Behavior of rubber-sleeved stud shear connectors under fatigue loading

Construction and Building Materials 244 (2020) 118386

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Behavior of rubber-sleeved stud shear connectors under fatigue loading Xiaoqing Xu a,b,⇑, Xuhong Zhou a,b, Yuqing Liu c a

School of Civil Engineering, Chongqing University, Chongqing 400045, China Key Laboratory of New Technology for Construction of Cities in Mountain Area (Ministry of Education), Chongqing University, Chongqing 400045, China c Department of Bridge Engineering, Tongji University, Shanghai 200092, China b

h i g h l i g h t s
Fatigue push-out tests on rubber-sleeved stud shear connectors were conducted.
S-N curves based on nominal shear stress for rubber-sleeved stud shear connectors were established.
Rubber sleeves decrease the fatigue strength of shear connectors and increase the relative slip growth rate.
A static shear stiffness degradation model for rubber-sleeved stud shear connectors was established.

a r t i c l e

i n f o

Article history: Received 8 August 2019 Received in revised form 21 January 2020 Accepted 7 February 2020

Keywords: Fatigue Rubber-sleeved stud Rubber Shear connector Headed stud Shear stiffness

a b s t r a c t The fatigue performance of the rubber-sleeved stud shear connector, which is a composite of ordinary stud and rubber sleeve, is not clear yet, which limits its application in steel and concrete composite structures subjected to fatigue loading. In this paper, fatigue push-out tests on nine shear connector specimens were conducted to provide insight into the influence of shear stress range and rubber sleeve height on the fatigue performance of shear connectors. Nominal shear stress-based fatigue strength curves for rubbersleeved stud shear connectors were established. It was observed that the fatigue strength of shear connectors decreases with the rubber sleeve height. In addition, rubber sleeves with low stiffness lead to a larger relative slip growth rate of rubber-sleeved stud shear connectors. However, the static stiffness degradation laws of the ordinary stud and rubber-sleeved stud shear connectors are similar, and a unified static shear stiffness degradation model was established. Moreover, fatigue failure mechanism of rubbersleeved stud shear connectors was analyzed. The results illustrated in this paper can provide reference for the fatigue design of rubber-sleeved stud shear connectors and support their application in steel and concrete composite structures. Ó 2020 Elsevier Ltd. All rights reserved.

1. Introduction Shear connectors are the essential component of steel and concrete composite structures for ensuring the composite action. Headed stud shear connector is the most common type of shear connector [1]. The behavior of a headed stud shear connector depends not only on the stud details (height, diameter and material property), but also the concrete environment, such as concrete properties and reinforcement detailing [2]. According to this basic law, the headed stud wrapped with rubber sleeve, named ‘‘rubbersleeved stud’’, was proposed by Xu et al. [3,4]. For the rubbersleeved stud shear connector (Fig. 1), concrete around the stud root is replaced with rubber of lower stiffness and higher ductility. As shown in Fig. 2, the effect of rubber sleeves on the shear strength ⇑ Corresponding author. E-mail address: [email protected] (X. Xu). https://doi.org/10.1016/j.conbuildmat.2020.118386 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.

of rubber-sleeved stud shear connectors is negligible, but the shear stiffness of the connectors markedly decreases with the rubber sleeve height and rubber-sleeved stud shear connectors have higher maximum slip capacities than ordinary stud shear connectors [3–6]. By utilizing rubber-sleeved stud shear connectors with different shear stiffness, the shear stiffness of the steel and concrete interface can be designed, thereby optimizing the shear force distribution in the connectors and improving the overall behavior of the composite structures [7]. In addition, rubber-sleeved stud shear connectors are expected to be used in high strength concrete to improve the ductility of the interface. It is worth noting that the cost of achieving these performance benefits is low since the cost and time to manufacture and install rubber sleeves is significantly low. Under fatigue loading, the fatigue failure of headed studs is the main mode of fatigue failure of composite structures and should be considered in structural design [8–11]. Therefore, a prerequisite of

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X. Xu et al. / Construction and Building Materials 244 (2020) 118386

Nomenclature

K Kcon kf kf,max kf,min ks ks,1 ks,N kSR m n N Nf R spl sf,max

sf,min Stdv tr V Vmax Vmin Vr Vu xi xk xm Z0

fatigue crack size cross-sectional area of stud shank a constant diameter of stud shank elastic modulus of concrete elastic modulus of steel loading frequency a correction factor for stress intensity factor concrete cylinder compressive strength height of rubber sleeve height of headed stud a modification factor to allow for the survival probability of 95% stress intensity factor modulus of concrete foundation dynamic stiffness maximum dynamic stiffness minimum dynamic stiffness static stiffness initial static stiffness static stiffness after N fatigue cycles shear stiffness of rubber-sleeved stud shear connectors a constant sample size of the fatigue data number of fatigue cycles fatigue life fatigue load ratio plastic slip maximum slip in one cycle

a b d DK DN Dsf Dsf,max Ds Dsc Dsck Dscm DV

g r s smax smin

the application of rubber-sleeved stud shear connectors in structures under fatigue loading is the knowledge of their fatigue behavior. The fatigue behavior of the ordinary headed stud shear

connectors has been extensively investigated since the fatigue push-out tests by Slutter and Fisher in 1966 [12]. Studies have shown that the stud geometry, shear stress range, concrete material properties, stud welding process, fatigue test methods, etc. affect the fatigue performance of the shear connectors [13–27]. As a result of these researches, design codes on composite structures have specified fatigue strength curves of headed stud shear connectors based on nominal shear stress [28–31]. However, whether the fatigue strength evaluation method of ordinary headed stud shear connectors is suitable for rubber-sleeved stud shear connectors is still unknown and thus, fatigue tests on this new type of shear connector are required to provide valuable insights into its fatigue behavior and help to establish a fatigue strength curve. So far, the researches on rubber-sleeved stud shear connectors are mainly aimed at their static performance, and there are few

Fig. 1. Rubber-sleeved studs with different rubber sleeve heights [4].

20

160

Shear stiffness (kN/mm)

Shear strength (kN)

120

minimum slip in one cycle standard variance ofxi thickness of rubber sleeve fatigue load of one shear connector maximum fatigue load of one shear connector minimum fatigue load of one shear connector residual shear capacity of one shear connector static shear strength of headed stud shear connectors results calculated from the left side of Eq. (2) characteristic value ofxi mean value ofxi a coefficient for static stiffness of shear connectors a fitting parameter for static stiffness degradation curve a fitting parameter for static stiffness degradation curve growth rate of the maximum dynamic relative slip the range of stress intensity factor fatigue cycle increment relative slip increment increment of the maximum slip shear stress range shear stress range at N = 2  106 characteristic shear stress range at N = 2  106 mean shear stress range at N = 2  106 fatigue load range in one shear connector relative static stiffness the reference stress shear stress maximum shear stress minimum shear stress

90

Max Mean Min

60

30

0

0

25

50

Rubber sleeve height (mm)

(a) Shear strength

75

Maximum slip capacity (mm)

a As C ds Ec Es f F0 fc hr hs k

Max Mean Min

120

80

40

15

10 Max Mean Min

5

0

0

0

25

50

Rubber sleeve height (mm)

(b) Shear stiffness

75

0

25

50

Rubber sleeve height (mm)

(c) Maximum slip capacity

Fig. 2. Effect of rubber sleeves on the static behavior of stud shear connectors of 19 mm diameter.

75

3

X. Xu et al. / Construction and Building Materials 244 (2020) 118386 Table 1 Fatigue test specimens. Specimens

hr/ mm

tr/ mm

smin/MPa

smax/MPa

Ds/MPa

Vmin/kN

Vmax/kN

DV/kN

R

f/Hz

S-120 S-140 RS25-30 RS25-50 RS25-70 RS25-90–1 RS25-90–2 RS50-50 RS50-70

– – 25 25 25 25 25 50 50

– – 5 5 5 5 5 5 5

12.0 12.0 12.0 12.0 12.0 12.0 52.2 12.0 12.0

132.0 152.0 42.0 62.0 82.0 102.0 142.2 62.0 82.0

120.0 140.0 30.0 50.0 70.0 90.0 90.0 50.0 70.0

3.4 3.4 3.4 3.4 3.4 3.4 14.8 3.4 3.4

37.4 43.1 11.9 17.6 23.2 28.9 40.3 17.6 23.2

34.0 39.7 8.5 14.2 19.8 25.5 25.5 14.2 19.8

0.09 0.08 0.29 0.19 0.15 0.12 0.37 0.19 0.15

4 2 5 4 4 4 4 4 4

(a) Front view

(b) Side view

(c) Plan view

Fig. 3. Details of specimens (mm).

(a) 25mm high rubber sleeve

(b) 50 mm high rubber sleeve

Fig. 4. Details of rubber sleeves (mm).

reports in the literature concerned with its fatigue performance. Xu et al. [3] conducted eighteen push-out tests on 19 mm rubbersleeved stud shear connectors with different heights and thicknesses of rubber sleeves under monotonic loading and uniaxial cyclic loading. Nonlinear finite element models were developed to simulate the failure process of shear connectors. The effect of rubber sleeves on the static behavior and the shear mechanism of the shear connector was clarified. Afterwards, Xu et al. [4] established an analytical model based on the ‘‘beam on elastic foundation” theory to calculate the shear stiffness. Moreover, finite element models were developed to study the influence of the welded collar on the shear stiffness. In the past two years, studies on the deformation performance of 19 mm and 25 mm rubbersleeved stud shear connectors under cyclic loading were reported [5,6]. However, the number of load cycles adopted in the above studies does not exceed 30, and it is difficult to determine the fatigue performance of the shear connector. The intent of the present study is to assess the influence of shear stress range and rubber sleeve height on the fatigue performance of rubber-sleeved stud shear connectors and establish the fatigue strength curve. Nine push-out specimens were fabricated and tested. Fatigue failure modes were revealed, and fatigue strength curves were proposed. Load-slip relationships were obtained, and stiffness degradation laws were described and analyzed. In addition, fatigue failure mechanism of rubber-sleeved stud shear connectors was analyzed.

2. Experiment description 2.1. Fatigue push-out test program

Fig. 5. 25 mm and 50 mm high rubber sleeves.

The behavior of shear connectors against shear loads can be revealed through tests on either push-out specimens or steel–concrete composite beam specimens. The limited data from fatigue

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X. Xu et al. / Construction and Building Materials 244 (2020) 118386

Load

Actuator Actuator Steel plate LVDT

Rubber sheet Steel beam

Steel plate LVDT Steel beam Gypsum plaster Gypsum plaster

(a) Schematic diagram

(b) Photo Fig. 6. Test setup.

Load

Static

Fatigue

Static

Fatigue

Vmax … ∆V Vmin O

Number of cycles Fig. 7. Loading procedure.

Shear stress R=τmin/τmax

T=1/f

τmax

τmin

O

Time

Fig. 8. Main parameters in fatigue loading.

tests on beams generally show that the fatigue performance of the studs is better than in push-out tests [18]. Fatigue design criteria based on push-out test results are in the safe side. Moreover, push-out specimens have smaller sizes and lower cost. Therefore, push-out test method was adopted in this study. (1) Test specimens Nine push-out specimens were tested with shear stress range and rubber sleeve height as the main parameters. In rubbersleeved stud shear connectors, the elastic modulus of the rubber sleeve around the stud root is negligible compared to the concrete, and it is difficult for the rubber sleeve to resist the deformation of the stud. Larger deformation will adversely affect the fatigue performance of the shear connector. It has been reported that the deformation of the stud increases with the rubber sleeve height [3]. Therefore, rubber sleeve height was expected to be the key parameter instead of the thickness. The details of specimens are summarized in Table 1. In the specimen labels, ‘‘S’’ and ‘‘RS’’ are identified for ordinary studs and rubber-sleeved studs, respectively. ‘‘RS250 ’ and ‘‘RS500 ’ are identified for studs with rubber sleeve height (hr) of 25 mm and

50 mm, respectively. Also, the shear stress range of a single stud (Ds) during fatigue loading is given in the label. All headed studs are 19 mm in diameter (ds) and 100 mm in height (hs), and the rubber sleeves are 5 mm in thickness (tr). The load values (Vmin, Vmax, DV) in the table refer to the load applied to one shear connector. Vmin is the minimum fatigue load, Vmax is the maximum fatigue load, and DV is the fatigue load range. The shear stress in the stud (s) is calculated as s = V/As, where As is the sectional area of the stud and V is the fatigue load. smin is the minimum shear stress, and smax is the maximum shear stress. The stress ratio (R) is calculated as R = smin /smax. f is the loading frequency. Vmin of all the specimens except SR25-90–2 are 3.4kN. Vmin of SR25-90–2 specimen is increased to 14.8kN in order to study the effect of maximum fatigue load on the fatigue life. Except for S-120 and RS2530 specimens which were statically loaded to failure after the preset fatigue cycles in order to measure the residual static shear capacities, all the other specimens were loaded until fatigue failure occurred. The dimensions of the specimens are shown in Fig. 3. The steel component made up of two T-shaped steel members was assembled using two splice plates and six high-strength bolts. A row of two studs were welded on the T-shaped steel member, and rubber sleeves of different heights were set. The thickness of the steel plates of T-shaped steel member was 20 mm. The dimension of concrete slabs were 500  460  150 mm. Four layers of /14mm steel rebars were placed in the concrete slab. The rubber sleeves were made of NR45° natural rubber with the hardness of 45 (Shore A). As shown in Fig. 4 and Fig. 5, the thickness of the rubber sleeves was 5 mm, and the heights were 25 mm and 50 mm. Considering the weld collar at the stud root, the inner diameter of the rubber sleeve root in the height range of 6 mm was increased from 19 mm to 25 mm to facilitate completely wrapping the stud root. (2) Test setup The test setup is shown in Fig. 6. A servo hydraulic testing machine with a capacity of 1000kN was used to load the specimens. The load was applied to the two flanges of the steel component of the specimen through a 30 mm thick distribution steel plate, so that the shear connectors were under the pure shear load. Moreover, the specimens were bedded in using a layer of high strength gypsum plaster, which resulted in an even contact with the distribution steel plate. In order to avoid large vibrations or movement of the specimen under the fatigue load, the bottom of both sides of the specimen was restricted by steel beams and rubber sheets. The time and the load from the machine load cell were recorded. Two linear variable displacement transformers (LVDTs)

5

X. Xu et al. / Construction and Building Materials 244 (2020) 118386

(a)Rubber sleeve installation

(b) Arrangement of reinforcing bars

(c) Concrete casting and curing Fig. 9. Photos for specimen fabrication.

Table 2 Mix proportions of concrete (kg/m3). Cement

Water

Sand

Stone

Water-reducing agent

605.7

202.9

545.1

1090.2

6.1

Table 3 Material properties of concrete (MPa). Cubic compressive strength

Prism compressive strength

Tensile splitting strength

51.35

38.78

3.33

with a resolution of 1 lm were placed on each steel flange to measure the longitudinal relative slips between each concrete slab and the steel component. All the data was collected by a data acquisition system. (3) Loading and measurement scheme The loading procedure was divided into static and fatigue loading as shown in Fig. 7. The main parameters in fatigue loading are shown in Fig. 8. Displacement control and force control were used in the static loading process. The loading speed was controlled under 10kN/min or 1 mm/min. The displacement control was used in the failure stage of S-120 and RS25-30 specimens when significant reduction of the stiffness was observed. Force-controlled static loading was adopted to measure the static performance of the specimens after a certain number of fatigue cycles (such as 1000 cycles, 10,000 cycles, 50,000 cycles, etc.). The applied maximum static loads were equal to the maximum fatigue loads. The fatigue

loading was carried out in load control using a continuous sinusoidal waveform with a loading frequency of 2, 4, or 5 Hz. A higher frequency would lead to larger vibrations of the specimens and affect the measurement of the LVDTs. Therefore, the loading frequency was adjusted according to the rigidity of the specimen and the maximum fatigue load. The testing machine can preset the upper and lower limits of the fatigue load and automatically record the number of fatigue cycles. Corresponding to the loading procedure, static tests were periodically performed to evaluate the load and relative slip of the specimen after a certain number of fatigue cycles, while the fatigue tests were conducted to obtain the maximum and minimum relative slip during one fatigue cycle. The data acquisition is at a sampling rate of 200 Hz.

2.2. Specimen fabrication The studs were welded onto the steel plates using current automatic welding machines. The rubber sleeves were cut, opened and bonded to the studs by cyanoacrylate super glue, as shown in Fig. 9. Taking the effect of concrete casting direction into account, the specimens were cast upward to ensure the quality of the concrete slabs and the right position of the rubber sleeves. The surfaces of steel plates in all specimens were greased to weaken the natural bond between the steel components and concrete slabs. To obtain the concrete compressive strength and tensile strength, 150 mm square prisms with a length of 300 mm and standard cubes with a length of 150 mm were cast with the push-out specimens simultaneously.

Table 4 Material properties of NR45° natural rubber. Hardness (Shore A)

Elongation (%)

Tensile strength (MPa)

Brittleness temperature (°C)

Tensile modulus of elasticity (MPa)

45

404

18

40

7.89

6

X. Xu et al. / Construction and Building Materials 244 (2020) 118386

Table 5 Fatigue tests results. Specimens

Ds/MPa

smin/MPa

smax/MPa

R

Nf/103 cycles

Vr/kN

S-120 S-140 RS25-30 RS25-50 RS25-70 RS25-90–1 RS25-90–2 RS50-50 RS50-70

120.0 140.0 30.0 50.0 70.0 90.0 90.0 50.0 70.0

12.0 12.0 12.0 12.0 12.0 12.0 52.2 12.0 12.0

132.0 152.0 42.0 62.0 82.0 102.0 142.2 62.0 82.0

0.09 0.08 0.29 0.19 0.15 0.12 0.37 0.19 0.15

453.3 163.8 2015.0 759.5 178.5 74.3 121.9 365.5 83.7

105.0 – 49.5 – – – – – –

150 120

(MPa)

90 60

S, hr=0mm RS25,hr=25mm RS50,hr=50mm Eurocode 4

30

10

4

10

5

N

10

6

10

7

Fig. 10. Fatigue lives of shear connectors under different shear stress ranges.

2.3. Material properties The reinforcement bars were HRB400E steel bars. The steel components were made of steel Q345. Based on the tensile tests, the mean yield strength and the ultimate tensile strength of headed stud were determined as 410 MPa and 450 MPa, respectively. The mix proportion of concrete is listed in Table 2. The concrete compressive strength was achieved from the cube and the prism compression tests together, and tensile splitting strength was obtained by tensile splitting tests on cube specimens. Table 3 shows the material properties of concrete which were tested at the age of 185 days when the fatigue tests started. Table 4 shows the material properties of the rubber. 3. Test results and discussion 3.1. Fatigue life Table 5 summarizes the numbers of cycles (Nf) and the residual shear capacities (Vr). Except for S-120 and RS25-30 specimens

which were tested for the residual shear capacities after a preset number of fatigue cycles, the fatigue cycle numbers of other specimens are the number of cycles when they failed by fatigue, that is, their fatigue lives. The fatigue lives of S-120 and RS25-30 specimens are larger than the preset cycle numbers as presented in Fig. 10. The fatigue stress range of S-140 specimen is twice those of RS25-70 and RS50-70 specimens, but its fatigue life is close to that of RS25-70 specimen and is about twice that of RS50-70 specimen. Meanwhile, the fatigue life of the RS25 specimen is 2.1 times that of the RS50 specimen under the same fatigue stress range. It can be concluded that the fatigue life of the rubber-sleeved stud shear connector is smaller than that of the ordinary stud shear connector, and the fatigue life of the shear connector decreases with the rubber sleeve height. Comparing the fatigue lives of RS2590–1 and RS25-90–2 specimens, it is known that the effect of maximum shear stress on the fatigue life is not significant. A comparison between test results and design values according to Eurocode 4 [28] is presented in Fig. 10. The fatigue lives of rubber-sleeved stud shear connectors are shorter than the design values. 3.2. Fatigue failure modes The fatigue failure process of all specimens was similar. As the number of fatigue cycles increased, the relative slip and separation between steel and concrete gradually increased. When the fatigue fracture was approached, the specimen was gradually inclined to the side where the relative slip and separation was larger. Along with the fracture of headed studs at that side, the concrete slab was totally separated from the specimen as shown in Fig. 11. Fig. 12 shows the state of the stud and its surrounding rubber sleeve, concrete and steel plate after the fracture of the stud. The left sides of the figures show the studs embedded in the concrete slabs while their corresponding residues on the steel plates are presented in the right side of the figures. Cavities were observed vertically below the studs. For rubber-sleeved studs, the rubber underneath the stud was greatly deformed by compression, and the rubber sleeves in some specimens were broken, such as

Steel part

(a) Front view of the specimen

Concrete part

(b) Two separated parts Fig. 11. Failure mode of one specimen.

X. Xu et al. / Construction and Building Materials 244 (2020) 118386

(a)S-120

(b)S-140

(c)RS25-30

(d)RS25-50

(e)RS25-70

(f)RS25-90-1

(g)RS25-90-2

(h)RS50-50

7

(i)RS50-70 Fig. 12. Failure modes of studs and rubber sleeves.

RS25-30 specimen. The lower half of weld collars of all studs was completely retained on the steel plates, indicating that the crack initiated at the weld collar/shank interface and propagated through the shank. This failure mode is consistent with the type

A failure mode reported by Hallam [13] as shown in Fig. 13. The fracture surface of the failed stud was substantially flush with the surface of the steel plate. Most areas of the fracture surface of the stud were dull, which was caused by fatigue crack growth

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X. Xu et al. / Construction and Building Materials 244 (2020) 118386

Push-out direction

100

Fatigue cracks

90.0

80

Weld collar

(MPa)

Concrete confinement

c

Fig. 13. Illustration of failure mode A [13].

150

RS25,hr=25mm Eq.(2), Ps=50% Eq.(7), Ps=95%

120

(MPa)

30.6

0 S

RS25

RS50

60 cm

Fig. 17. Effect of rubber sleeves on the fatigue strength at 2 million cycles.

=38.5MPa

=32.6MPa

30

ck

10

4

10

5

N

10

6

2 10

6

10

7

Fig. 14. S-N curves for RS25 shear connectors.

150

90

and was referred to as the forced fracture zone. The forced fracture zones could be clearly found in S-140 and RS25-30 specimens, which were related to static tests on the residual shear strengths of the specimens. 3.3. S-N curves The S-N curve reveals the relationship between the fatigue life and stress range. Extensive studies have been conducted on the fatigue behavior of ordinary stud shear connectors, and various fatigue life prediction formulas have been proposed. Johnson [18] summarized that there are three distinct models: ‘‘EC model”, ‘‘BS model” and ‘‘Peak Load model”. The ‘‘EC model”, Eq. (1), takes no account of the static shear strength of the stud, and is more widely accepted and is used in Eurocode 4 [28] and Chinese code for highway steel–concrete composite bridges [31].

RS25,hr=25mm RS50,hr=50mm Eq.(2), Ps=50% Eq.(8), Ps=50%

120

(MPa)

38.5 40 20

90

60

logN þ mlogDs ¼ C

30

10

4

10

5

N

10

6

10

7

Fig. 15. S-N curve for RS50 shear connectors.

150 120

Eurocode 4

ð2Þ

A survival probability no less than 95% is demanded for fatigue design. Thus, the regression curve should be modified. Firstly, the slope of the fatigue design curve was assumed to be the same as that of the mean regression curve, which is 3.700. Then, the corresponding value of each set of test data, xi , was calculated from the left side of Eq. (2). The mean and standard variance of xi were given by

60 Eq. (7) S, hr=0mm RS25,hr=25mm

30

ð1Þ

where N is the number of fatigue cycles, m is the slope of the S-N curve, Ds is the stress range, and C is a constant. By performing a linear curve-fitting analysis on the fatigue test results obtained in this study, S-N curves using EC model were proposed for rubbersleeved stud shear connectors. (1) For shear connectors with 25 mm high rubber sleeves The test data is plotted in a log–log coordinate system as show in Fig. 14. Linear regression analysis of logDs on logN was carried out, and the mean regression curve with a 50% survival probability (Ps) was

logN þ 3:700logDs ¼ 12:166

90

(MPa)

60

P 10

4

10

5

N

10

6

10

7

Fig. 16. Comparison between the S-N curves for RS25 and S shear connectors.

and were referred to as the fatigue fracture zone. This shows that fatigue crack growth was the main cause of specimen failure. Only a small area was bright, which was caused by forced shear fracture

xm ¼

xi n

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ðxm  xi Þ2 Stdv ¼ n1

ð3Þ

ð4Þ

where n is the sample size of the fatigue data, xm is the mean value and Stdv is the standard variance. Since RS25-30 specimen did not fail in fatigue, it was not included in the analysis, and thus n was

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X. Xu et al. / Construction and Building Materials 244 (2020) 118386

2.0

0.5 A-Min A-Max B-Min B-Max

1.6

Relative slip (mm)

Relative slip (mm)

0.4

A-Min A-Max B-Min B-Max

0.3

0.2

1.2

0.8 0.4

0.1

0.0

0.0 0

10

20

30

40

0

50

8

12

Number of cycles (x10 )

(a)S-120

(b)S-140

16

2.5

0.8 A-Min A-Max B-Min B-Max

0.6

A-Min A-Max B-Min B-Max

2.0

Relative slip (mm)

Relative slip (mm)

4

4

4

Number of cycles(x10 )

0.4

0.2

1.5

1.0 0.5

0.0 0

50

100

150

0.0

200

0

40

60

Number of cycles (x10 )

(c)RS25-30

(d)RS25-50

80

4

3

1.5 A-Min A-Max B-Min B-Max

Relative slip (mm)

Relative slip (mm)

20

Number of cycles (x104)

1.0

0.5

0.0 0

4

8

12

16

A-Min A-Max B-Min B-Max

2

1

0 0

4

Number of cycles (x10 )

2

4

6

8

Number of cycles (x104)

(e)RS25-70

(f)RS25-90-1 Fig. 18. Dynamic relative slip.

taken as 4. xm and Stdv were calculated to be 12.166 and 0.107, respectively. Then, the characteristic value of xi , xk , was estimated from

xk ¼ xm  k  Stdv

ð5Þ

  1 k ¼ 1:645  1 þ pffiffiffi n

ð6Þ

where k is a modification factor to allow for the survival probability of 95% and is related to the number of specimens [32]. xk was calculated to be 11.901. Thus, the S-N curve with a 95% survival probability for fatigue design was

logN þ 3:700logDs ¼ 11:901

ð7Þ 6

Eqs. (2) and (7) are plotted in Fig. 14. At N = 2  10 , two equations give the mean shear stress rangeDscm = 38.5 MPa and the characteristic oneDsck = 32.6 MPa, respectively.

10

X. Xu et al. / Construction and Building Materials 244 (2020) 118386

2.0 A-Min A-Max B-Min B-Max

6

Relative slip (mm)

Relative slip (mm)

8

4

2

A-Min A-Max B-Min B-Max

1.5

1.0

0.5

0.0

0 0

4

8

0

12

5

10

15

20

25

Number of cycles (x10 )

Number of cycles (x104)

(g)RS25-90-2

(h)RS50-50

4

30

Relative slip (mm)

8

6

4 A-Min A-Max B-Min B-Max

2

0 0

2

4

6

8

4

Number of cycles(x10 )

(i)RS50-70 Fig. 18 (continued)

Shear force Static test

S120 S140 RS25-30 RS25-50 RS25-70 RS25-90-1 RS25-90-2 RS50-50 RS50-70

400

Fatigue test

…

∆V

kf

Vmin

O

Dynamic stiffness (kN/mm)

Vmax

ks spl

sf,min sf,max

Slip

Fig. 19. Method for determining the static stiffness and dynamic stiffness.

(2) For shear connectors with 50 mm high rubber sleeves The fatigue test data for RS50 shear connectors is limited. By assuming that RS50 shear connectors have similar fatigue behavior as RS25, the slope of the S-N curve for RS50 shear connectors was assumed to be 3.700. Then, the linear regression curve was obtained

logN þ 3:700logDs ¼ 11:799

ð8Þ

Eq. (8) is plotted in Fig. 15. At N = 2  106, it givesDscm = 30.6 MPa. The comparison with Eq. (2) clearly shows that RS50 shear connectors have lower fatigue lives than RS25 shear connectors. (3) Comparison with the S-N curve for ordinary stud shear connectors

300

200

100

0 0.0

0.2

0.4

0.6

0.8

1.0

N/Nf Fig. 20. Evolution of dynamic stiffness.

In Eurocode 4 [28], the S-N curve recommended for fatigue design is

logN þ 8logDs ¼ 21:935

ð9Þ

The curve is plotted in Fig. 16. The fatigue lives of ordinary stud shear connectors measured in this study are greater than the predicted values of Eq. (9). It indicates that the fatigue test method and results are reasonable. The comparison between the S-N curve

11

X. Xu et al. / Construction and Building Materials 244 (2020) 118386 Table 6 Minimum and maximum dynamic shear stiffness and their ratio.

kf,min (kN/mm) kf,max (kN/mm) kf,min/kf,max

S-120

S-140

RS25-30

RS25-50

RS25-70

RS25-90–1

RS25-90–2

RS50-50

RS50-70

204.3 316.7 0.65

109.9 239.0 0.46

33.4 136.2 0.25

42.7 111.0 0.38

95.3 193.8 0.49

50.2 108.0 0.46

110.2 157.5 0.70

20.2 65.3 0.31

25.0 53.3 0.47

for RS25 shear connectors and that for S shear connectors further shows that the fatigue performance of S shear connectors is better than that of RS25 shear connectors, and rubber sleeves have an adverse effect on the fatigue performance. (4) Effect of rubber sleeves on fatigue strength at 2 million cycles The stress ranges at 2 million cycles (Dsc ) for three types of shear connectors were compared to show the effect of rubber sleeves on fatigue strength. For RS25 and RS50 shear connectors, the fatigue strength was estimated from the S-N curves with a 50% survival probability, while the fatigue strength for S shear connectors was taken as 90.0 MPa which is recommended by Chinese code [31]. The results are presented in Fig. 17. The fatigue strengths of RS25 and RS50 shear connectors are only 42.8% and 34.0% of that of S shear connectors, respectively. The rubber sleeves cause the fatigue strength of the shear connectors to decrease. Moreover, the fatigue strength of RS50 shear connectors is 20.5% lower than that of RS25 shear connectors, indicating that the decrease of fatigue strength is not linear to the increase of rubber sleeve height, and the fatigue strength reduction significantly decreases after the rubber sleeve is larger than 25 mm. 3.4. Results of relative slip in fatigue tests and discussion (1) Results of relative slip in fatigue tests Fig. 18 plots the test results of maximum and minimum relative slips at both sides (A side and B side) of the specimen with the number of loading cycles. The dynamic relative slip values at one loading cycle on A and B sides were quite different in some specimens, but the evolution laws were basically the same. In the early stage of fatigue loading, the relative slip increased approximately linearly with the number of fatigue cycles, and the growth was slow. When the fatigue failure was approached, the relative slip growth increased, and the relative slip on the side where the failure occurred increased more rapidly. There were differences in the evolution laws of the three types of shear connectors. It can be explained by comparing S-140, RS25-70 and RS50-70 specimens. Though the shear stress range of S-140 specimen was twice as the other two specimens, S-140 specimen had the smallest slip growth rate. Meanwhile, the rate of RS50-70 specimen was larger than that of RS25-70, which indicated that the rubber sleeve height influences the evolution law. (2) Dynamic shear stiffness degradation law Dynamic shear stiffness, as given by Eq. (10), characterizes the deformability of shear connectors during fatigue loading.

kf ¼

Ds f sf;max  sf;min ¼ DV DV

ð10Þ

where Dsf is the slip range in one cycle, DV is fatigue load range, and sf;max and sf;min are the maximum and minimum slip in one cycle, respectively, as shown in Fig. 19. Here, a linear relation between slip and load was assumed for the upper and lower load within the fatigue cycle. As shown in Fig. 20, the dynamic shear stiffness of all specimens deteriorated approximately linearly with the fatigue cycles, which is consistent with the research by Oehlers and Coughlan [15]. The RS50-70 and RS25-90–2 specimens are special cases where the

stiffness increased with the fatigue cycles after the fatigue cycle number was greater than a certain value. The common feature of the two specimens was that the relative slip exceeded 5 mm (as refered to Fig. 18), that is, the thickness of the rubber sleeve. Part of the rubber sleeve was squashed. This caused that the concrete below the rubber sleeve started to restrict the deformation of the stud, thereby increasing the stiffness of the shear connectors. The shear connectors with rubber sleeves of larger height have larger dynamic stiffness. Table 6 summarizes the minimum and maximum dynamic shear stiffness (kf,min and kf,max) of the specimens, and the ratios of the two stiffness values are presented. It is found that the ratio is generally less than 0.5, and the mean value of the ratios of specimens tested to fatigue failure is 0.47. The effect of shear stress ranges on the dynamic stiffness is not clear. For ordinary stud shear connectors, the stiffness of S-140 specimen is smaller than that of S-120 specimen. However, for the rubber-sleeved stud shear connectors, the stiffness of specimens under larger shear stress ranges, such as RS25-90–1, RS2590–2 and RS25-70 specimens, are greater. The possible cause is the difference in loading rate. Both steel and concrete materials are rate-dependent materials. Specimens under higher loading rates shall have greater stiffness. For example, the S-140 specimen has a loading frequency of 2 Hz, which is half of the S-120 specimen, so the loading rate is also close to half and the dynamic stiffness is lower. The RS25 specimens are loaded at the same frequency, so the specimen under a larger shear stress range has a higher loading rate and thus larger dynamic stiffness. (3) Maximum dynamic relative slip evolution law Many researchers have analyzed the growth law of the maximum dynamic relative slip with the number of fatigue cycles for ordinary stud shear connectors, and proposed a variety of analytical models. By referring to previous research methods, this paper quantitatively studies the growth law of rubber-sleeved stud shear connectors in order to analyze the influence of rubber sleeve height. In 1976, Hallam [13] proposed an equation to calculate the growth rate of the maximum dynamic relative slip based on the fatigue test data of shear connectors in normal strength concrete, as given by Eq. (11). The ratio of shear force range to shear strength was thought to be the only influencing factor.

logd ¼ - 10 þ 12:99

DV Vu

ð11Þ

where d is the growth rate of the maximum dynamic relative slip, DV is the shear force range and V u is the static shear strength. Then, in 1986, an equation, Eq. (12), was determined by Oehlers and Coughlan [15] derived from the fatigue lives of 99 unidirectionally loaded specimens, and it was assumed that the change of slip per cycle and the stiffness per cycle is constant and the energy released per cycle is proportional to the crack extension per cycle [14].

d ¼ 1:70  10

- 5

 4:55 DV ds Vu

ð12Þ

where ds is the stud diameter. Valente [21] proposed an equation in 2007 similar to that by Hallam [13] for 13 mm diameter studs under low cycle fatigue:

12

X. Xu et al. / Construction and Building Materials 244 (2020) 118386

2.0

x10

-5

8 S-120 S-140

-5

RS25-30 RS25-50 RS25-70 RS25-90-1 RS25-90-2

6

(mm/cycle)

(mm/cycle)

1.5

x10

1.0

0.5

4

2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

N/Nf

0 0.0

0.2

0.6

0.8

1.0

N/Nf

(a)S specimens x10

0.4

(b)RS25 specimens -5

30 RS50-50 RS50-70

(mm/cycle)

25 20 15 10 5 0 0.0

0.2

0.4

0.6

0.8

1.0

N/Nf

(c)RS50 specimens Fig. 21. Growth rate of the maximum dynamic relative slip.

Table 7 Experimental results of average growth rate. Specimens

DV/kN

Vu/kN

DV/Vu

d/mm/cycle

S-120 S-140 RS25-30 RS25-50 RS25-70 RS25-90-1 RS25-90-2 RS50-50 RS50-70

34.03 39.70 8.50 14.18 19.85 25.53 25.53 14.18 19.85

124.4 124.4 124.4 124.4 124.4 124.4 124.4 124.4 124.4

0.27 0.32 0.07 0.11 0.16 0.21 0.21 0.11 0.16

4.844 6.988 1.832 2.527 4.874 2.925 3.318 5.919 8.944

logd ¼ - 7:11 þ 5:79

DV Vu

ð13Þ

Recently, Cao et al. [25] analyzed the growth rate data of studs in ultra-high performance concrete (UHPC) and proposed the corresponding equation:

logd ¼ - 10:574 þ 14:053

DV Vu

ð14Þ

It was found that the slip rate of the headed studs in UHPC is lower than that of the headed studs in normal concrete, which is attributed to the high strength and stiffness of UHPC [25]. Studies by Liu et al. [27] on the slip growth rate of headed studs in the engineered cementitious composites (ECC) showed that the rate

        

107 106 107 106 106 105 105 106 105

logd 6.315 5.156 6.737 5.597 5.312 4.534 4.479 5.228 4.048

is close to that in the lightweight concrete, but higher than that in the normal concrete. The higher growth rate was thought to be associated with the relatively low elastic modulus of ECC. The elastic modulus of rubber is much smaller than that of any type of concrete. The following analysis was performed to obtain an equation similar to that by Hallam [13] for predicting the growth rate of RS shear connectors and to show the influence of rubber sleeves on the growth rate by comparing with S shear connectors. First, the static shear strength of shear connectors was estimated. Rubber sleeves has negligible effect on the static shear strength. Therefore, it was estimated by the equation (Eq. (15)) proposed by Wang and Liu [33], which is based on the worldwide 255 push-out test results of ordinary stud shear connectors.

X. Xu et al. / Construction and Building Materials 244 (2020) 118386

-2

log

sleeved studs have the highest growth rate. It can be concluded that the restraint conditions provided by the materials surrounding the studs during the deformation of the studs affect the relative slip growth rate. The greater the strength and stiffness of the surrounding materials, the stronger the restraint conditions and the lower the relative slip growth rate. Finally, linear regression analysis of (logd) on (DV/Vu) was performed for the data of RS25 specimens. Fitting the data of five specimens gives the Eq. (17), where the symbols have the same meaning as above. The analysis shows that the coefficient of determination is 0.95, indicating that the linear correlation is high.

S, hr=0mm RS25,hr=25mm RS50,hr=50mm Eq.(17)

-4

Hallam [13]

-6

-8

-10 0.0

Cao et al. [25] Valente [21] Oehlers and Coughlan [15] 0.1

0.2

0.3

logd ¼ - 7:54 þ 14:55 0.4

V Vu Fig. 22. Comparison of experimental and calculated results of slip growth rate.

8 > <

qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi 0 0 V u ¼ 0:50As Ec f c Ec f c 6 700 qffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffi 0 > : V ¼ 0:20A E f 0 þ 210:0A Ec f c > 700 u s c c s

Dsf;max DN

DV Vu

ð17Þ

The slope of the above formula is close to that of Eq. (12) by Hallam [13], but the vertical axis intercepts differ by about 3, that is, the maximum dynamic relative slip growth rates differ by nearly three orders of magnitude. 3.5. Results of relative slip in static tests and discussion

ð15Þ

where V u is the shear strength of headed stud shear connector; As 0 is the cross section area of a stud; f c is the concrete cylinder compressive strength, which is assumed to be equal to the prism compressive strength in this study; Ec is the elastic modulus of concrete. The strength of one stud shear connector was calculated to be 124.4kN. The calculated value is slightly larger than the average value of test results in the literature [3], 101.7kN. This is reasonable because the concrete strength in this study is 38.78 MPa, which is slightly larger than 34.1 MPa in that literature. Then, d was to be calculated. In view of the similar law of relative slip growth on both sides of the specimen, the relative slip on A and B sides were averaged. Subsequently, the fatigue life was divided into several stages with similar fatigue cycle numbers (DN), and relative slip increments (Dsf;max ) were calculated. Thereby the corresponding growth rate can be obtained:

d¼

13

ð16Þ

As shown in Fig. 21, the growth rate was not constant during the fatigue loading process. For most specimens, the rate increased with the fatigue cycle number. The maximum value of the rate was found in the RS50-70 specimen, which was 2.64 mm per 10,000 cycles. In the same type of shear connector, the rate obviously increased with the shear stress range. The values of d at all stages were averaged and the logarithmic results of the average values are presented in Table 7. The comparison between the experimental results and the calculation results of the existing formulas is shown in Fig. 22. The results of S specimens are close to the predicted values of the existing three formulas for studs in normal strength concrete, and the predicted values of the three formulas for the larger fatigue stress range tend to be consistent with each other. This shows that S specimens exhibit the typical fatigue characteristics of ordinary stud shear connectors. Except for the RS23-30 specimen, the growth rates of the remaining RS specimens are larger than the predicted values of the formulas, further indicating that the growth rate of RS shear connectors is greater than that of S shear connectors. At the same time, under the same shear stress range, the growth rate of RS50 shear connectors is greater than RS25 shear connectors, indicating that the growth rate increases with the rubber sleeve height, which will then lead to the reduction of fatigue life. Studs in UHPC have the lowest growth rate, while rubber-

(1) Results of relative slip in static tests After the fatigue loading was suspended, the static test was carried out on the specimen. After the relative slips on both sides of the specimen were averaged, the static load-relative slip curves after different number of fatigue cycles were obtained, as shown in Fig. 23. The loading and unloading curves were approximately linear because the maximum fatigue loads applied to the specimens were small relative to their static shear strengths. At the beginning of the fatigue test, the loading curves were convex. They gradually tended to be concave with the increase of fatigue cycle number. Meanwhile, the slope of the loading curve gradually decreased, revealing that the shear stiffness degraded after fatigue loading. The unloading curves were always concave. After the load was completely removed, the relative slip value basically returns to the initial value, and the residual relative slip generated by one loading and unloading cycle was small. (2) Static shear stiffness degradation law In order to analyze the stiffness degradation law of the shear connector during the fatigue loading process, the secant stiffness from the starting point to the highest point of the static loadrelative slip curve was calculated as the static shear stiffness, and the results are shown in Fig. 24. In the figures, the abscissa is the cycle number as a proportion of the fatigue life of the specimen. Although the stiffnesses of the three types of shear connectors differed, the stiffnesses of all specimens were clearly degraded, which is different from that reported by Oehlers and Foley [14] who found that the stiffness remained constant during fatigue loading. Then, the stiffness value was divided by the initial value, and the result, which was the relative stiffness, is shown in Fig. 25. The stiffness was significantly degraded in the early stage of fatigue loading (N/Nf less than 0.06). The reason for this is that the natural bond between steel and concrete was destroyed at the beginning of fatigue life and the slip at the interface increased [25]. Then, during most of the loading process, the specimen’s stiffness decreased linearly with the number of cycles. This is similar to the existing fatigue test results for ordinary stud shear connectors. However, no sudden decrease in stiffness was observed near the fatigue failure in this study. The experimental results show that the static stiffness degradation laws of the S shear connectors and the RS shear connectors were similar, and the same mathematical model can be used to quantitatively analyze the stiffness degradation. In Fig. 26, test data of relative static stiffness for all specimens except S-120 and RS25-30 specimens are plotted against (N/Nf). A model proposed by Hanswille et al. [22,23] was used to fit this data:

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X. Xu et al. / Construction and Building Materials 244 (2020) 118386

50

40

40

N=1 N=1000 N=10000 N=50000 N=100000 N=250000 N=333354

20

10

0 0.0

0.1

0.2

0.3

Load (kN)

Load (kN)

30

30

N=1 N=1000 N=10000 N=60000 N=100000 N=150000

20 10

0 0.0

0.4

0.3

Relative slip (mm)

0.6

(a)S-120

1.2

(b)S-140 20

15

12

15 N=1 N=1000 N=10000 N=50000 N=625000 N=1075000 N=1525000 N=2015000

9

6 3

0 0.0

0.1

0.2

0.3

Load (kN)

Load (kN)

0.9

Relative slip (mm)

N=1 N=1000 N=10000 N=50000 N=100000 N=200000 N=550000 N=750000

10

5

0 0.0

0.4

0.3

0.6

0.9

1.2

1.5

Relative slip (mm)

Relative slip (mm)

(c)RS25-30

(d)RS25-50

25

30

N=1 N=1000 N=10000 N=35583 N=100000 N=150000

15

10 5

0 0.0

0.3

0.6

0.9

20

Load (kN)

Load (kN)

20

N=1 N=1000 N=10000 N=50000 N=74315

10

0

1.2

0

Relative slip (mm)

2

4

6

8

Relative slip (mm)

(e)RS25-70

(f)RS25-90-1 Fig. 23. Evolution of load-slip curves.

k g ¼ s;N ¼ ks;1

(

 1 N ¼ 1 1  1 0 < N < Nf N=N

a þ bln

ð18Þ

f

where, g is the relative static stiffness, ks;N is the static stiffness after N fatigue cycles, ks;1 is the initial static stiffness, and a and b are the fitting parameters. After fitting, a and b were obtained as 0.60 and 0.08, respectively, and the fitted curve is shown in Fig. 26. The coefficient of determination was 0.76. The figure also shows the fitted curves for

ordinary stud shear connectors by other researchers. The stiffness degradation curve proposed by Liu et al [27] for studs in ECC is close to that proposed in this study. Cao et al. [25] studied the stiffness degradation law of studs in UHPC, but the scatter of results was large, and the upper and lower curves (Curve 1 and 2 in the figure) were given respectively. The curve in this study lies between the two curves and is closer to the upper curve. As a summary, the proposed model can predict the stiffness degradation of both ordinary stud shear connectors and rubber-sleeved stud shear connectors.

15

X. Xu et al. / Construction and Building Materials 244 (2020) 118386

20

50

15

30

N=1 N=1000 N=10000 N=50000 N=100000

20

Load (kN)

Load (kN)

40

5

10

0 0

1

2

3

N=1 N=1000 N=10000 N=50000 N=150000 N=300000

10

0 0.0

4

0.5

Relative slip (mm)

1.0

1.5

2.0

Relative slip (mm)

(g)RS25-90-2

(h)RS50-50

25

Load (kN)

20 15

N=1 N=1000 N=10000 N=35000

10 5

0 0

1

2

3

4

5

Relative slip (mm)

(i)RS50-70 Fig. 23 (continued)

300

1.0

200

100

0 0.0

0.2

0.4

0.6

0.8

S-120 S-140 RS25-30 RS25-50 RS25-70 RS25-90-1 RS25-90-2 RS50-50 RS50-70

1.2

S-120 S-140 RS25-30 RS25-50 RS25-70 RS25-90-1 RS25-90-2 RS50-50 RS50-70

Relative static stiffnes

Static stiffness (kN/mm)

400

1.0

N/Nf Fig. 24. Evolution of static stiffness.

4. Fatigue failure mechanism The shear mechanism and failure process of rubber-sleeved stud shear connectors under monotonic loading have been clarified by Xu et al. [3]. Through the calculated results from the analytical model based on ‘‘beam on elastic foundation’’ theory and finite element analysis, it has been observed that when the shear connectors are under the same shear force, the bending moment in the

0.8 0.6 0.4 0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

N/Nf Fig. 25. Evolution of relative static stiffness.

stud increases with the height of the rubber sleeve [4]. As a result, the roots of rubber-sleeved studs suffer greater strain and stress, and the bending deformation of the stud and the relative slip increase, as shown in Fig. 27. The change in the shear mechanism caused by the rubber sleeve affects the fatigue life of the shear connectors. For both ordinary stud and rubber-sleeved stud shear connectors, the fatigue failure mode is the fracture of the stud shank. The fatigue crack starts at

16

X. Xu et al. / Construction and Building Materials 244 (2020) 118386

1.0

Relative static stiffness

stress intensity factor is in proportion to the reference stress. Since the rubber-sleeved stud is at higher stress state than the ordinary stud, it can be speculated that the reference stress in the rubbersleeved stud is higher. As a result, the rubber-sleeved stud has a higher crack propagation rate and a lower fatigue life. If the stud is assumed to be a beam on an elastic foundation, as shown in Fig. 28, then the shear stiffness degradation of the shear connector is the result of the reduction of both the beam section and the foundation stiffness. For rubber-sleeved stud shear connectors, the formula for static shear stiffness is as following [4]:

Test data Fitted curve Curve by Liu et al. [27] Curve 1 by Cao et al. [25] Curve 2 by Cao et al. [25]

1.2

0.8 0.6 0.4

  hr 3=4 kRS ¼ exp 0:648 ðK con ds Þ Es1=4 ds Z 0 ds

0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

N/Nf Fig. 26. Static stiffness degradation model.

the stud root and propagates until the strength of the remaining steel is weaker than the maximum shear load. Therefore, the fatigue crack propagation rate determines the fatigue life. This rate can be expressed by the Paris equation [34],

da ¼ C ðDK Þm dN

ð19Þ

where a is the crack size; N is the crack propagation life; DK is the range of the stress intensity factor; C and m are material constants. The stress intensity factor can be calculated by the following formula [35]:

K ¼ Fr

pffiffiffiffiffiffi pa

ð20Þ

where F is a correction factor dependent on the specimen and crack geometry; r is the reference stress in the uncracked condition. The

S shear connector

where kRS is the shear stiffness of rubber-sleeved stud shear connectors; hr is the rubber sleeve height; ds is the stud shank diameter; K con is the modulus of concrete foundation, which is a function of Ec ; Es and Ec are the elastic modulus of steel and concrete, respectively; Z 0 is a near constant coefficient. The stiffness of the beam section is determined by Es and ds , while hr and K con undoubtedly reflect the effects of the foundation stiffness on the shear stiffness of the connectors. As the area of the fatigue crack at the stud root increases, the stiffness of the cracked section decreases. However, the stiffness reduction of individual sections has a limited influence on the shear stiffness of the connectors, because the relative slip is the result of the overall deformation of the stud. On the other hand, the deterioration of the foundation along the stud caused by the fatigue damage in concrete leads to an increase in the bending deformation of the stud. As a result, the stress in the stud gradually increases and the cross sections of the stud continuously yield. Thus, the bending stiffness of the stud decreases, eventually leading to the stiffness degradation of shear connectors. Since the stiffness degradation laws of the two types of shear connectors are similar, it can be inferred that although the concrete compression zone and damage degree are different (Fig. 27), the degradation law of the

RS shear connector

(a) Mises stress in stud (MPa)

S shear connector

ð21Þ

RS shear connector

(b) Compressive damage in concrete Fig. 27. Numerical results of shear connectors at the load of 30kN [3].

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X. Xu et al. / Construction and Building Materials 244 (2020) 118386

Push-out direction

da dN

C

K

m

Q0

EsIs

M0

Kr=0

a Rubber

(a) Rubber-sleeved stud with a fatigue crack

x

Kcon

hr

y

Concrete

Stud

hef - hr

(b) “Beam on elastic foundation’’ model [4]

Foundation stiffness

Area of the cracked section

Kcon

As a O

a

(c) Reduction in area of the cracked section

O

N/Nf

(d) Degradation of concrete foundation stiffness

Fig. 28. Fatigue failure mechanism of rubber-sleeved stud shear connectors.

foundation stiffness may be the same. Moreover, for different types of concrete, the degradation law seems to be consistent. 5. Conclusions Through the fatigue push-out tests on nine specimens of shear connectors with different rubber sleeve heights under different shear stress ranges, the shear fatigue performance of the rubbersleeved stud shear connector was studied, and the following conclusions were obtained: (1) The fatigue life of rubber-sleeved stud shear connector is smaller than that of the ordinary stud shear connector, and the fatigue life of the shear connector decreases with the rubber sleeve height. The fatigue failure of specimens was caused by the fracture of the headed studs. The fatigue cracks in all the specimens initiated at the weld collar/shank interface and propagated through the shank. (2) Nominal shear stress-based S-N curves for shear connectors with 25 mm and 50 mm high rubber sleeves were proposed through the statistical analysis of fatigue life data. The proposed S-N curves lie below the S-N curve specified in Eurocode 4 for ordinary stud shear connectors. Based on the curve equations, the fatigue strengths of RS25 and RS50 shear connectors at two million cycles were calculated to be 38.5 MPa and 30.6 MPa, respectively, which are lower than that of ordinary stud shear connectors specified in the Chinese code, 90 MPa. The rubber sleeve leads to the decrease in the fatigue strength of shear connector. (3) Rubber sleeves with low stiffness have influence on the evolution law of dynamic relative slip. Through the quantitative analysis on the growth rate of the maximum dynamic relative slip of rubber-sleeved stud shear connectors, it was found that the rubber sleeve which provides a weaker restraint to stud deformation than concrete leads to a larger relative slip growth rate. The greater the strength and stiffness of the materials surrounding the studs, the stronger the restraint conditions and the smaller the growth rate. (4) The static shear stiffnesses of all specimens were clearly degraded during the fatigue tests. The static stiffness degradation laws of ordinary stud shear connectors and rubbersleeved stud shear connectors were similar. A unified static

shear stiffness degradation model for two types of shear connectors was established by nonlinear fitting of the test results. (5) Fatigue failure mechanism of rubber-sleeved stud shear connectors was analyzed. The shear stiffness degradation of the shear connector is the result of the reduction of both the stud sections and the concrete stiffness. Rubber-sleeved studs suffer greater strain and stress than ordinary studs. As a result, the rubber-sleeved stud has a higher crack propagation rate and a lower fatigue life. All the findings up to now contribute to the understanding of the behavior of rubber-sleeved stud shear connectors under fatigue loading and would provide reference for their fatigue design. However, the formulas proposed in this study are empirical. In the future, additional numerical and theoretical studies will be conducted to evaluate the proposed fatigue failure mechanism of rubber-sleeved stud shear connectors. Moreover, fatigue tests on steel–concrete composite beams will be executed. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors gratefully acknowledge the financial support provided by National Natural Science Foundation of China (No. 51808069), China Postdoctoral Science Foundation (No. 2019M653339) and Chongqing Postdoctoral Science Special Foundation (No. XmT2018035). CRediT authorship contribution statement Xiaoqing Xu: Conceptualization, Investigation, Methodology, Writing - original draft, Writing - review & editing, Funding acquisition. Xuhong Zhou: Supervision. Yuqing Liu: Supervision. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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References [1] D. Oehlers, M. Bradford, Elementary behaviour of composite steel and concrete structural members, Butterworth-Heinemann, 1999. [2] L. An, K. Cederwall, Push-out tests on studs in high strength and normal strength concrete, J. Constr. Steel Res. 36 (1) (1996) 15–29. [3] X. Xu, Y. Liu, J. He, Study on mechanical behavior of rubber-sleeved studs for steel and concrete composite structures, Constr. Build. Mater. 53 (2014) 533– 546. [4] X. Xu, Y. Liu, Analytical and numerical study of the shear stiffness of rubbersleeved stud, J. Constr. Steel Res. 123 (2016) 68–78. [5] B. Zhuang, Y. Liu, F. Yang, Experimental and numerical study on deformation performance of Rubber-Sleeved Stud connector under cyclic load, Constr. Build. Mater. 192 (2018) 179–193. [6] B. Zhuang, Y. Liu, Study on the composite mechanism of large Rubber-Sleeved Stud connector, Constr. Build. Mater. 211 (2019) 869–884. [7] X. Xu, Y. Liu, M. Yuan, W. Ren, Application of rubber-sleeved studs on steel and concrete composite deck in railway bridges, in: H. Furuta, D.M. Frangopol, M. Akiyama (Eds.), Proceedings of the Fourth International Symposium on Lifecycle Civil Engineering, IALCCE, Tokyo, Japan 2014, pp. 780-783. [8] M. Shariati, N.H. Ramli Sulong, M. Suhatril, A. Shariati, M.M. Arabnejad Khanouki, H. Sinaei, Comparison of behaviour between channel and angle shear connectors under monotonic and fully reversed cyclic loading, Constr. Build. Mater. 38 (2013) 582–593. [9] Y.H. Wang, J.G. Nie, J.J. Li, Study on fatigue property of steel–concrete composite beams and studs, J. Constr. Steel Res. 94 (2014) 1–10. [10] M. Sjaarda, T. Porter, J.S. West, S. Walbridge, Fatigue behavior of welded shear studs in precast composite beams, J. Bridge Eng. 22 (11) (2017) 04017089. [11] A. El-Zohairy, H. Salim, A. Saucier, Fatigue tests on steel-concrete composite beams subjected to sagging moments, J. Struct. Eng. 145 (5) (2019) 04019029. [12] R.G. Slutter, J.W. Fisher, Fatigue strength of shear connectors, Highway Research Record 147 (1966) 65–88. [13] M.W. Hallam, The behaviour of stud shear connectors under repeated loading, Research report no. R281 Sydney, (Australia), University of Sydney, School of Civil Engineering, 1976. [14] D.J. Oehlers, L. Foley, The fatigue strength of stud shear connections in composite beams, Proceedings Institution of Civil Engineers 79 (2) (1985) 349–364. [15] D.J. Oehlers, C.G. Coughlan, The shear stiffness of stud shear connections in composite beams, J. Constr. Steel Res. 6 (4) (1986) 273–284. [16] D.J. Oehlers, Deterioration in strength of stud connectors in composite bridge beams, J. Struct. Eng. 116 (12) (1990) 3417–3431. [17] N. Gattesco, E. Giuriani, Experimental study on stud shear connectors subjected to cyclic loading, J. Constr. Steel Res. 38 (1) (1996) 1–21. [18] R.P. Johnson, Resistance of stud shear connectors to fatigue, J. Constr. Steel Res. 56 (2) (2000) 101–116.

[19] C.S. Shim, P.G. Lee, S.P. Chang, Design of shear connection in composite steel and concrete bridges with precast decks, J. Constr. Steel Res. 57 (3) (2001) 203–219. [20] P.G. Lee, C.S. Shim, S.P. Chang, Static and fatigue behavior of large stud shear connectors for steel–concrete composite bridges, J. Constr. Steel Res. 61 (9) (2005) 1270–1285. [21] Valente MI. Experimental studies on shear connection systems in steel and lightweight concrete composite bridges, PhD Dissertation, University of Minho, Portugal; 2007. [22] G. Hanswille, M. Porsch, C. Ustundag, Resistance of headed studs subjected to fatigue loading: Part I: Experimental study, J. Constr. Steel Res. 63 (4) (2007) 475–484. [23] G. Hanswille, M. Porsch, C. Ustundag, Resistance of headed studs subjected to fatigue loading Part II: Analytical study, J. Constr. Steel Res. 63 (4) (2007) 485– 493. [24] H. Higashiyama, K. Yoshida, K. Inamoto, S. Matsui, H. Kaido, Fatigue of headed studs welded with improved ferrules under rotating shear force, J. Constr. Steel Res. 92 (2014) 211–218. [25] J. Cao, X. Shao, L. Deng, Y. Gan, Static and fatigue behavior of short-headed studs embedded in a thin ultrahigh-performance concrete layer, J. Bridge Eng. 22 (5) (2017) 04017005. [26] C. Xu, K. Sugiura, Q. Su, Fatigue behavior of the group stud shear connectors in steel-concrete composite bridges, J. Bridge Eng. 23 (8) (2018) 04018055. [27] Y. Liu, Q. Zhang, Y. Bao, Y. Bu, Static and fatigue push-out tests of short headed shear studs embedded in Engineered Cementitious Composites (ECC), Eng. Struct. 182 (2019) 29–38. [28] EN 1994-1-1. Eurocode 4: Design of composite steel and concrete structures, Part 1-1: General rules and rules for buildings, CEN, Brüssel, 2010. [29] American Association of State Highway and Transportation Officials, LRFD Bridge design specifications, 7th ed., AASHTO, Washington, DC, 2017. [30] Ministry of Housing and Urban-Rural Construction of the People’s Republic of China and General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, Code for design of steel and concrete composite bridges GB 50917-2013. Beijing, China Planning Press, 2014. [31] Ministry of Transport of the People’s Republic of China, Specifications for design and construction of highway steel-concrete composite bridge JTG/T D64-01-2015. Beijing, China Communications Press, 2015. [32] H. Hobbacher, Recommendations for the fatigue design of welded joints and components, Springer, 2016. [33] Q. Wang, Y. Liu, Experimental study of shear capacity of stud connector, J. Tongji University (Natural Science) 5 (2013). [34] P. Paris, F. Erdogan, A critical analysis of crack propagation laws, J. Basic Eng. 85 (4) (1963) 528–533. [35] Y. Murakami, Stress intensity factors handbook, Pergamon, 1992.