Virtual pre-assembly method for bridge tower crossbeam lifting based on temperature effect analysis and 3D laser scanning technology

Abstract

By transferring on-site construction operations to a controlled factory environment, prefabricated construction technology has significantly reduced the adverse interference of factors such as transportation and weather conditions on the construction process. However, factors including fabrication and assembly inaccuracies, along with the deformation of components, have the potential to reduce the precision of prefabricated assembly. To address these challenges, this study proposes a virtual pre-assembly method for bridge tower crossbeam lifting, integrating temperature effect analysis with 3D laser scanning technology. The method begins with a theoretical investigation into the deformation behavior of bridge towers and crossbeams under different temperature gradient patterns. Radiative heat transfer theory is then employed to compute the thermal profile of a bridge tower, which is introduced into a finite element model to analyze and validate the time-dependent displacement characteristics of the structure. High-precision point cloud data of crossbeam connection interfaces are acquired via 3D laser scanning. These data are aligned using point cloud registration techniques to achieve accurate spatial integration of the crossbeam and bridge tower. By incorporating the time-varying displacement data obtained from thermal analysis, the spatial positions of key control points in the point cloud are adjusted to simulate deformations encountered during actual construction. This virtual pre-assembly approach provides a visual and quantitative assessment of alignment tolerances with daily periods, enabling more accurate monitoring and control of the crossbeam lifting process.

Keywords

virtual pre-assembly temperature analysis thermal deformation 3D laser scanning crossbeam lifting

Introduction

Prefabricated structures offer several significant advantages over traditional cast-in-place structures. Prefabricated construction transfers most of the site work involved in cast-in-place construction to factories, with only the lifting and connection processes carried out on-site. This effectively reduces the impact of weather conditions such as rain, snow, and wind on construction and improves the working environment for laborers. Additionally, the components are standardized and produced in factories, which can significantly reduce the generation of construction waste, minimize noise and dust pollution to the surrounding environment, and contribute to a more sustainable and eco-friendly approach. However, the implementation of prefabricated construction also poses challenges in practical applications, such as discrepancies between the actual dimensions of components and the design specifications, installation dimensional deviations caused by construction, and size changes or component deformation due to factors like temperature. These issues can influence the construction precision of prefabricated structures. Therefore, resolving the problems that arise during the lifting and installation of prefabricated structures is crucial to promoting the widespread use of this construction approach.

Scholars both domestically and internationally have conducted extensive research on the construction of prefabricated structures. Wang et al. (2022) proposed a fault-tolerant interval inversion framework to address the tolerance of deviations in prefabricated construction, which greatly enhanced the constructability of the assembly process, reduced on-site time, and minimized delays. Hu et al. (2024a) established a 3D heat transfer model to precisely calculate the temperature field during the construction phase of CFST truss arch bridges, providing a detailed analysis of the deformation changes and offering a reference for accurate closure during construction. Nguyen et al. (2024) developed a BIM-based prefabricated bridge DfMA (design for manufacturing and assembly) pre-assembly analysis system to address issues related to manufacturing errors and assembly deviations in prefabricated structures. This system enhances information exchange, identifies, and reduces assembly errors. Solving the manufacturing errors and installation deviations caused by various factors will contribute to the wider adoption of prefabricated structures (Liu et al., 2024; Chen et al., 2025; Daly et al., 2025).

With the development of bridge structural health monitoring technology, a large amount of on-site monitoring data has made it feasible to study the temperature effects on bridges (Xia et al., 2020; Anastasopoulos and Reynders, 2023; He et al., 2023; Chen et al., 2024; Hu et al., 2024a; Hu et al., 2024b; Jing et al., 2024; Li et al., 2023a; Zhang et al., 2023). Xia et al. (2022) arranged temperature sensors on bridges and used on-site monitoring data to calculate the temperature variations and responses, with the developed method enabling automated and effective analysis of the thermal behavior of bridges. Yang et al. (2024) examined the correlation between structural temperature and bridge support displacement using on-site monitoring data, which helps improve the understanding of the operational patterns of steel truss continuous girder bridges. Zhang et al. (2024) proposed an effective method for calculating temperature and temperature differences based on structural health monitoring data and conducted a detailed analysis of road-rail steel truss cable-stayed bridges. Xu and Liu (2025) developed a temperature-induced strain prediction framework based on deep kernel regression, significantly enhancing the performance and practicality of health monitoring systems for long-span bridges. Due to the tendency of bridge main girder to generate uneven temperature fields and noticeable local thermal effects, which may lead to excessive thermal stresses and structural damage. Research based on temperature monitoring data has provided valuable insights for bridge construction monitoring and subsequent operation and maintenance.

The temperature effects on the crossbeam lifting process are mainly reflected in the following aspects. First, temperature changes can cause deformations of the bridge tower and crossbeam, leading to changes in the gap size during crossbeam lifting. Second, the temperature gradient effect can induce bending and torsion of the bridge tower and crossbeam, further altering the spatial positions of key lifting control points and increasing the difficulty of the crossbeam lifting process. Therefore, it is essential to fully consider the influence of temperature effects to ensure assembly accuracy and safety during crossbeam lifting construction.

High-precision and efficient 3D laser scanning technology can effectively monitor bridge construction (Serwa and Saleh, 2021; Li et al., 2023; Xu et al., 2024; Wang et al., 2025). By real-time acquisition of high-precision point cloud data from the bridge surface, the component dimensions and spatial positions during the construction process can be obtained. Combined with displacement prediction values derived from temperature effects, this will effectively guide the crossbeam lifting construction. Yoon et al. (2018) used a 3D laser scanner to capture scanning data of deck panels and precast beams, extracting the positions and dimensions of prefabricated components to determine the optimal placement of deck panels relative to the main beams. Xu et al. (2022) studied the use of laser scanning for monitoring the orientation of concrete bridge piers and provided guidance for the installation of precast concrete piers, showing the potential of laser scanning technology to improve installation efficiency and accuracy. Wang et al. (2024) proposed an automatic cable shape measurement method for large-span suspension bridges, addressing the time-consuming and labor-intensive challenges of using total stations for cable measurements. This method enables rapid spatial positioning and geometric information retrieval of cable clamps. Therefore, employing 3D laser scanning technology to acquire high-precision 3D point cloud data of beam surfaces and bridge tower facades during the construction phase offers essential data support for temperature deformation monitoring and beam lifting tasks.

Based on the above background, this study proposes a virtual pre-assembly method for crossbeam lifting construction that combines temperature effect analysis with measured point cloud data. The method predicts the time-varying displacement of the bridge tower and crossbeam on the day of construction through theoretical derivation and finite element analysis. It then utilizes 3D laser scanning technology to obtain measured point cloud data and combines it with temperature effect analysis to predict deformations, ultimately guiding the precise beam lifting operation. This study elaborates on the implementation process of this method and verifies its effectiveness and feasibility through practical application. The method not only effectively solves the issue of construction delays caused by continuous temperature change observations but also eliminates assembly and fabrication errors, significantly improving the accuracy and efficiency of crossbeam lifting construction.

Methodology

Under temperature effects, the bridge tower experiences cyclic thermal deformation, while temperature differences also cause dimensional changes in the crossbeam. This results in gaps or misalignments at the crossbeam–tower interface, making lifting operations difficult and requiring repeated adjustments. To address this problem, a virtual pre-assembly method for the bridge tower and crossbeam is proposed, which predicts temperature displacement with temporal changing to correct the spatial coordinates of the control points in the point cloud model. The deformation behavior of the bridge tower and crossbeam is first analyzed theoretically. Then, structural temperatures are calculated and used as input thermal loads in a finite element model to obtain time-varying displacement predictions for the construction day. By leveraging high-precision measured point cloud data and integrating it with deformation predictions derived from temperature analysis, precise guidance is furnished for the girder lifting and assembly procedure. The proposed method is illustrated in Figure 1.

Figure 1.

Methodological framework.

Analysis method of temperature effect during installation of prefabricated bridge tower and crossbeam

Bridge profile and the lifting of the crossbeam

The cable-stayed Bridge adopts a high and low tower double cable-stayed surface with the total length 535.4 m. The bridge tower is a frame-type tower composed of two hollow columns and two crossbeams. Taking the low tower as an example, the height of the low tower is 92 m, the lower crossbeam is cast-in-situ prestressed concrete structure, and the upper crossbeam is prefabricated steel structure. The size of the upper crossbeam is 24 m (length) ×7.492 m (width) ×2.236 m (height) and its weight is 168.1 t, the upper crossbeam is lifted and installed by a 610 t floating crane (Figure 2).

Figure 2.

Schematic of the bridge (unite: cm) (a) dimensional drawing of bridge (b) bridge tower.

The lifting construction of the upper crossbeam of the low tower is scheduled for July, and the highest temperature on site reaches 37°C. Under the influence of sunshine temperature around the bridge tower for one day, there is a large temperature difference between the inner and outer surfaces, and inducing temperature deformation. The steel beam is prefabricated in the factory and the segment size has been determined. The surface temperature of steel beam may exceed 50°C during lifting construction. Affected by temperature, both the crossbeam and the bridge tower will have large temperature deformation (Zhou et al., 2020), which will lead to the changes of the coordinates of control points between the crossbeam and the two towers. Due to the influence of temperature, there is a deviation between the size of the beam and the reserved position between the two towers, which leads to the need to quickly cut or weld the steel beam in the floating state, which greatly increases the difficulty and time of operation. Thermal-induced deformations in both the crossbeam and bridge tower cause substantial displacement of control points between these structural elements. These temperature-driven dimensional variations create misalignment between the crossbeam dimensions and the predetermined clearance between the tower columns. Consequently, construction teams must perform on-site steel crossbeam modification—either cutting or welding, substantially increasing both the operational difficulty and construction time (Figure 3).

Figure 3.

Case of crossbeam lifting.

The key problem is how to accurately predict the coupling deformation law of bridge tower and crossbeam. If the displacement of the bridge tower and the crossbeam in all directions caused by the temperature can be quickly calculated according to the real-time environmental temperature on site before the steel crossbeam lifting construction, the reserved space between the splicing joints of the steel crossbeam can be predicted, so as to guide the steel crossbeam to complete cutting and welding on the ground before lifting, reduce the floating crane operation time, ensure the smooth construction and restore the navigation channel.

Theoretical analysis on bridge tower and crossbeam

Under the influence of solar radiation, environmental temperature and other factors, the temperature distribution of structural sections can be classified into uniform temperature, linear temperature and nonlinear temperature (Xia et al., 2018). For slender and flexible super-tall structures, the tower column can be regarded as a cantilever beam. The following analyzes the temperature deformation modes of bridge tower structures using three types of temperature models.

①The cantilever beam model with the change of uniform temperature distribution ( ${∆ T}_{U}$ ), as shown in Figure 4. It has a height of $H$ , and it expands $δ_{U}$ under the change of uniform temperature load.

δ_{U} = α {∆ T}_{U} H

(1)

where

δ_{U}

is tower expansion under uniform temperature distribution

{∆ T}_{U}

and

α

is coefficient of thermal expansion.

②The cantilever beam model is subjected to a linear temperature gradient ( $T_{L}$ ), which linear change along the cross-section as shown in Figure 4. The unrestrained rotation is caused by deformation when there are no rotational restraints at cantilever beam ends. The liner temperature gradient completely generates the bending deformation,

λ_{T_{L}} = H θ_{T}

(2)

where

θ_{T} = \frac{α (T_{1} - T_{2}) H}{h}

is the rotation at the beam ends;

h

is height of cross-section;

T_{1}

T_{2}

are the temperature of the top and bottom surface, respectively.

③The cantilever beam model with the change of uniform temperature distribution ( $T_{y}$ ). Structural deformation not only occurs but also generates temperature-induced self-stress as shown in Figure 4. The axial deformation and bending deformation that will be generated in the structure are respectively expressed as,

δ_{T_{y}} = ε_{T_{y}}^{N} H

(3)

λ_{T_{y}} = \frac{M_{T_{y}} H^{2}}{2 E I}

(4)

where

N_{T_{y}}

and

M_{T_{y}}

is the equivalent of axial force and bending moment on the cross-section;

ε_{T_{y}}^{N} = \frac{N_{T}}{E A}

and

ε_{T_{y}}^{M} = \frac{M_{T_{y}} \cdot y_{0}}{E I}

is the axial and bending deformation;

y_{0}

is the distance to the neutral axis;

E A

and

E I

is axial stiffness and bending stiffness.

Figure 4.

Temperature induced deformation of bridge tower and crossbeam.

Based on a comprehensive analysis of structural deformation patterns using three thermal models, the spatial variation in the sun’s position induces non-uniform temperature changes across all directions of the bridge tower structure. This thermal gradient leads to complex spatial deformation of the bridge tower, where both axial and bending deformations can be expressed as the superposition of deformations in different directions.

δ_{T o w e r} = δ_{U} + δ_{T_{y}}

(5)

λ_{T o w e r} = λ_{T_{L}} + λ_{T_{y}}

(6)

During construction, the temperature on the upper surface of the crossbeam can reach as high as 50°C. Such a significant temperature difference is lead to complex structural deformations inevitably. Considering that the beam ends are free and unconstrained during the lifting process of the steel crossbeam, a simply supported beam model is adopted for thermal analysis. Due to the relatively short length of the crossbeam, the bending deformation caused by the non-linear temperature gradient is minimal and can be neglected here. The axial deformation at one end of the crossbeam is expressed as:

δ_{B e a m} = \frac{L}{2} (α Δ T_{U} + ε_{T_{y}}^{N})

(7)

Comprehensive analysis of temperature effects

By considering the temperature induced deformation of the bridge tower and crossbeam, the construction procedure for lifting the tower and crossbeam can be simplified as illustrated in Figure 4.

Analysis of the temperature effects

Heat transfer analysis on bridge tower and crossbeam

The heat transfer process of the bridge tower is shown in Figure 5. Based on the information in Table 1, the solar altitude angles at all times during the day can be calculated by MATLAB, and the solar trajectory at different times on the day of beam lifting construction can be simulated by combining the latitude, longitude and azimuth of the bridge tower (Zhou et al., 2024), as shown in Figure 6(d). The orientation diagram of the low tower is shown in Figure 6(c). The x and y directions in the figure are consistent with the coordinate axes in the sunlight radiation model and the coordinate axes in the subsequent ANSYS finite element model (Figure 6(a)). The Z-axis is located between the east and west towers of the low tower, perpendicular to the XOY plane and pointing to the top of the low tower. According to the direction of the bridge and the design of the bridge tower, there is an included angle of about 8.25° between the positive direction of the X axis and the due south direction in the coordinate system. The geographical parameters and physical parameters of the bridge tower are shown in Table 1 and Table 2, respectively.

Figure 5.

The heat transfer processes occur on the boundary surfaces.

Table 1.

Geographical parameters of cable-stayed bridge.

Geographical parameters	Symbol	Numerical value
Longitude	JD	119.76
Latitude	$\emptyset$	29.87
Azimuth		8.25°
Fate	D	187 (July 6th)
Atmospheric transparency coefficient	P	0.8
Solar constant	$I_{0}$	1362 W/m2
Noon sun height angle	Hmax	82.83°

Figure 6.

FEM and simulation on virtual solar (a) FEM of the bridge tower (b) FEM of the crossbeam (c) virtual solar trajectory (d) virtual sun space location.

Table 2.

Physical parameters of thermal analysis materials for tower of cable-stayed bridge.

Parameter	Steel Q370qD	Concrete C55
$k$ coefficient of heat conduction (W/(m·°C))	58.2	1.28
$ρ$ density (kg/m³)	7850	2600
$E$ modulus of elasticity (kPa)	2.1 × 10⁸	3.6 × 10⁷
Poisson’s ratio	0.3	0.2
$C$ specific heat capacity (J/kg·°C)	480	970
Coefficient of linear expansion (1/°C )	1.2 × 10^-5	1.0 × 10^-5
Absorptivity	0.3	0.65

Establishment of finite element model of bridge tower and crossbeam

A 3D finite element model (FEM) was developed using the commercial FE analysis software ANSYS 16.0. The bridge tower model (including 49,352 nodes and 37,012 elements) was extracted separately for analysis as shown in Figure 6(a). In the heat-transfer analysis, SOLID 70 three-dimensional solid thermal element is adopted for the bridge tower. The element has eight nodes, each node has a degree of freedom of temperature, and can be used for three-dimensional steady-state or transient thermal analysis problems. In the subsequent structural field analysis, this element can be replaced by an equivalent structural element SOLID 45. The temperature distribution of the bridge will be calculated and verified using the monitoring temperature data. In the structural analysis, the configuration and mesh of the FEM remain unchanged, and the 3D thermal elements change to 3D mechanics elements. The calculated temperature in the previous step will be assigned to the FEM automatically, and the temperature-induced responses such as displacement will be obtained. Taking the lifting day as an example, the sun’s path is shown in Figure 6(d). The typical solar radiation and ambient air temperature on that day are illustrated in Figure 7.

Figure 7.

Solar radiation and air temperature (a) solar radiation intensity (b) ambient temperature.

Calculation of equivalent temperature

The equivalent temperature accounts for both solar radiation and ambient air temperature. The calculation equation is as follows:

T^{*} = T_{a} + \frac{α I}{h}

(8)

T^{*}

represents the combined temperature;

T_{a}

is the ambient temperature;

h

is the overall heat transfer coefficient at the structure’s surface;

α

is the solar radiation absorption coefficient, and

α_{s t e e l}

is 0.82 for steel,

α_{c o n}

is 0.65 for concrete; and

I

is the solar radiation intensity.

After calculating the overall heat transfer coefficient, ambient air temperature, solar radiation intensity, and the angle factor for each surface at different times, the equivalent temperature of each surface of the bridge tower and crossbeam can be obtained. These equivalent temperatures are then applied as thermal loads in the ANSYS model to simulate the temperature field. The variation curves of equivalent temperature for the surfaces of the bridge tower and crossbeam are shown in Figure 8.

Figure 8.

Equivalent temperature (a) equivalent temperature of bridge tower (b) equivalent temperature of the crossbeam.

Calculation of thermal deformation

After the temperature field is calculated, it can be used in the structural analysis to calculate temperature-induced displacements of the bridge tower and crossbeam.

The displacement changes of the tower control points are shown in Figure 9(a). (1) Starting from 6:00 a.m., when the towers are first exposed to sunlight, deformation begins to appear in the Y-direction, with both tower columns deformed to the westward. As the sun rises and solar radiation increases, the displacement is constantly increasing. By 11:00 a.m., the Y-direction displacement reaches its peak, about 6 mm. (2) After 12:00 p.m., the sun begins to shine directly on the west side of the towers. As the west side becomes hotter than the east side, the westward displacement gradually decreases. By around 4:00 p.m., the Y-direction displacement nearly returns to its initial state. (3) At this time, the sun is still above the horizon and continues to shine on the west side. The towers start to eastward deflection. At 6:00 p.m., when the sun sets, the eastward displacement reaches about 5 mm. (4) From the Y-direction displacement of the tower, it can be seen that when the tower shifts westward, the displacement of the east column is greater than that of the west column at the same height. When the towers shift eastward, the displacement of the west tower is greater than that of the east tower. This is because the two tower are built with a slight inward tilt. When exposed to sunlight from the east, the east side of the east tower receives sunlight at a smaller angle of incidence compared to the east side of the west tower. As a result, the angle factor is larger, and the temperature effect is more significant. Similarly, under sunlight from the west, the west side of the west tower experiences a signification temperature effect than the west side of the east tower. As shown in Figure 9(b), the three-direction displacement of the control points over a ten-day construction period indicates a general upward trend in ambient temperature. Therefore, the displacement of the control points on the bridge tower shows a spiral rising pattern over time.

Figure 9.

Temperature deformation patterns of the bridge tower and beam (a) tower control point displacement variation (b) three-dimensional displacement variation of the tower control point over 10 days (c) crossbeam elongation results.

The temperature-induced displacement at the crossbeam ends is shown in Figure 9(c). After continuous solar radiation, the crossbeam shows noticeable thermal deformation, which increases with rising temperature. Among all directions, the deformation along the longitudinal axis of the crossbeam (Y-direction) is the most significant, indicating thermal expansion. At 14:00 in the afternoon, the maximum displacement occurs at the top surface of the crossbeam end, reaching 3.64 mm.

Due to solar exposure, a nonlinear temperature gradient between the top and bottom plates of the crossbeam, causing vertical bending. The top plate expands more than the bottom plate, resulting in the crossbeam’s end face no longer being perfectly vertical but forming a slight angle. This angular misalignment is a critical factor that must be carefully considered during crossbeam lifting and installation.

Virtual pre-assembly of the crossbeam considering temperature effects

Point cloud data acquisition

During the crossbeam lifting process of bridge, both the tower column and the steel crossbeam deform due to temperature effects. This deformation requires adjustments to the crossbeam during installation, which greatly increases construction difficulty. To reduce the time, labor, and material costs of crossbeam lifting, 3D laser scanning technology was applied in the virtual pre-assembly study of the crossbeam installation.

The point cloud data was collected using a Riegl VZ-400i 3D laser scanner, which has a maximum range of 800 m and a repeatability accuracy of 3 mm. The laser emission frequency is 1200 kHz. The scanner was placed on side span of the bridge tower, as shown in Figure 10.

Figure 10.

Schematic diagram of scanner station layout.

Point cloud data processing

Point cloud data processing is a key step in the pre-assembly process. After collecting the raw point cloud data, initial cleaning is performed using the RiSCAN Pro software. This includes cropping, denoising, and thinning to remove irrelevant information and noise, improving the quality of the point cloud. A coarse registration is first done using point cloud features, followed by fine registration using the ICP (Iterative Closest Point) algorithm to obtain an accurate point cloud model.

The method for extracting key points from the point cloud is explained using the crossbeam to be lifted as an example. The point cloud of contains 3D coordinate information. A principal component analysis (PCA) algorithm is used to reduce the dimensions of the preprocessed point cloud data, and the projection distance is minimized by optimizing the objective function $\sum_{i = 1}^{m} {‖ {\hat{x}}^{(i)} - x^{(i)} ‖}_{2}^{2}$ .

The principal component can be written as follows, where $X_{1}, X_{2}, \dots, X_{p}$ are the original variables, and $u_{1}, u_{2}, \dots, u_{p}$ are the corresponding weights.

t_{p} = u_{1 p} X_{1} + u_{2 p} X_{2} + \dots + u_{p p} X_{p}

(9)

\sum_{i = 1}^{m} {‖ {\hat{x}}^{(i)} - x^{(i)} ‖}_{2}^{2} = - tr (W^{T} X X^{T} W) + \sum_{i = 1}^{m} {(x^{(i)})}^{T} x^{(i)}

(10)

Since the thickness of the steel crossbeam is much smaller than its length, the main component lies along the longitudinal plane. Therefore, the secondary principal component $t_{2}$ is used to extract the crossbeam’s cross-section.

For boundary detection and key point extraction, the Canny edge detection algorithm is applied to identify the outline of the bridge structure. The edge strength $G$ and orientation $θ$ can be computed using the following formulas:

G = \sqrt{G_{x}^{2} + G_{y}^{2}}

(11)

θ = \arctan (\frac{G_{y}}{G_{x}})

(12)

where

G_{x}

and

G_{y}

represent the gradients of the point cloud in the x and y directions, respectively.

Then, the Hough transform algorithm is used to detect straight lines from the edge points. For each point $(x_{i}, y_{i})$ in the point cloud, its perpendicular distance $d$ to the line $y = m x + c$ is given by:

d = \frac{| m x_{i} - y_{i} + c |}{\sqrt{m^{2} + 1}}

(13)

The intersection points of these lines are identified as the control points, as shown in Figure 11(d). Once the control points are identified, their spatial coordinates can be used for the subsequent calculation of the cutting quantity.

Figure 11.

Edge detection algorithm and control point extraction for point cloud data (a) point cloud data of the crossbeam (b) point cloud data after dimensionality reduction (c) edge detection (d) line detection based on Hough transform (e) extraction of control points.

Simulation of crossbeam assembly based on temperature-dependent displacement predictions

This study proposes a virtual pre-assembly method for crossbeam lifting that combines temperature effect analysis with 3D laser scanning technology. The goal is to improve assembly accuracy and construction control. The workflow is shown in Figure 12. First, the deformation mechanisms of the bridge tower and crossbeam are analyzed based on temperature theory. Then, a FEM is used to calculate the displacement changes of key control points. Through point cloud processing, the corresponding control points on the tower and crossbeam are extracted. The calculated temperature-induced displacements are then used to quantify the time-varying spatial positions of these control points on the day of construction.

Figure 12.

Virtual pre-assembly technology process flow diagram.

The crossbeam has a total length of 24 m. When considering deformation caused by temperature effects and changes in the spacing between bridge towers, adjustments are required based on the relationship between crossbeam length and tower spacing. If the total crossbeam length exceeds the tower spacing, cutting of the crossbeam at control points is necessary. Conversely, if the crossbeam length is shorter than the spacing, additional segments must be welded to compensate.

After the crossbeam is lifted and adjusted into position, one side is welded, while the other side is trimmed to compensate for length deviations caused by temperature effects before final welding as shown in Figure 13(a) and (b).

Figure 13.

Schematic diagram of crossbeam cutting quantity at different lifting times (a) the crossbeam is lifted and welded to one side for fixation (b) cutting and weldding another side of crossbeam (c) cutting quantity at the upper control point (d) cutting quantity at the lower control point.

Therefore, the cutting quantity for the four control points of the crossbeam needs to be predicted. Based on the previously analyzed temperature effects, the gap distance between bridge towers can be calculated using the coordinates of control points and equation (14). $(x_{m}, y_{m}, z_{m})$ and $(x_{n}, y_{n}, z_{n})$ represent the coordinates of the corresponding control points, while $(∆ x, ∆ y, ∆ z)$ denote the coordinate changes caused by temperature variation.

d_{gap} = \sqrt{{(x_{m} + Δ x_{m} - x_{n} - Δ x_{n})}^{2} + {(y_{m} + Δ y_{m} - y_{n} - Δ y_{n})}^{2} + {(z_{m} + Δ z_{m} - z_{n} - Δ z_{n})}^{2}}

(14)

The actual length of the crossbeam needs to account for axial elongation caused by temperature effects, where $l_{0}$ is the original length of the crossbeam, and $∆ l$ is the elongation due to temperature variation.

l_{c r o s s b e a m} = l_{0} + ∆ l

(15)

The calculation of the cutting quantity for the control points is given as follows,

d_{c u t t i n g} = l_{c r o s s b e a m} {- d}_{g a p}

(16)

However, due to the temperature gradient caused by sunlight on the top plate of the crossbeam, the crossbeam experiences vertical bending, with the elongation of the top plate being greater than that of the bottom plate. Since the cutting quantities for the two control points on the same side (either upper or lower) are nearly identical, this study primarily focuses on predicting the cutting quantity for the two control points on the upper side and the lower side as shown in Figure 13(c) and (d). Since beam installation is typically concentrated within a specific construction day, the deformation over a period of ten days before and after the installation is analyzed. Unless extreme weather conditions, such as heavy rainfall, cause a sudden temperature drop, the temperature change during this period is relatively steady. The final results show that the cutting quantity at the upper control points is significantly greater than that at the lower control points due to temperature effects. The maximum average cutting quantity at the upper control points is approximately 5 mm, while at the lower control points, it is about 0.9 mm. Thus, the predicted cutting quantity for the crossbeam provide the average value, upper limit, and lower limit at any given time, offering a reliable guide for cutting during the installation operation within any construction period.

Conclusion

The uneven spatial and temporal distribution of temperature fields can induce periodic thermal deformations in bridge tower and simultaneously cause thermal expansion and contraction effects in the structure. This coupled action results in non-uniform gaps or misalignment deviations at the connection interface between the crossbeam and the bridge tower, severely constraining the precise lifting and installation operations of large-scale components. In response to the aforementioned technical bottleneck, this article proposes a virtual pre-assembly technology for bridge tower and crossbeam based on time-varying temperature-induced displacement prediction. By integrating multi-physics field coupling analysis with point cloud modeling technology, dynamic control of assembly accuracy in complex temperature field environments is achieved.

1. The variation patterns of non-uniform gaps formed at the connection interface between the bridge tower and the crossbeam were studied from two perspectives: the analysis of the theoretical temperature effect model and the finite element numerical model.

2. A point cloud model of corresponding control points for the bridge tower and crossbeam was established based on laser scanning technology. The calculated temperature-induced displacements were utilized to quantify the time-varying spatial position characteristics of the control points on the day of construction, enabling the quantification of crossbeam lifting and cutting amounts at different time intervals. Considering daytime construction conditions, the average cutting quantity of upper control points ranges from 1 to 5 mm, with the maximum reaching 6.4 mm, highly approximate to the actual cutting quantity 7 mm. In contrast, the average cutting quantity of lower control points is basically within 1 mm. The adoption of predicted cutting quantity in construction can reduce the time for lifting and cutting. This approach enhances assembly accuracy and improves construction control efficiency.

Footnotes

ORCID iDs

Qi Xia

Jian Zhang

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors wish to express appreciation for the funding support of this research from the National Natural Science Foundation of China (Grant No: 52208305), Natural Science Foundation of Jiangsu Province (Grant No. BK20220852); the Research Fund for Advanced Ocean Institute of Southeast University (Key Program) Project (Grant No. KP202407), and the Jiangsu Provincial Double-Innovation Doctoral Program (Grant No. JSSCBS20210129).

Declaration of conflicting interests

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

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