Full-scale fatigue tests on a novel box-shaped steel rod of a spatial arch bridge for fatigue assessment

Abstract

A novel leaning-type spatial arch bridge without thrust was designed as a landmark in a major urban city. In order to alleviate the higher negative reaction force at side span and enhance the lateral stability, commonly the case within this type bridge, a large-size replaceable box-shaped steel rod with pinned connections was introduced. The fatigue behaviour of the box-shaped steel rod and related upper and lower anchorage segments was investigated through a full-scale constant-amplitude fatigue test under axial loading. In comparison to the fatigue test results, the fatigue evaluation based on Eurocode 3 nominal stress design curve FAT56 considerably overestimated the fatigue strength of critical welded detail in box-shaped steel rod, which was underrated according to the universal International Institute of Welding effective notch stress design curve FAT225. The presented full-scale programme also validated the applicability of the latter method, which presented conservative results, to large-size thick-plate (80 mm) welded joints. The conclusion based on the test and theoretical results may provide a reference for the fatigue design of adopting box-shaped steel rod in spatial arch bridges.

Keywords

effective notch stress fatigue test full-scale spatial arch bridge welded joints

Introduction

On areas with soft soil in cities, it is rather troublesome to build an arch bridge with thrust for huge foundations are normally required to balance the horizontal thrust. In addition, unavoidable non-uniform settlement of foundation would bring secondary internal force in structures. It is even worse for bridges with long-span or wide decks or both. Accordingly, tied-arch bridges have been commonly adopted to eliminate the thrust, by means of different forms of tied-chord (De Backer et al., 2014; Malm and Andersson, 2006; Uzgider et al., 2009). However, this type of bridges may raise connecting issues between tied-chord and other components of bridge, such as floor beams and hangers, in terms of fabrication and design. In this case, a set of novel spatial arch bridges without thrust emerged in landmark demand under the soft soil condition at the city centre (Manterola et al., 2011; Sarmiento-Comesías et al., 2013). These new-type bridges improve both aesthetics and distinction from existing bridges over the same river at the heart of the city.

One of the widely adopted spatial types is a leaning-type arch bridge featured with two sets of convergent non-braced arches, consisting of a main arch (vertical) and a vice-arch (leaning). The first application was on Bac de Roda Bridge in 1987, Spain, proposed by Santiago Calatrava (Cerver, 1989). Its thrust is directly transferred to main girders, working together with the main arch ribs as an arch–beam composite system. In contrast, its leaning arch ribs are fixed at both ends to form an indeterminate structure with thrust. In this case, the foundations support the thrust. On the commencement of this innovation, a number of leaning-type bridges were also built in China. Examples are Kangfu Bridge (main span of 120 m), Chaozhou Jinshan Bridge (main span of 160 m), Xingchun Bridge (main span of 73.5 m) and Kunshan Yufeng Bridge (main span of 110 m) (Feng and Xu, 2004; Gu et al., 2006; Xiao et al., 2005; Zhou et al., 2005). In comparison with original scheme Bacde Road Bridge, the thrust of these four bridges was balanced by tie-rod/tied-beam or cables underneath the deck for the first three and the last one, respectively. This leaning-type of spatial arch bridge aforementioned enables an advantageous broader view through removing the braces between the main arches, which, however, causes a disadvantage in lateral stability (Liu et al., 2015; Sarmiento-Comesías et al., 2011).

To accommodate the geological condition and to achieve both aesthetics and novelty, a design of leaning-type steel arch bridge without thrust and adoption of tied-chord was introduced (Figure 1). The two sets of leaning arches consist of a cluster spatial arch ribs both in plan and in elevation and were transversely connected by coupling beam (Figure 1(b)). With the removal of complex tied-chord and colossal ballast, the horizontal thrust was eliminated by a closed load transfer system. The support condition for arches was set as one fixed bearing at the pier of one arch spring, while sliding bearings were set at the rest of the piers. In this way, the traffic load is able to be first transferred to main arch, then through steel castings and inclined struts and eventually to be passed on to main girders of side span (Figure 1(a)). However, a problem arises that higher negative reaction force will occur at piers of side span and at the intersection of inclined struts with side span’s main girders. The conventional tensional bearings cannot safely withstand such high force level, especially for the shorter side span. The spatial main arch (Figure 1(b)) adopted in this new design, merged with inclined struts at arch spring through steel casting. Bearing joint, instead of rigid connection, was employed in this case between steel casting and piers. This turns overall superstructure of this bridge into a simply supported structure, which also raises doubts about its lateral stability.

Therefore, a novel large-size box-shaped steel rod (BSSR) was introduced to decrease the higher negative reaction force in side span and ensure the lateral stability of bridge. Installed near the middle of side span, it divided side span into two shorter spans. Hence, the negative reaction force was transferred from main girders to substructure through BSSR. The lateral stability was attained by the strong torsion restraint of main girders, which was provided by four BSSRs transversely distributed at each end. For the higher safety consideration, all BSSR were designed as replaceable through pinned connection with the upper anchorage segment (UAS) and lower anchorage segment (LAS): the main girders and the anchorage foundation, respectively.

The failure of BSSR component system, namely, the BSSR and related anchorage segments, will endanger the whole bridge structural system, as no redundant load path exists. The reason is that the load transfer system BSSR involved in is the main load transferring path of this newly designed bridge. This novel BSSR component was designed to undertake large tensional force range in service. Additionally, the configuration of the BSSR contains complex welded joints which cannot be simply classified according to standards or codes, in terms of fatigue design. One questionable point lies in conventional fatigue design because these complex welded joints are not normally covered by standards owing to their large scale (80-mm-thick plate). Therefore, the fatigue safety of this novel BSSR becomes a major concern of this bridge.

For that matter, fatigue assessment of BSSR was performed in this research based on the effective notch stress approach (ENSA). This method, considering the strength reduction due to notches, was proposed by Radaj et al. (2013) and has been widely applied to fatigue assessment of welded joints (Baptista et al., 2017; Marulo et al., 2017; Sonsino et al., 2012). Recently, there are more researches on fatigue evaluation of welded joints using ENSA in various industries (Bruder et al., 2012; Fricke et al., 2009, 2012; Pedersen et al., 2010), and a simplified calculation procedure regarding ENSA was proposed and verified (Pradana et al., 2015, 2017a, 2017b). However, there is still scanty evidence of fatigue experimental data of large-scale welded joints with thick plate (e.g. plate thickness t > 40 mm) in the literature to validate this method. Moreover, the large-scale experimental data which the universal reference S-N curve (FAT225) recommended in International Institute of Welding (IIW) guideline (Hobbacher, 2015) derived from was confined to plate thickness mostly less than 20 mm (Fricke and Paetzold, 2010). Therefore, large-scale component fatigue test is needed to investigate the applicability of ENSA in the field of thick-plate welded joints.

The aim of this article is to investigate the fatigue behaviour of BSSR and ancillary anchorage segments from a novel design spatial arch bridge. A representative large-size full-scale fatigue experimental programme was conducted under axial tensile loading. The fatigue test data were then compared with the results evaluated by nominal stress approach according to Eurocode 3 (EN 1993-1-9, 2005) and ENSA defined in IIW recommendations (Hobbacher, 2015). Finite element (FE) models were constructed to examine the stress concentration conditions and obtain the effective notch stress of hot spot (HS). In terms of the results of experimental and assessment based on ENSA, some design modifications of critical fatigue detail were proposed at the end of this article.

Proposed BSSR structure

This novel design of spatial arch bridge, as depicted in Figure 1, a 220-m main span with 42-m side spans, is under construction in Tianjin, the northeast of China. The novel BSSR structure separates the side span into two spans of 20+22 m. It is laid out in the way that each end of the bridge has four in transverse direction (Figure 1(b)). The 40.5-m-wide deck carries six traffic lanes and two footpaths.

Figure 2 shows a representative sketch of the BSSR and related segments, the UAS and LAS. The three components connected in series by the pin shafts. The upper lifting lugs (plate thickness, t = 80 mm), evolved from extended thick (t = 80 mm) web plates of box girder, were welded to top and bottom slabs as well as standard web plates. The negative reaction force was mainly transferred from the non-load-carrying cruciform welded joints to pin shaft, then to BSSR, shown in Figure 2. Hence, the box girder worked with gusset plates (t = 40 mm) in both longitudinal and transverse directions and with two floor beams (t = 60 mm) to form a whole UAS.

The lower lifting lugs (t = 80 mm) were welded to the embedded plate (t = 80 mm) acting as load-carrying T-joints and were enhanced by gusset plates (t = 40 mm) by full penetration. In this case, the T-joints were employed to transfer all the load undertaken by BSSR to substructure, through prestressed reinforcing bars, studs, shear plates and filled concrete (Figure 2).

The pinned connections play a crucial role as connectors in load transfer of BSSR structure. Therefore, in order to alleviate the stress level around the contact area between pin shaft and associated plates’ inboard edge, cap plates were welded to outer and inner surfaces of lugs and BSSR’s ear-plates, respectively.

With the advent of the BSSR structure, the following advantages and characteristics were anticipated:

The UAS was slightly modified from the box girder, by extending web plates as well as adding gusset plates and floor beams. There are minor costs in design alteration and construction in comparison to traditional box girder, with anchorage function safely attained.

The whole BSSR structure serves more as intermediate piers in the side spans, as both contribute to lowering the negative reaction force.

The replaceable design of BSSR bounded by both ends of pinned connection reduces time and costs of restoration. In addition, the design of BSSR alone could be revised along the updated service requirements in future.

However, there are some concerns relating to fatigue safety of BSSR structure:

The load-carrying T-joints between lower lifting lugs and embedded plate, in LAS, were designed to undertake almost the entire forces from BSSR to underground structure.

There may be fretting fatigue issues underlying critical pinned connections, which will not be discussed in this article.

The critical welded joints of BSSR, in terms of their large size (80-mm-thick plate) and the close position between several welds, become a major concern in this study.

Experimental programme

The main objectives to be achieved in this research programme are as follows: (1) to investigate the fatigue behaviour of the proposed BSSR in terms of fatigue strength and critical fatigue-sensitive spot and (2) to investigate the fatigue behaviour of LAS and UAS.

To achieve the above objectives, a full-scale BSSR structure has been designed to be tested. More details about the experiment were reported by Cai and Chen (2016).

Test specimens

The test BSSR structure is comprised of three parts assembled by pinned connections: the BSSR, the LAS and the UAS. As illustrated in Figure 3, the test specimens were placed right to left horizontally corresponding to top to down in practical (Figure 2). The test UAS simply adjusts the gusset plates in quantity and locations, while the rest, such as cruciform welded joints, floor beams, remain the same as in the practice (Figure 3(a)). The whole specimen of UAS was welded to a large thick base plate (t = 60 mm), which was anchored to reaction floor by bolts.

The test BSSR (Figure 3(b)) was fabricated the same as practical bridge. The specimen was shortened from 7.39 to 8.63 m in actual bridge to 2.5 m (centre distance of two pin holes), under the premise that the mechanics performance of specimen is consistent with the actual structure.

The test LAS was manufactured the same as practical case except for the transition components (Figure 3(c)). Thus, the critical fatigue detail, load-carrying T-joints, was retained. However, what are arranged under the embedded plate in the practice (corresponded to its right part in test), that is, studs, shear plates, prestressed reinforcing bars and filled concrete, were substituted by numerous stiffened plates in both longitudinal and transverse directions. It should be noted that the bolts for test LAS were high-strength bolts connected to actuators.

The steel used in this test were all graded as Q345qD in Chinese National Standard (CNS) (2008), with a yield strength of 345 MPa. The pin shaft was made of 40Cr whose yield strength was 785 MPa (CNS, 1999).

Test load

One of the main objectives of this full-scale fatigue test is to verify the fatigue safety of proposed BSSR structure under the stress history throughout the entire life cycle of bridge. However, it is not feasible to obtain the actual stress history of a bridge not yet built. An alternative method is to use numerical method based on weigh-in-motion (WIM) data established on site with similar traffic situations (Zhang et al., 2016). Thus, we could define the fatigue test load based on numerical simulation, of which the procedure is as follows:

Step 1. Mont Carlo approach was used to simulate the traffic flow (24-h traffic-flow monitoring on the site of reference);

Step 2. Stress history of BSSR was obtained by applying virtual traffic flow (from Step 1) to FE model of the entire bridge;

Step 3. The fatigue prone details were classified according to Eurocode 3 (EN 1993-1-9, 2005) using the nominal stress approach, and the cumulative damage of these details was calculated within 100 years of designed service life;

Step 4. The results of cumulative damage of 100 years in Step 3 was then converted into equivalent stress range Δσ_eq at 2 × 10⁶ cycles as equations (1) and (2), according to equivalent damage theory. Eventually, the maximum test load range, needed to fail specimen at 2 × 10⁶ cycles, could be directly calculated based on Δσ_eq

Δ σ_{eq_total} = {[\sum \frac{n_{i}}{N_{total}} \cdot Δ σ_{i}^{m}]}^{1 / m}

(1)

Δ σ_{eq} = \frac{N_{total}}{2 \times 10^{6}} \cdot Δ σ_{eq_total}

(2)

where m is slope of fatigue strength curve, n_i is number of cycles for stress range Δσ_i, N_total is total number of cycles and Δσ_{eq_total} is equivalent stress range for total number of cycles.

The most vulnerable fatigue prone detail and corresponding detail category/fatigue class (FAT) defined in Eurocode 3 (EN 1993-1-9, 2005) are shown in Figure 4. The calculated cumulative damage of this detail exceeds 1 (D > 1). Under the premise of these assumptions, for the most critical detail (Figure 4), in terms of D = 1, the equivalent stress range is 56 MPa (FAT) at 2 × 10⁶ cycles, thus the equivalent load is 4480 kN. Therefore, in terms of the minimum and maximum loads the test apparatus is capable of providing, the test procedure is set as follows:

During the first phase, the specimens were loaded under the tensile load range of 700–3900 kN which was confined to ability of test apparatus, and were observed for whether the specimen has a fatigue-initiated crack or not till 2 × 10⁶ cycles. If no failure is detected, the test goes on to the next stage;

In the second phase, the tensile load range was increased to 200-4680 kN loading till failure to determine the fatigue strength.

Test setup

A test setup was prepared to simulate the boundary and connection conditions of the BSSR structure. The specimen BSSR structure was bolted to reaction floor and to six hydraulic actuators at each end, respectively, as depicted in Figure 5. The actuators were arranged in two rows, and each row was comprised of one 500-kN and two 1000-kN actuators. The actuators were anchored to reaction wall by bolts. To investigate the stress distribution and concentration condition in fatigue critical locations, a sufficient number of strain gauges were installed (Figure 6).

Axial fatigue loading was applied as a sinusoidal wave at a frequency of 1 Hz, with a load ratio of R = 0.179 (700–3900 kN). For fatigue detail A (Figure 4), the corresponding nominal stress range (test load range divided by net section area) is 40 MPa. As the occurring of crack initiation is hard to define and observe, the final failure criterion at which the fatigue test is terminated is defined as through-thickness cracking being visually observed.

Experimental results

The fatigue test on BSSR structure was terminated at 1.77 × 10⁶ cycles due to failure observed in BSSR, while no fatigue cracks were observed in the rest part, that is, the UAS and LAS, and the sites around pinned connections. The structural stresses at the HS of specimens obtained from measurement, excluding the strength reduction due to the local notch effect compared with effective notch stress (Doerk et al., 2003; Dong, 2001), were also discussed in the following. The structural HS stresses could be extrapolated by two measured strains at 0.4t and 1.0t away from weld toe line, σ_hs= 1.67σ_0.4t − 0.67σ_1.0t, avoiding time-consuming FE analysis, according to IIW recommendations (Hobbacher, 2015).

The UAS and LAS

The UAS owns a structural stress range state at an extremely low level of 10.61 MPa (7.69–18.30 MPa) at location (1) under test load (Figure 6(a)). The bottom corner site location (2) read a nominal stress range of 3.3–14 MPa and 4.2–15.2 MPa for gauge 3 and gauge 4, respectively. This detail of non-load carrying cruciform welded joint was classified as FAT100 in Eurocode 3 and in IIW recommendations based on structural HS stress approach. Both constant-amplitude fatigue limits (CAFLs) of FAT100, 73.7 MPa at 5 million cycles for the Eurocode 3 and 58.5 MPa at 10 million cycles for IIW recommendations, are far greater than the stress range measured in the test. Likewise, the LAS saw a steady low stress state during the whole fatigue test process. The measured maximum structural stress range (Figure 3(c)) of load-carrying T-joint is 32.12 MPa (9.77–41.89 MPa) for location (6) and a relatively low value of 12.81 MPa (3.13–15.94 MPa) for location (9) (Figure 6(c) and (e)). This fatigue detail was also classified as FAT100 in Eurocode 3 and in IIW recommendations, of which the CAFLs are still far above the measured structural stress ranges indicating an infinite fatigue life under test. The test results of these two anchorage segments prove their equal possession of a high fatigue reliability under test load. This is mainly due to the large and thick plates adopted in critical welded joints, leading to a rather lower stress state.

Pinned connections

The strain gauge placed at surface of lifting lug’s cap plate around the pin hole shows that the maximum vertical tension stress (y-direction; Figure 3) was 93.7 MPa at the beginning of the test and was changed to a slightly higher value of 95.8 MPa at the end. Strain gauge placed at the same plate near pin hole in line of central axis got the maximum longitudinal compression stress (x-direction) at 33 MPa. These indicate that the plates interacting with pin shaft have a lower stress level and are safe for the static limit state. The magnetic particle inspection at the end of the test shows no sign of cracks in all plates around the pin hole.

BSSR

The strain measurement after 1×10⁶ cycles shows that the strain gauge 9 (Figure 6(c)) near the HS2 was read to have decreased to nearly zero, indicating the possibility of an initial crack at this location. This was verified by subsequent magnetic particle inspection. The exact initial spot was at HS1 in Figure 7(a). It can be concluded that the fatigue initiation life of this HS was less than 1 million cycles. Afterwards, the crack propagation phase went on. With a further 779,535 cycles, the crack has propagated through both the thickness (80 mm) and the width (500 mm) of the entire ear-plate simultaneously. As shown in Figure 7(b), the crack was propagated along a straight line penetrating half thickness and then twisted in waves with an angle of 45° at the end. Along the width of the web plate, it twisted at an angle of 45° at the beginning, and further propagated approximately along the vertical direction (Figure 8). The crack initiation spot was located on the minimum section of BSSR where the flange plate ended, only leaving the two longitudinal thick web plates (80 mm) to undertake the whole load. In addition, this site was also the joint of several weld lines (Figures 5 and 7), which significantly intensified the stress concentration of this HS. The maximum axial stress (x-direction) calculated from strain gauge near the crack initiation spot HS2 is 192.61 MPa, with a corresponding nominal stress (maximum test load divided by net section area) of 48.75 MPa. The rather high stress concentration factor of 3.95 identifies a significant stress concentration situation. However, this value did not exclude the effect of weld profile. The following FE analysis also indicates the maximum stress (x-direction) occurred at this site.

Failure mechanisms

For most fatigue evaluation of welded joints under high-cycle fluctuation forces, the propagation life in calculating the total fatigue life was commonly neglected. In this failure process, the fatigue initiation life N_i versus propagated life N_p is nearly equal (1/0.779). One reason contributing to this result is that the main load-carrying plates are made by thick plate (80 mm) which brings more cycles for thorough propagating compared with thin plate (less than 40 mm). The second reason is that the BSSR is a complex box-shaped structure, of which the web plate was bounded by top and bottom flange. It should be noted that the prediction of fatigue propagation life is limited by the drawbacks of monitoring apparatus. Since the initiation crack was usually detected by visual inspection, cracks have already been propagated for a while once they were detected by routine inspection. For a complex and huge impact structures like bridges undertaking daily heavy traffic in the city centre, it will be too late to prevent the failure of an entire bridge if the propagation life is too short. Therefore, the risk control of bridge management can be benefit from BSSR structure’s advantage of its longer propagation life.

Numerical investigation

FE model

In order to acquire the stress distribution in the complex BSSR structure and to form the basis for calculating the effective notch stress, a two-step analysis, the global model and the refined sub-models, was conducted using ANSYS, Inc. (2015). Due to the symmetry in the three directions and the high reliability of two anchorage segments aforementioned, only 1/8 of the global model (Figure 9(a)) was simulated in this study, including the BSSR component, lifting lug plate and associated pinned connection. All components were modelled using a three-dimensional (3D) linear elastic element – solid 185 (eight-node linear displacement function).

The mechanism of load transfer, from anchorage segment to BSSR by pinned connection or the reverse, was simulated by contact pairs in FE model. The contact regions were identified as follows:

Contact pair 1: between the pin shaft and ear-plate of BSSR;

Contact pair 2: between the pin shaft and lifting lug of anchorage segment.

Contact element TARGE170 was used in the modelling of all these interfaces for contact surfaces on pin shaft, and CONTA174 for surfaces on ear-plate and lifting lug. The symmetric boundary condition was applied on each symmetrical plane of the 1/8 global model, and the pressure was loaded at the end of lifting lug section (Figure 9(a)). The element size near critical location (detail A) was 5 mm, and the size away from it was 10–20 mm.

The sub-models were used to investigate the effective notch stress at fatigue critical location. By trial and error, it was found that spurious stresses occurred at the cut boundary locations when the contact regions were not included. Applying displacements as cut boundaries, which results in over constraining of the sub-model, may account for this. Therefore, the strategy in this case was to cut only the right part of section, while maintaining the region surrounding the critical location, the whole left part, that is, the lifting lug and cap plate (Figure 9(b)). The welds were added in sub-models, and fictitious notch radius of 1 mm was used to replace the actual notch radius of weld toe (Radaj et al., 2013). The element types were employed in the same way as those for global model. The fillet welds between cap plate (weld lines 3 and 4)/flange plate (weld lines 1 and 2) and ear-plate were added in sub-models (Figures 5 and 9(b)). As a result of the linear displacement function of the solid 185, the element mesh size around the fictitious notch was set as 0.14 mm in all three directions (Figure 9(c)), according to mesh density requirements (Fricke, 2012).

The material property of steel adopted Young’s modulus E = 206,000 MPa and Poisson’s ration ν = 0.3. The material property of spin shaft is in Young’s modulus E = 206,000 MPa and Poisson’s ration ν = 0.3. The friction coefficient between the contact surface is µ = 0.5.

Validation of FE model

The numerical results obtained from the FE analysis were compared with the experimental results. As is illustrated in Figure 10, the FE results generally remain consistent with measured data, except for first measured data due to a retarded force distribution. These two opposite gauges (Figure 6c) read a very close results. This shows that the specimens were undertook a symmetrical stress state during the whole test process, which verified the implementation of 1/8 global model. The calculated axial stresses (x-direction) are slightly above the measured ones in each side’s web plate surface, leading to conservative results for FE model. Therefore, it is a convincing result that the FE model is reliable in predicting the mechanical performance of BSSR structure.

Numerical results

The effective notch stresses σ_k obtained from sub-models and the corresponding modified nominal stresses σ_{n_m} from global models are tabulated in Table 1. Figure 11 illustrates the FE stress contours and the corresponding HS locations in each model. The effect of the weld profile was excluded from the modified nominal stress. As shown in Table 1, the elastic notch stress concentration factor K_f (the effective notch stress divided by modified nominal stress) of HS2 and of HS3 is just a half or less of HS1, 1.27 and 1.61 versus 2.95 (taking the unfavourable values under 3900 kN for discussion), respectively. This identifies HS1 as the most vulnerable location under fatigue load. It should be noted that the nominal stress used in some parametric equations to estimate K_f (Pachoud et al., 2017; Radaj et al., 2013) is lower than that tabulated in Table 1.

Table 1.

Calculated effective notch stresses (the maximum principle stress) under tensile load range of 700–3900 kN.

Hot spot	700 kN			3900 kN
	Global model σ_{n_m} (MPa)	Sub-model σ_k (MPa)	K_f = σ_k/σ_{n_m}	Global model σ_{n_m} (MPa)	Sub-model σ_k (MPa)	K_f = σ_k/σ_{n_m}
HS1	32.5	92.8	2.85	170.8	503.8	2.95
HS2	28.9	35.3	1.22	153.8	194.8	1.27
HS3	22.0	34.7	1.58	118.6	190.9	1.61

Fatigue evaluation results, predicted by nominal stress and ENSA, are listed in Table 2 in comparison with test results. The nominal stress σ_n defined here was the average stress in plate at weld toe. The fatigue life N_f depending on the failure criteria was defined as merely crack initiation phase (N_i) or through-thickness cracking (N_i + N_p) which could be 1×10⁶ and 1.77×10⁶ cycles, respectively. For HS2 and HS3, as the crack did not initiate from these two locations, it could be just roughly deducted that the fatigue life of these two HSs are beyond that of HS1. The fatigue evaluation based on nominal stress approach generates an un-conservative result compared with experimental results (with a ratio of 9 to 1 or 9 to 1.7 according to different failure criteria), leading to a risk in the structure design and maintenance. It indicates that the actual category of this detail was lower than 56 MPa. In contrast, the fatigue life predicted by ENSA compared with test results is rather conservative, with a ratio of 0.32 to 1 or 0.32 to 1.77. For HS2 and HS3, the predicted life based on ENSA was much higher than that of HS1, a seventeenth of the prior values, which indicates that these two locations were not the within concern of BSSR fatigue design and evaluation.

Table 2.

Predicted fatigue life compared to test results under tensile load range of 700–3900 kN.

Hot spot	Nominal stress approach			Effective notch stress approach(the maximum principle stress)			Test results
	Δσ_n (MPa)	Fatigue class	Predicted fatigue life	Δσ_k (MPa)	Fatigue class	Predicted fatigue life	N_i	N_i + N_p
HS1	33.9	56	9.02E+06	411	225	0.33E+06	1.00E+06	1.77E+06
HS2	33.9	56	9.02E+06	159.5	225	5.61E+06	–	–
HS3	33.9	56	9.02E+06	156.2	225	5.98E+06	–	–

The fatigue assessment, relating the effective notch stress range Δσ_k calculated by FE analysis to test results N_f, is illustrated in Figure 12. Regardless of how the failure criterion was defined, the test results of HS1 are all above those of the single universal S-N curve (FAT225) recommended by IIW. HS1 has a fatigue strength curve equivalent to FAT326 or FAT395, regarding crack initiation or through-thickness cracking criteria, respectively. It is certain that more test data are needed to verify this result. As aforementioned, test results were not possible as crack was not initiated from these locations in HS2 and HS3. Therefore, the comparison between the actual fatigue strength of these two HSs and design curve (FAT225) remains a mystery. In general, from Table 2 and Figure 12, the fatigue evaluation relating effective notch stress to design S-N curve of FAT225 produces a conservative outcome.

Conclusion

A large-size full-scale experimental investigation on the fatigue behaviour of the proposed novel BSSR structure has been carried out. The specimen includes the LAS and UAS, the BSSR and the pinned connection between three segments in series. The following conclusions can be drawn as follows:

The UAS and LAS have a much longer fatigue life than designed service life under predicted load history. This is mainly due to the large and thick plate adopted in welded joint of these two segments, which significantly alleviated the stress at weld toe to an extremely lower level.

There is a potential danger that the BSSR may fail during service if it was not replaced at regular intervals. As the most vulnerable spot of BSSR, HS1 is probed by the FE results and the test results to be the location of crack initiation. Conversely, both HS2 and HS3 have a much longer fatigue life than HS1 according to the prediction using notch stress approach based on design curve of FAT 225 and can serve safely during the service life.

The fatigue evaluation of thick-plate welded structure (BSSR, t = 80 mm) based on ENSA presents a conservative result, by adopting a single universal S-N curve (FAT225), while the nominal stress approach overestimates the fatigue life of welded joints of BSSR. However, Aygül et al. (2013) analysed five types of welded joints typically used in steel bridges and found no obvious discrepancy in magnitude of standard deviations for most of these details, in spite of adopting any method. There might be a size effect in this proposed structure. In this case, the test results evaluated by ENSA are more in line with the results from Cai et al. (2017) and Park and Miki (2008), presenting an S-N curve for both investigated welded joints generally beyond the FAT300.

In general, the proposed BSSR structure contains a critical detail prone to fatigue during the service life. Change in the weld profile of this detail to get a longer fatigue life is in need to enable successful application of BSSR structure into practice. The following measures can be adopted: (1) modification of the cap plate into a round shape to distancing the weld line 3 from weld line 2 or (2) modification of the angle between flange plate and web plate featured in detail A into a mild obtuse angle to alleviating the stress concentration of HS1. It can also be validated by FE model using the ENSA.

Footnotes

Appendix 1 Acknowledgements

The authors thank Mr Zhengxing Wang from Key Laboratory of Bridge Structure Health and Safety, Wuhan, China, for his assistance in conducting the experiment.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This research was funded by the Science and Technology Support Program of Tianjin (Grant No. 02202530267).

References

ANSYS, Inc. (2015) Ansys 13.0 Documentation. Canonsburg, PA: ANSYS, Inc.

Aygül

Bokesjö

Heshmati

et al . (2013) A comparative study of different fatigue failure assessments of welded bridge details. International Journal of Fatigue 49: 62–72.

Baptista

Kannuna

Oliveira Pedro

et al . (2017) Fatigue behaviour of CHS tubular bracings in steel bridges. International Journal of Fatigue 96: 127–141.

Bruder

Störzel

Baumgartner

et al . (2012) Evaluation of nominal and local stress based approaches for the fatigue assessment of seam welds. International Journal of Fatigue 34(1): 86–102.

Cai

Chen

(2016) An experimental study on the fatigue behaviour of a novel box-shaped steel rod for an arch bridge. In: Proceedings of the 11th Pacific structural steel conference, Shanghai, China. 31 October.

Cai

Chen

Kashani

et al . (2017) Fatigue life assessment of large scale T-jointed steel truss bridge components. Journal of Constructional Steel Research 133: 499–509.

Cerver

(1989) New Bridges: Arco Colour Thematic Architecture. Acro Editorial, pp. 77–78.

Chinese National Standard (CNS) (1999) Alloy Structural Steel (GB/T 3077-1999). Beijing, China: CNS.

Chinese National Standard (CNS) (2008) High Strength Low Alloy Structural Steels (GB/T 1591-2008). Beijing, China: CNS.

10.

De Backer

Outtier

Van Bogaert

(2014) Buckling design of steel tied-arch bridges. Journal of Constructional Steel Research 103: 159–167.

11.

Doerk

Fricke

Weissenborn

(2003) Comparison of different calculation methods for structural stresses at welded joints. International Journal of Fatigue 25(5): 359–369.

12.

Dong

(2001) A structural stress definition and numerical implementation for fatigue analysis of welded joints. International Journal of Fatigue 23(10): 865–876.

13.

EN 1993-1-9 (2005) Eurocode 3: Design of Steel Structures: Part 1-9: Fatigue. Brussels: European Committee for Standardization.

14.

Feng

(2004) Jiangyin Xinchun bridge-design of a basket bowstring arch bridge. Nanjing Municipal 1: 18–21 (in Chinese).

15.

Fricke

(2012) IIW Recommendations for the Fatigue Assessment of Welded Structures by Notch Stress Analysis: IIW-2006-09 (International Institute of Welding). Cambridge: Woodhead Publishing, pp. 11–12.

16.

Fricke

Paetzold

(2010) Full-scale fatigue tests of ship structures to validate the S–N approaches for fatigue strength assessment. Marine Structures 23(1): 115–130.

17.

Fricke

Paetzold

Zipfel

(2009) Fatigue tests and numerical analyses of a connection of steel sandwich plates. Welding in the World 53(7): R151–R157.

18.

Fricke

von Lilienfeld-Toal

Paetzold

(2012) Fatigue strength investigations of welded details of stiffened plate structures in steel ships. International Journal of Fatigue 34(1): 17–26.

19.

Chen

(2006) Stability analysis of the Chaozhou Hanjiang river northern double X-shape arch bridge. Journal of Highway and Transportation Research and Development 23(3): 100–103 (in Chinese).

20.

Hobbacher

(2015) Recommendations for Fatigue Design of Welded Joints and Components. New York: Springer.

21.

Liu

A-R

Huang

Y-H

J-Y

et al . (2015) Experimental research on stable ultimate bearing capacity of leaning-type arch rib systems. Journal of Constructional Steel Research 114: 281–292.

22.

Malm

Andersson

(2006) Field testing and simulation of dynamic properties of a tied arch railway bridge. Engineering Structures 28(1): 143–152.

23.

Manterola

Gil

MÁ

Muñoz-Rojas

(2011) Spatial arch bridges over the Galindo and Bidasoa rivers. Structural Engineering International 21(1): 114–121.

24.

Marulo

Baumgartner

Frendo

(2017) Fatigue strength assessment of laser welded thin-walled joints made of mild and high strength steel. International Journal of Fatigue 96: 142–151.

25.

Pachoud

Manso

Schleiss

(2017) New parametric equations to estimate notch stress concentration factors at butt welded joints modeling the weld profile with splines. Engineering Failure Analysis 72: 11–24.

26.

Park

Miki

(2008) Fatigue assessment of large-size welded joints based on the effective notch stress approach. International Journal of Fatigue 30(9): 1556–1568.

27.

Pedersen

Mouritsen

OØ

Hansen

et al . (2010) Re-analysis of fatigue data for welded joints using the notch stress approach. International Journal of Fatigue 32(10): 1620–1626.

28.

Pradana

Qian

Swaddiwudhipong

(2015) An extrapolation method to determine the effective notch stress in welded joints. Fatigue & Fracture of Engineering Materials & Structures 38(9): 1118–1135.

29.

Pradana

Qian

Swaddiwudhipong

(2017a) Simplified effective notch stress calculation for non-overlapping circular hollow section K-Joints. Marine Structures 55: 1–16.

30.

Pradana

Qian

Swaddiwudhipong

et al . (2017b) An extrapolation method to determine the effective notch stress in circular hollow section X-joints. Fatigue & Fracture of Engineering Materials & Structures 40(2): 160–175.

31.

Radaj

Lazzarin

Berto

(2013) Generalised Neuber concept of fictitious notch rounding. International Journal of Fatigue 51: 105–115.

32.

Sarmiento-Comesías

Ruiz-Teran

Aparicio

(2011) Structural behavior of inferior-deck spatial arch bridges with imposed curvature. Journal of Bridge Engineering 17(4): 682–690. Available at: http://ascelibrary.org/doi/10.1061/%28ASCE%29BE.1943-5592.0000282

33.

Sarmiento-Comesías

Ruiz-Teran

Aparicio

(2013) State-of-the-art of spatial arch bridges. Proceedings of the Institution of Civil Engineers: Bridge Engineering 166(3): 163–176. Available at: http://www.icevirtuallibrary.com/doi/10.1680/bren.11.00010

34.

Sonsino

Fricke

de Bruyne

et al . (2012) Notch stress concepts for the fatigue assessment of welded joints – background and applications. International Journal of Fatigue 34(1): 2–16.

35.

Uzgider

Aydogan

Caglayan

et al . (2009) Performance of a tied-arch reinforced concrete railway bridge: rating, safety assessment, and bond length evaluation. Journal of Performance of Constructed Facilities 23(5): 366–371.

36.

Xiao

Sun

Jia

et al . (2005) Kunshan Yufeng bridge-design of the first long-span leaning-type arch bridge without thrust. China Civil Engineering Journal 38(1): 78–83 (in Chinese).

37.

Zhang

Chen

(2016) Load effect and fatigue damage of bridges under combined actions of traffic and wind: a case study. Stahlbau 85(4): 281–291.

38.

Zhou

Meng

Chen

(2005) The modeling analysis of concrete filled steel tube arch bridge with no wind bracing system. Journal of Central South Forestry University 25(6): 8–11 (in Chinese).