1. Introduction
The incremental launching construction method is widely used in bridge construction due to its advantages of simple construction machinery and equipment, good structural integrity, and savings in construction land [1,2,3,4]. Since its introduction in the 19th century, numerous scholars have conducted analyses and research on the incremental launching process of concrete box girders [5,6]. However, due to the thin-walled structure of steel box girders, issues of local stability and stress concentration are more prominent during the incremental launching construction process compared to concrete box girders [7,8]. This specific challenge has been referred to as the “local deformation problem” by several researchers [9], leading to a series of studies on the topic [10,11,12]. Previous research on local deformation has predominantly focused on the ultimate bearing capacity of isolated structural members such as I-beams [13,14,15], slender plate beams [16,17], or other components [18,19]. The findings indicate that excessive local deformation leads to noticeable local stress concentration and eventual plastic deformation, which can impact the overall structural stress [20]. Therefore, it becomes essential to incorporate local deformation into steel box girder launching construction, and to analyze and optimize the deformation in the area of local stress concentration.
The Qilu Yellow River Bridge, currently under construction, holds the title of the world’s widest network suspender arch bridge. Its construction adopts the method of building the beam first and the arch later, with the main girder constructed using a combination of walking-type and dragging-type pushing methods. The walking-type pushing method involves incremental movements to ensure precise positioning of the main girder segments during construction. This method allows for careful adjustments and alignment checks after each step to maintain stability and accuracy. On the other hand, the dragging-type pushing method utilizes a dragging mechanism to move the main girder segments into place. This approach focuses on controlled traction to smoothly position the girder sections, ensuring they align correctly with the overall bridge structure. These combined methods of construction facilitate the precise assembly of the Qilu Yellow River Bridge’s main girder, supporting its claim as the world’s widest network suspender arch bridge under construction. However, both jacking construction methods exhibit a phenomenon where there is a small area of concentrated stress on the bottom plate of the steel box girder, known as the “local deformation problem”. Moreover, the bridge’s extraordinary width and large span result in a significantly heavy weight of the steel box girder and large distances between temporary piers, making the local deformation problem particularly pronounced during construction. Existing research findings have shown that local deformation can lead to local stress concentration on the web and bottom plate of the steel box girder [21]. Real-time monitoring of the Qilu Yellow River Bridge has shown that at the initial construction stage, noticeable local deformation occurred in the area of stress concentration on the bottom plate of the steel box girder. More importantly, during the subsequent arch rib installation, the application of the arch rib’s self-weight and construction loads will exacerbate the stress concentration phenomenon in the steel box girder’s bottom plate. Therefore, it is imperative to systematically analyze the local deformation law of the contact area and to reasonably optimize the launching construction scheme.
Traditional research methods for analyzing bridge construction typically involve in situ measurements [22,23] and model tests [24,25,26]. However, in recent years, the finite element method (FEM) has gained popularity due to its high accuracy and cost-effectiveness [27,28]. In this study, a multi-scale FEM approach was employed to create a macro overall model of the entire incremental launching construction process, focusing on the local key research area [29,30]. The macro model was then integrated into a local fine model through appropriate connections to simulate the intricate boundary conditions of the local structure. This approach allowed for the revelation of the local stress and deformation patterns of the steel box girder bottom plate during the incremental launching construction process. The study also analyzed the factors influencing the local deformation of the bottom plate and proposed effective measures to enhance its performance. The insights gained from this research can provide valuable guidance for future steel box girder launching constructions.
2. Project Background
2.1. Introduction to Main Bridge
The Qilu Yellow River Bridge is a three-span, continuous-network suspender arch bridge. The total length of the main bridge is 980 m and the span arrangement is 280 m + 420 m + 280 m. The section of the main girder is a steel box girder, and an orthotropic composite deck has been adopted. The full width of the standard section is 60.7 m, which constitutes the widest network suspender arch bridge under construction in the world. The construction method of beam before arch has been adopted for the main bridge, and a combination of walking-type pushing and dragging-type pushing has been employed for the main beam. The temporary support for the launching construction includes one launching platform and eleven temporary piers. The launching platform is a temporary support platform between permanent pier P19 and temporary pier LD1, which provides an operation platform for the rear assembly and welding of the steel box girder. Elevation diagrams of the launching construction are presented in Figure 1.
2.2. Incremental Launching Construction Technology
The main girder of Qilu Yellow River Bridge is pushed by a combination of dragging-type and walking-type launching. Among them, the dragging-type launching system is mainly located within the launching platform. As can be seen from Figure 2, the dragging-type launching system is mainly provided by the traction cables to provide the reaction force to guide the steel box girder to slide forward over the tank wheel group. And the walking-type launching system is set on the top of the temporary pier. As shown in Figure 2, the walking-type launching system mainly consists of cushion block and walking jack. The cushion block mainly plays the role of stress dispersion to avoid the concentrated force at the top of the walking jack from causing large damage to the bottom of the steel box girder. The walking jack has the functions of upward jacking and forward and backward walking at the same time. The specific working principle of the walking jacking system includes: 1. the vertical lifting oil cylinder lifts the box girder; 2. the horizontal oil cylinder pushes the box girder forward with the slide system; 3. the vertical lifting oil cylinder drops the box girder onto the temporary support; and 4. the horizontal oil cylinder is reset.
2.3. Problems in Construction
During the launching construction of the steel box girder with the first span of 280 m, when the main girder was pushed forward by 120.8 m; that is, the front end of the steel guide girder was lapped to the top of temporary pier LD3, and an obvious local deformation of the steel box girder bottom plate was observed on the site. As indicated in Figure 3, the local deformation has created a longitudinal trace, roughly located beneath the mediastinal plate unit, coinciding with the positions of the walking jack and tank wheel set. Because the contact area of the walking jack and tank wheel that makes direct contact with the deformation area is small and the applied reaction force is large, the stress concentration in the contact area is large and a corresponding local deformation also appears. The appearance of local deformation affects the overall mechanical performance of the steel box girder, and this has a significant impact on the safety and stability of the incremental launching construction and subsequent construction.
3. Finite Element Model
In this study, the multi-scale FEM was used to simulate the pushing process from a macro perspective [31]. The detailed model of the box girder was analyzed using parameters including the material and size of the elastic cushion block of the walking jack, the width of the tank wheel, and the distance of the stiffener.
3.1. Multi-Scale FEM
In traditional local fine FEM analysis, key parts of the entire structure are typically isolated as the local model, with specific boundary conditions and stress states defined using strong boundary conditions. However, when the local model is fully defined, the forces and boundary conditions can become very complex, requiring a more nuanced approach than a single strong boundary condition. Consequently, the analysis may display a distorted region or F-zone (fuzzy region) near the boundary of the local model. According to Saint-Venant’s principle, the analysis results in the region far from the boundary in the local model are considered scientifically reliable; this region is known as the S-zone (Saint-Venant region). The boundary between the F-zone and S-zone is known as the S–F boundary. Due to the uncertainty and fuzziness of the S–F boundary, it becomes challenging to determine whether the F-zone in the local model will impact the results in the S-zone, potentially compromising the reliability of the FE analysis results.
In this study, a multi-scale FEM approach was utilized. By examining the overall structure, the elastic boundary conditions for the local fine model of the steel box girder were determined. These elastic boundary conditions were then implemented in the local fine model to conduct detailed investigations.
3.2. Integral FEM
The entire whole process of incremental launching construction before the deformation of the steel box girder bottom plate was simulated and analyzed using the FE software Midas Civil 2020. According to the equivalence principle of the section area, bending stiffness, torsion stiffness, and shear area, the steel box girder and steel guide beam were simplified as three-dimensional beam elements [32,33]. The standard section length of the steel box girder was 9 m, and the length of the steel guide beam was 39 m. Both the steel box girder and steel guide beam were Q345 steel, with an elastic modulus of E = 2.06 × 105 MPa and a Poisson’s ratio of v = 0.3. The simulation was carried out according to the principle of the pier moving and beam not moving. The key points of the modeling were as follows:
(1). Plane assumption: The temporary piers and main piers are set in pairs, and the reactions at the temporary piers and main pier supports upstream and downstream are equal. The model is calculated based on a plane bar system.
(2). One-step incremental launching construction: No further assembly or adjustment of the main girder structure is considered during incremental launching.
(3). Compression-only constraint: A compression-only elastic connection was used to simulate the support effect between the launching platform and temporary pier. The platform length was 90 m, and ten groups of tank wheels were set at the top with equal spacing. Therefore, the temporary support of the platform was simulated using ten elastic connections only under pressure.
To clarify the elastic boundary of the subsequent multi-scale local FEM, the overall model focused on the parameters such as the temporary support reaction, steel box girder bending moment, and steel box girder shear force and displacement.
Figure 4a depicts the reaction diagram of the temporary pier and launching platform during the process of the incremental launching construction, where T1 to T9 represent the reaction of the tank wheel support on top of the launching platform, and LD1 to LD3 represent the reaction of the temporary pier support. The overall incremental launching process could be divided into three stages. In stage I, the front end of the steel guide beam was placed on top of temporary pier LD1, and the steel box beam was pushed forward by 39 m to the first section and placed on pier LD1; in stage II, the first steel box girder was pushed 48 m forward to the top of temporary pier LD2; in stage III, the entire structure was pushed forward by 33 m, and the front end of the steel guide beam was placed on top of temporary pier LD3, which means that data on the LD3 support reaction force will only appear in the final construction stage specifically, as depicted by a single data point in Figure 4a.
Based on Figure 4a, when the steel box girder is positioned above the walking jack, the most unfavorable condition occurs during the 41st construction stage, with the 24th section of the steel box girder located at the top of LD2. As shown at point A, the maximum reaction force on the walking jack is 11,698.25 kN. On the other hand, when the steel box girder is positioned above the tank wheel, the most unfavorable condition arises during the 25th construction stage, with the 39th section of the steel box girder atop tank wheel T5. As indicated at point B, the maximum reaction force on the tank wheel is 3083.65 kN. Therefore, the 24th and 39th sections of the steel box girder were selected as local multi-scale FEMs to study the influence of the walking jack and tank wheel on the bottom plate of the steel box girder.
Figure 4b shows the shear force and bending moment for steel box girders in the 24th and 39th sections. It can be seen that the fluctuation of shear force and bending moment of the steel box girder in the 24th section is larger than that in the 39th section, and the timing of the fluctuation of the values is earlier. This is because the 24th section box girder is located in front of the 39th section box girder and will be pushed to the temporary pier first. Figure 4c shows the displacements at the front and rear ends of the steel box girders in the 24th and 39th sections. It can be seen the displacement of the 24th section box girder fluctuates, but the maximum fluctuation value does not exceed 1 mm, while the displacement of the 39th section box girder is almost unchanged. This is also due to the position of the 34th section box girder, which is behind.
According to Figure 4, the bending moment, shear force, displacement, and other elastic boundary conditions of the 24th and 39th sections of the steel box girder in the most unfavorable positions were obtained, as listed in Table 1.
3.3. Local FEM
The refined local FEM of the standard section of the steel box girder was analyzed using the FE software ABAQUS 2020. This section describes the material parameters, element types, contact and boundary conditions, loading methods, and mesh size sensitivity of the model.
The shell–solid contact hybrid element was used in the FEM. The steel box girder was defined as an S4R shell element made of Q345 steel, with an elastic modulus of E = 206 GPa and a Poisson’s ratio of ν = 0.3. The component composition of the steel box girder is presented in Figure 5.
A C3D8R solid element was used to simulate the elastic cushion of the walking jack and tank wheel. The tank wheel material was steel, the elastic modulus was 2.06 GPa, and the Poisson’s ratio was 0.3. According to engineering practice, a rubber cushion, polytetrafluoroethylene (PTFE) cushion, and steel cushion with compression moduli of 500 MPa, 1.42 GPa, and 2.06 GPa, respectively, were selected for the elastic cushion of the walking jack.
All components of the steel box girder were assembled and integrated into one unit [34]. The elastic boundary condition described in Section 3.2 was used as the boundary condition for the fine model of the local steel box girder. Shell–solid contact was adopted between the elastic cushion, tank rotation, and steel box girder.
The elastic cushion model of the walking jack with an initial size of 1 × 2 m and rubber cushion material was selected for sensitivity analysis to determine the optimal mesh size [35]. The results of sensitivity analysis are presented in Figure 6. It can be observed that the deformation value of the bottom plate of the steel box girder in contact with the central point of the cushion increased with the reduction in the mesh size of the steel box girder. Considering the calculation cost and measured value error, the mesh size of the steel box girder was selected as 200 mm, whereas the mesh size of the elastic cushion block of the walking jack was selected as 125 mm.
4. Parameter Analysis
A total of 23 FEMs with the elastic cushion material, size, tank wheel width, and launching stiffener spacing as parameters were analyzed to explore the influence law of the different parameters on the stress and local deformation of the steel box girder bottom plate. The von Mises stress and deformation results obtained from ABAQUS are depicted in Figure 7. It can be seen that a stress concentration area resembling the shape of the cushion block appeared on the bottom plate of the steel box girder, with the highest stress occurring at the short edges of the cushion block. This is attributed to the short side of the cushion block spanning the mediastinal plate unit, which has greater stiffness. In contrast, the maximum deformation of the bottom plate occurs at the long edges of the cushion block. This is because the long side of the pad is further away from the stiffener and the mediastinal plate unit, where the stiffness is lower.
The evaluation parameter λ of the deformation size was introduced, the expression of which is as follows:
(1)
Moreover, the evaluation parameter ρ of the deformation uniformity was introduced as follows:
(2)
The influence of the pushing equipment on the deformation degree of the steel box girder bottom plate was considered to be positive proportional to the deformation value, the main deformation area (the width of both the pad block and tank wheel), and the deformation uniformity. Therefore, the comprehensive evaluation parameter ε of the influence degree of the bottom plate deformation was introduced, which is expressed as follows:
(3)
where mi is the deformation value of the ith node in ABAQUS, n is the number of ABAQUS grid nodes, and a is the width of the elastic cushion or tank wheel in the transverse direction of the bridge.4.1. Influence of Elastic Cushion Material
This section presents the comprehensive analysis of the influence of the three elastic cushion material types of the walking jack on the stress and deformation of the steel box girder. Table 2 displays the maximum von Mises stress of each part of the steel box girder when the three elastic cushion types were used. It can be observed from Table 2 that the maximum von Mises stress of the contact area and stiffener element decreased continuously with the increase in the stiffness of the elastic cushion, and the maximum decreases reached 40.72% and 49.12%, respectively. However, the maximum von Mises stress of the mediastinal plate element increased continuously by 14.31%, compared to the elastic cushion with a smaller stiffness. The maximum stresses of all parts of the steel box girder were within the allowable range.
Figure 8a presents the deformation diagram of the contact area between the bottom plate of the steel box girder and the elastic cushion. It can be observed that the deformation along the transverse direction of the bridge was large on both sides and small in the middle. This is because the center of the elastic cushion was placed under the mediastinal plate of the steel box girder and the stiffness of the diaphragm plate was relatively high, so that the deformation value near this area was relatively low. According to Saint-Venant’s principle, as the stiffness of the bottom plate of the steel box girder far from the mediastinal plate area was low, it would produce large deformation. The deformation changed in a small wave shape along the longitudinal direction of the bridge because the existence of the launching stiffener enhanced the bottom plate stiffness in the nearby area, which caused a trough to appear in the deformation of the bottom plate. The area far from the launching stiffener had a lower stiffness, and a wave crest appeared.
According to Figure 8a, the relationship among the deformation values at the center of the transverse bridge was S > T > R. When moving from the center to both sides along the transverse bridge, the relationship among the deformation values gradually became R > T > S. There was a large gap between the deformation values of groups R, S, and T and a small gap between the deformation values of groups S and T. According to the evaluation parameters in Table 2 and Figure 8b, the maximum and minimum deformation values, evaluation parameter λ of the deformation size, evaluation parameter ρ of the deformation uniformity, and comprehensive evaluation parameter ε all exhibited the relationship of R > T > S. Among these, the evaluation parameter ε comprehensively considered the deformation size, degree of uniformity, and deformation area size. Furthermore, it could be used as the main parameter to evaluate the influence of the elastic cushion material on the bottom plate deformation. When the elastic cushion material was changed from rubber to PTFE, the ε value decreased by 72.5%. When the elastic cushion material was changed from PTFE to steel, the ε value decreased by 18.0%. Therefore, greater stiffness of the elastic cushion of the walking jack resulted in a smaller deformation degree of the steel box girder bottom plate. Moreover, the reduction in the stiffness of the elastic cushion could effectively alleviate the deformation degree of the steel box girder bottom plate.
4.2. Influence of Elastic Cushion Size
As the area directly contacting the steel box girder bottom plate, the influence of the cross-section size of the elastic cushion for the walking jack on the local stress and deformation of the steel box girder bottom plate cannot be ignored. Therefore, this section presents the analysis of the influence of the elastic cushion size. Moreover, the local stress and deformation law of the steel box girder bottom plate was investigated according to the size change in the cross-section length and width.
Table 2 displays the maximum von Mises stresses of various components of the steel box girder with different elastic cushion sizes. It can be observed that the maximum von Mises stresses of various components of the steel box girder were within the allowable range when the length and width of the elastic cushion changed. The difference between the maximum von Mises stress of the bottom plate contact area and the launching stiffener of the steel box girder was small, but the maximum von Mises stress of the mediastinal plate was much greater than that of the bottom plate contact area and push stiffener.
Figure 9a,b presents the deformation diagrams of the bottom plate contact area with different elastic cushion sizes. It can be observed that (1) when the cross-section width changed, the deformation values of the bottom plate contact area of the steel box girder at the same spatial position exhibited a significant difference, namely, W-0.7 > W-0.8 > W-0.9 > W-1.0 and W-1.1 > W-1.2 > W-1.3 > W-1.0, and (2) when the cross-section length changed, the deformation values of the bottom plate contact area of the steel box girder at the same spatial position roughly conformed to the size relationships of L-1.4 > L-1.6 > L-1.8 > L-2.0 and L-2.2 > L-2.4 > L-2.6 > L-2.0. However, in certain areas, the relationship between groups L-1.4 and L-1.6, groups L-2.2 and L-2.4, and groups L-2.6 and L-2.0 was the opposite to the above.
Table 2 displays the deformation evaluation parameters of the steel box girder bottom plate contact area with the changes in the elastic cushion size. In combination with Figure 10, it can be observed that the differences between the maximum and minimum values of the five evaluation parameters were 22.5%, 55.8%, 63.6%, 23.9%, and 15.8%, respectively, when the width changed and 13.5%, 17.6%, 33.8%, 13.8%, and 14.7%, respectively, when the length changed. The deformation of the bottom plate of the steel box girder was more sensitive to the change in the cross-section length than the change in the width. The minimum value of λ appeared when the width was 1 m and the length was 2 m. However, λ was only used as the evaluation parameter for the deformation of the contact area between the elastic cushion and bottom plate of the steel box girder, and the deformation area was not considered. After introducing the range and uniformity of the deformation area, the minimum value of ε appeared when the width was 0.7 m and the length was 1.8 m. Therefore, considering the deformation size, deformation uniformity, and deformation influence range, the elastic cushion with a cross-section size of 0.7 m × 1.8 m should be the optimal size.
4.3. Influence of Distance between Launching Stiffeners
The push stiffener is a steel plate that is welded onto both sides of the mediastinal plate in the original design, which can improve the stiffness of the base plate in the area nearby and the deformation-resistance ability of the base plate.
Three stiffener distances, namely 1.8 m, 0.9 m, and 0.45 m, were considered to study the influence of different stiffener spacings on the stress and deformation of the bottom plate. The size of the elastic cushion was 1 m × 2 m and the material was steel.
Table 3 displays the maximum von Mises stress of each component of the steel box girder with different distances of the push stiffeners. It can be observed that when the spacing of the push stiffeners was reduced from 1.8 m to 0.9 m, the peak stress of the components decreased by 22.90%, 7.56%, and 0.93%, respectively. When the spacing of the push stiffeners was reduced from 0.9 m to 0.45 m, the peak stress of the components decreased by 9.46%, 15.41%, and 21.11%, respectively. Thus, the stress level of each part of the steel box girder decreased with the increase in the number of stiffeners.
Figure 11a presents the deformation diagram of the bottom plate contact area with different spacings of the launching stiffeners. It can be observed from the diagram that the deformation when the spacing of the stiffeners was 0.45 m was obviously less than that when the spacing was 1.8 m and 0.9 m, but the difference between the deformation when the spacing was 1.8 m and 0.9 m was small, and the difference between the two was not obvious with the same spatial position.
According to Figure 11b, the evaluation parameters decreased with the decrease in the spacing of the launching stiffeners. When the distance between the launching stiffeners was reduced from 1.8 m to 0.9 m, the comprehensive evaluation parameter ε decreased by 8.0%, and when the distance between the launching stiffeners was reduced from 0.9 m to 0.45 m, the comprehensive evaluation parameter ε decreased by 86.1%. Therefore, smaller spacing of the launching stiffeners resulted in a smaller deformation degree of the bottom plate of the steel box girder. Thus, the deformation of the bottom plate of the steel box girder can be significantly alleviated by setting the spacing of the launching stiffeners to 0.45 m.
4.4. Influence of Tank Wheel Width
According to the calculation results in Section 2.2, the reaction force of the tank wheel support was substantially smaller than that of the elastic cushion of the walking jack; however, in the actual construction process, there were also traces of the tank wheel running at the bottom plate of the steel box girder. Thus, for the analysis in this section, the width of the tank wheel was used as the parameter so as to avoid excessive disturbance caused by the large track of the tank wheel.
Table 4 displays the maximum von Mises stress of each part of the steel box girder with different widths of the tank wheel. It can be observed that with the increase in the tank wheel width, the maximum von Mises stress of the contact area and stiffener element decreased continuously, whereas the maximum von Mises stress of the mediastinal plate element changed little, and it was substantially larger than those of the above two parts.
Figure 12a presents the deformation diagram of the steel box girder bottom plate contact area with different tank wheel widths. It can be observed that the relationship of the deformation of the steel box girder bottom plate contact area under the same spatial position was T-0.8 > T-0.9 > T-1.0. According to Figure 12b, all of the evaluation parameters decreased with the increase in the tank wheel width, and the comprehensive evaluation parameter ε decreased by 5.41% and 2.14%, respectively. Therefore, a greater width of the tank wheel resulted in a smaller deformation degree of the steel box girder bottom plate. Thus, the deformation of the steel box girder bottom plate can be alleviated when the tank wheel width is set to 1.0 m, and the disturbance to the subsequent walking push can be reduced.
5. Improved Measures and Monitoring Results of Launching
Based on the above research results, the following optimization adjustments have been made to the launching construction scheme for the subsequent launching construction of the beam section:
(1). The PTFE cushion above the walking jack is replaced by a steel cushion composed of multiple I-beams, and the rubber cushion between the original PTFE plate and steel box girder is removed, as illustrated in Figure 13a. The rubber layer wrapping the tank wheel is removed and the steel tank wheel makes direct contact with the bottom plate of the steel box girder, as shown in Figure 13b.
(2). The original elastic cushion size of 1 m × 2 m is optimized to 0.7 m × 1.8 m.
(3). When the steel box girder is assembled, the launching stiffener is welded to double the stiffener spacing from 0.9 m to 0.45 m, as illustrated in Figure 13c.
(4). The original tank wheel with a width of 0.8 m is replaced by one with a width of 1.0 m, as shown in Figure 13d.
After implementing the above improvement measures, a good construction effect was achieved. The equivalent stress of each part of the steel box girder was less than the allowable stress, and the deformation of the contact area decreased significantly.
The entire process of the incremental launching construction of Qilu Yellow River Bridge was monitored. The stress of the main part of the girder and deformation of the bottom plate contact area were measured.
A total of 120 strain gauges and a further 100 gauges were used to measure the stress of the beam. During the launching process of the box girder, the strain was measured and then converted into stress, and the results were compared with the FE results. The results demonstrate that the stress of each part of the steel box girder was less than the allowable stress.
The deformation value of the box girder bottom plate contact area was measured at the top of the temporary pier using the field measurement method with a level ruler and feeler gauge. As deformation measurements could be carried out between the two temporary piers, the deformation value of the box girder bottom plate of the entire line was observed by combining the measured and predicted values. The GM (1, 1) prediction model of Gray’s theory was used to predict the deformation value [36,37], and the predicted deformation value was compared with the data of the FE model before and after optimization.
Figure 14 depicts the deformation value of the middle line in the contact area of the bottom plate of the standard section steel box girder at the top of temporary pier LD10. It can be observed that the measured value of the deformation within 2.7 m of the top of the temporary pier was in good agreement with the predicted value of the GM (1, 1) prediction model. The predicted value of the standard segment bottom plate deformation was basically consistent with the optimized FEM data. Moreover, the predicted and measured values were slightly lower than the FE value. Compared to the FE deformation value before optimization, the optimized predicted deformation value decreased by 48.32% on average. The analysis and optimization method described in this study substantially reduced the deformation degree of the bottom plate, and the optimization goal of the local deformation of the steel box girder was successfully achieved.
6. Conclusions
In this study, an improved incremental launching construction scheme for steel box girders is proposed, effectively addressing the issue of significant elastic–plastic deformation in stress concentration areas under local deformation. The following conclusions were drawn from this study.
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(1). The choice of elastic cushion material and size significantly impacts the deformation of the steel box girder bottom plate during incremental launching. Specifically, a stiffer cushion material and larger cushion size lead to reduced deformation.
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(2). The spacing of launching stiffeners and the width of the tank wheel play crucial roles in minimizing bottom plate deformation. Decreasing the spacing of launching stiffeners and increasing the width of the tank wheel effectively reduces deformation.
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(3). Implementing optimized measures such as replacing the cushion material with steel, selecting specific cushion sizes, adjusting pushing stiffener spacing, and setting the tank wheel width resulted in a notable 48.32% reduction in average bottom plate deformation, as evidenced by monitoring data during the launching process.
Conceptualization, L.Z.; investigation, R.X.; supervision, Y.W.; writing—review and editing; formal analysis, C.T.; supervision, K.Q. All authors have read and agreed to the published version of the manuscript.
The original contributions presented in the study are included in the article material. Further inquiries can be directed to the corresponding authors.
Author Lin Zhao was employed by Shandong Expressway Construction Management Group Co. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflicts of interest.
Footnotes
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Enlarge this image.Figure 4. Elastic boundary conditions of the (a) support reaction, (b) shear force and bending moment, and (c) displacement.
Enlarge this image.Figure 7. FE operation results of the (a) stress nephogram, (b) deformation nephogram.
Enlarge this image.Figure 9. Three-dimensional deformation of bottom plate about the (a) width of the elastic cushion, (b) length of the elastic cushion.
Enlarge this image.Figure 10. Evaluation parameters about the (a) width of the elastic cushion, (b) length of the elastic cushion.
Enlarge this image.Figure 13. (a) Elastic cushion of material replaced. (b) Rubber layer removed from outside of tank wheel. (c) Spacing of stiffeners reduced. (d) Spacing of stiffeners reduced.
Elastic boundary conditions.
| Elastic Boundary | Shear Force (kN) | Bending Moment (kN·m) | Front End Displacement (mm) | Rear End Displacement (mm) | Support Reaction (kN) |
|---|---|---|---|---|---|
| Section24 | 10,336.69 | −165,023.5 | −0.22032 | −0.00234 | 11,698.25 |
| Section 39 | 3106.156 | 5346.362 | 0.0109 | 0.0109 | 3083.65 |
FE results of different cushion block materials and sizes.
| No. | Model Type Notation | * YE (MPa) | Stiffener Spacing (m) | Size (m) | Maximum | Evaluation Parameters | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| * C | * S | * M | λ | ρ | ε | Max | Min | |||||
| 1 | R | 500 | 0.9 | 1 × 2 | 232.06 | 288.93 | 272.92 | 11.40 | 2.941 | 67.03 | 16.21 | 6.53 |
| 2 | T | 1420 | 0.9 | 1 × 2 | 147.76 | 180.69 | 285.85 | 8.70 | 1.057 | 18.44 | 10.16 | 6.49 |
| 3 | S | 2060 | 0.9 | 1 × 2 | 137.56 | 147.02 | 318.51 | 8.43 | 0.901 | 15.12 | 9.47 | 6.48 |
| 4 | W-0.7 | 2060 | 0.9 | 0.7 × 2 | 157.50 | 164.75 | 295.12 | 9.74 | 0.927 | 6.33 | 10.99 | 7.60 |
| 5 | W-0.8 | 2060 | 0.9 | 0.8 × 2 | 155.43 | 169.73 | 299.24 | 9.67 | 0.976 | 7.55 | 10.96 | 7.48 |
| 6 | W-0.9 | 2060 | 0.9 | 0.9 × 2 | 149.93 | 167.41 | 294.46 | 9.45 | 0.952 | 8.10 | 10.67 | 7.34 |
| 7 | W-1.0 | 2060 | 0.9 | 1 × 2 | 137.56 | 147.02 | 318.51 | 8.43 | 0.901 | 15.12 | 9.47 | 6.48 |
| 8 | W-1.1 | 2060 | 0.9 | 1.1 × 2 | 182.61 | 169.65 | 267.72 | 9.36 | 0.870 | 8.96 | 10.18 | 7.29 |
| 9 | W-1.2 | 2060 | 0.9 | 1.2 × 2 | 178.19 | 165.44 | 260.93 | 9.17 | 0.829 | 9.13 | 10.00 | 7.22 |
| 10 | W-1.3 | 2060 | 0.9 | 1.3 × 2 | 168.58 | 163.66 | 259.16 | 9.14 | 0.804 | 9.56 | 9.98 | 7.24 |
| 11 | L-1.4 | 2060 | 0.9 | 1 × 1.4 | 127.53 | 131.07 | 289.79 | 10.71 | 1.425 | 15.26 | 12.18 | 7.70 |
| 12 | L-1.6 | 2060 | 0.9 | 1 × 1.6 | 108.61 | 189.04 | 319.08 | 10.13 | 1.208 | 12.24 | 11.48 | 7.51 |
| 13 | L-1.8 | 2060 | 0.9 | 1 × 1.8 | 105.32 | 150.21 | 258.23 | 8.81 | 0.630 | 5.55 | 9.52 | 7.44 |
| 14 | L-2.0 | 2060 | 0.9 | 1 × 2 | 137.56 | 147.02 | 318.51 | 8.43 | 0.901 | 15.12 | 9.47 | 6.48 |
| 15 | L-2.2 | 2060 | 0.9 | 1 × 2.2 | 139.00 | 161.50 | 318.75 | 9.20 | 1.034 | 9.51 | 10.35 | 7.13 |
| 16 | L-2.4 | 2060 | 0.9 | 1 × 2.4 | 128.95 | 159.31 | 289.75 | 8.88 | 1.006 | 8.93 | 10.06 | 6.99 |
| 17 | L-2.6 | 2060 | 0.9 | 1 × 2.6 | 126.07 | 166.84 | 317.96 | 8.30 | 0.777 | 6.45 | 9.27 | 6.82 |
Note: * YE: Elastic modulus; * C: Contact area; * S: Launching stiffener; * M: Mediastinal plate.
FE results of different launching stiffener distances.
| No. | Model Type Notation | * YE (MPa) | Stiffener Distance (m) | Size (m) | Maximum Equivalent Stress (MPa) | Evaluation Parameters | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| * C | * S | * M | λ | ρ | ε | Max | Min | |||||
| 1 | S-0.45 | 2060 | 0.45 | 1 × 2 | 124.54 | 124.36 | 251.26 | 5.09 | 0.799 | 1.06 | 6.02 | 3.37 |
| 2 | S-0.9 | 2060 | 0.9 | 1 × 2 | 137.56 | 147.02 | 318.51 | 8.43 | 0.901 | 7.60 | 9.47 | 6.48 |
| 3 | S-1.8 | 2060 | 1.8 | 1 × 2 | 178.41 | 159.05 | 321.50 | 8.47 | 0.975 | 8.26 | 9.69 | 6.44 |
Note: * YE: Elastic modulus; * C: Contact area; * S: Launching stiffener; * M: Mediastinal plate.
FE results of different tank wheel widths.
| No. | Model Type Notation | * YE (MPa) | Stiffener Spacing (m) | Width of Tank Wheel (m) | Maximum | Evaluation Parameters | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| * C | * S | * M | λ | ρ | ε | Max | Min | |||||
| 1 | T-0.8 | 2060 | 0.9 | 0.8 | 100.08 | 61.85 | 151.92 | 1.75 | 0.106 | 0.148 | 1.89 | 1.54 |
| 2 | T-0.9 | 2060 | 0.9 | 0.9 | 93.66 | 54.46 | 152.00 | 1.72 | 0.088 | 0.140 | 1.84 | 1.53 |
| 3 | T-1.0 | 2060 | 0.9 | 1.0 | 89.23 | 53.83 | 151.99 | 1.71 | 0.082 | 0.137 | 1.83 | 1.52 |
Note: * YE: Elastic modulus; * C: Contact area; * S: Launching stiffener; * M: Mediastinal plate.
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