 123.95FSCB-5 114.6 30 84.6 207 119.16FSCB-6 110 20 90.0 34.8 126.77FSCB-7 101.1 20 80.1 220 112.82

2.16

6 W. Yu-Hang et al. / Journal of Constructional Steel Research 94 (2014) 1–10

where C1 and C2 were the parameters given below:

C1 ¼ 0:104 exp 3:95Pmax=Pu;0

� �ð9Þ

C2 ¼ 0:664 Pmin=Pu;0 þ 0:029 ð10Þ

where Pmax, Pmin and Pu,0 were the maximal shear force, minimal shearforce and the static shear bearing capacity of the stud respectively. Themethods in reference [13]was used for calculating the static shear bear-ing capacity Pu,0 of the stud:

Pu;0 ¼ 0:43As

ffiffiffiffiffiffiffiffiffiffiEc f c

q≤0:7 f uAs ð11Þ

where fc was the compressive strength of the concrete, and fu was thetensile strength of the steel material of studs.

In steel–concrete composite beams, the curvatures of the concreteslab and steel beamwere identical due to the composite action providedby studs. Furthermore, the residual slip δr on the interface at mid-spanwas zero due to the symmetry, and the differential quotient of the slipδr′ at the end of the beamwas also zero due to the boundary condition.

Using the differential equation of slip proposed in reference [13], theformula for calculating the residual slip on the interface of concrete andsteel was derived and simplified and expressed as:

δr xð Þ ¼ kδpl;nx l−xð Þ=l2 ð12Þ

where x was the distance from the calculation section to the mid-span,l was the span of the beam and k = 10.11 was the dimensionlessparameter. Then the residual deflection fr at mid-span can be obtainedthrough serious derivations. Firstly, differentiating Eq. (12), the strainon the interface caused by the residual slip was calculated as:

εr xð Þ ¼ δ0r xð Þ ¼ kδpl;n l−2xð Þ=l2: ð13Þ

Fatigue crack expansion area

Static shear failure area

Fig. 9. Shear failure surface of studs.

As shown in Fig. 12, the additional curvature of the section due to thestrain on the interface was obtained.

Δϕr xð Þ ¼ εr xð Þ=h ¼ kδpl;n l−2xð Þ= l2h� �

ð14Þ

where h was the section height of the composite beams.Then the curvature–deflection relation was used, which was shown

below:

Δϕr xð Þ ¼ d2 f rð Þdx2

: ð15Þ

lgN +12.43lg = 32.12

2.00

2.04

2.08

2.12

5.50 6.00 6.505.75 6.25lg N

Fig. 10. Relations between lg Δτ and lg N of specimens.

0 20 40 60 80 100 1200

5

10

15

20

25

Loa

d (k

N)

Deflection (mm)

FSCB-1FSCB-2FSCB-3FSCB-4FSCB-5FSCB-6FSCB-7

Fig. 11. Residual load versus deflection relations of specimens.

7W. Yu-Hang et al. / Journal of Constructional Steel Research 94 (2014) 1–10

Finally, integrating Eq. (15), introducing the two boundary condi-tions d f rð Þ

dx jx¼0 ¼ 0 and fr|x = l/2 = 0, the residual deflection of the com-posite beam at mid-span can be obtained as:

f r ¼ kδpl;nl= 12hð Þ: ð16Þ

3.2. Test verification

In order to verify the precision of the proposedmethods for calculat-ing the deflection of composite beams, the comparisons were madebetween the test results and predicted results based on the transformedsection method without consideration of the influence of the fatigueload and the proposed method. The detailed comparison results wereillustrated in Table 3.

From the results listed above, it can be seen that the deflectionscalculated based on the transformed section method was much smallerthan the real deflection of composite beams anddid not changewith theloading cycles, leading to the unsafe results. The results calculated bythe proposed methods with consideration of the influence of fatigueload had good agreement with the test results, and the reasonableprediction can be observed about the deflection changingwith the load-ing cycles increasing.

3.3. Influencing factors analysis

In order tomake a comprehensive discussion on the influence of thefatigue load on the rigidity of the composite beams, the number n ofloading cycles, the flexure rigidity EI of the section, the static shear

Conc

Steel beam

Fig. 12. Strain distribution on the

bearing capacity Pu0 of studs, the fatigue load ratio Pmax/Pmin andthe fatigue load amplitude ΔP were chosen for the parameter analy-sis. The basic composite section for calculations was the same as thatin the reported test. Using the proposed method in this paper, theinfluences of various parameters on the deflection of steel–concretebeams subjected to fatigue load were calculated, and the resultswere illustrated in Fig. 13, where EI0 was the rigidity of the basic sec-tion, ΔP0 = 100kN, f was the deflection of the composite beam atmid-span, f1 was the deflection of the composite beam at initial load-ing state.

From Fig. 13(a) and (b), it can be observed that the deflection ofcomposite beams increased as the loading cycles increased. For varioussection rigidity and fatigue load amplitude, the growth rate was fast atthe initial loading, and became slow when the loading cycles graduallyincreased. Meanwhile, the influence of the fatigue load on the growthrate of the deflection of composite beams can be reduced by the bigrigidity, and was more obvious when the fatigue load amplitude waslarge. We can see from Fig. 13(c) that the deflection of compositebeams increased slowly with the loading cycles increasing when thefatigue load ratio was relatively lower, and then increased moreobviously. The curves in Fig. 13(d) indicated that the static shear bear-ing capacity of studs also had important influence on the deflectionof composite beams. As the static shear bearing capacity of studsincreased, the deflection of composite beams decreased rapidly whenthe static shear bearing capacity of studs was close to the upper limitof the fatigue load, and then decreased gradually as the static shearbearing capacity of studs increased.

Therefore, in practical design, the fatigue load amplitude, fatigueload ratio and static shear bearing capacity of studs should be strictly

h

rete slab

Normal strain distribution

section of composite beams.

Table 3Comparison of test results and predicted results of deflections of composite beams.

Specimen no. Loading cycles(104)

Δtest (mm) Δcal (mm) Δcal/Δtest

Transformed section method Proposed method Transformed section method Proposed method

FSCB-2 0 6.80 4.35 6.70 0.64 0.981 7.61 4.35 7.92 0.57 1.0410 7.97 4.35 8.76 0.55 1.1020 8.27 4.35 9.02 0.53 1.0950 8.59 4.35 9.41 0.51 1.10100 9.70 4.35 9.78 0.45 1.01125 9.72 4.35 9.93 0.45 1.02150 10.07 4.35 10.10 0.43 1.00175 10.09 4.35 10.32 0.43 1.02200 10.27 4.35 10.83 0.42 1.05

FSCB-3 0 7.21 4.91 6.71 0.68 0.931 7.91 4.91 8.52 0.62 1.0810 9.36 4.91 9.40 0.52 1.0020 9.56 4.91 9.71 0.51 1.0250 9.87 4.91 10.31 0.50 1.04

FSCB-5 0 6.80 4.93 6.48 0.73 0.951 7.88 4.93 7.69 0.63 0.9810 7.93 4.93 8.52 0.62 1.07100 9.01 4.93 9.53 0.55 1.06200 10.41 4.93 10.54 0.47 1.01

FSCB-6 0 6.40 4.76 6.77 0.74 1.061 8.39 4.76 8.76 0.57 1.0410 10.67 4.76 9.57 0.45 0.90

FSCB-7 0 7.10 4.22 6.77 0.59 0.951 7.87 4.22 8.80 0.54 1.1210 8.02 4.22 9.67 0.53 1.2122 10.59 4.22 10.49 0.40 0.99

Statistical results Average value 0.54 0.98 1.03Standard derivation 0.09 0.08 0.06

(a) Loading cycles and rigidity

(c) Load ratio (d) Static shear bearing capacity of studs

(b) Loading cycles and load amplitude

Fig. 13. Influence of various factors on deflection of composite beams.

8 W. Yu-Hang et al. / Journal of Constructional Steel Research 94 (2014) 1–10

Table 4Parameters in Codes.

m C

Euro code 4 8 21.395CSCCB 8.55 23.42AASHTO 10 26.15

Lee Hanswille Lo Oehlers Slutter Maeda

70.9%

67.9%

Lee Hanswille Lo Oehlers Slutter Maeda

103

103

104

105

106

107

108

109

104 105 106 107 108 109

84.2%

Lee Hanswille Lo Oehlers Slutter Maeda

Nt

Nc

(a) Euro code 4

(b) Japanese code

(c) AASHTO

103 104 105 106 107 108 109

Nt

103

104

105

106

107

108

109

Nc

103

104

105

106

107

108

109

Nc

103 104 105 106 107 108 109

Nt

Fig. 14. Comparison between predicted results and test results of fatigue life of studs.

9W. Yu-Hang et al. / Journal of Constructional Steel Research 94 (2014) 1–10

controlled, in order to obtain the reasonable rigidity design of steel–concrete composite beams subjected to fatigue load.

4. Investigation on fatigue life of studs

Up to now, most of the Codes for the design of steel–concrete com-posite beams mainly focused on the fatigue life of the studs, and thecalculation equations were given below:

lgN þm lgr ¼ C ð17Þ

where,Nwas the fatigue life of studs, rwas the shear stress amplitude orthe ratio of shear stress to the static shear bearing capacity of studs, andm andCwere the constant parameters to control the shape of equations,which were differently defined in various codes.

4.1. Equations in Codes

In Euro code 4, Japanese code for steel–concrete composite beam(JCSCCB in brief) and AASHTO, only the shear stress amplitude ofstuds was considered, so the symbol in Eq. (17) represented the shearstress amplitude Δτ and the parameters m and C in the three codeswere illustrated in Table 4.

From Table 4 we can see that the different values of parameters mand C were the main distinction between various specifications. Thevalue of parameter m had an important reflection on the fatigue loadspectrum, so the value of parameter m for studs subjected to low-cycle fatigue load was larger than that for studs subjected to high-cycle fatigue load, which can be observed in practical highway bridgestructures. The value of parameter C represented the guarantee rate ofthe equation for calculating the fatigue life of studs, and the guaranteerate increased as the value of parameter C decreased.

Furthermore, besides the shear stress amplitude, the fatigue life ofstuds was also affected by other factors, which had been considered insome codes as following.

The British code for bridge structures (BS5400) specified that thefatigue life of studs can be calculated as:

lgN þ 8 lg ΔP=Puð Þ ¼ 1:29 ð18Þ

where ΔP was the shear force amplitude of studs, and Pu was the staticshear bearing capacity.

The provisions in the Japanese code for high speed railway showedthat the shear force amplitude of the stud could not exceed themaximalshear force:

ΔP ¼ 9:5dh f ckð Þ0:5 1–0:7ρð Þ ð19Þ

where ΔP was the allowable shear stress amplitude when the fatiguelife of studs is 2 × 106, dwas the diameter of the studs, hwas the heightof studs, fck was the cylinder concrete compressive strength, andρ = τmin/τmax was the ratio of theminimal shear stress to themaximalshear stress of studs.

The maximal shear force amplitude in American code for railwaysteel bridge was defined as:

ΔP ¼ 1:117� 105d2: ð20Þ

10 W. Yu-Hang et al. / Journal of Constructional Steel Research 94 (2014) 1–10

From Eq. (18) to Eq. (20), it can be seen that the influences of geo-metrical dimension, the material property and the shear stress ratioon the fatigue life of studs were also considered in some codes.

4.2. Evaluation on formulae in codes

Based on a large number of test data on the fatigue life of studscollected in references [1,5,6,14–16], the comparison of the predictedfatigue life of studs calculated from various codes was made, as shownin Fig. 14.

From the comparison results in Fig. 14, the equation in AASHTO hadthe highest guarantee rate for predicting the fatigue life of studs, and the84.2% of the predicted results were safe. The guarantee rate of the equa-tions in Euro code 4 and Japanese code for steel–concrete compositebeam was similar.

Although the guarantee rate of the equations in various codes wasrelatively high, the large discreteness still existed in the predictedresults comparedwith the test results. Thiswasmainly due to the differ-ent stress states caused by the different loading modes and devices inthe reported literatures. Meanwhile, the discreteness of the materialfatigue property of studs and concrete also affected the test results ofstuds subjected to fatigue shear load. Furthermore, the fatigue behaviorof studswas affected bymany other factors, such as the initial imperfec-tion of material, the crack propagation paths, which were very difficultto be determined.

5. Conclusions

(1) The fatigue failure mode of steel–concrete composite beams inthe reported test was the shear fatigue failure of studs, withgood ductility. The fatigue life was significantly affected by theshear stress amplitude of studs.

(2) Themethod for calculating the deflection of steel–concrete com-posite beams was proposed, and the good agreement can beobserved compared with the test results. Furthermore, theinfluencing factors of various parameters on the deflection ofsteel–concrete composite beams subjected fatigue load were

also analyzed.(3) The investigation on the fatigue life of studs was made by com-

paring the results from equations in various equations and alarge number of test results from literatures and the high dis-creteness can be observed. The equation in AASHTO was thesafest equation for predicting the fatigue life of studs in practicaldesign.

References

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