Study on Mechanical Performance of Steel Truss–Concrete Composite Girder During Post-Rotation Jacking Process

Abstract

Post-rotation jacking is a critical construction stage for load-path reconstruction and alignment adjustment in rotation-constructed bridges, particularly for ultra-wide double-deck composite girder systems. Taking a two-span continuous steel truss–concrete composite girder bridge with spans of 2 × 85 m as the engineering background, this study investigates the mechanical behavior during post-rotation jacking through theoretical derivation, finite element simulation, and on-site monitoring. Based on the force method of structural mechanics, a linear relationship between vertical synchronous jacking force and displacement is derived, and an analytical formulation for bearing reaction redistribution under laterally asynchronous jacking is established by considering the coupling effects of vertical bending, torsion, and transverse multi-bearing support. A full-bridge spatial finite element model was developed in MIDAS Civil NX 2024 V1.1 to analyze the redistribution of bearing reactions and the stress response of the concrete crossbeam under different jacking conditions. The results show that, for the investigated bridge, the jacking force–displacement response remains highly linear during synchronous jacking. The B-axis middle bearing is more sensitive to jacking displacement than the two side bearings, with its fitted stiffness being approximately 2.19 times the average stiffness of the side bearings. Eccentric jacking causes reaction concentration at the jacked point and reaction reduction at adjacent supports, and the magnitude of reaction variation increases approximately linearly with jacking displacement. When the transverse non-uniform jacking magnitude reaches 20 mm, a tensile stress of 0.3 MPa appears at the bottom flange of the concrete crossbeam; therefore, a project-specific stroke-difference limit of 20 mm is recommended for this bridge, while the actual construction achieved a stroke control accuracy of ±0.5 mm and a transverse elevation difference within 1 mm. Field monitoring results validate the proposed analytical and numerical methods. The Pearson correlation coefficients of the measured jacking forces with the finite element and theoretical results are 0.9987 and 0.9988, respectively, and the corresponding mean relative errors are 3.84% and 4.23%. For stress responses, the measured and calculated values show a strong correlation, with a Pearson correlation coefficient of 0.9980 and a mean relative error of 12.77%; the critical mid-span monitoring point shows a relative error of only 0.65%. The final bridge alignment deviation is controlled within ±3 cm. The overall mean verification coefficient is 0.968, with a 95% empirical agreement range of [0.888, 1.048], indicating that the proposed mechanical analysis framework and combined force–displacement control strategy can provide a useful reference for refined construction control of similar ultra-wide double-deck composite girder bridges with comparable span arrangement and transverse bearing layout.

1. Introduction

Steel truss–concrete composite girders combine the tensile strength of steel with the compressive strength of concrete, representing an ideal structural form for the construction of long-span continuous rigid-frame bridges [1,2,3]. The rotation construction method is widely employed in bridges crossing busy transportation corridors due to its minimal disruption to existing traffic and high level of safety [4,5,6]. After rotation, however, the bridge is not yet in its final load-transfer state [7]. The girder is generally supported by temporary restraints, jacks, and partially engaged permanent bearings, and the load path must be reconstructed through staged jacking, temporary-support removal, permanent-bearing engagement, and alignment adjustment [8,9]. Therefore, post-rotation jacking is not merely an elevation-correction operation but a critical construction stage involving bearing reaction redistribution, structural deformation compatibility, and local stress control.

Previous studies on rotation-constructed bridges have mainly addressed swivel-system design, closure construction, and construction-stage monitoring. For swivel-system design, Xu et al. investigated the effects of unbalanced moment, bridge self-weight, friction coefficient, and spherical-hinge curvature on the stress state of the spherical hinge. Their results showed that, when the friction coefficient and bridge self-weight were kept constant, increasing the unbalanced moment from 400 to 800 kN·m had little influence on the maximum stress of the spherical hinge, indicating that the hinge stress is governed by multiple mechanical parameters rather than the unbalanced moment alone [10]. Quan et al. further pointed out that neglecting the unbalanced moment in spherical-hinge design may result in insufficient safety reserve or difficulty in subsequent rotation, and proposed a design method that explicitly considers the unbalanced moment [11]. For closure construction, Zhang reported that the early-age shrinkage stress of newly cast closure concrete increases with the age difference between old and new concrete and with the box-girder width, and suggested delayed tensioning of partial transverse prestressing tendons and pre-wetting of adjacent existing concrete to reduce the risk of longitudinal cracking [12]. In terms of construction-stage monitoring, Liu et al. developed a spatial-pose monitoring and real-time visualization method for swivel bridges, enabling real-time acquisition of rotation angle, displacement, and spatial attitude during the rotation process [13]. These studies have significantly improved the safety and accuracy of rotation construction and closure control; however, their focus remains mainly on the rotation stage, closure cracking, and spatial attitude monitoring, while the mechanical behavior of post-rotation jacking-induced system conversion has not been quantitatively clarified.

Beyond rotation construction, bridge jacking and lifting have been widely used for bearing replacement, elevation correction, bridge rehabilitation, and staged construction [14]. Existing studies and engineering guidelines generally emphasize jacking force estimation, synchronization control, temporary support safety, and construction-stage monitoring [15]. For example, bridge lifting studies have combined finite element analysis with monitoring data to determine construction control values, while studies on continuous girder jacking have examined the influence of asynchronous jacking on girder deformation and stress response [16]. These investigations provide valuable references for jacking construction; however, most of them focus on conventional girder bridges, bearing replacement, or general lifting operations, and rarely address the coupled vertical bending, torsional deformation, transverse multi-bearing reaction redistribution, and local stress response of ultra-wide double-deck steel truss–concrete composite girders during post-rotation jacking.

Although considerable progress has been made in the design of swivel systems, closure construction, and construction-stage monitoring of rotation-constructed bridges, the mechanical behavior associated with post-rotation jacking has not been sufficiently clarified. In particular, after rotation is completed, the bridge is still supported by temporary restraints and jacks before the permanent bearings are fully engaged. The removal of temporary supports and the staged application of jacking forces inevitably lead to load-path transformation and redistribution of bearing reactions. For ultra-wide double-deck steel truss–concrete composite girders, this process becomes more complicated because vertical bending stiffness, torsional stiffness, transverse stiffness, and multi-point bearing reactions are strongly coupled. Existing studies on bridge jacking and construction monitoring have mainly focused on alignment adjustment, bearing replacement, or qualitative safety verification, whereas limited quantitative attention has been paid to the relationship among jacking displacement, jacking force, bearing reaction redistribution, and local stress response in such complex composite girder systems.

To address this gap, this study investigates the post-rotation jacking process of a two-span continuous steel truss–concrete composite girder bridge with spans of 2 × 85 m. The main scientific contribution is the establishment of a mechanical analysis framework for jacking-induced system conversion, including the vertical jacking force–displacement relationship and the bearing reaction redistribution under laterally asynchronous jacking. A refined finite element model and field monitoring data are then used to verify the analytical results and to clarify the response characteristics of the investigated bridge. Based on the calculated and measured responses, practical control indicators, including a project-specific differential stroke limit and a combined force–displacement control strategy, are proposed for refined construction control of similar ultra-wide double-deck composite girder bridges.

2. Analytical Formulation for Jacking-Induced System Conversion and Bearing Reaction Redistribution

2.1. Basic Mechanical Model and Assumptions

Based on the characteristics of steel truss–concrete composite girders, the transformed section method is employed to account for the composite action between steel and concrete, whereby the truss structure is idealized as a continuous beam possessing equivalent flexural stiffness EI and equivalent torsional stiffness GJ [17,18]. The longitudinal direction of the girder is defined as the x-axis, the transverse direction as the y-axis, and the vertical direction as the z-axis. Upward jacking displacement and upward jack force are taken as positive. The bearing reactions discussed in this section are defined as incremental reactions relative to the initial post-rotation state unless otherwise specified. To facilitate analysis, a theoretical computational model is established as illustrated in Figure 1. The following fundamental assumptions are adopted:

(1)

The main girder operates within the elastic range; the material constitutive behavior obeys Hooke’s Law, and neither geometric nonlinearity nor second-order effects are considered.

(2)

The equivalent flexural stiffness EI of the transformed section of the main girder is assumed constant along the span length. In the transverse analysis, the equivalent torsional stiffness GJ is additionally considered, while the effects of shear deformation and axial deformation are neglected.

(3)

In the vertical analysis, the two-span continuous girder is simplified as a hyperstatic structure supported at the intermediate pier top and the two end abutments. At the intermediate pier, the temporary bearings and permanent bearings jointly sustain the self-weight of the girder.

(4)

In the transverse analysis, the main girder and the piers are collectively treated as a rigid frame in the horizontal plane. The transverse force distribution is governed jointly by the transverse flexural stiffness of the main girder and the lateral thrust stiffness of the piers. For the case involving multiple bearings within the same cross-section, the main girder is idealized as an elastic beam with equivalent flexural stiffness and equivalent torsional stiffness.

2.2. Force Method Analysis of Synchronous Jacking

The essence of system conversion lies in the removal of temporary supports and the smooth transfer of the support reaction to the permanent bearings. During the jacking process, the total reaction R at the support point is borne jointly by the temporary bearing and the jack, and is ultimately transferred entirely to the permanent bearing.

Prior to jacking, the temporary bearing sustains the entire reaction R, while the jacking force is zero. During jacking, the jacking force F_v progressively increases, and the temporary bearing reaction R_temp correspondingly decreases. The relationship among the three satisfies the condition of static equilibrium:

$$R=F_{\mathrm{v}}+R_{\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}}$$

(1)

The synchronous jacking process can be regarded as an imposed-displacement problem of a once-hyperstatic continuous girder. By selecting the vertical reaction increment at the jacking support as the redundant unknown, the force method can be used to establish the compatibility relationship between the imposed jacking displacement and the corresponding reaction increment [19]. Adopting the force method, the intermediate support constraint is treated as the redundant restraint, yielding a primary statically determinate system. A unit redundant force X = 1 is applied at the intermediate support location, and the resulting vertical displacement at that point is denoted as ${\delta }_{\mathrm{v}}$. According to the condition of deformation compatibility, the actual jacking displacement ${\delta }_{\mathrm{v}}$ is equal to the displacement induced by the combined action of the redundant force (i.e., the increment in support reaction ΔR caused by jacking) and the external loads:

$${\delta }_{\mathrm{v}}=\Delta R{\delta }_{11}+{\delta }_{1\mathrm{p}}$$

(2)

where ${\delta }_{1\mathrm{p}}$ represents the displacement at the intermediate support point in the primary system caused by the external loads. At the instant when jacking causes the temporary bearing to fully disengage, ΔR equals R, and the corresponding ${\delta }_{\mathrm{v}}$ represents the theoretical liftoff displacement. From this, the vertical equivalent stiffness k_v of the structure can be determined as:

$$k_v={\displaystyle \frac{1}{{\delta }_{11}}}={\displaystyle \frac{\Delta R}{{\delta }_v-{\delta }_{1\mathrm{p}}}}$$

(3)

For a two-span continuous beam with equal span lengths L, it is known from structural mechanics that:

$${\delta }_{11}={\displaystyle \frac{2L^3}{3EI}}$$

(4)

Substituting this expression yields the theoretical relationship between jacking force and displacement:

$$F_{\mathrm{v}}=k_{\mathrm{v}}{\delta }_{\mathrm{v}}={\displaystyle \frac{3EI}{2L^3}}$$

(5)

As indicated by the above equation, the relationship between jacking force and displacement is linearly proportional, with the proportionality coefficient determined by the span length L and the flexural stiffness EI of the structure.

2.3. Formula for Bearing Reaction Distribution Under Asynchronous Jacking

For multiple bearings arranged transversely on the same bridge pier, when vertical jacking is performed using jacks with unequal stroke displacements, the main girder undergoes torsional deformation and transverse bending deformation, thereby inducing a redistribution of the bearing reactions. Taking the case of three bearings as an example, a theoretical analysis model is established.

2.3.1. Displacement Decomposition and Stiffness Matrix

Since the three forces act on the same cross-section but at different locations, their influence on the main girder can be decomposed into three fundamental modes:

(1)

Overall vertical displacement mode: Induced by the average displacement $\overline{\delta }={(\delta }_1+{\delta }_2+{\delta }_3)/3$, this mode corresponds to vertical flexural deformation of the main girder and produces a uniform bearing reaction component.

(2)

Torsional deformation mode: Induced by the torsional displacement difference ${\Delta \delta =(\delta }_3-{\delta }_1)/(2d)$, this mode corresponds to torsion of the main girder about its longitudinal axis and produces a bearing reaction component proportional to the y-coordinate.

(3)

Distortional deformation mode: Induced by the distortional displacement ${\delta }_d={({\delta }_1+\delta }_3-{2\delta }_2)/2$, this mode corresponds to transverse bending deformation of the main girder cross-section (i.e., change in cross-sectional shape) and produces a self-equilibrating bearing reaction component.

According to the principle of linear superposition, the laterally asynchronous jacking problem is formulated in an incremental form. The initial bearing reaction vector before jacking is denoted as $R_0$, and the reaction increment induced by differential jacking displacement is denoted as $\Delta R$. The total bearing reaction during jacking is therefore

$$R=R_0+\Delta R$$

(6)

For the three bearings arranged in the transverse direction, their coordinates are defined as$:y_1=-d$, $y_2=0$, $y_3=d$.

The incremental jacking displacement vector and the corresponding reaction increment vector are expressed as

$$\Delta \delta =\left(\begin{array}{c}{\Delta \delta }_1\\ {\Delta \delta }_2\\ \Delta {\delta }_3\end{array}\right)$$

(7)

$$\Delta R=\left(\begin{array}{c}{\Delta R}_1\\ {\Delta R}_2\\ {\Delta R}_3\end{array}\right)$$

(8)

The three-point displacement pattern can be decomposed into three independent components: the average vertical displacement, the torsional rotation of the transverse section, and the local transverse distortion. These components are defined as

$$\overline{\delta }={\displaystyle \frac{{\Delta \delta }_1+\Delta {\delta }_2+{\Delta \delta }_3}{3}}$$

(9)

$$\theta ={\displaystyle \frac{\Delta {\delta }_3-{\Delta \delta }_1}{2d}}$$

(10)

$$\eta ={\Delta \delta }_1-2\Delta {\delta }_2+{\Delta \delta }_3$$

(11)

where $\overline{\delta }$ represents the overall vertical jacking mode, $\theta$ represents the torsional mode, and $\eta$ represents the local transverse distortion mode.

If only the rigid-section vertical translation and torsion are considered, the transverse section has only two independent deformation modes, and the three-bearing reaction redistribution problem cannot be uniquely determined. Therefore, a local transverse distortion component associated with the deformation of the concrete crossbeam and transverse girder system is introduced. This component reflects the self-equilibrating reaction mode among the three bearings and ensures that the flexibility matrix is nonsingular.

2.3.2. Formulation of the Flexibility Matrix

The flexibility matrix F is defined through unit-load cases. Its element f_ij represents the vertical displacement at bearing j caused by a unit vertical force applied at bearing i. According to Maxwell’s reciprocal theorem, f_ij = f_ji, and the flexibility matrix is symmetric. The incremental displacement and reaction vectors satisfy

$$\Delta \delta =F\Delta R$$

(12)

$$F=\left(\begin{array}{ccc}a& b& c\\ b& d& b\\ c& b& a\end{array}\right)$$

(13)

where $a=f_{11}=f_{33}$; $b=f_{12}=f_{21}=f_{23}=f_{32}$; $c=f_{13}=f_{31}$; $d=f_{22}$.

The corresponding stiffness relationship is

$$\Delta R=K\Delta \delta$$

(14)

$$K=F^{-1}$$

(15)

The main girder is idealized as a beam with an overhang: the left pier location at x = 0 is a free end, while the intermediate pier at x = L and the right pier at L_x = 2L serve as vertical hinge supports. When a unit vertical force (directed downward) is applied at the centroid of the left pier cross-section (y = 0), the vertical displacement at that point can be obtained from structural mechanics as:

$$\omega ={\displaystyle \frac{2L^3}{3EI}}$$

(16)

When a unit torque (about the x-axis) is applied to the left pier cross-section, the resulting angle of twist θ depends on the torsional boundary conditions of the structure. For free torsion, assuming that the intermediate and right piers provide no torsional restraint, the angle of twist of the left pier cross-section under a unit torque can be approximated as:

$$\theta ={\displaystyle \frac{2L}{GJ}}$$

(17)

This expression assumes that the torque is uniformly distributed along the girder length and that both ends are free of torsional restraint; in practical applications, adjustments may be necessary according to the actual torsional capacity of the bearings.

Considering a unit force acting at y = d, this force can be decomposed into a unit force acting at the centroid (producing displacement ω) and a torque T = 1 × d (producing angle of twist θ). The displacement produced at the point of application (y = d) is therefore:

$$f_{33}=\omega +\theta d^2$$

(18)

The displacement produced at the point y = −d is:

$$f_{31}=\omega -\theta d^2$$

(19)

And the displacement produced at the point y = 0 is:

$$f_{32}=\omega$$

(20)

Similarly, when a unit force acts at y = 0, no torque is generated, and the displacement at all points is ω. Consequently:

$${f_{22}=f_{12}=f}_{32}=\omega$$

(21)

Thus, the elements of the flexibility matrix are:

$$a=\omega +\theta d^2$$

(22)

$$b=\omega$$

(23)

$$c=\omega -\theta d^2$$

(24)

$$d=\omega$$

(25)

2.3.3. Stiffness Matrix and Bearing Reaction Expressions

Introducing the coefficient of vertical flexural stiffness $k_{\mathrm{v}}=1/\omega$ and the coefficient of torsional stiffness $k_{\mathrm{t}}=1/\theta$ the elements of the flexibility matrix can be expressed as:

$$a={\displaystyle \frac{1}{k_{\mathrm{v}}}}+{\displaystyle \frac{d^2}{k_{\mathrm{t}}}}$$

(26)

$$b={\displaystyle \frac{1}{k_{\mathrm{v}}}}$$

(27)

$$c={\displaystyle \frac{1}{k_{\mathrm{v}}}}-{\displaystyle \frac{d^2}{k_{\mathrm{t}}}}$$

(28)

$$d={\displaystyle \frac{1}{k_{\mathrm{v}}}}$$

(29)

Inverting the flexibility matrix yields the stiffness matrix K:

$$K=\left(\begin{array}{ccc}-{\displaystyle \frac{k_{\mathrm{v}}}{2}}+{\displaystyle \frac{k_{\mathrm{t}}}{4d^2}}& k_v& -{\displaystyle \frac{k_{\mathrm{v}}}{2}}-{\displaystyle \frac{k_{\mathrm{t}}}{4d^2}}\\ k_{\mathrm{v}}& -2k_{\mathrm{v}}& k_{\mathrm{v}}\\ -{\displaystyle \frac{k_{\mathrm{v}}}{2}}-{\displaystyle \frac{k_{\mathrm{t}}}{4d^2}}& k_{\mathrm{v}}& -{\displaystyle \frac{k_{\mathrm{v}}}{2}}+{\displaystyle \frac{k_{\mathrm{t}}}{4d^2}}\end{array}\right)$$

(30)

The relationships between the three bearing reactions and the jacking displacements are thereby obtained:

$$F_1=\left(-{\displaystyle \frac{k_{\mathrm{v}}}{2}}+{\displaystyle \frac{k_{\mathrm{t}}}{4d^2}}\right){\delta }_1+k_v{\delta }_2+\left(-{\displaystyle \frac{k_{\mathrm{v}}}{2}}-{\displaystyle \frac{k_{\mathrm{t}}}{4d^2}}\right){\delta }_3$$

(31)

$$F_2=k_{\mathrm{v}}{\delta }_1-2k_{\mathrm{v}}{\delta }_2+k_{\mathrm{v}}{\delta }_3$$

(32)

$$F_3=\left(-{\displaystyle \frac{k_{\mathrm{v}}}{2}}-{\displaystyle \frac{k_{\mathrm{t}}}{4d^2}}\right){\delta }_1+k_{\mathrm{v}}{\delta }_2+\left(-{\displaystyle \frac{k_{\mathrm{v}}}{2}}+{\displaystyle \frac{k_{\mathrm{t}}}{4d^2}}\right){\delta }_3$$

(33)

The above formulas provide an analytical relationship between bearing reactions and jacking displacements, wherein the vertical flexural stiffness coefficient k_v and the torsional stiffness coefficient k_t reflect the global stiffness characteristics of the structure. In practical engineering applications, due to the complexity of cross-sections and the diversity of boundary conditions, analytical formulations cannot fully capture the behavior with complete accuracy, and it is necessary to employ finite element methods for refined simulation.

3. Finite Element Simulation Analysis

3.1. Engineering Overview

The investigated double-deck bridge crossing a railway features an upper deck designated for an expressway and a lower deck for an urban arterial road. The upper and lower decks are constructed according to the standards for an eight-lane expressway and a six-lane urban arterial road, respectively, with auxiliary lanes provided as dictated by site conditions on either side. The main bridge structure adopts a 2 × 85 m continuous steel truss web–plate truss composite structural system, arranged as a full-width single unit. The upper deck employs a steel truss girder, with all truss members fabricated from structural steel, while the lower deck consists of a ribbed-slab concrete girder. The design elevation difference between the upper and lower bridge decks is 14.8 m. Transversely, three main trusses are spaced at 18.35 m centers. Longitudinally, the truss is of the Warren type, with a panel length of 14 m. The main truss height is 14.879 m. The general layout of the bridge is presented in Figure 2. The actual photograph of the main bridge after rotation is shown in Figure 3.

The bridge was constructed using the rotation method. After rotation into position and subsequent locking, jacks were arranged on the top surface of the side pier lower-level cap beam to perform jacking at the girder ends on each side. Following the installation of the side pier bearings and removal of the jacking equipment, the system conversion was completed.

3.2. Model Establishment

A full-bridge three-dimensional beam–plate finite element model was established using MIDAS Civil NX 2024 V1.1. The model consisted of approximately 4948 elements and 3247 nodes. The orthotropic steel deck of the upper level and the concrete deck of the lower level were modeled using plate elements, whereas the truss chords, diagonal members, vertical members, longitudinal ribs, and transverse ribs were modeled using beam elements. The full-bridge finite element model is shown in Figure 4. Material parameters were adopted according to actual values: the elastic modulus of steel E_s = 2.06 × 10⁵ MPa, the elastic modulus of concrete E_c = 3.45 × 10⁴ MPa, and Poisson’s ratios of 0.3 and 0.2, respectively. For ease of description, the positions of the main bridge components and the reference axes are presented in Figure 5.

The bases of the bridge piers were fully fixed. Temporary bearings were simulated using compression-only elastic link elements with a vertical stiffness of 1.0 × 10⁸ kN/m. Permanent bearings were modeled according to their design restraint conditions. In the vertical direction, the permanent bearings were represented by elastic supports with a vertical stiffness of 5.0 × 10⁷ kN/m. The jacks were modeled as vertical displacement-controlled supports at the corresponding jacking locations. The analysis was performed within the linear elastic range, and material nonlinearity and geometric nonlinearity were not considered.

In the construction-stage jacking analysis, the loads considered mainly included permanent actions and imposed jack displacements. The permanent actions consisted of structural self-weight and superimposed dead loads. The unit weights of concrete and steel were taken as 26.5 kN/m³ and 78.5 kN/m³, respectively. In the global model, the weight of steel members was calculated according to their system-line lengths and multiplied by a structural coefficient of 1.35 to account for the additional weight of gusset plates, splice plates, diaphragms, and other connection details. The superimposed dead loads were determined according to the actual material quantities of the bridge deck pavement, barriers, and ancillary facilities. Since the bridge was not open to traffic during the jacking operation, traffic loads were not included in the construction-stage jacking simulations discussed in this study. In the synchronous jacking cases, equal vertical displacements were imposed at the three transverse jacking points. In the eccentric jacking cases, a prescribed vertical displacement was imposed at one selected support point, while the remaining support points were kept at their current elevations, so as to simulate the stroke differences among individual jacks.

The construction-stage simulation was performed in the following sequence: (1) completion and locking of bridge rotation; (2) activation of temporary bearings and application of permanent actions; (3) staged synchronous jacking at the side-pier supports; (4) transverse eccentric jacking analysis to evaluate the influence of non-uniform jack strokes; (5) verification of excess jacking amounts of 5 mm, 10 mm, and 20 mm; (6) removal of temporary bearings and activation of permanent bearings; and (7) stepwise unloading of the jacks after the permanent bearings were installed. The main load cases used in the analysis are summarized in

Table 1. Construction-stage load cases used in the finite element analysis.

Load Case	Structural State	Active Boundary Condition	Applied Action
LC1	Post-rotation locked state	Temporary bearings active; permanent bearings inactive	Self-weight + superimposed dead load + shrinkage and creep
LC2	Synchronous jacking	Jacks activated at side-pier support points	Equal vertical jack displacement
LC3	Eccentric jacking at side support	One side support point jacked; other support points unchanged	Prescribed eccentric displacement of 0–50 mm
LC4	Eccentric jacking at intermediate support	Intermediate support point jacked; side support points unchanged	Prescribed eccentric displacement of 0–50 mm
LC5	Excess jacking verification	Jacks and temporary bearings jointly active	Non-uniform excess jacking of 5 mm, 10 mm, and 20 mm
LC6	Support transfer	Temporary bearings removed; permanent bearings activated	Permanent actions + support-boundary conversion
LC7	Jack unloading	Permanent bearings active; jacks unloaded step by step	Jack force/displacement release

.

3.3. Longitudinal Redistribution Pattern of Bearing Reactions

The essence of the jacking process is the active transfer of the load path. In the initial state following rotation completion, the self-weight of the main girder is primarily supported by the six bearings arranged atop the two piers. Once longitudinal jacking commences, the jacks progressively engage and bear load, while the reactions at the temporary bearings correspondingly decrease. As illustrated in Figure 6, the jacking force exhibits a favorable linear relationship with displacement, consistent with the theoretical formulation presented in Section 2.2. During jacking, the reaction at the intermediate support increases rapidly, whereas the reaction at the side supports decreases more gradually. For synchronous jacking within a range of 10 cm, each centimeter of jacking displacement results in an increase of 9.4% in the intermediate support reaction relative to its initial value, an increase of 4.3% in the side support reaction, and a decrease of 1.9% in the main pier reaction. After the main girder attains the design elevation, the side support reaction approaches twice the magnitude of the intermediate support reaction, with the side support reaction accounting for 5.39%, the intermediate support reaction for 2.81%, and the main pier reaction for 72.82% of the total.

3.4. Transverse Redistribution Pattern of Bearing Reactions

To investigate the relationship between jacking force and jacking displacement, as well as the redistribution of bearing reactions between the main pier and side pier supports under excessive jacking at the side pier support points, eccentric jacking was applied individually at the side pier support points, taking the design elevation after rotation positioning as the initial reference elevation. In the case of eccentric jacking at the side support point, a 5 cm eccentric displacement was imposed at side support point A as an example, while the remaining support points were held in their original positions. In the case of eccentric jacking at the intermediate support point, a 5 cm eccentric displacement was imposed at intermediate support point B as an example, with the other support points remaining stationary. The relationship between jacking force and jacking displacement at the side support point is shown in Figure 7a, while the corresponding relationship and the proportion of bearing reaction to total weight at the intermediate support point are presented in Figure 7b.

As illustrated in Figure 7a, during eccentric jacking at side support point A, the reaction at side support point B decreases at a comparable rate, the reaction at side support point C exhibits a slight increase, and the main pier reaction decreases marginally. When the eccentric jacking at side support point A reaches 2 cm, the reaction at point A increases by 0.85%, the reaction at intermediate support point B decreases by 0.85%, the reaction at left side support point C decreases by 0.24%, and the main pier reaction decreases by 0.39%. As shown in Figure 7b, during eccentric jacking at intermediate support point B, the reactions at side support points A and C decrease at a similar rate, while the main pier reaction exhibits a slight decrease. When the eccentric jacking at left intermediate support point B reaches 2 cm, the reaction at that point increases by 2.01%, and the reactions at left side support points A and C each decrease by 0.87%. The observed pattern of reaction variation under eccentric jacking is qualitatively consistent with the bearing reaction distribution formula derived in Section 2.3: when an outer support point is jacked, the reaction at that point increases, whereas the reactions at adjacent support points decrease, with the magnitude of change being proportional to the jacking displacement.

3.5. Determination of Excess Jacking Magnitude and Analysis of Control Methods

3.5.1. Analysis of Excess Jacking Magnitude

During jacking construction, the elastic compression of temporary bearings, construction assembly clearances, and additional elastic deformation of the main girder cannot be eliminated solely through the theoretical liftoff displacement. Consequently, excess jacking is required to achieve complete disengagement of the temporary bearings. The theoretical value of the excess jacking magnitude is the summation of the bearing elastic compression, the construction clearance compensation, and the additional structural elastic deformation. In the absence of deformation cancellation effects, these three deformation components are superimposed directly, and the calculation formula is expressed as:

$${\delta }_{\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}}={\delta }_{\mathrm{b}}+{\delta }_{\mathrm{g}}+{\delta }_{\mathrm{s}}$$

(34)

where ${\delta }_{\mathrm{b}}$ is the elastic compression recovery of the bearing, ${\delta }_{\mathrm{g}}$is the construction gap compensation, and ${\delta }_{\mathrm{s}}$ is the additional elastic deformation of the girder induced by excess jacking.

The methods for determining each deformation component are as follows:

(1) Bearing Elastic Compression δ_b

$${\delta }_{\mathrm{b}}={\displaystyle \frac{Fh}{EA}}$$

(35)

where

F: actual girder load sustained by the bearing (kN);

h: vertical height of the elastomeric bearing (mm);

E: elastic modulus of the elastomeric bearing (MPa);

A: compressive cross-sectional area of the bearing (mm²).

(2) Construction Clearance Compensation δ_g

The construction clearance compensation accounts for the contact gaps between the bearing and the cap beam as well as between the bearing and the girder soffit, together with the operational clearances required for jack installation and temporary support removal. Its value is determined based on site construction procedures and experience from similar projects.

(3) Additional Structural Elastic Deformation δ_s

The additional structural elastic deformation refers to the extra elastic deflection induced in the main girder by the jacking force at the instant the theoretical liftoff displacement is attained. Based on the mechanical model of the synchronous jacking force method presented in Section 2.2, and in conjunction with the equivalent flexural stiffness EI of the 2 × 85 m two-span continuous girder of the present bridge, the vertical equivalent stiffness of the structure is calculated using the formula $k_{\mathrm{v}}={\displaystyle \frac{2L}{33EI}}$. The additional elastic deformation of the main girder at the pier top during the jacking process is subsequently derived from this stiffness.

3.5.2. Finite Element Simulation Verification of Excess Jacking Magnitude

Based on the full-bridge spatial finite element model established in Midas Civil as described in Section 3.2, multiple loading cases with varying gradients of excess jacking magnitude were configured to verify the rationality of the theoretical excess jacking value and to determine the optimal excess jacking magnitude and its upper limit for engineering application. The stress at the bottom flange of the concrete crossbeam was selected as the evaluation criterion.

The bridge is equipped with three bearings arranged transversely. Owing to the distribution of transverse structural stiffness and the bearing layout configuration, the vertical load sustained by the side bearings is smaller than that sustained by the middle bearing, and the force response sensitivity of these two bearing types to jacking displacement differs. Employing a uniform excess jacking magnitude during construction may readily lead to imbalanced redistribution of bearing reactions and induce additional structural stresses. Therefore, to accommodate the transverse multi-bearing configuration of this bridge, supplementary eccentric excess jacking simulation cases were introduced to analyze the influence of excess jacking deviation on the additional tensile stresses in the concrete girder. Three excess jacking conditions (5 mm, 10 mm, and 20 mm) were established for the two outer support points atop Pier No. 6. The extreme values of stresses at the top and bottom flanges of the concrete longitudinal girders and crossbeams under these three conditions are presented in

Table 2. Extreme stress values in longitudinal and crossbeams (MPa).

Non-Uniform Jacking Distance	Concrete Longitudinal Girder				Concrete Crossbeam
	Top Flange		Bottom Flange		Top Flange		Bottom Flange
	Max	Min	Max	Min	Max	Min	Max	Min
5 mm	−11.9	−2	−15.5	−1.4	−13.9	−1.7	−16.9	−3.9
10 mm	−11.4	−1.9	−14.7	−1.3	−14.6	−1.6	−17	−2.5
20 mm	−10.7	−1.7	−13.2	−1.1	−16.2	−1.6	−17	0.3

.

As indicated in Table 2, when non-uniform excess jacking is applied to the two outer support points atop Pier No. 6, the stress in the concrete longitudinal girders decreases, whereas the stress in the concrete crossbeam increases. When the non-uniform excess jacking reaches 20 mm, the maximum compressive stress in the concrete longitudinal girder decreases from 15.5 MPa to 13.2 MPa; the maximum compressive stress at the top flange of the concrete crossbeam decreases from 11.9 MPa to 10.7 MPa, while a tensile stress of 0.3 MPa begins to appear at the bottom flange of the concrete crossbeam. Although this tensile stress is small in magnitude, the concrete crossbeam in the jacking stage was controlled according to the principle that tensile stress should not occur in the concrete. Therefore, the appearance of tensile stress indicates that the stress state of the bottom flange has changed from a fully compressive state to a locally tensile state, which may increase the risk of crack initiation under construction uncertainty and local stress redistribution. The reinforcement in the crossbeam can provide post-cracking tensile resistance and crack-control capacity, but it should be regarded only as a structural reserve rather than as a basis for relaxing the synchronization requirement of the jacks. Accordingly, 20 mm is adopted as the project-specific upper limit for transverse non-uniform jacking. In actual construction, the computerized synchronous jacking system achieved a stroke control accuracy of ±0.5 mm and controlled the transverse elevation difference within 1 mm, which is much stricter than the calculated upper limit and provides an additional construction control margin.

3.6. Comparison and Selection of Jacking Control Methods

3.6.1. Displacement Control

Displacement control employs the theoretical jacking displacement and the excess jacking magnitude as target values, achieving jacking through synchronized control of the stroke of each jack. Its principal advantages lie in its operational simplicity and its capacity to accurately ensure the structural alignment, effectively averting torsional deformation induced by non-uniform jacking.

However, displacement control alone cannot directly reflect the load-transfer state between the temporary bearings, jacks, and permanent bearings. In other words, even if the measured jack strokes are consistent, residual contact force may still remain in the temporary bearings, or the support reactions may be unevenly distributed due to local stiffness differences. This limitation is especially important for the present bridge, because the transverse stiffness and support reaction sensitivity are not uniform among the three bearing axes. Compared with conventional rotation bridges discussed in previous studies, the ultra-wide double-deck composite girder studied herein requires stricter attention to transverse synchronization, since non-uniform jack strokes may produce additional torsional deformation and local tensile stress in the concrete crossbeam.

The numerical results further showed that when the non-uniform jacking amount reached 20 mm, tensile stress began to appear at the bottom flange of the concrete crossbeam. Therefore, for this specific bridge, the stroke difference among individual jacks should be limited to less than 20 mm as a safety control threshold. In actual construction, a computerized synchronous jacking system was adopted, with a stroke control accuracy of ±0.5 mm and a transverse elevation difference controlled within 1 mm. This actual control accuracy was much stricter than the calculated allowable threshold, providing an additional safety margin for construction.

3.6.2. Force Control

Force control uses the jacking force or the residual reaction of temporary bearings as the main control index. Its main advantage is that it can directly reflect the load-transfer process during system conversion. In the early stage of jacking, the structural response is dominated by the gradual transfer of dead load from temporary bearings to jacks. Therefore, force control is effective for identifying whether the jacks have been fully engaged and whether the temporary bearings have been sufficiently unloaded.

However, force control alone is also insufficient for this bridge. Due to the large transverse width and the different reaction sensitivities of the intermediate and side bearings, force adjustment at one jack may induce displacement incompatibility among adjacent jacking points. If the jacking force is used as the only control objective, the bridge alignment may deviate from the target profile, and additional transverse bending or torsional deformation may be introduced. This explains why previous force-based control methods for conventional jacking construction cannot be directly applied to the present bridge without considering deformation compatibility.

Therefore, force control is more suitable for the initial stage of jacking, during which the main objective is to overcome the structural self-weight and complete the transfer of reactions from temporary bearings to jacks. During this stage, the jacking force was applied in graded increments according to the design bearing reactions under dead-load conditions. The loading sequence was divided into levels of 0.2T, 0.4T, 0.6T, 0.8T, and 1.0T, and each level was maintained for observation to confirm that the structural response remained stable.

3.6.3. Combined Control Strategy

Based on the above comparison, neither displacement control nor force control alone can fully satisfy the requirements of post-rotation jacking for the investigated ultra-wide double-deck composite girder bridge. Displacement control is advantageous for alignment adjustment and deformation compatibility, whereas force control is advantageous for identifying the load-transfer state and the unloading degree of temporary bearings. The two methods are therefore complementary rather than mutually exclusive.

Accordingly, a staged combined control strategy was adopted in this study. In the early stage, force control was used as the primary control mode, supplemented by displacement observation. This stage focused on the safe and gradual transfer of the structural self-weight from the temporary bearings to the jacks. When the jacking force approached the design reaction level and the temporary bearings were substantially disengaged, the control objective changed from load transfer to alignment adjustment.

In the later stage, displacement control was used as the primary control mode, supplemented by force monitoring. Synchronous jacking was then performed in increments of 3 mm per level until the main girder approached the design elevation. During this process, the stroke difference among individual jacks and the transverse elevation difference in the support points were continuously monitored to avoid torsional deformation and local stress concentration. After the target alignment was achieved, a fine adjustment of 1 mm was carried out, the permanent bearings were installed, and the jacks were unloaded step by step.

The proposed combined control method differs from conventional single-index jacking control in that it explicitly considers the stage-dependent mechanical characteristics of the bridge. In the early stage, the dominant issue is load-path conversion, and force control is therefore more reliable. In the later stage, the dominant issue becomes deformation compatibility and alignment accuracy, and displacement control becomes more appropriate.

4. On-Site Bridge Monitoring

4.1. Monitoring Scheme and Measurement Point Layout

4.1.1. Three-Dimensional Visualization Monitoring System for Bridge Rotation and Jacking

To achieve digitalized and visualized management and control throughout the entire rotation and jacking process, a three-dimensional visualization monitoring system for bridge rotation construction, based on B/S architecture, was developed and successfully deployed in this bridge project. The system is built upon a core framework of “485 sensors + hubs + DTU + cloud storage + Internet of Things + Web interface,” and leverages web technologies to construct a lightweight BIM model and an integrated data visualization platform. The system integrates diverse heterogeneous data sources, including surrounding terrain, bridge-site meteorology, traction system parameters, main girder displacements, multi-angle ground-based video feeds, and aerial drone imagery, thereby enabling comprehensive situational awareness on a unified display. In conjunction with relevant specifications and design documentation, graded early-warning thresholds are pre-configured, allowing real-time assessment and alerting for indicators such as jacking force, stroke differential, and stresses at critical cross-sections. The main interface of the monitoring system is shown in Figure 8.

4.1.2. Main Girder Stress Monitoring

Main girder stress monitoring enables real-time observation of structural stresses at critical control sections during construction, thereby ensuring the safety and controllability of the main bridge. Welded vibrating-wire strain sensors are employed for the steel structural members, while embedded vibrating-wire strain gauges, corroborated by surface-mounted strain gauges for dual-path verification, are utilized for the concrete bridge deck. The sensors are connected to automated data acquisition units, which perform a measurement cycle every minute, and non-stress meters fabricated from the same material are installed to provide temperature compensation. The monitoring sections are selected at the intermediate bridge span sections, the mid-span sections, and additional sections exhibiting relatively high stress levels. The sensor layout for each section is illustrated in Figure 9. For horizontal chords, the lower concrete slab, and diagonal members, sensors are installed at the center of the bottom surface of the cross-section; for vertical posts, sensors are installed at the center of the “王”—shaped cross-section, with all sensors oriented along the longitudinal axis of the respective member.

4.1.3. Layout of Main Girder Displacement Measurement Points

Alignment monitoring of the entire bridge is conducted using a precise level. Elevation control points on the deck segments of both the upper and lower bridge levels are surveyed after rotation and both before and after jacking closure. Reference points are respectively arranged at the center of the upper and lower decks at Section A7, as illustrated in Figure 10. During each construction stage, elevation data from the alignment control points along Axes A, B, and C are acquired for the upper deck sections spanning from A1 to A13.

4.1.4. Monitoring of Jacking Force and Girder-End Displacement

Jacking force is monitored by connecting high-precision oil pressure sensors in series within the hydraulic circuit of each jacking cylinder. The exerted jacking force is converted in real time based on the oil pressure–jacking force relationship curve obtained through laboratory calibration. Data from the oil pressure sensors are sampled at a frequency of 1 Hz via a dynamic acquisition module and transmitted to the on-site monitoring host through an RS485 bus, as illustrated in Figure 11a.

To precisely monitor the local vertical deformation and rotation of the main girder soffit at the pier top during the jacking process, an array of dial gauges is arranged vertically on the underside of the main girder at each jacking location. The specific layout configuration is as follows: one dial gauge is installed vertically on the jacking-advancing side, one on the side opposite to jacking, and one each on the left and right sides oriented at 90 degrees to the jacking direction, thereby forming an orthogonal monitoring group consisting of four dial gauges in total, as depicted in Figure 11b. The dial gauges possess a measuring range of 50 mm and a resolution of 0.01 mm. They are secured to the top surface of the cap beam using magnetic stands, with their probes bearing against pre-embedded steel plates affixed to the girder soffit.

4.2. Data Comparison and Analysis

4.2.1. Comparison of Jacking Force–Displacement (P-δ) Curves

Figure 12 compares the measured jacking force–displacement curve, the finite element result, and the theoretical result for the middle bearing of the left side pier. The three curves all exhibited an approximately linear relationship between jacking force and displacement, indicating that the structural response remained within the linear elastic range during synchronous jacking. To provide a more transparent validation of the numerical model, representative data points were extracted from the curves and are summarized in

Table 3. Quantitative comparison of jacking force–displacement responses at the middle bearing of the left side pier.

Jacking Displacement (mm)	Absolute Error Between Measured and FE (kN)	Relative Error Between Measured and FE (%)	Absolute Error Between Measured and Theoretical Value (kN)	Relative Error Between Measured and Theoretical Value (%)
5	143	2.38	188	3.14
10	169	1.36	99	0.79
15	65	0.35	30	0.16
20	1105	4.71	1225	5.22
25	1979	6.88	2124	7.39
30	1222	3.44	1482	4.1

.

The error was calculated using the measured value as the reference. Based on all valid data points from 1 mm to 30 mm, the Pearson correlation coefficient between the measured and finite element jacking forces was 0.9987, while that between the measured and theoretical jacking forces was 0.9988. The mean relative error between the measured and finite element results was 3.84%, and the mean relative error between the measured and theoretical results was 4.23%. These results indicate that both the finite element model and the theoretical formulation can accurately capture the force–displacement relationship during synchronous jacking.

The observed linear relationship is consistent with the force method derivation in Section 2.2, in which the jacking force is governed primarily by the vertical equivalent stiffness of the structural system. Similar linear force–displacement behavior has also been reported in previous studies on beam-end jacking and closure-stage construction control of rotation bridges. However, compared with conventional concrete T-frame or single-deck bridge systems, the present ultra-wide double-deck steel truss–concrete composite girder exhibited a more evident transverse differentiation in support response, as further shown in Figure 13. This difference is mainly attributed to the large transverse spacing of the three main trusses, the coupling between vertical bending and torsional deformation, and the non-uniform stiffness distribution among the transverse bearing positions.

Figure 13 presents the measured jacking force–displacement curves of the three transverse bearings at the left side pier. To further quantify the transverse difference in bearing response, linear regression was performed for the three measured curves, as summarized in

Table 4. Linear fitting results of jacking force–displacement curves for three transverse bearings of the left side pier.

Bearing Axis	Linear Fitting Slope (kN/mm)	Pearson Correlation Coefficient, r	Coefficient of Determination, R2	Measured Jacking Force at 30 mm (kN)
A-axis side bearing	529.31	0.9976	0.9953	16,697
B-axis middle bearing	1178.01	0.9986	0.9972	35,568
C-axis side bearing	548.14	0.9983	0.9965	16,318

.

The jacking force–displacement curves of the three bearings showed strong linear correlations, with Pearson correlation coefficients greater than 0.997. The linear fitting slope of the B-axis middle bearing was 1178.01 kN/mm, whereas those of the A-axis and C-axis side bearings were 529.31 kN/mm and 548.14 kN/mm, respectively. The slope of the middle bearing was approximately 2.19 times the average slope of the two side bearings. At a jacking displacement of 30 mm, the measured jacking force of the middle bearing was 35,568 kN, which was approximately 2.13 times that of the A-axis side bearing and 2.18 times that of the C-axis side bearing.

This trend indicates that the intermediate bearing was more sensitive to jacking displacement than the side bearings. The nearly symmetric responses of the A-axis and C-axis bearings demonstrate that the transverse synchronous jacking system maintained good coordination during construction. The significantly larger response of the B-axis bearing can be explained by the higher vertical load-transfer stiffness near the middle support line and the transverse load-sharing mechanism of the ultra-wide composite girder. Therefore, for bridges with similar ultra-wide double-deck composite configurations, the middle bearing should be treated as the primary force control point, while the side bearings should be monitored carefully to prevent transverse elevation differences and local reaction redistribution.

4.2.2. Comparative Analysis of Stresses

The measured stress variations during the post-rotation jacking process were compared with the corresponding calculated values. The quantitative comparison is listed in

Table 5. Quantitative comparison of measured and calculated stress variations at selected monitoring points.

Location	Measured Stress Variation (MPa)	Calculated Stress Variation (MPa)	Absolute Error (MPa)	Relative Error (%)
side pier location	51.98	59.18	7.2	13.85
	40	45.3	5.3	13.25
	20	22.6	2.6	13
	−13.4	−15.2	1.8	13.43
mid-span location	−74.88	−75.37	0.49	0.65
	−58	−65.4	7.4	12.76
	−43.5	−48.9	5.4	12.41
	−34	−38.2	4.2	12.35
intermediate pier location	−30.02	−36.99	6.97	23.22

.

The measured and calculated stress variations at the selected monitoring points showed consistent overall trends. The Pearson correlation coefficient between the measured and calculated stress responses was 0.9980, indicating a strong linear selected monitoring points showed consistent overall trends. The Pearson correlation coefficient between the measured and calculated stress responses was 0.9980, indicating a strong linear correlation. For the nine monitoring data pairs listed in Table 5, the mean absolute error was 4.60 MPa, the maximum absolute error was 7.40 MPa, and the mean relative error was 12.77%. Although the relative error of the stress response was higher than that of the jacking force response, the calculated results captured the distribution pattern and variation trend of the measured stresses with good accuracy.

The absolute magnitudes of the measured stress variations were generally smaller than those of the calculated values. This difference may be attributed to several factors. First, the finite element model was established based on idealized linear elastic assumptions and did not fully account for local stiffness redistribution at joints, construction clearances, and possible minor interface slip between steel and concrete. Second, stress measurements are more sensitive to sensor installation accuracy, local welding effects, temperature compensation, and the difference between local measured strain and sectional average stress. Third, partial stress redistribution may have occurred during staged jacking and unloading, resulting in slightly smaller measured stress variations than the calculated values.

Among the selected monitoring points, the maximum compressive stress variation occurred at the mid-span location, where the measured and calculated values were −74.88 MPa and −75.37 MPa, respectively, with an absolute error of 0.49 MPa and a relative error of only 0.65%. This indicates that the finite element model captured the dominant stress response at the critical section with high accuracy. The maximum relative error was 23.22%, occurring at the intermediate pier location, but the corresponding absolute error was 6.97 MPa, and the overall stress variation trend remained consistent. No abrupt stress change was observed at any monitoring point, suggesting that the temporary bearings were unloaded smoothly and that no abnormal local constraint or sudden load transfer occurred during the jacking process. Therefore, the stress monitoring results reasonably support the reliability of the finite element model and the proposed construction control method.

4.2.3. Alignment Analysis

In this study, the elevations of the bridge deck along Axes A, B, and C were successively measured after main girder jacking and during the jack unloading process to analyze the alignment before and after jacking closure. The elevation variations in the bridge deck during the beam-end jacking stage and the jack unloading stage are presented in Figure 14. As can be observed from Figure 14, no abrupt displacement changes occurred at any node of the main girder during the jacking and girder lowering processes, and the displacement variation trends are consistent with the theoretical values. The maximum deviation of the longitudinal deck alignment is −2.5 cm, with all deviations controlled within ±3 cm, thereby satisfying the requirements of the relevant specifications.

4.2.4. Definition and Statistical Analysis of the Verification Coefficient

To quantitatively evaluate the reliability of the theoretical analysis methods, a verification coefficient ζ is defined as follows:

$$\zeta ={\displaystyle \frac{\mathrm{M}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}}{\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}}}$$

(36)

where the theoretical calculated values encompass both the finite element simulation results and the values derived from the simplified theoretical formulas. Based on the monitoring data acquired throughout the entire jacking construction process of this bridge, a total of 114 valid data pairs were obtained. These data pairs were categorized and statistically analyzed according to parameter type, and the results are presented in

Table 6. Statistical analysis of monitoring data verification coefficients.

Parameter Type	Sample Size	Mean ζ	Std. Dev. ζ	Max ζ	Min ζ	95% Empirical Agreement Range
Jacking Force	54	0.984	0.042	1.062	0.901	[0.902, 1.066]
Steel Truss Stress	42	0.958	0.036	1.028	0.892	[0.887, 1.029]
Concrete Slab Stress	18	0.941	0.044	1.015	0.876	[0.855, 1.027]
Overall	114	0.968	0.041	1.062	0.876	[0.888, 1.048]

.

As indicated in Table 6, the overall mean verification coefficient is 0.968, which is close to 1.0, and the 95% empirical agreement range is [0.888, 1.048]. This demonstrates that the theoretical analysis methods employed in this study possess relatively high reliability and are capable of accurately predicting the structural response during the jacking construction process of this bridge. The mean verification coefficient for jacking force is 0.984, approaching 1.0 and exhibiting relatively small dispersion. This is attributable to the fact that force parameters can be directly measured via jack oil pressure, possess a clear physical interpretation, and are less susceptible to localized effects, thereby yielding higher simulation accuracy. The mean verification coefficient for steel truss stress is 0.958, slightly lower than that for the force parameters, and the dispersion is somewhat greater. This is primarily because stress is more sensitive to factors such as joint stiffness, weld residual stresses, and temperature variations. Furthermore, minor deviations in strain gauge placement can also introduce measurement errors. The mean verification coefficient for concrete slab stress is the lowest, and its dispersion is the largest. In addition to the aforementioned reasons, factors such as the incomplete stabilization of concrete shrinkage and creep and steel-concrete interface slip may also contribute to measured values being lower than theoretical predictions. The measured values are generally slightly smaller than the theoretical values, indicating that the actual structure possesses a certain safety margin during the jacking process, that the design is conservative, and that the construction control has incorporated a reasonable degree of redundancy.

5. Conclusions

Taking a two-span continuous steel truss–concrete composite girder bridge with spans of 2 × 85 m as the engineering background, this study has conducted a systematic investigation into the mechanical behavior of the structure during rotation jacking construction through an integrated approach combining theoretical derivation, finite element simulation, and on-site bridge monitoring. The following principal conclusions are drawn:

(1)

Based on the force method of structural mechanics, a linear analytical relationship between synchronous jacking force and displacement was established, and a theoretical model for bearing reaction distribution under laterally asynchronous jacking was derived by considering the combined effects of vertical bending, torsion, and transverse multi-bearing support. The proposed model reveals the redistribution mechanism of bearing reactions during jacking and provides a theoretical basis for construction control.

(2)

Finite element analysis shows that during synchronous jacking, the increase in reaction force at the middle bearing is significantly greater than that at the side bearings. For the investigated bridge, each centimeter of synchronous jacking displacement results in an increase of approximately 9.4% in the middle-bearing reaction and 4.3% in the side-bearing reaction relative to their initial values. Under transverse eccentric jacking, the reaction force at the jacking position increases while those at adjacent supports decrease, and this effect is more pronounced when eccentric jacking occurs at the middle bearing.

(3)

The analysis of key control indicators indicates that when the transverse non-uniform jacking displacement reaches 20 mm, a tensile stress of approximately 0.3 MPa develops at the bottom flange of the concrete crossbeam. Therefore, the differential stroke among individual jacks should be controlled within 20 mm for the investigated bridge. In the actual construction process, the computerized synchronous jacking system maintained a stroke control accuracy of ±0.5 mm and a transverse elevation difference within 1 mm, ensuring a sufficient safety margin.

(4)

Field monitoring results verify the accuracy of both the theoretical analysis and finite element simulation. The measured jacking force–displacement relationships agree well with the calculated results. The Pearson correlation coefficients between the measured jacking forces and the finite element and theoretical predictions are 0.9987 and 0.9988, respectively, with corresponding mean relative errors of 3.84% and 4.23%. The completed bridge alignment deviation was controlled within ±3 cm. In addition, the fitted stiffness of the B-axis middle bearing is approximately 2.19 times the average stiffness of the A-axis and C-axis side bearings, indicating that the middle bearing should be regarded as the key force control point during jacking. The measured and calculated stress responses also exhibit consistent variation trends, with a Pearson correlation coefficient of 0.9980 and a mean relative error of 12.77%. No abrupt stress variation was observed during jacking or unloading, demonstrating a stable load-transfer process.

(5)

Statistical evaluation of the verification coefficients yields an overall mean value of 0.968 and a 95% empirical agreement range of [0.888, 1.048], indicating good agreement between the measured and calculated results. The integrated research approach combining theoretical analysis, numerical simulation, and field monitoring can effectively support the refined control of post-rotation jacking construction. Although the quantitative indicators obtained in this study are specific to the investigated bridge, the proposed analytical framework and force–displacement combined control strategy can provide useful references for similar ultra-wide steel truss–concrete composite girder bridges.