Numerical Study on the Mechanical Performance of a Flexible Arch Composite Bridge with Steel Truss Beams over Its Entire Lifespan

Abstract

Steel truss–arch composite bridge systems are widely used in bridge engineering to provide sufficient space for double lanes. However, a lack of research exists on their mechanical performance throughout their lifespan, resulting in uncertainties regarding bearing capacity and the risk of bridge failure. This paper conducts a numerical study of the structural mechanical performance of a flexible arch composite bridge with steel truss beams throughout its lifespan to determine the critical components and their mechanical behavior. Critical vehicle loads are used to assess the bridge’s mechanical performance. The results show that the mechanical performance of the bridge changes significantly when the temporary piers and the bridge deck pavement are removed, substantially influencing the effects of the vehicle loads on the service life. The compressive axial force of the diagonal bar significantly increases to 33,101 kN near the supports during the two construction stages, and the axial force in the upper chord of the midspan increases by 4.1 times under a critical load. Moreover, the suspender tensions and maximum vertical displacement are probably larger than the limit of this bridge system in the service stage, and this is caused by the insufficient longitudinal bending stiffness of truss beams. Therefore, monitoring and inspection of critical members are necessary during the removal of temporary piers and bridge deck paving, and an appropriate design in steel truss beams is required to improve the life cycle assessment of this bridge system.

1. Introduction

A steel truss–arch composite bridge system has high stiffness and bearing capacity and a long lifespan, providing space for double lanes to alleviate traffic pressure, which significantly improves green engineering and transportation. There is a lack of research on the mechanical behavior of these bridges during construction, resulting in uncertainties in their mechanical performance and bearing capacity and posing potential safety risks [1]. Therefore, it is necessary to study the mechanical performance of this bridge system throughout the construction and service stages.

Many scholars have conducted extensive research on beam–arch composite bridges. Parida and Talukdar found the dynamic amplification factor of the steel truss bridge by taking into account the bridge–vehicle dynamics [2]. Buitrago et al. experimentally analyzed the robustness of riveted steel truss bridges and defined practical recommendations for early detection of local failures before they cause progressive collapse [3]. Huang and Yang proposed a theoretical equation for calculating the load distribution of the beam, arch, and boom of beam–arch composite bridges. They analyzed the factors affecting the load-sharing ratio and the bending moment ratio [4]. Li conducted a comprehensive safety evaluation of a prestressed concrete continuous beam–arch composite bridge and analyzed the synergistic interactions between the main beam and composite arches subjected to railway loads [5]. Li et al. investigated the impact factors of continuous beam–arch composite bridges and provided a regression equation to estimate the impact factors for main beams with similar structures [6]. Fu et al. studied the deformation and repair of beam–arch composite bridges under extreme temperature conditions and found that the cause of the abnormal bridge deformation was an inconsistent temperature field between the top and bottom plates [7]. Stojanovic et al. assessed a nonlinear, coupled system of beam–arch composite bridges [8]. Shi et al. found that the arch ribs in continuous beam arch bridges amplify the lateral displacement of the beams, unlike in continuous beam bridges of equal mass [9]. He et al. investigated the mechanical behavior of perforated steel plate–concrete-filled tubular arch feet in concrete girder–steel arch composite bridges [10]. Zhou et al. studied the crack resistance of concrete-filled steel tubes and found that the radial stress resulted in significant hoop tensile stress in the surrounding concrete, exposing the arch feet to a high risk of early-age cracking [11]. Parisi et al. described a method for locating damage in steel truss railway bridges through machine learning classification tools [12]. Valiullin and Chizhov assessed the stiffness of trusses bolted connections in railway bridges and proposed formulas to determine rotation angles of the truss element joint sections [13]. Nettis et al. evaluated the applicability and effectiveness of DBA (displacement-based assessment) and nonlinear static procedures for multi-span railway steel truss bridges [14]. Zhu et al. accurately mapped the temperature-induced responses of long-span steel truss arch bridges with spherical bearings, considering the bearing properties and temperature distribution [15]. Guo et al. analyzed the static aerodynamic coefficients of a girder using computational fluid dynamics numerical simulations and a wind tunnel test to determine the wind resistance of a sea-crossing arch bridge [16]. Yang et al. found that a beam–arch bridge had high stability in out-plane and in-plane buckling [17]. Shao et al. proposed a conceptual design of an ultra-high-performance fiber-reinforced concrete composite truss arch bridge with a main span of 1000 m. They addressed excessive self-weight and difficulty in constructing super-long-span arch bridges [18]. Liu et al. found that the chord members added to stiffen the structure substantially enhanced the bridge’s fatigue performance [19]. Crognale et al. developed a methodology for a preliminary description of the damage in steel railway bridges induced by fatigue phenomena [20]. Banerjee et al. proposed a real-time crack localization algorithm for a truss beam and validated it using the AE (acoustic emission) technique [21]. Wen et al. proposed a design for the Seagull Bridge, a two-span continuous aluminum alloy truss arch bridge [22]. Qiu et al. built a test bridge to demonstrate the superiority of a truss arch bridge with multi-point elastic constraints [23]. Xie et al. proposed a method that considered vehicle–bridge coupled vibration to evaluate the technical status of concrete truss–arch bridges [24]. Trochymiak et al. studied the incremental launching of a bridge using BIM (building information modeling) technology [25]. López et al. presented a methodology to identify triggering events leading to progressive collapse on truss-type bridges [26]. Ren et al. found that the dominant failure type of the arch of a steel truss–arch composite structure (STACS) was out-of-plane failure under in-plane loading, which differed from the failure modes of traditional fixed steel arches [27]. Shangguan et al. described the technical characteristics of three-truss, rigid-arch, and rigid-beam structures and the synchronous construction of the arch and beam [28]. Zhang et al. revealed that the radial grid number of single-layer reticulated shells significantly affected steel consumption [29]. Rajchel and Siwowski assessed the fatigue of a 100-year-old riveted truss railway bridge by determining the full spectrum of railway loads [30].

Most studies have focused on the mechanical behavior of the entire bridge but have not considered the construction process. This paper conducts a numerical study on the mechanical performance of flexible arch composite bridges with steel truss beams during construction to determine the critical members. The mechanical behavior of the bridge is examined under vehicle loads. The research results provide insights into the critical components for health monitoring, design optimization, and maintenance of these bridge types during their lifespan, which improves the life cycle assessment of this bridge system.

2. Flexible Arch Composite Bridges with Steel Truss Beams

2.1. Bridge Configuration

A steel truss–arch bridge with a span of (1 × 202) m and a width of 45 m, with the measured section A, is shown in Figure 1 and Figure 2. The bridge has two decks. The upper deck is an eight-lane highway, and the lower deck is an eight-lane road with a sidewalk. The main beam consists of three truss beams with a spacing of 21.75 m. Three arch ribs are placed on the truss beams with six transverse braces and 3 × 11 = 33 suspenders, as shown in Figure 2. The stringers are welded to the orthotropic deck, and the lateral beam is connected to the truss joints with a spacing of 3.05 m (3.06 m at the end of the beams). The bridge has six supports, including one fixed support, three unidirectional movable supports, and two bidirectional movable supports, as shown in Figure 3.

The design strength values of the steel for the trusses, bridge decks, and arches are listed in

Table 1. Material properties.

Component	Grade	Elasticity Modulus (MPa)	Thickness (mm)	fd (MPa)	fvd (MPa)
Truss, Arch, Crossbeam, Bridge deck	Q355D	2.06 × 105	≤16	305	175
			16–40	290	170

Note: f_d: design value of tensile strength, compressive strength, and flexural strength. f_vd: design value of shear strength.

. The suspenders are parallel steel wire ropes with a standard strength of 1860 MPa and an elastic modulus of 1.95 × 10⁵ MPa. The symbols of the members are shown in

Table 2. Symbols of members.

Symbol	Members
L/M/RU1-16	Upper chord
L/M/RL1-16	Lower chord
L/M/RV1-16	Vertical bar
L/M/RD1-17	Diagonal bar
L/M/RS1-11	Suspender

Note: The prefixes L, M, and R represent the position of the members on the left, middle, and right sides of the truss, respectively.

and Figure 4.

2.2. Construction Procedure

The construction consisted of two stages: incremental launching of the steel trusses one each side and the installation of the steel arch. Four temporary piers were used in the first stage. Subsequently, the arch ribs were installed, and the suspenders were tensioned after constructing the steel truss beam. The four temporary piers were then removed, and the pavement was installed, as shown in

Table 3. Construction steps.

Step	Content	Construction Elevation Layout (unit: m)
1–3	The guide beam was installed. Each of the three trusses was assembled and incrementally launched. Each launch covered a distance of 12.2 m.
4–9	The six trusses were assembled and incrementally launched, with each launch covering a distance of 24.4 m.
10–11	The two trusses were assembled and incrementally launched, with each launch covering a distance of 12.2 m.
12	The steel truss was launched into position (30.3 m). The guide beam was removed, and the permanent supports were installed.
13	The arch ribs were installed.
14–25	The suspenders were tensioned.
26	Four temporary piers were removed
27	The bridge deck pavement was installed.
28	The forces in some suspenders were adjusted.

.

3. Numerical Study

3.1. Numerical Study of the Construction Procedure

A 3D finite element model of the flexible arch composite bridge with the steel truss beam was established in MIDAS/Civil software. The truss and arch were simulated by beam elements, and the suspenders and bridge deck were simulated by truss elements and plate elements, respectively. Elastic support nodes with X and Y translation constraints were used to represent the interaction between the pile and the soil. General supports with complete translational constraints were used to simulate soil consolidation at the end of the piles. General supports with Y and Z translation constraints were used to simulate the temporary piers, and rigid connections were used to simulate the permanent supports between the truss and piers, as shown in Figure 5.

The launching support was fixed, and the guide beams and steel trusses moved forward during bridge launching. This was achieved by continuously changing the position of the constraints to simulate the launching process, as shown in Figure 6.

3.2. Verification of the Numerical Model

In order to verify the reliability and accuracy of the numerical model, the strain gauges were used to measure the strains of the upper chord in section A of the middle truss after the construction step 2 finished, as shown in Figure 1 and Figure 7. Four strain gauges are arranged in Section A (Figure 8b), with the measured and theoretical stresses in

Table 4. Measured and finite element model stresses.

Measuring Point	Measured Stress/MPa	FE Model Stress/MPa	Relative Difference
1	−0.63	−0.65	3.08%
2	−0.62	−0.65	4.62%
3	−4.25	−4.3	1.16%
4	−4.09	−4.3	4.88%

. Noticeably, the maximum relative difference in measured and theoretical stresses is merely 4.88%; thus, this numerical model is accurate in its analysis of the mechanical performance of this bridge.

4. Analysis of the Construction Phase

4.1. Incremental Launching

The construction steps 3, 9, 11, and 12 are critical for the steel truss beams during incremental launching. The mechanical performance of the trusses in the construction steps is shown in Figure 9, Figure 10, Figure 11 and Figure 12.

Construction step 3 was the third assembly and incremental launching of the truss beams. The front end of the guide beam reached temporary pier L1. Most truss members were compressed, with 1122 kN, 1011 kN, and 1618 kN of maximum pressure in chord MU13, diagonal bar MD16, and vertical bar MV17, respectively. The maximum bending moment was 3970 kN·m in chord ML13.

Construction step 9 was the assembly of the ninth section of the truss and the incremental launching of the truss with a distance of 24.4 m. The truss reached the temporary pier L2. The maximum tensile and compressive axial forces were 2412 kN and 3909 kN in chords MU11 and MU9, 4007 kN and 5102 kN in diagonal bars MD15 and MD11, and 1111 kN and 4254 kN in vertical bars MV12 and MV16, respectively. The maximum bending moment was 6748 kN·m in chord ML15.

Construction step 11 was the completion of the assembly and launching of the truss. The front end of the guide beam reached support L3. The maximum tensile and compressive axial forces were 4500 kN and 4270 kN in chords MU15 and ML13, 4319 kN and 6242 kN in diagonal bars MD13 and MD15, and 1087 kN and 2769 kN in vertical bars MV12 and MV14, respectively. The maximum bending moment was 6367 kN·m in chord ML13.

Construction step 12 included launching the truss with a distance of 30.3 m, the removal of the guide beam, and the installation of the permanent supports. The maximum tensile and compressive axial forces were 3288 kN and 4504 kN in chords ML4 and ML15, 4795 kN and 7105 kN in diagonal bars MD5 and MD1, and 1220 kN and 3133 kN in vertical bars MV2 and MV6. The maximum bending moment was 7667 kN·m in chord ML11.

The axial force and bending moment of the steel trusses increased during incremental launching, with the largest values for the diagonal bars and lower chords, respectively.

4.2. Installation of Arch Ribs

The maximum tensile and compressive axial force after installing the arch ribs were 4370 kN and 3577 kN in chords ML4 and MU15, 5264 kN and 10,988 kN in diagonal bars MD5 and MD1, and 1220 kN and 3490 kN in vertical bars MV14 and MV6, respectively. The diagonal bars MD5 and MD1 had the maximum tensile and compressive axial forces. They were 10% and 55% higher, respectively, than before the installation of the arch ribs. However, the installation of the arch ribs had a negligible effect on the bending moment of the steel truss members (Figure 13).

The pressure was lower on the side than in the middle of the arch ribs after their installation. The maximum pressure was 4922 kN at the foot of the middle arch rib. This decreased to the minimum value at the top of the arch. The maximum bending moment of the middle arch rib was −5727 kN·m at the arch foot, increasing to the maximum value and (2345 kN·m) at 1/7 of the span away from the arch foot, as shown in Figure 14.

4.3. Tensioning the Suspenders

The initial tension forces of the side and middle suspenders followed the same trend, as shown in

Table 5. Initial tension in suspenders (unit: kN).

Order	Suspenders	Initial Tension	Order	Suspenders	Initial Tension
1	MS6	1350	7	LS6, RS6	950
2	MS5, MS7	1850	8	LS5, LS7, RS5, RS7	1450
3	MS4, MS8	1815	9	LS4, LS8, RS4, RS8	1415
4	MS3, MS9	1800	10	LS3, LS9, RS3, RS9	1400
5	MS2, MS10	1700	11	LS2, LS10, RS2, RS10	1300
6	MS1, MS11	1550	12	LS1, LS11, RS1, RS11	1150

. The lowest initial tension occurred at suspender S6 located at the crown of the arch, and the largest value was observed at suspenders S5 and S7. The initial tension forces decreased from suspenders S5 and S7 toward the arch foot. The middle (side) suspender had a minimum tension of 1350 kN (950 kN) and a maximum tension of 1850 kN (1450 kN). The initial forces in the middle suspenders were about 400 kN larger than those in the side suspenders.

After tensioning the middle suspenders, the maximum tensile and compressive axial forces of the upper chord were 3229 kN and 1813 kN in chords MU11 and MU16, respectively. The lower chords from 1/4 span to ¾ span were under compression, with maximum tensile and compressive axial forces of 6398 kN and 1078 kN in chords ML1 and ML11, respectively. Similar axial forces were observed in the upper chords. The maximum tensile force of the lower chord was 11% higher (7116 kN) than that of chord LL15. The bending moment was similar due to tension in the suspenders, as shown in Figure 15, Figure 16, Figure 17 and Figure 18.

Due to the tension in the suspenders, diagonal bar MD1 had the maximum pressure. It was 67% higher than that before tension in the suspenders (18,326 kN). The bending moment of the steel truss was not significantly different before and after tensioning (Figure 19). Therefore, the tensioning of the suspenders significantly affected the axial forces of the truss but had a negligible effect on the bending moment.

The tension of the suspenders resulted in significantly higher pressure in the arch ribs, with maximum and minimum pressure values of 17,909 kN and 14,932 kN at the foot and crown in the middle arch rib (Figure 20). The axial force was 2.6 times larger after tensioning the suspender than before, with maximum and minimum pressure values of 14,907 kN and 12,486 kN at the foot and crown in the side arch ribs, respectively. The maximum negative bending moment of the arch rib was −9251 kN·m at the 1/14 span of the middle arch rib. This value was approximately 62% larger than before tensioning the suspenders. The maximum positive bending moment was 2745 kN·m at the middle arch rib close to suspenders MS5 and MS7. There were slight differences in the bending moment before and after tensioning.

4.4. Removal of Temporary Piers

The removal of the temporary piers significantly altered the distribution of the steel truss’ axial forces. The compressive axial forces in the truss beams are shown in Figure 21. The maximum tensile and compressive axial forces were 9818 kN and 1759 kN in chords ML1 and MU16, 3257 kN and 25,264 kN in diagonal bars MD2 and MD1, and 1249 kN and 2203 kN in vertical bars MV11 and MV17, respectively. Thus, the maximum tensile and compressive axial force of the truss was 38% and 37%, higher, respectively, after the removal of the temporary piers. The axial force of the end diagonal bar MD1 was much greater than that of the other members. However, the maximum bending moment of the steel truss was 6561 kN·m in chord MU16, similar to before the removal of the temporary piers.

The axial force of the arch ribs was approximately 40% larger after the removal of temporary piers, as shown in Figure 22. The maximum and minimum pressure values were 25,226 kN and 21,345 kN at the foot and crown in the middle arch rib and 20,592 kN and 17,423 kN at the foot and crown in the side arch ribs. The bending moment was negative at the arch foot and positive at the arch rib, reaching a maximum of 3356 kN·m.

The removal of temporary piers caused a significant increase in the cable forces in most suspenders. The cable forces were about 30% higher in suspenders S1 and S11 after the removal, as shown in Figure 23. The minimum and maximum tensile forces in the side suspenders were 797 kN and 1904 kN in suspenders LS6, LS5 (LS7) and 905 kN and 2185 kN in suspenders MS6, MS5 (MS7) in the middle suspenders, respectively.

4.5. Secondary Dead Load

After the secondary dead load, the maximum tensile and compressive axial forces were 12,965 kN and 2056 kN in chords ML1 and MU9, 5583 kN and 33,101 kN in diagonal bars MD2 and MD1, and 1326 kN and 2908 kN in vertical bars MV11 and MV17, respectively. The maximum tension of the lower chord and the pressure of the diagonal bar were 32% and 31% higher, respectively, after applying the secondary dead load. The members with the largest bending moment remained unchanged, and the maximum bending moments were 8448 kN·m and −8572 kN·m in chords ML15 and MU16, 50% and 31% higher, respectively, after applying the secondary dead load (Figure 24).

The pressure of the arch ribs was 23% higher, with a maximum pressure of 31,106 kN at the arch foot of the middle rib, as shown in Figure 25. Installing the bridge deck pavement significantly affected the bending moment at the arch foot. It was 1.7 times higher after installing the pavement (8908 kN·m).

The force in the side (middle) cable was 410 kN (540 kN) higher after paving the bridge deck, resulting in a large difference between the tensile forces in the side and middle suspenders, with a range of 250 kN to 589 kN (Figure 26). The minimum and maximum forces were 1210 kN and 2316 kN in suspenders LS6 and LS5 (LS7) and 1460 kN and 2725 kN in the middle suspenders MS6 and MS5 (MS7), respectively.

4.6. Adjusting the Tension in the Suspenders

A tension of 2268 kN was applied to suspenders L (R)S5 and L (R)S7, and a tension of 2965 kN was applied to suspenders MS5 and MS7, resulting in slight differences in the maximum axial force and bending moment of the chord members and the diagonal and straight bars. The maximum tensile force and pressure of the steel truss were 12,997 kN in chord ML1 and 33,184 kN in diagonal bar MD1, which were similar to the values before adjusting the cable tension. Therefore, adjusting the cable tension had a negligible influence on the steel truss’ mechanical performance (Figure 27).

Adjusting the cable tension had a slight effect on the mechanical performance of the arch rib. The maximum and minimum pressure values were 31,316 kN and 21,391 kN at the arch foot and crown, respectively. The maximum positive and negative bending moments were 9140 kN·m and −9496 kN·m at the arch foot and the 1/14 span of the middle arch rib, as shown in Figure 28.

Adjusting the tension in the suspenders resulted in a 10% lower tension in suspender S6 and a 10% higher tension in suspenders S5 and S7. The tensions were 1332 kN and 1209 kN in suspenders M (L\R) S6 and 2970 kN and 2972 kN in suspenders S5 and S7, respectively. However, the tension adjustment had a negligible effect on the other suspenders (Figure 29).

The adjustment of the suspender tension slightly affected the crossbeams’ mechanical performance, as shown in Figure 30. The effect was larger on the bending moments than on the axial forces. The bending moments were 729 kN·m at the lower end of the crossbeam, indicating that the former was significantly larger than the latter.

4.7. Axial Forces during Construction

The change in the bridge structure affects the axial forces of the critical members. Chords MU9 and ML1, diagonal bar MD1, and vertical bar MV17 exhibited the largest axial forces (Figure 31).

The axial forces of the critical members during construction are shown in Figure 32. The axial force varied significantly, ranging from 1827 kN to −3474 kN in chord MU9 during construction step 12, as the trusses were launched with a distance of 30.3 m, and the guide beam and permanent supports were removed. As the suspenders were tensioned (Steps 14–25), the axial force decreased from −2926 kN to −66 kN. The removal of the temporary piers (Step 26) and bridge deck paving (Step 27) resulted in a significant increase in the axial force to −2057 kN (Figure 32a). Therefore, the inspection could be conducted for chord MU9 as the truss beam reached maximum cantilever (Step 9). The axial force in chord ML1 increased as the arch ribs and suspenders were installed (Steps 13–25) and sharply increased from 7045 kN to 9817 kN as the temporary piers were removed (Step 26). Paving the bridge deck (Step 27) caused a further increase to 12,996 kN in chord ML1 (Figure 32b). Similarly, the compressive axial force increased to −33,184 kN in diagonal bar MD1 and increased further as the temporary piers were removed (Step 26) and the bridge deck was paved (Step 27) (Figure 32c). The axial force ranged from −613 kN to −1977 kN in vertical bar MV17 during the incremental launching (Steps 1–11), changed slightly during suspender tensioning (Steps 14–25), and increased significantly to 2908 kN during bridge deck paving (Step 27) (Figure 32d). The axial force was much higher in diagonal bar MD1, a critical member, than in the other members, indicating this member should be inspected in all construction procedures, especially during bridge deck paving.

The pressure significantly increased from −4921 kN to −16,886 kN at the arch foot during the tensioning of the middle suspenders (Steps 14–19). It increased to −17,909 kN as the side suspenders were tensioned (Steps 20–25). The removal of the temporary piers (Step 26) and bridge deck paving (Step 27) resulted in a significant increase of approximately 37% and 24% to −25,208 kN and −31,081 kN, respectively. The axial force reached −31,291 kN at the arch foot during the adjustment of the suspender tension (Step 28) (Figure 33a). The bending moment significantly fluctuated at the arch foot during suspender tensioning (Steps 14–25) and remained positive after removing the temporary piers (Step 26). Subsequently, it increased significantly from 2459 kN·m to 8908 kN·m during bridge deck paving (Step 27) (Figure 33b).

Suspender MS5 is the most critical one. Its initial tension was 1855 kN, and it decreased to 1500 kN after tensioning suspender MS4 (Step 16). Subsequently, the tension changed slightly during the tensioning of the other suspenders. The removal of the temporary piers (Step 26) significantly increased the tension from 1525 kN to 2184 kN, followed by a further increase to 2970 kN due to bridge deck paving (Step 27) and the adjustment of the suspender tension (Step 28) (Figure 34).

The removal of the temporary piers (Step 26) and bridge deck paving (Step 27) significantly affected the mechanical performance. The axial force and bending moment of the critical members are listed in

Table 6. Axial force and bending moment of critical members.

Critical Members	Axial Force (kN)	Bending Moment (kN·m)
MD1	−33,184	−6218
ML1	12,997	4920
MU9	−1999	1226
MS5	2970	/
Foot in middle arch rib	−31,316	9140
End crossbeam	−259.7	−729

. Therefore, the inspection and monitoring of these members are necessary during the two construction phases.

5. Service Period

Six loading scenarios (intermediate and eccentric) were evaluated using a standard vehicle to determine the members’ critical loads (Figure 35, Figure 36 and Figure 37) [31].

The compressive axial forces of chord MU9 were 10,272 kN and 5686 kN under the critical intermediate and eccentric loads, respectively (Figure 38). The tensile axial forces of chord ML1 were 24,021 kN and 18,206 kN under the critical intermediate and eccentric loads, respectively. These were the largest forces (Figure 39). Therefore, chords MU9 and ML1 were critical members under the intermediate load. The axial forces were 4.1 times and 85% higher than the truss beam forces in chords MU9 and ML1, respectively, under the critical load. Therefore, inspections of chords MU9 and ML1 should be conducted to avoid damage to these members.

As the maximum force, the compressive axial forces are 63,762 kN and 46,759 kN in diagonal bar MD1 subjected to critical intermediate and eccentric load, with an increase of about 92% and 40.8%, as shown in Figure 40. That is to say, under the eccentric load, the maximum axial force is still in the members in the middle truss beam with sufficient bending stiffness in crossbeams. Additionally, inspection of diagonal bar MD1 is necessary for avoiding damage within its service life.

The maximum compressive axial forces at the foot of the middle arch were 52,750 kN and 41,638 under the critical intermediate and eccentric loads, respectively. These values were 69% and 36% higher than for the completed bridge (Figure 41a and Figure 42a). The bending moments at the foot of the middle arch were 32,952 kN·m and 20,254 kN·m under the critical intermediate and eccentric loads, respectively (Figure 41b and Figure 42b). Notably, the bending moment at the foot of the side arch was 23,411 kN·m under the critical eccentric load, which was 16% larger than that at the foot in the middle arch and 86% larger than that at the foot of the other side arch.

The maximum tension in the most critical suspender (MS5) was 5011 kN under the critical intermediate load, approaching a fracture tension of 7803 kN in suspender [32]. This value was 69% larger than that after bridge completion, with a difference of 738 kN to 1357 kN between the tension in the middle and side suspenders (Figure 43a). The tension was larger in suspender MS5 (3930 kN) than in suspender LS5 (3467 kN) under the critical eccentric load, indicating sufficient bending stiffness in the crossbeams. The difference between the tensions in the two side suspenders was 914 kN to 953 kN (Figure 43b). Noticeably, the tensions are larger than the limit of 2434 kN and 3121 kN in most suspenders, indicating that improvement and inspection are critically necessary for suspenders and longitudinal bending stiffness in truss beams [32].

The maximum bending moment was the dominant internal force. It was −2600 kN·m and −5247 kN·m at the end of the crossbeam subjected to the critical intermediate and eccentric loads, indicating that these were critical members (as shown in Figure 44).

The largest vertical displacements of chord MD9 in the loading scenarios were 0.34 m and 0.28 m in the midspan of the middle and side trusses under the critical intermediate and eccentric loads. Both the maximum vertical displacements were larger than the limit (l/800 = 0.253 m), indicating that this bridge system is probably lacking longitudinal bending stiffness, necessitating improvement in the longitudinal bending stiffness of truss beams [33]. The maximum difference between the vertical displacement of the two sides of the bridge under an eccentric load was 0.11 m, indicating the sufficient bending stiffness of the crossbeams (Figure 45).

The critical members, including diagonal bar MD1, chords ML1 and MU9, and suspender MS5 at the foot of the middle arch rib and the end crossbeam were the most sensitive to the vehicle load. Suspender tensions and vertical displacement are larger than the limit of the bridge in critical load scenarios, caused by the lack of longitudinal bending stiffness in truss beams. Thus, it is recommended that the height of truss beams is increased to improve their longitudinal bending stiffness to decrease the deformation of bridges under vehicle load, and monitoring and inspection of those critical members are necessary to improve structural safety during the service stage. Moreover, the axial forces in the diagonal bracings, arch ribs, and suspenders on the eccentric loading side were smaller than those in the middle truss and arch due to the sufficient bending stiffness of the crossbeams. Thus, the eccentric load did not cause anomalous mechanical behavior in the bridge, and no adverse effects were observed.

6. Conclusions

To improve life cycle assessment in steel truss–arch composite bridge system, this paper conducted a numerical study on the mechanical behavior of a flexible arch composite bridge with steel truss beams to determine the critical components and the evolution of mechanical performance during construction. Furthermore, the bridge’s mechanical behavior was investigated in critical load scenarios. The following conclusions were obtained.

(1)

The axial force and bending moment of the steel truss members increased during incremental launching. The removal of the guide beam and the installation of the permanent supports caused significant changes in the axial force of the critical chords MU9 and ML1 from 1827 kN and 104 kN to −3474 kN and 2492 kN, respectively. The removal of the temporary piers and the bridge deck paving resulted in significant increases in the axial forces to −2057 kN and 12,964 kN, as well as a significant increase to 33,101 kN in diagonal bar MD1.

(2)

Tensioning the suspenders caused a significant increase in the compressive axial force at the foot of the middle arch from 4920 kN to 17,909 kN. The removal of the temporary piers caused increases in the forces and bending moment to 31,291 kN and 8908 kN·m, respectively. Therefore, the removal of the temporary piers and bridge deck paving significantly influenced the bridge’s mechanical performance. Thus, monitoring and inspection of critical members is necessary in both construction phases.

(3)

The axial forces of the critical members, including declining bar MD1 and chords ML1 and MU9, increased by 92%, 85%, and 4.1 times, respectively, in the critical load scenarios. The vehicle loads significantly affected the critical members’ mechanical performance, necessitating monitoring and inspection of these members to increase the bridge’s safety and sustainable service life.

(4)

The suspender tensions and maximum vertical displacement are probably larger than the limit in service stage, triggered by the insufficient longitudinal bending stiffness of truss beams, which could be resolved by increasing the height of these trusses. Besides, the maximum difference in the vertical displacement between the two sides of the bridge under a critical eccentric load was only 0.11 m due to the sufficient bending stiffness of the crossbeams.