Experimental study on fatigue performance of composite beam with steel-plate-concrete composite decks

Construction and Building Materials 188 (2018) 833–849

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Experimental study on fatigue performance of composite beam with steel-plate-concrete composite decks Ruyue Liu ⇑, Yong Yang, Xianwei Zhou Department of Civil Engineering, Xi’an University of Architecture and Technology, Shaanxi 710055, China

h i g h l i g h t s
A new type of composite deck was used in the composite beam.
The calculation method for stiffness of composite beam under fatigue loading was proposed.
The fatigue behavior of composite beam under positive and negative bending moment was tested and analyzed, respectively.

a r t i c l e

i n f o

Article history: Received 31 May 2018 Received in revised form 9 August 2018 Accepted 17 August 2018

Keywords: Composite beam Steel-plate-concrete composite deck Fatigue performance Failure mode Experimental study

a b s t r a c t In order to study the fatigue performance of composite beam with steel-plate-concrete composite deck under fatigue load, both static test on two specimens and fatigue test with constant-amplitude fatigue load on six specimens were conducted. The influence of the upper limit and lower limit of fatigue load as well as the amplitude of fatigue load on the failure mode and failure damage was studied both under sagging moment and hogging moment. In addition, for the tested specimens under fatigue load, the dynamic deflection, residual deflection, strains of concrete and steel plates, strain of steel beam, residual capacity and the flexural stiffness were recorded and analyzed. The experimental results demonstrated that the failure mode of specimens under sagging moment was the fracture of steel plate of composite beam, resulting in the concrete crush in compression region, however, the specimens under hogging moment developed good fatigue behavior with comparatively high bearing capacity and stiffness and no fatigue failure was found finally. The fatigue life was directly affected by the stress amplitude of fatigue load while the upper limit and lower limit of fatigue load had little influence on it. The conclusion obtained in the paper was helpful for the design of this type of composite beam. Ó 2018 Elsevier Ltd. All rights reserved.

0. Introduction As an innovative type of composite beam with steel-plateconcrete composite deck (abbreviated as composite beam in this paper for brevity), the H-shaped steel beam was connected with the composite deck by studs (shown as Fig. 1a), and for the composite deck, the steel plate was connected with concrete by steel plate with openings (shown as Fig. 1b). This new type of composite beam takes the advantage of component materials, obtains efficient lightweight components, and solves the problem of temporary framework and scaffoldings with the steel plate, reducing the construction period and saving costs. Moreover, with steelplate-concrete composite deck, the composite beam could be used

⇑ Corresponding author. E-mail address: [email protected] (R. Liu). https://doi.org/10.1016/j.conbuildmat.2018.08.108 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.

in beam with larger span without necessary excessive secondary beams. It is known to us that for steel-plate-concrete composite deck, it is important to ensure the shear force transferring between the steel plate and the concrete, therefore, it is of significance to set up reliable interaction between these two members. For the steel-plate-concrete composite deck mentioned in this paper, a type of perforbond shear connector (abbreviated as PBL shear connector in this paper for brevity) was used to connect the steel plate and the concrete together with the steel-plate with openings. The PBL shear connector could be used as stiffeners for the flat steelplate under construction to enhance the flexural stiffness and bending capacity. Besides, considering that the PBL shear connector could work together well with the concrete and develop significant stress under external load, it could be taken as the transverse reinforcement. Therefore, it is unnecessary for other reinforcing bars and reduces the construction cost, and it could also effectively

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(a) composite beam

(b) composite deck

Fig. 1. Details of configuration of composite beam with composite deck.

solve the problem of insufficient shearing capacity of concrete in case of unsuitable configuration of transverse reinforcing. Because of the advantages of this new type of composite beam, it has been gradually applied in the civil construction and industrial construction especially for the large-span bridges [1]. With the rapid development of transportation, it is common that the bridge always suffered from the cyclic load and dynamic load and the demand on tonnage and speed of the vehicles over the bridges grows as well. Although many researches on static performance or the seismic performance of the composite beam have been conducted [2–4], rare study of the fatigue behavior of the composite beam due to the repeated load or dynamic load was performed. According to the statistics, until the end of 2006, a large quantities proportion of 500 thousands existed bridges were designed without taking the fatigue into consideration. If the structure which suffered from fatigue load was designed only with static load, it was of high possibility that unexpected fatigue failure would occur during service period and put threat on the life safety and even brought undesirable losses. Consequently, it was of great significance to study the fatigue performance of composite bridge decks to better understand the mechanism of the fatigue performance of the composite decks and the vibration mechanism under dynamic load [5]. It would be helpful to ensure the safety of the composite beams in service period, and improve the durability and the fatigue-resistance capacity based on the study of fatigue behavior [6]. Strength degradation and stiffness degradation caused by the loss of bounding between concrete and shear stubs were studied [7,8] and the fatigue behavior of stub shear connectors and the crack on concrete deck were also studied [9,10]. The residual deflection behavior of steel-concrete composite beam under negative bending moment was analyzed and the analytical model for the residual deflection was put forward and verified [11]. In addition, considering that different strengthened method were used in

old structures to improve the fatigue behavior, Nie and Yu also performed experimental research on the strengthened reinforced concrete beams [12,13]. However, these researches concentrated on the mechanical behavior under positive bending moment. For continuous composite structural members, the composite components would experience both positive and negative bending moment, and it is unfavorable that the composite deck would generate tensile stress under negative bending moment, resulting in serious cracking of concrete and the final collapse. Therefore, it is essential to investigate the fatigue behavior of the composite beam and the influence of negative bending moment on the mechanical behavior of composite deck to ensure the normal working function, the life safety and service life of bridges [14,15]. It had been verified that both the incremental slip at the interface of steel beam and concrete deck and the cracking of the concrete deck would impair the durability and service life of composite beam [16,17]. Besides, combining the influence of sagging moment and high-cycle repeated loadings, the decrease of both static and fatigue resistance would be serious and the ductility and service life of composite beams might be unfavorably affected. Based on this background, a series of fatigue tests with 3 composite beams under sagging moment and 3 specimens under hogging moment were conducted. Besides, static test for specimen under sagging moment and hogging moment and the final static test after fatigue test were also performed to furthermore investigate the influence of different load pattern on the fatigue behavior of such type of composite beams. 1. Test program 1.1. Specimens design Eight composite beams were designed for the test, including 2 for the static test and 6 for the fatigue test. Table 1 listed the major

Table 1 Parameters of composite beam specimens. Specimen No.

L/mm

T/mm

W/mm

k

Layout of stubs

steel plate with openings

Longitudinal reinforcement

fcu/MPa

CBP-1200-0 CBP-1200-1 CBP-1200-2 CBP-1200-3

3300 3300 3300 3300

350 350 350 350

1200 1200 1200 1200

3.41 3.41 3.41 3.41

U16  65@50 U16  65@50 U16  65@50 U16  65@50

14  70  565@240 14  70  565@240 14  70  565@240 14  70  565@240

2,15U12 2,15U12 2,15U12 2,15U12

17.48

CBN-1200-0 CBN-1200-1 CBN-1200-2 CBN-1200-3

3300 3300 3300 3300

350 350 350 350

1200 1200 1200 1200

3.85 3.85 3.85 3.85

U16  65@50 U16  65@50 U16  65@50 U16  65@50

14  70  565@240 14  70  565@240 14  70  565@240 14  70  565@240

2,15U12+1,4U10 2,15U12+1,4U10 2,15U12+1,4U10 2,15U12+1,4U10

34.12

Note: For CBP(N)-1200-X, CSB = the composite beam, P = the positive bending moment and N = the negative bending moment, X = the number of specimen; L = span of slab; T = thickness of slab; W = width of slab; t = thickness of steel plate; k = nominal shear span ratio; fcu = average compressive strength of cubic concrete.

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parameters of all tested specimens and Table 2 listed the material property of the concrete, steel plate and reinforcement used for the specimens. For the 6 specimens in fatigue test, they were classified into 2 categories, series 1 included specimen CBP-1200-1 CBP-1200-3 designed under sagging moment while series 2 included CBN1200-1 CBN-1200-3 designed under hogging moment. Concrete with grade of C25 and C45 for used for series 1 and series 2, respectively. Transverse steel-plate with opening was used to connect the bottom flat steel-plate and concrete, and the thickness of the transverse steel-plate was 14 mm and the diameter of the opening on it was 40 mm, the opening was set with space of 240 mm. H-shaped steel beam of HM250  175 was used and connected with the upper steel-plate-concrete composite deck with stubs. The specification of stubs was U16  85, the space of stubs in series 1 was 120 mm and 80 mm for series 2. Fig. 2 and Fig. 3 demonstrated the details of configuration of composite beam and connection.

1.2. Test set-up 1.2.1. Loading scheme For specimen CBP-1200-0 and CBN-1200-0, static failure test was performed to obtain the ultimate bearing capacity under static load, and the result was used as the basis of the fatigue test. For the remaining 6 specimens, fatigue test with constant fatigue amplitude was applied to furthermore study the fatigue behavior of composite beams, and 3 specimens were tested under positive bending moment while the other 3 specimens were tested under negative bending moment. The set-up for static test was shown as Figs. 4 and 5, Fig. 6 demonstrated the test-up for fatigue test (specimen under negative bending moment was inverted installed). As shown in Figs. 4 and 5, the specimen was restrained at one end with fixed hinged support and the other with roller support. For static test, the vertical load was applied symmetrically at 2 points by hydraulic jack while for

Table 2 Material property of composite beam specimens. Specimen No.

CBP-1200-X CBN-1200-X

Flat steel-plate

U10

Steel plate with openings

U12

fcu/MPa

fy/MPa

fu/MPa

fy/MPa

fu/MPa

fy/MPa

fu/MPa

fy/MPa

fu/MPa

310 310

434 434

304 304

497 497

474.3 474.3

604.8 604.8

373.6 373.6

523.8 523.8

17.48 34.12

Note: fy = yielding strength; fu = ultimate strength; fcu = average compressive strength of cubic concrete.

(a) Schematic profile of composite beam

(b) Layout of reinforcement

Fig. 2. Details of configuration of composite beam under positive bending moment.

(a) Front view

(a) Top view

Fig. 3. Configuration of composite beam. Note:1-PBL shear connector of 14 mm; 2-shear stubs; 3-concrete deck; 4-stiffeners of 10 mm; 5-reinforcing bar of 12 mm; 6-reinforcing bar of 10 mm; 7-flat bottom steel plate; 8-side steel plate; 9-end plate of 10 mm.

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(a) Specimen CBP-1200-0(sagging moment)

(b) Specimen CBN-1200-0(hogging moment)

Fig. 4. Schematic of set-up for static test.

(a) Specimen CBP(sagging moment)

(b) Specimen CBN(hogging moment)

Fig. 5. Schematic of set-up for fatigue test.

For the fatigue test, the loading frequency was 5 Hz and the target loading cycle was 2 million times. The intermediate static test was carried out again after every critical cyclic loading and the evolution of fatigue damage was determined based on the subsequent static test with upper limit of fatigue load after fatigue test (loading cycles equaled to 1  104, 3  104, 5  104, 10  104, 20  104, 50  104, 100  104, 150  104). Table 3 demonstrated the detailed procedures of fatigue test, while Table 4 briefly summarized the parameters of fatigue test, and Fig. 6 showed the fatigue test setup. Subsequent final static test would be performed on the specimens to study the static loading behavior of composite beam after fatigue loading if fatigue failure did not occur during fatigue loading, and the residual bearing capacity and residual stiffness of composite beam was obtained. Fig. 6. Fatigue test set-up.

fatigue test, the vertical was applied at the distributed beam at the midpoint and the upper and lower limit of fatigue load was applied based on the test result of static test. Table 3 listed the test result of static test and details of fatigue load for all specimens.

1.2.2. Measurement scheme Preloading was conducted to ensure the normal working condition of loading equipment and check if the measurement equipment was in good condition. During the tests, the deflection of composite beam, strain of steel plate (both at bottom and at side), strain of H-shaped steel beam and strain of concrete was measure by LVDTs. In addition, the dynamic deflection and residual deflec-

Table 3 Loading procedures for fatigue test. 1 2 3 4 5 6 7 8 9

Before fatigue test Fatigue test (Fatigue Fatigue test (Fatigue Fatigue test (Fatigue Fatigue test (Fatigue Fatigue test (Fatigue Fatigue test (Fatigue Fatigue test (Fatigue Fatigue test (Fatigue

load: load: load: load: load: load: load: load:

Pf, Pf, Pf, Pf, Pf, Pf, Pf, Pf,

10,000cycles) 30,000cycles) 50,000cycles) 100,000cycles) 200,000cycles) 500,000cycles) 1000,000cycles) 2000,000cycles)

Intermediate Intermediate Intermediate Intermediate Intermediate Intermediate Intermediate Intermediate Intermediate

static static static static static static static static static

test test test test test test test test test

(static (static (static (static (static (static (static (static (static

load: load: load: load: load: load: load: load: load:

Ps) Ps) Ps) Ps) Ps) Ps) Ps) Ps) Ps)

Note: Ps = Pf = 100 kN for specimens CBP-1200-1, CBP-1200-2, CBN-1200-1, CBN-1200-2; Ps = Pf = 65 kN for specimens CBP1200-3, Ps = Pf = 150 kN for specimens CBN-1200-3.

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R. Liu et al. / Construction and Building Materials 188 (2018) 833–849 Table 4 Summary of parameter of fatigue test. Specimen No.

P s =kN

P u;s =kN

P f =kN

P f ;limit =kN

Ratio of fatigue loading

CBP-1200-1 CBP-1200-2 CBP-1200-3 CBN-1200-1 CBN-1200-2 CBN-1200-3

630 630 630 416 416 416

315 315 315 200 260 260

100 100 65 100 100 150

215–315 125–225 250–315 100–200 160–260 110–260

0.34P s –0.5P s 0.2P s –0.36P s 0.4P s –0.5P s 0.24P s –0.48P s 0.38P s –0.63P s 0.26P s –0.63P s

Note: P s = ultimate static load;P u;s = load for initial static loading;P f = fatigue load;P f ;limit = lower and upper limit of fatigue load.

Fig. 7. Layout of strain gauges of composite beam.

tion at the mid-span of composite beam was also recorded. The layout of LVDTs could be seen from Fig. 4 and the strain gauges were demonstrated in Fig. 7. LVDTs labeled from D41 to D44 was installed at mid-span of beam and the loading points to record the deflection at different location; D45 and D46 was to measure the deformation of beam end; D47 and D48 were placed at two ends of the specimens to measure the slip between the H-shaped steel beam and concrete slab. Strain gauges labeled from S1 to S7 was to measure the strain of concrete while S11 to S16 to measure the strain of flat steel plate of composite deck. Strain of web and flange of H-shaped steel beam was recorded at both sides.

2. Test results and analysis

since that all the steel-plate-concrete composite deck was covered by the steel plate expect for the top of concrete. The development of the cracks for static test was demonstrated in Fig. 8. For specimen CBP-1200-0 and CBN-1200-0, composite beam cracked at on the order of 0.7 P u 0.8P u , and the concrete gradually cracked with load increasing and the previous crack extended from loading point to the end of decks. Fig. 8 demonstrated the cracking development of specimen CBN-1200-0 as an example and it was observed that initial cracks generated in the concrete adjacent to the tension region and with test going on, the tensile stress of concrete increased and the cracking of concrete finally occurred as the tensile stress exceeded the ultimate tensile strength. It was also observed that all the specimens in static test experienced typical flexural failure, and no obvious slip was found, indicating that the layout of PBL connectors and shear stubs was reasonable.

2.1. Test phenomenon 2.1.1. Static test 2.1.1.1. Development of cracking. During the test, it was found that the crack concentrated on the concrete slab of composite beam

2.1.1.2. Failure mode. According to the observation during test, it was found that for the specimen under static test, the final failure of specimen was due to the concrete crush at the mid-span of beam under large bending moment and the reinforcement in concrete

Fig. 8. Crack development and distribution of specimen CBN-1200-0.

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R. Liu et al. / Construction and Building Materials 188 (2018) 833–849

(a) Global failure of composite beam

(b) Failure of steel beam

(b) Failure of steel bar

Fig. 9. Failure mode of specimen CBP-1200-0.

2.1.1.3. Analysis of strain development. Fig. 10 demonstrate the strain development of bottom steel plate of composite beam under different cases and Fig. 11 illustrated the strain development and distribution along upper flange of steel beam. From the development of strain of bottom steel plate at different locations, it could be seen that the development of strain grew slowly with the increasing of load and the strain at different location differed slightly when applied loading enhanced initially, however, the strain increased quickly and the difference of strain at different location was obvious (Fig. 10a) after 400 kN. For specimen CBN1200-0, before 200 kN, the strain grew with load increasing and the strain at location where was close to web of steel beam increased more quickly, moreover, it remained growing while strain at location close to the end of flange was deduced with the load increasing, and the difference of strain at opposite location concerned, which was caused by the bias of loading during the experiment. In addition, from the analysis of strain along upper flange of steel beam, it could be known that the strain of upper flange of steel beam was almost the same when the load was small initially. However, for specimen CBP-1200-0, the difference was increased when load achieved 400 kN with the strain at position close to

1200

2.1.2. Fatigue test 2.1.2.1. Development of cracking. In terms of other specimens under fatigue test, no cracks occurred after static test, but the concrete gradually cracked after certain fatigue load level for specimens under positive bending moment, and the cracks of specimen CBP-1200-3 developed more seriously. However, for specimen under negative bending moment, visible transverse crack was found near the mid-span of beam and the cracks developed quickly at the beginning of fatigue test with new cracks in the shearbending zone and pure bending zone occurring. The evolution of development in fatigue test was similar with that in static test. The development of crack became stable finally and then the subsequent static test was performed until the failure of specimen, the cracks developing and distributing symmetrically. Fig. 12 partially illustrated the development of crack in specimens during fatigue test. 2.1.2.2. Failure mode. Based on the proposed fatigue loading scheme, the final failure mode of specimens in fatigue test was sort of different and the failure mode of every specimen was summarized in Table 5. No significant slip between PBL shear connectors and concrete or H-shaped steel beam and steel-plate-concrete

50kN 100kN 200kN 300kN 400kN 450kN 500kN 550kN 600kN

strain/(με)

1400

the centroid of steel beam was larger than that at location close to the end of flange. It could be also observed that due to the serious bias of loading at steel beam during loading, the strain gauges of specimen CBN-1200-0 failed, resulting in erratic strain measurement.

1000 800

350 300 250 200 150

600

100

400

50

200

-550

-300

-50

0

50kN 100kN 200kN 300kN 400kN 416kN

strain/(με)

buckled upwards after removing the casting concrete. At ultimate load, load decreased abruptly with deflection of beam growing quickly, resulting in the outwards buckling of side steel plate (shown in Fig. 9). The object of static was to get the ultimate fatigue strength of specimens.

-550 50

300

550

-300

0 -50 -50

50

300

-100

Distance to centroid of beam/mm

Distance to centroid of beam/mm

(a) Specimen CBP-1200-0

(b) Specimen CBN-1200-0 Fig. 10. Strain of bottom steel-plate.

550

839

-60

-45

-30

3600

-4000

strain/(με)

50kN 100kN 200kN 300kN 400kN 450kN 500kN 550kN

2400

50kN 100kN -3500 200kN 300kN -3000 400kN 416kN -2500

2000

-2000

1600

-1500

1200

-1000

800

-500

400

0

3200 2800

-15

0

0

15

30

45

60

Distance to centroid of beam/mm

-60

-45

-30

500 -15 0

strain/(με)

R. Liu et al. / Construction and Building Materials 188 (2018) 833–849

15

30

45

60

Distance to centroid of beam/mm

(a) Specimen CBP-1200-0

(b) Specimen CBN-1200-0

Fig. 11. Strain of upper flange of steel beam.

(a) specimen CBP-1200-2

(a) specimen CBP-1200-3

Fig. 12. Crack development and distribution of specimen in fatigue test.

Table 5 Summary of results for static test and parameters for fatigue test. Specimen No.

P res =kN

CBP-1200-0 CBP-1200-1 CBP-1200-2 CBP-1200-3 CBN-1200-0 CBN-1200-1 CBN-1200-2 CBN-1200-3

630

620 416 428 475 434

P f =kN

P f ;limit =kN

Cycle times/(1 0 4)

100 100 65

215–315 125–225 250–315

142 115 211

100 100 150

100–200 160–260 110–260

200 215 356

Failure mode Static failure Fatigue fracture Fatigue fracture Static failure after Static failure Static failure after Static failure after Static failure after

fatigue test fatigue test fatigue test fatigue test

Note: P res = residual load for subsequent static failure test; P f = fatigue load; P f ;limit = lower and upper limit of fatigue load.

composite deck was observed, indicating that there was reliable stress transferring between different members. For specimen CBP-1200-1 and CBP-1200-2, fatigue failure mode was observed at 142  104 cycle times and 115  104 cycle times, respectively. The failure was caused by the fatigue fracture at the flange of Hshaped steel beam. Fatigue crack initiated at the one side of flange and then extended and developed quickly along the web and in the end, the whole web fractured for CBP-1200-1 leading to the concrete collapsing in the compression zone while the top flange of CBP-1200-2 remained intact. However, specimen CBP-1200-3 did

not suffer fatigue failure. As a result, the failure mode of specimens under positive bending moment could be summarized as fatigue fracture of flange and subsequent crush of concrete. Nevertheless, for specimens under negative bending moment, similar cracks with that of CBN-1200-0 was found at initial static test, but none experienced fatigue failure even though the steel beam buckled significantly. The development of crack was different because of different force mechanism. For specimen CBN1200-1, it had similar crack distribution with static test and no obvious strength degradation was found during static test after

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R. Liu et al. / Construction and Building Materials 188 (2018) 833–849

specimen CBP-1200-2

specimen CBP-1200-3

specimen CBN-1200-2

(a) Failure of steel beam

specimen CBP-1200-2

specimen CBP-1200-3

specimen CBN-1200-2

(b) Failure of composite deck Fig. 13. Failure mode of specimen in fatigue test.

fatigue, and the residual bearing capacity was 428 kN. Similarly, for specimen CBN-1200-2 and CBN-1200-3, the residual bearing capacity was 475 kN and 434 kN, respectively. Fig. 13 demonstrated the final failure mode of specimen under positive bending moment and negative bending moment. Table 5 also summarized the results for subsequent static failure test and parameters for fatigue test. 2.2. Analysis of test results Considering that the failure mode of specimen under positive and negative bending moment was different, in this section, the behavior of specimen under positive and negative bending would be discussed. In addition, experimental results of static test were analyzed, and it was the basis of the study of fatigue test. 2.2.1. Deflection analysis 2.2.1.1. Static test. The flexural stiffness, bearing capacity and deformation capacity were investigated during static test. Fig. 14

demonstrated the curve of load vs. deflection for specimens under positive and negative bending moment, respectively. It could be conducted that the performance of composite beam under positive bending moment was better than that under negative moment, and it had higher bearing capacity and better deformation capacity. The elastic limited load was on the order of 400 kN and 350 kN for positive and negative cases, respectively. The difference in performance of composite beam under positive and negative bending moment was caused by the difference in stress mechanism. When under positive bending moment, the steel beam yielded as soon as the concrete crush, however, the steel beam yielded prior to the concrete crushed when suffered negative bending moment. 2.2.1.2. Fatigue test. Intermediate static test with upper limit of fatigue load was conducted at different critical level of fatigue loading cycles and the deflection was recorded. Before fatigue loading, initial static test (0 cycles in figures) was conducted and if no fatigue failure was generated during fatigue test, then the speci-

500

700

CBN-1200-0

CBP-1200-0 600

400

400

Load/kN

Load/kN

500

300

300

200

200

100

100 0

0

25

50

75

100

125

0

0

25

Deflection/mm

(a) Specimen CBP-1200-0

50

75

Deflection/mm

(b) Specimen CBN-1200-0

Fig. 14. Curve of load vs. deflection in static test.

100

841

R. Liu et al. / Construction and Building Materials 188 (2018) 833–849

350

250 200

0 1*104 cycles 3*104 cycles 5*104 cycles 9*104 cycles 33*104 cycles 70*104 cycles 100*104 cycles 140*104 cycles 200*104 cycles

200

Load/kN

300

Load/kN

250

0 3*104 cycles 5*104 cycles 25*104 cycles 60*104 cycles 100*104 cycles

150

150

100

100

50

50

CBN-1200-1

CBP-1200-1 0

0

2

4

6

8

0

10

0

1

2

Mid-span Deflection/mm 350

200 150

200

100

150 100

0

2

4

6

0

8

0

2

Mid-span Deflection/mm

200 150 100

6

8

0 3*104 cycles 5*104 cycles 10*104 cycles 35*104 cycles 50*104 cycles 94*104 cycles 150*104 cycles 215*104 cycles

250 200

Load/kN

250

4

Mid-span Deflection/mm 300

0 1*104 cycles 3*104 cycles 5*104 cycles 10*104 cycles 35*104 cycles 50*104 cycles 105*104 cycles 150*104 cycles

300

Load/kN

6

CBN-1200-2

CBP-1200-2

350

150 100 50

50

CBN-1200-3

CBP-1200-3 0

5

50

50 0

4

0 1*104 cycles 3*104 cycles 5*104 cycles 9*104 cycles 33*104 cycles 70*104 cycles 100*104 cycles 140*104 cycles 200*104 cycles

250

Load/kN

250

Load/kN

300

0 1*104 cycles 3*104 cycles 7*104 cycles 10*104 cycles 33.5*104 cycles 50*104 cycles 104*104 cycles

300

3

Mid-span Deflection/mm

0

2

4

6

8

10

Mid-span Deflection/mm

0

0

2

4

6

8

10

Mid-span Deflection/mm

Fig. 15. Curves of load vs. deflection for composite beams.

mens would be loaded statically with the upper fatigue load until failure in order to get the residual bearing capacity and the test would not terminate until either the maximum stroke of loading equipment was reached or the bearing capacity dropped abruptly. Fig. 15 demonstrated the deflection at the mid-span of beam under different fatigue load and the curve was reflection of the degradation of stiffness of composite beam. It could be found that the curve moved up and down initially, and this might be caused by the unstable interaction between the specimens and loading machine. For specimens under positive bending moment, the maximum fatigue load was less than 350 kN, while the maximum fatigue load less than 300 kN for specimens under negative bending

moment, and it implied that all the specimens under fatigue test remained elastic since that the maximum fatigue load was less than the elastic limited load. The negative flexural specimens developed smaller capacity might be because that the concrete deck was in tensile and it could not develop as much as capacity as it in compression. Besides, stiffness of composite beam did no change much with the increase of repeated load cycles, indicating that no practical difference was found during fatigue test when the fatigue load limited to the ultimate elastic resistance. By comparison of load corresponding to 2 mm in deflection, it could be deduced that the stiffness of specimens under positive bending moment was larger

R. Liu et al. / Construction and Building Materials 188 (2018) 833–849

Mid-span Deflection/mm

Mid-span Deflection/mm

Mid-span Deflection/mm

842

8.5

9.0

8.0

8.5

7.5

8.0 7.5

7.0

7.0

6.5

6.5

6.0

6.0

5.5 5.0

5.5

loading cycle=0 0

50

100

150

200

250

300

5.0

9.5

10.0

9.0

9.5

8.5

9.0

8.0

8.5

7.5

8.0

7.0

7.5

6.5

50

6.5

4

loading cycle=5*10 times 0

50

100

150

200

250

300

6.0

10.0

10.0

9.5

9.5

9.0

9.0

8.5

8.5

8.0

8.0

7.5

7.5

7.0

100

150

200

250

300

200

250

300

200

250

300

loading cycle=25*104 times 0

50

100

150

7.0

6.5 6.0

0

7.0

6.0 5.5

loading cycle=3*104 times

6.5

loading cycle=60*104 times 0

50

100

150

200

250

300

6.0

loading cycle=100*104 times 0

50

100

150

Fig. 16. Dynamic deflection in critical time of fatigue tests for specimen CBP-1200-1.

than that of specimens under negative bending moment. It was presumable caused by the cracking on the concrete deck in tension under large fatigue load. Fig. 16 gave the dynamic deflection result at critical fatigue loading level for specimen CBP-1200-1 as an example to discuss the damage development during fatigue test, and the maximum and minimum dynamic deflection was obtained. From the curves, it could be conducted that after the crack initiated at the flange of steel beam, the dynamic deflection developed more quickly and increased to 3 times of previous deflection in short time and it kept increasing until the failure of composite beam. Therefore, it could be hypothesized that the judgement for the fatigue failure

of composite beam was to check if the fracture of flange of steel beam and the stiffness degradation as well as the abrupt change in dynamic deflection occurred during the fatigue test. Fig. 17 showed the curve of dynamic deflection, including the maximum deflection, minimum deflection difference between the maximum and minimum deflection, vs. fatigue loading cycles for specimen CBP-1200-1 and specimen CBN-1200-3 and Table 6 listed the details of deflection at every critical fatigue load. Based on the observation from test, it was known that only specimen CBP-1200-1 and CBP-1200-2 experienced fatigue failure. From the figures, it was seen that for specimen CBP-1200-1, the deflections increased significantly when the load approached to the ulti-

20

12

Mid-span Deflection/mm

Mid-span Deflection/mm

Maximum deflection Minimum deflection Difference in deflection

16

12

8

4

0

0

30

60

90

120 4

Loading Cycles/(10 )

(a) CBP-1200-1(fatigue failure)

150

Maximum deflection Minimum deflection Difference in deflection

9

6

3

0

0

50

100

150

200 4

Loading Cycles/(10 )

(b) CBN-1200-3

Fig. 17. Curve of deflection vs. number of loading cycles.

250

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R. Liu et al. / Construction and Building Materials 188 (2018) 833–849 Table 6 Result of dynamic at main fatigue load cycles. Specimen

No.

Cycle times/(1 0 4)

dmax =mm

dmin =mm

ðdmax  dmin Þ=mm

dres =mm

dres =mm

CBP-1200-1

1 2 3 4 5 6 7 8

0 1 3 5 25 60 100 141

– 10.435 10.495 10.365 10.715 20.730 10.720 17.045

– 7.670 7.880 7.980 8.190 8.240 8.275 14.360

– 2.765 2.615 2.385 2.525 2.490 2.445 2.685

– 1.980 2.140 2.250 2.150 2.245 2.315 –

1.480 2.015 2.190 2.260 2.160 2.250 2.320 –

CBN-1200–3

1 2 3 4 5 6 7 8 9 10

0 1 3 5 10 36.75 50 94 150 215

– 10.690 1.640 10.745 10.780 10.790 10.910 10.915 11.095 11.980

– 5.485 5.580 5.640 5.660 5.590 5.805 5.725 5.950 5.820

– 5.205 5.060 5.105 5.120 5.200 5.105 5.190 5.145 5.160

– 2.630 2.670 2.685 2.745 2.850 2.905 2.935 2.945 3.015

1.800 2.605 2.650 2.670 2.745 2.840 2.890 2.290 2.930 3.005

Fatigue test

Static test

Note: N = the times of fatigue load; dmax = the maximum dynamic deflection; dmin = the minimum dynamic deflection; dres = the residual deflection.

mate fatigue failure load, but for specimen without fatigue failure, the deflection developed stably, which could be observed from Fig. 15(b). The maximum and minimum deflection increased linearly with the increasing of fatigue loading cycles, but the deflection of CBP-1200-1 grew more quickly than CBN-1200-3. The difference between the maximum and minimum deflection did not change significantly, meaning that no obvious degradation of the flexural stiffness occurred. Moreover, Fig. 18 demonstrated comparison of residual deflection at mid-span of beam between the cases of static test and fatigue test. It could also be seen that for specimen with fatigue failure, the loading cycles had obvious influence on the fatigue residual deflection when load was about the ultimate load, but the residual deflection almost remained the same for specimen without failure test. Fig. 19 also illustrated comparison of the ratio of residual deflection to the maximum deflection for the specimens under positive bending moment and negative bending moment, respectively. It could be found that the residual deflection ration increased quickly initially, besides, it developed significantly after fatigue failure and could be up to the 50% of the maximum deflection. With reference to the analysis in Table 6, it could be con-

ducted that under same fatigue stress, specimen with higher upper fatigue load limit could achieve higher ratio, while for the case with same upper fatigue load limit, the ratio of specimen with higher fatigue stress was larger. 2.2.2. Strain analysis During the fatigue test, the strain of the static test after corresponding fatigue test but not the stress during fatigue loading was used to reflect the development of dynamic stress and change of residual stress. Therefore, the stress analysis discussed in the following was only used to approximately reflect the stress and its development. 2.2.2.1. Analysis of strain distribution along section height at mid-span of beam. Fig. 20(a) illustrated the strain distribution along the section height at mid-span of beam in static test and Fig. 20(b) illustrated the strain distribution along the section height at the final static test before fatigue failure. The strain distributed linearly along the height, indicating that the strain development in fatigue could still satisfy the requirement of plane-section assumption. The strain gauges destroyed at the later stage of loading and could

2.5

3.5 3.0

Mid-span Deflection/mm

Mid-span Deflection/mm

2.0

Static residual deflection Fatigue residual deflection

1.5

1.0

0.5

0.0

0

30

60

90

120

2.5

Static residual deflection Fatigue residual deflection

2.0 1.5 1.0 0.5 0.0

0

50

100

150

Loading Cycles/(104)

Loading Cycles/(104)

(a) CBP-1200-1

(b) CBN-1200-3

Fig. 18. Curve of residual deflection vs. number of loading cycles.

200

250

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R. Liu et al. / Construction and Building Materials 188 (2018) 833–849

50

30

CBP-1200-1 CBP-1200-2 CBP-1200-3

25

Residual deflection ratio

Residual deflection ratio

40

30

20

10

0

0

50

100

150

200

250

20

CBN-1200-1 CBN-1200-2 CBN-1200-3

15 10 5 0

0

50

Loading Cycles/(104)

100

150

200

250

Loading Cycles/(104)

Fig. 19. Curve of residual deflection ratio vs. number of loading cycles.

350

400

50kN 100kN 150kN 200kN 250kN 300kN

200

250

Load/kN

Load/kN

300

300

50kN 100kN 150kN 200kN 250kN

200 150 100

100

50 -600 -300

0

0

300 600 900 1200 1500 1800 2100 2400

-1500 -1200 -900

-600

Strain/(με)

-300

0

0

300

600

900

Strain/(με)

Specimen CBP-1200-1

Specimen CBN-1200-3

(a) Distribution of strains for static test 350

400

50kN 100kN 150kN 200kN 250kN 300kN

200

250

Load/kN

Load/kN

300

300

50kN 100kN 150kN 200kN 250kN

200 150 100

100

50 -600

-300

0

0

300

600

900

1200

1500

-1200

-900

-600

Strain/(με)

-300

0

0

Strain/(με)

Specimen CBP-1200-1

Specimen CBN-1200-3

(b) Distribution of strains for static test after fatigue test Fig. 20. Distribution of strains along section heights at mid-span of beam.

300

600

845

180

50kN 100kN 150kN 200kN 250kN 300kN

150 120

Strain/(με)

Strain/(με)

R. Liu et al. / Construction and Building Materials 188 (2018) 833–849

50kN 100kN 150kN 200kN 250kN

-1200 -1000 -800 -600

90

-400

60

-200 30

-600

-400

-200

0

-60 0

200

400

-45

-30

0

-15

0

15

30

45

60

200

600

Distance to centroid of beam/mm

Distance to centroid of beam/mm

(a) Specimen CBP-1200-1

(b) Specimen CBN-1200-3

Fig. 21. Distribution of flat bottom steel-plate at mid-span of beam.

Strain/(με)

2.2.2.2. Analysis of strain distribution along flat bottom steel-plate. The flat bottom steel-plate of composite beams was generally subjected to steadily increasing number of fatigue loading cycles and it might lead to the fatigue fracture of steel-plate. Fig. 21 showed the result of strain distribution of the flat bottom steel-plate for typical specimen CBP-1200-1 and specimen CBN-1200-3 under different loading level. It was shown that the change of stress of negatively flexural specimens was more significant For specimen CBP-1200-1, the stress at the location close to beam centroid was smaller, and the increment of stress at the region away from beam centroid. When suffered from negative bending moment such as specimen CBN-1200-3, the stress differed significantly at different location, and for the region adjacent to beam centroid, the stress at the same location increased more -700

quickly with load developing than the stress at the location far away from beam centroid.

2.2.2.3. Analysis of strain of concrete at mid-span of beam. Fig. 22 showed the result of concrete at mid-span of beam for typical specimen CBP-1200-1 and specimen CBN-1200-3. The curves showed that the strain distributed uniformly and with load increasing, the strain increased as well. However, for specimens under negative bending moment, due to the influence of steel beam, the strain of concrete deck distributed nonuniformly. Under negative bending moment, the concrete deck was in tensile and the tensile stress of concrete deck decreased to zero as concrete cracked, resulting in more tensile stress sustained by reinforcing bar. The tensile stress of reinforcing bar grew suddenly and led to the slippage between concrete and reinforcing bar. Nevertheless, with the bonding effect between concrete and reinforcing bar, the concrete was confined and the relative slippage was reduced. The concrete cracked finally when the tensile stress of concrete due to bending moment exceeded the ultimate tensile strength of concrete. Consequently, the stress redistributed with the development of cracking and the curve of the stress distribu-

50kN 100kN 150kN 200kN 250kN 300kN

-600 -500 -400

50kN 100kN 150kN 200kN 250kN

Strain/(με)

not record the precise strain and it could not be used in the validation of plane-section assumption. It was also noted that the stress was smaller for the static test after fatigue test, even though it was tested with the same amplitude load of static load before fatigue load and the strain distributed more linearly along the section height for the case of the static test after fatigue test.

400

300

200 -300 -200

100

-100

-600

-400

-200

0

0

200

400

600

-600

-400

-200

0

0

200

400

Distance to centroid of beam/mm

Distance to centroid of beam/mm

(a) Specimen CBP-1200-1

(b) Specimen CBN-1200-3

Fig. 22. Distribution of strains along section heights at mid-span of beam.

600

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R. Liu et al. / Construction and Building Materials 188 (2018) 833–849

tion undulated. But the space between cracking was generally equal and the development of cracking became stabile with no new cracking emerging. 2.2.3. Residual deflection Table 7 listed the maximum residual deflection of composite beam and it showed that the maximum average residual deflection of specimens under positive bending moment and negative bending moment was 2.155 mm and 2.430 mm, respectively. Compared to the maximum deflection obtained in static failure test, which was 28.80 mm and 21.30 mm for specimen CBP-1200-0 and CBN-1200-0, respectively, it could be calculated that the residual deflection accounted for 7.48% and 11.41% of the deflection. The fatigue residual deflection ratio was significant enough for beams with span of 3.3 m only. Therefore, it should be paid attention to the residual deflection caused by fatigue load when studied the fatigue behavior of composite beams.

2.3. Analysis of residual bearing capacity During fatigue test, it was found that for specimen CBP-1200-3 and all negatively flexural specimens did not suffer fatigue failure finally. The specimens without fatigue failure were performed with static test after fatigue test to get the residual bearing capacity. Specimen CBP-1200-3 and CBN-1200-2 were chosen as typical specimen for illustration. Fig. 23 demonstrated the failure mode of two typical specimens, respectively. It could be known that the final failure mode of composite beam was of ductile flexural failure. It was observed that after fatigue test, compressive concrete of specimen CBP-1200-3 crushed at the ultimate load and the cracking of the concrete of negatively flexural specimens distributed symmetrically and the flange of steel beam buckled significantly. Fig. 24 showed the curve for load vs. deflection in initial static test before fatigue loading and the curve obtained for the final sta-

Table 7 Maximum residual deflection during fatigue test. Specimens

Residual deflection/mm

Average residual deflection/mm

Number of repeated load cycles

CBP-1200-1 CBP-1200-2 CBP-1200-3

2.320 2.105 2.040

2.155

100  104 104  104 211  104

CBN-1200-1 CBN-1200-2 CBN-1200-3

1.565 1.950 3.775

2.430

200  104 150  104 356  104

(a) Specimen CBP-1200-3

(b) Specimen CBN-1200-2

Fig. 23. Failure mode of specimens.

500

700

static test before fatigue loading static test after fatigue test

static test before fatigue loading static test after fatigue test

600

400

400

Load/kN

Load/kN

500

300

300

200

200

100

100 4

211*10 cycles of fatigue loading 0

0

4

8

12

16

215*104 cycles of fatigue loading 20

0

0

3

Mid-span Deflection/mm

(a) Specimen CBP-1200-3

6

9

Mid-span Deflection/mm

(b) Specimen CBN-1200-2

Fig. 24. Curve of load vs. deflection before failure.

12

15

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R. Liu et al. / Construction and Building Materials 188 (2018) 833–849

700

500

static failure test static test after fatigue test

600

400

400

Load/kN

Load/kN

500

300

static failure test static test before fatigue loading

300

200

200 100

100 0

0

4

8

12

16

20

0

24

0

100

200

300

400

500

600

700

800

Mid-span Deflection/mm

Mid-span Deflection/mm

(a) Specimen CBP-1200-3

(b) Specimen CBN-1200-2

Fig. 25. Comparison of curve of load vs. deflection.

500

700 600

400

CBP-1200-0 CBP-1200-3

400

Load/kN

Load/kN

500

300

CBN-1200-0 CBN-1200-1 CBN-1200-2

300

200

200

100

100 0

0

20

40

60

80

100

120

0

140

0

15

Mid-span Deflection/mm

30

45

60

75

90

Mid-span Deflection/mm

(b) Negative bending moment

(a) Positive bending moment

Fig. 26. Curve of residual load and deflection.

tic test after last fatigue loading and Fig. 25 illustrated the comparison between the curve for load vs. deflection in static failure test and the curve obtained for the static test after last fatigue loading. From the comparison, it was known that no significant degradation of the residual bearing capacity occurred after fatigue test, implying that the composite beam could develop excellent fatigue behavior without significant degradation in strength. However, due to the failure of strain gauges, it could not be verified whether the stress distribution agreed with the plan-section assumption or not and the load could not be calculated as a result. In addition, the flexural stiffness did not degrade while the ductility capacity reduced a bit. Fig. 26 demonstrated the curve of residual bearing capacity vs. deflection. From the comparison between specimen CBP-1200-0 and CBP-1200-3, together with specimen CBN-1200-0 and CBN1200-2, it could be concluded that the stiffness decreased slowly with increment of loading cycles, indicating that the fatigue loading had little effect on the stiffness under the case without fatigue failure. Under the same loading, the deformation of specimen with fatigue test was larger than that of specimen in static failure test. The stiffness dropped seriously with more fatigue damage and finally remained constant until the composite action between concrete deck and steel beam completely lost.

3. Calculation method for stiffness According to the previous analysis of stiffness development, it was deduced that the stiffness of composite beams was influenced by number of repeated load cycles. For composite beams in serviceability status, the deformation was not only induced by static load but also repeated load, therefore, the calculation of deformation based on static load would be smaller than the actual deflection and resulted in potential in unsafety. Consequently, the influence of fatigue load should be taken into consideration in the design of composite beam under fatigue load. The determination of flexural stiffness (EI) was key to calculation of deflection of composite beam. Nie had proposed the calculation method of stiffness using the reduced stiffness [18] to considered the effect of slip on the stiffness:

B¼

EI 1þn

ð1Þ

where, flexural stiffness (EI) was determined by the steel beam and concrete deck; n means the stiffness reduction coefficient. In addition, the effect of fatigue loading and strength of steel beam should also be considered. The following session discussed the influence of fatigue stiffness modulus and fatigue strength of

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R. Liu et al. / Construction and Building Materials 188 (2018) 833–849 Table 8 Stiffness of composite during fatigue test (unit:107 N=mm2 ). Specimen

Number of repeated load cycles

Fatigue test under positive bending moment Static stiffness

Fatigue stiffness

Bf =Bs

CBP-1200-1

0 3 10 50 100

4.080 4.080 4.080 4.080 4.080

4.080 4.077 4.076 4.068 4.047

1.0 0.9993 0.9990 0.9971 0.9919

CBP-1200-2

0 3 10 50 104

4.080 4.080 4.080 4.080 4.080

4.080 4.077 4.071 4.078 4.078

1.0 0.9993 0.9978 0.9995 0.9995

CBP-1200-3

0 3 10 50 100 150 211

4.080 4.080 4.080 4.080 4.080 4.080 4.080

4.080 4.078 4.077 4.075 4.072 4.069 4.064

1.0 0.9995 0.9993 0.9988 0.9980 0.9973 0.9961

concrete, steel beam, steel-plate as well as shear stub, and the stiffness calculation. (a) Concrete components In the calculation of stiffness of composite beams under repeated load, the fatigue stiffness modulus of concrete should be used, and the fatigue stiffness modulus Ecf was calculated from Eq. (2):

Ecf ¼ E1 ¼ E0 ½0:96 þ 0:078lnð1 

n1 Þ N1F

ð2Þ

where, E0 was the initial static stiffness of concrete component; n1 was the number of fatigue loading cycles; N 1F was the fatigue life, and it could be calculated by the following formula: 1S

lgN1F ¼ 17  1Sk;max þ 0:23 k;min

Sk;max ¼ rk;max =f c Sk;min ¼ rk;min =f c

ð3Þ

In the formula, Sk;max and Sk;min was the stress on the concrete flange corresponding to the upper limit and lower limit of fatigue load; rk;max and rk;min was the maximum and minimum stress for each loading cycle; f c was the initial concrete strength and the fatif

gue strength f c was taken as 0.88 f c . (b) Steel components Considering that the stress-strain curve under repeated load was approximately linear both in tension and in compression, and it was also parallel to the initial stress-strain curve, therefore, the fatigue stiffness modulus of steel Esf was taken as Es . However, for the stiffness of shear stub, it was found that the envelop curve of load-slip under repeated load was similar to the load-deflection under monotonic load, as a result, the shear resistance of shear stub under fatigue load was calculated by formula (4):

Ncv ¼ 0:43As

qffiffiffiffiffiffiffiffiffiffi f Ecf f c 6 0:7As cf s

ð4Þ

As and f s was the cross section area and yielding strength of shear stub, c was the ratio of minimum tensile strength to yielding strength. (c) Calculation of stiffness Fatigue test involved specimens under sagging moment and hogging moment, and for negative flexural specimens, the concrete deck was in tension and it was hypothesized that the concrete was out of work when in tension, therefore, the fatigue stiffness of composite beam under negative bending moment was same as static stiffness. However, for specimens under positive bending moment,

considering the influence of concrete and steel components under repeated load, the corresponding fatigue stiffness could be calculated using the proposed calculation method. In calculation, the stiffness reduction coefficient n was valued as 0.3 based on the study of static test [19] and Table 8 listed the detailed calculation results for 3 specimens under different critical repeated load cycles. It could be found from the calculation result that the stiffness degraded with the increasing of number of repeated load cycles but the degradation of stiffness was not obvious in general, which agreed with the observation during fatigue test. 4. Conclusions Fatigue tests with different repeated loads under different mechanical patterns were conducted and the final subsequent static tests were performed. Detailed experimental results were recorded at each intermediate static test after corresponding critical cycles of fatigue loading, including the cracking development, load-deflection response, strain development of flat bottom steelplate and concrete, strain distribution along beam section as well as the residual deflection and residual bearing capacity. Based on the analysis of experimental results presented herein, some conclusions could be drawn as followings: (1) Specimens in static test suffered typical flexural failure and slip between composite concrete deck and steel beam was insignificant, indicating that the layout of PBL and shear stubs was reasonable and the interaction was reliable. (2) The damage of specimens under positive bending moment in fatigue test generally initiated from the fracture of bottom flange of steel beam, subsequent crack of web and final concrete crush, and the final failure was dependent on the fatigue load amplitude. No fatigue failure of specimens under negative bending moment suffered fatigue failure finally, indicating that it had better fatigue performance when the ultimate limit of fatigue was same. (3) No stiffness degradation was observed during fatigue test with the repeated load limited to ultimate limit of elastic capacity, and the development of cracks tended to be stabile after certain number of repeated load cycles. But the stiffness of specimens under positive bending moment was larger than that of specimens under negative bending moment. It was presumable caused by the cracking on the concrete deck in tension under large fatigue load.

R. Liu et al. / Construction and Building Materials 188 (2018) 833–849

(4) In the final static test after fatigue test, it was found that the bearing capacity did not drop significantly while the stiffness decreased a bit. This also indicated that the fatigue test did not affect the static loading behavior of composite beam if the repeated load was limited to ultimate limit of elastic capacity. Conflict of interest None. Acknowledgements It is gratefully acknowledged for the financial support from The National Key Research and Development Program of China, China (Grant No. 2016YFC0701403), as well as the support from National Natural Science Foundation of China, China (Grant No. 50708040). However, all the opinions and conclusions presented in this paper are only those of the authors and do not necessarily represent the perspectives of the funding institute mentioned herein. References [1] B. Stankiewicz, Bridge structures with GFRP composite deck, Open J. Civ. Eng. 05 (1) (2015) 53–62. [2] Y. Xing, Q. Han, J. Xu, et al., Experimental and numerical study on static behavior of elastic concrete-steel composite beams, J. Constr. Steel Res. 123 (2016) 79–92. [3] Y. Yang, P.J. Zhou, J.G. Nie, et al., Experimental on static and fatigue behavior of steel plate-concrete composite bridge decks, China J. Highway Transp. 22 (4) (2009) 78–83. [4] Y. Yang, Y.L. Yu, X.W. Zhou, C.W. Roeder, X.D. Huo, Study on mechanism performance of composite beam with innovative composite slabs, Steel Compos. Struct. 21 (3) (2016) 537–551.

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