1. Introduction
Composite bridges composed of concrete and steel are mostly steel girder-concrete slab composite bridges [
1], steel web (member)-prestressed concrete (PC) composite bridges [
2], and ST truss composite bridges [
3], as shown in
Figure 1. At present, the steel girder-concrete slab composite bridges and steel web (member)-PC composite bridges are mainly used in medium and short span lengths, since buckling failure of webs or premature cracking of concrete deck affecting the durability of the bridges may occur [
1,
2,
3]. ST truss composite bridges have been introduced and widely adopted to overcome the aforementioned shortcomings of the two other types of composite bridges, not only addressing the deck and web cracking problems but also improving the load bearing capacity and durability of bridges [
4]. However, investigations revealed that the stress existing in the joints of ST truss composite bridges is complex, leading to severe stress concentration problems [
5,
6,
7,
8]. In addition, the stress generated by live loads at the joints account for a large proportion of the whole stress in the structures [
9], giving rise to the fact that the fatigue cracks appear in the ST truss composite joints of existing bridges, which seriously affects the durability of the bridge structures. To comprehensively improve and optimize the fatigue performance of ST composite truss girders, while retaining their favorable properties by replacing the truss web members in composite girders with CSW, a kind of improved composite girder has been put forward. The new structure above is referred to as the composite girder with CSW and ST truss [
10] and has been widely adopted over the last decade [
11], as shown in
Figure 1d.
As for the studies on the fatigue performance of the composite girders with CSW, to obtain the fatigue performance of web-flange weld of corrugated web girders, model tests and theoretical analysis have been conducted. The influence of web corrugation geometry and flange on web-flange weld toe stress was acquired; meanwhile, the calculation method for the fatigue performance of web-flange weld of corrugated web girders was also put forward [
12,
13]. By carrying out the fatigue performance test, the fatigue life of steel bridge I-girders with trapezoidal web corrugations was acquired. Moreover, combining the test results and the stipulation given in AASHTO specification [
14], the Category
B’ was suitable to be used in designing the fatigue life of the girders above [
15]. To study the fatigue performance of the welds between the steel plate and the CSW, model tests and FE analysis have been carried out. By combining the results obtained from model tests and FE analysis, the fatigue performance of the welds between the steel plate and the CSW with different types was acquired. Meanwhile, the calculation method for the fatigue life has been put forward [
16,
17,
18]. The research results above mainly focused on the welds between the steel plate and the CSW of composite girders, and whether the research results above are suitable to evaluate the fatigue performance of the welds between the steel tube and the CSW should be discussed in detail.
There were many studies on the mechanical properties of composite girders with CSW [
19,
20], however, existing studies on composite girders with CSW and ST truss were very limited. Based on the engineering case, model tests have been conducted to study the flexural performance of the composite girders with CSW and ST truss, and the calculation method for the flexural bearing capacity of the composite girders above under positive and negative bending moments has been put forward [
11,
21]. To analyze the shear lag effects, both model tests and FE analysis were carried out, and the calculation method for the shear lag effects of the composite girders above have been put forward [
22]. By combining the results obtained from the test and FE analysis, the influence of the geometric parameters on the torsional behavior of the composite girders has been studied [
23]. Taking the Maluanshan Park Viaduct in Guangdong Province, China as an object, the fatigue performance test has been conducted on the composite girders with corrugated steel web and concrete-filled steel tubular (CSW-CFST) truss chords, but its chord was filled with concrete, and the evaluation method on the composite girders with CSW-CFST truss chords was not established [
24]. As a result, there exists a relatively mature static theory for the composite girders with CSW and ST truss. However, the dearth of research on the fatigue performance of the composite girders with CSW and ST truss hinders practical engineering applications, and there are no fatigue performance evaluation methods for composite girders with CSW and ST truss available in the existing design specifications. The current state of knowledge not only does not allow for evaluation of the existing fatigue failure risks of the composite girders with CSW and ST truss but also fails to provide reasonable fatigue design methods, which slows technological advancements in the composite girders with CSW and ST truss. In conclusion, a systematic study on the hot spot stress distribution, fatigue failure mode, and fatigue life of the composite girders with CSW and ST truss will not only help in establishing a theoretical foundation for evaluating the fatigue performance, but can also provide a basis for the evaluation of the residual fatigue life of the existing composite girders with CSW and ST truss, which will offer guidance for the fatigue design of the type of bridges to be built in future.
3. Analysis on Test Results
3.1. Analysis of Hot Spot Stress Distribution
Figure 6a illustrates the change of stress gradient at the maximum stress monitoring point (CZ3) observed in the test at the peak load of 350 kN, where the abscissa represents the distance that the unidirectional strain gauge arranged on the substrate was from the weld toe. According to
Figure 6a, the stress gradient in the weld zone was essentially constant. The hot spot stress acquired by the linear extrapolation was slightly more (0.3%) than that by the quadratic extrapolation. Hence, linear extrapolation was considered to acquire the hot spot stress of the composite girders with CSW and ST truss based on the structural safety and facilitate to monitoring.
σr represents the hot spot stress. To obtain the hot spot stress, by combining the stress at the positions which were 4 mm and 6 mm away from the intersecting welding, the stress at the position which was zero mm away from the intersecting welding could be acquired by linear extrapolation, namely the hot spot stress.
Figure 6b illustrates the distribution rule of the hot spot stress which was obtained using linear extrapolation at the intersecting weld along the axis of the girder. It is implied that the hot spot stress exhibited essentially symmetric distribution in the axis of the girder with respect to the mid-span position, with the hot spot stress distribution at the left hand side of the chord practically equal to that at the right hand side (the maximum deviation of 6.1%), it can be concluded that the results obtained through the fatigue performance test can reflect the hot spot stress distribution and fatigue failure state of real bridges.
3.2. Analysis of Fatigue Performance Evolution
The load-strain relationship at CZ3 and load-displacement relationship at DZ2 up to the peak static load before the commencement of the cyclic fatigue testing are shown in
Figure 7a,b, respectively. It was implied that before the cyclic fatigue test started, both strain and displacement of the composite girder showed linear increments with the increase in load, demonstrating that up to the peak load, the composite girder was in an elastic stage, and therefore met the precondition for the fatigue performance test. The changing rule of the strain and displacement at key monitoring points under peak static loading with the increasing fatigue loading cycles is shown in
Figure 7c,d, respectively.
Figure 8 displayed the time histories of dynamic strain in the intersection zone, and how it changed under the peak static loading with the increasing fatigue loading cycles. The developing process of the fatigue crack is shown in
Figure 9a.
As shown in
Figure 7,
Figure 8 and
Figure 9, the evolution of fatigue performance of the test model could generally be divided into three phases, including initiation, propagation, and failure of the fatigue crack. The corresponding number of loading cycles was 0–1,266,000, 1,266,000–1,298,000, and 1,298,000–1,324,000, respectively. The fatigue crack initiated in the intersecting welds between the CSW and the chord, and with the increase of the number of loading cycles, the fatigue crack would develop along the three-dimensional direction of the chord and the CSW.
In the fatigue crack initiation phase, the relationships between the fatigue loading cycles and strain and displacement, and dynamic strain time histories were all essentially horizontal lines, i.e., neither strain nor displacement changed substantially with the increasing fatigue loading cycles, indicating that the test model did not experience fatigue cracking and its stiffness was unchanged in the fatigue crack initiation phase. When the fatigue loading cycles reached about 1,266,000, the strain at CZ3 and CY3 began experiencing clear changes with the increasing fatigue loading cycles, but the displacement at the mid-span position changed only slightly. By also considering the phased array detection results, it implied that a fatigue crack initiated near CZ3, and had a length, width, and depth of 1.3 mm, 0.2 mm, and 0.1 mm, respectively. After the number of fatigue loading cycles reached about 1,277,000, the strain changed markedly. At that time, the fatigue crack propagated inside the weld along the chord surface, and its length increased to 2.4 mm.
When the number of fatigue loading cycles reached about 1,298,000, a sudden drop appeared in the time histories at CZ3. However, the corresponding time histories measured at CY3 continued rising, indicating that after the fatigue crack was initiated, the stress redistribution occurred near the cracked section. In conjunction with the phased array detection results, it implied that the fatigue crack at CZ3 had already propagated to the CSW by spanning the weld, running through the chord thickness, and increasing its length at an accelerated rate. By the comparative analysis on relationships between the loading cycles and displacement, it was illustrated that the stiffness in the mid-span position of the test model developed a clear declining trend. When the loading cycles reached about 1,324,000, the bottom surface of the chord had already been propagated by the fatigue crack, the stiffness was severely reduced, and the flexural bearing capacity was essentially lost. Thus, the fatigue performance test was stopped at that time.
By analyzing the entire evolution of the fatigue performance of the composite girder, it can be observed that the initiation phase accounted for 95.6% of the whole loading cycles, i.e., most of the fatigue life. After the fatigue crack appeared, the mechanical properties of the composite girder deteriorated at a high rate, i.e., brittle failure was apparent. Hence, it was appropriate to define the loading cycles at the time of fatigue crack initiation (1,266,000) as the fatigue life.
3.3. Analysis of Fatigue Failure Mode
Figure 9b illustrates the failure mode of the composite girders with CSW and ST truss under the fatigue load, and it implied that during the fatigue performance test, the fatigue failure mainly occurred near the intersection of the point S near the pure bending segment, penetrated through the chord thickness and the intersecting weld. In this way, a uniform and smooth fatigue fracture surface was formed. Furthermore, as shown in
Figure 9b, the propagation path of the fatigue crack and the direction of the hot spot stress were perpendicular to the axis of the girder and the fracture surface of the fatigue crack, indicating that the fatigue crack was opening type I. Furthermore, the observed fatigue failure mode was similar to the typical fatigue failure mode of I-shaped beams, demonstrating that when the CSW was used to replace a flat steel plate web, the stress flow direction did not change, and the longitudinal tensile stress still played a dominant role.
5. Hot Spot Stress Sensitivity Analysis
5.1. Determination of Influencing Parameters
FE parametric analysis was conducted for different geometric parameters using the single variable method, so as to study the sensitivity of hot spot stress to the geometric parameters above. To minimize the size effect caused by scale, the full-scale real bridge parameters were used in the reference model for the parametric analysis. To highlight the key points of the analysis, the maximum value of the hot spot stress envelope within a single corrugation wavelength near the mid-span section of the pure bending segment was focused on.
5.2. Discussion of Sensitivity Analysis Results
The sensitivity of the hot spot stress distribution to the geometric parameters, including the chord (
Dc and
Tc) and the CSW (
Tb,
Rb, and
θb), was analyzed in
Figure 13a–e. The results showed that the hot spot stress distributions obtained by changing a single geometric parameter were essentially similar to each other, implying that the geometric parameters had no influence on the distribution rule of the hot spot stress. The maximum hot spot stress occurred near point S of the CSW, the location of which was slightly influenced by the change in geometric parameters. In addition,
Figure 13a showed that as
Dc increased, the wave crest at point S of the CSW became less sharp.
The sensitivity of the hot spot stress at point S to the geometric parameters including the chord (
Dc and
Tc) and the CSW (
Tb,
Rb, and
θb) was analyzed in
Figure 14a–e. It was observed that the hot spot stress was negatively correlated with
Dc,
Tc, and
Rb, and positively correlated with
Tb, while it had a more complex relationship with
θb. The hot spot stress of the composite girders exhibited the strongest sensitivity to
Dc, followed by
Tc.
Larger Dc, on the one hand, changed the position of the neutral axis, and it was gradually close to the chord surface. On the other hand, it reduced the ratio of the projection length of the inclined web in the chord section to the circumference length of the entire section, gradually approaching a flat steel plate and the chord, thereby reducing the out-of-plane bending moment borne by the inclined web, which was also the essential reason for the negative correlation of the hot spot stress with Dc. The wave crest at point S of the CSW became less sharp with the increase in Dc, and the hot spot stress distribution was gradually uniform along the length of the CSW.
Parameters
Tc and
Tb separately affected the radial stiffness of the chord and the axial stiffness of the intersecting welds. The axial stiffness of the intersecting welds is usually larger than the radial stiffness of the chord. As
Tc increased, the radial stiffness of the chord increased, and the difference from the axial stiffness of the intersecting welds was reduced, thus the hot spot stress in the composite girders was negatively correlated with
Tc. However, the axial stiffness of the intersecting welds increased with the increase in
Tb, further amplifying the difference from the axial stiffness of the intersecting welds, thus the hot spot stress of the composite girders with CSW and ST truss was positively correlated with
Tb. Moreover, the calculation methods of the radial stiffness of the chord and the axial stiffness of the intersecting welds were analyzed by Equations (4) and (5). Where
Ic and
Ib denote the radial stiffness of the chord and the axial stiffness of the intersecting welds, respectively,
Ec and
Eb are the modulus of elasticity of the chord and the CSW, respectively, and
Lb denotes the length of the intersecting welds. The results showed that when only
Tc or
Tb was varied, Equations (4) and (5) were both power functions, with the exponent of three and one, respectively, thus the sensitivity of the radial stiffness of the chord to
Tc was stronger than that of the axial stiffness of the intersecting welds to
Tb. This was the main reason why the sensitivity of the hot spot stress to
Tc was stronger than that to
Tb.
An increase in Rb further alleviated the sharp angle generated during bending of CSWs and ensured the smooth stress transition between the straight web and the inclined web, thus, increasing Rb reduced the hot spot stress.
Increasing θb enhanced the out-of-plane flexural stiffness of the inclined web and reduced the influence of the out-of-plane bending moment on the hot spot stress, but it also increased the axial stiffness of the intersecting welds, thus increasing the hot spot stress. As a result, the influence of θb on the hot spot stress of the composite girders with CSW and ST truss was the combined effect of the out-of-plane flexural stiffness of the inclined web and the axial stiffness of the intersecting welds, which produced the complex relationship between the hot spot stress and θb.
6. Fatigue Life Evaluation Method
Using the parameters of the test model,
Figure 15 has compared the theoretical fatigue life obtained from the evaluation method for the fatigue performance in AASHTO, CIDECT, and API with the test results, where Δ
σh represents the hot spot stress range. It was found that the deviation between the theoretical fatigue life obtained from the evaluation method for the fatigue performance in AASHTO, CIDECT, and API and the test results reached 21.0%, which illustrated that the evaluation method for the fatigue performance in AASHTO, CIDECT, and API was not suitable for the evaluation of the fatigue performance of the composite girder with CSW and ST truss.
The following basic computational model for the fatigue design
S-
N curve based on the hot spot stress range of the composite girders with CSW and ST truss was formulated according to the literature [
32]:
where
N represents the fatigue life,
m is the slope of the fatigue design
S-
N curve, and
C0 represents the constant of the fatigue design
S-
N curve, which is determined as follows:
The fatigue failure of the composite girders resulted from the fluctuating tensile stress range, and fatigue cracking was found at the intersecting welds (
Figure 9). The fatigue details of the composite girders with CSW and ST truss were shown in
Figure 16, and it could be seen from
Figure 16 that the welded joint of the composite girders with CSW and ST truss was composed of the welds between the CSW and the chord, and the construction details of the welds was the full penetration weld. Thus, it belonged to the T-shaped fully penetrable welded joint. Meanwhile, under the action of the load, the welded joint of the composite girders with CSW and ST truss played a vital role in transferring the load, namely that the welded joint of the composite girders with CSW and ST truss needed to bear the load. Therefore, according to the literature [
32], the strength grade of the fatigue details of the composite girders with CSW and ST truss could be classified into D type weld joint. Based on the relevant regulations [
32], the slope
m of the fatigue design
S-
N curve of the composite girders with CSW and ST truss was taken as 3. Considering the fact that the fatigue failure belonged to the brittle failure, the
S-
N curve used to evaluate the fatigue performance of the composite girder with CSW and ST truss, which should have a certain security surplus. Therefore, by referring to the literature [
33], a cut-off limit for the fatigue design was not adopted, and the slope
m of the fatigue design
S-
N curve was still taken as 3 after 10,000,000 cycles of fatigue loading.
Only the structural stress concentration in the intersecting welds was considered, and the influence of the shape of the intersecting welds on the hot spot stress was ignored. Therefore, according to the relevant provisions for the fatigue design
S-
N curve [
32], the basic fatigue strength Δ
σ0 after 2,000,000 cycles of loading could be determined based on the basic fatigue strength of the T-shaped fully penetrable welded joint. As per the requirements [
10], the intersecting welds of the composite girders with CSW and ST truss belonged to the T-shaped fully penetrable welded joint and should meet the stipulation of full penetration groove butt welding. Meanwhile, the weld toe should be ground after welding. Hence, the basic fatigue strength of the intersecting welds was taken as 100 MPa.
According to the literature [
10],
Tb should be between 9 mm and 40 mm. Therefore, from the perspective of the margin of safety, combined with the literature [
32], the wall thickness correction coefficients of the composite girders were assumed to be 0.889 and 1.000, respectively, when
Tb was no more than 25 mm. Furthermore, the fatigue failure of the composite girders with CSW and ST truss is usually caused by tensile stress, i.e., the stress ratio is usually positive. Hence, the basic fatigue strength of the composite girders with CSW and ST truss was not subjected to stress ratio correction. The fatigue design
S-
N curves could be obtained by further combining Equations (6) and (7), as shown in
Figure 17.
The applicability of the obtained fatigue design S-N curves was analyzed using the results of the test. Using the parameters of the test model, the theoretical fatigue life was determined as 1,390,000 cycles, i.e., close to the value of 1,266,000 cycles obtained in the test, with the difference of 9.8%, which suggests that an empirical calculation model of the S-N curve for the composite girder with CSW and ST truss was created, and compared with the test result obtained in this paper, it was proved that the empirical calculation model of the S-N curve has certain applicability. Under the premise that there was no fatigue design S-N curve given in the specification, the empirical calculation model of the S-N curve could be used as a reference for designing the composite girder with CSW and ST truss. Meanwhile, to improve the representation and applicability, more fatigue performance tests on the composite girder with CSW and ST truss should be conducted to carry out further verifications and validations of the empirical calculation model of the S-N curve put forward in the paper.
7. Conclusions
The fatigue performance of the composite girder with CSW and ST truss was revealed by carrying out a test and FE analysis. The fatigue failure mode and the sensitivities of the hot spot stress to the geometric parameters of the composite girder above were studied. Furthermore, a fatigue life evaluation method was discussed. It could be concluded that: (a) linear extrapolation is suitable to determine the hot spot stress of the composite girders with CSW and ST truss. The fatigue performance evolution comprised three stages, i.e., initiation, expansion, and failure of the fatigue crack, with corresponding numbers of fatigue loading cycles of 0–1,266,000, 1,266,000–1,298,000, and 1,298,000–1,324,000, respectively. The fatigue crack initiation stage in the test accounted for about 95.6% of the fatigue life. The fatigue cracks were opening type I; (b) both the maximum hot spot stress and fatigue cracks of the composite girders with CSW and ST truss occurred in point S, which happened mainly because the inclined web of the CSW had a small out-of-plane bending stiffness but had to withstand an out-of-plane bending moment; (c) the hot spot stress in the composite girders with CSW and ST truss exhibited negative correlations with Dc, Tc, and Rb, a positive correlation with Tb, and a more complex relationship with θb. It was most sensitive to Dc, followed by Tc; (d) based on the hot spot stress method and the fact that intersecting welds were a type of T-shaped fully penetrable welded joint, the basic fatigue strength of 100 MPa after 2,000,000 cycles of cyclic loading was recommended to establish the S-N curve of the joint. An empirical calculation model of the S-N curve for the composite girder with CSW and ST truss was created, and to improve the representation and applicability, more fatigue performance tests on the composite girder with CSW and ST truss should be conducted to carry out further verifications and validations of the empirical calculation model of the S-N curve put forward by this paper in the future; (e) due to the reason that the software of MIDAS/CIVIL was exactly suitable to conduct linear analysis, the results of the integral FE analysis on the composite girders with CSW and ST truss by the software of MIDAS/CIVIL were not very consistent with the test results. Thus, the simulation method based on the linear analysis of the composite girders with CSW and ST truss should be studied in further.