Synchronous closure method for multi-span continuous rigid frame bridge

Abstract

The invention discloses a synchronous closure method for a multi-span continuous rigid frame bridge, which comprises the following steps: (1) deflection calculation theory analysis under asynchronous closure, including the following sub-steps: a proportionality coefficient v formed at a K point in a Jth stage is a time function related to a loading period age psi; unifying the loading time and the actual time coordinate of the site; deflection calculation under the action of self weight, wherein deflection formed by prestress tension is calculated; calculating the deflection of the K point after the Jth section is tensioned under the asynchronous closure; (2) deflection calculation theoretical analysis under synchronous closure: the deflection calculation theoretical analysis under the synchronous closure of the bridge mainly considers the stress and deformation of the structure, a finite element method is adopted to discretize the bridge into a plurality of units, and a mechanical equilibrium equation is solved to solve the deflection; and (3) based on a finite element analysis platform, establishing a comparison model of a span-by-span closure process and a synchronous closure process. A construction scheme which is correct in line shape, reasonable in stress and fast in bridge forming is provided for the continuous rigid frame bridge.

Description

Technical Field

[0001] The invention relates to the technical field of synchronous closure of multi-span continuous rigid frame bridges, and in particular to a synchronous closure method for multi-span continuous rigid frame bridges. Background Art

[0002] In the field of transportation infrastructure, continuous rigid frame bridges are highly favored due to their strong spanning capacity, minimal supporting structures, high traffic flow efficiency, and good aesthetics. However, the traditional closure process has the disadvantage of a long construction period. More importantly, the differences in its closure process will have a significant impact on the final constant load internal force distribution of the multi-span continuous system. After closure, the bridge structure will change from a statically determinate structure to a statically indeterminate structure. The internal forces will be redistributed, and different closure processes will also cause large differences in the redistribution of internal forces due to creep and temperature, thus affecting the mechanical properties of the entire bridge. Therefore, how to optimize the bridge closure process, reduce the number of internal force redistributions, and simplify the calculation of structural internal forces has become an important research topic to promote the sustainable development of efficient construction in the bridge field.

[0003] Closure is one of the most critical construction steps in the construction of continuous rigid frame bridges. Based on the equivalent load method, Hu Zhijian et al. proposed a new closure technology that pre-tensions the box girder bottom plate, thereby eliminating the counterweight during closure. This can effectively eliminate disturbances during the closure process and achieve the goal of efficient construction. However, there is a lack of analysis of different closure sequences. Weng et al. developed eight closure schemes for a seven-span continuous rigid frame bridge based on the four principles of side spans first, middle spans second, middle spans first, side spans second, alternating closure of side spans and middle spans, and sequential closure. These schemes provide sufficient mechanical basis for the final closure construction plan, but do not involve research and analysis on the synchronous closure scheme for side spans and middle spans. Based on the study of synchronous closure of a four-span continuous rigid frame bridge, Yuan Hui et al. analyzed the internal forces, deflections, and post-bridge effects of span-by-span closure and synchronous closure, proving the feasibility of synchronous closure. From the perspective of construction technology, Wu Haishan et al. further proposed a method of using a hanging basket to simultaneously cast the straight sections and joint sections of the side spans. Studies have shown that this method has little effect on the force and deflection of the main beams on the middle span side, but it has a large disturbance on the side span main beams and does not consider the long-term stability of the bridge line shape.

[0004] In view of this, the present invention is based on the advantages that synchronous closure of continuous rigid frame bridges helps to control deflection, evenly distribute loads, and reduce the number of times of static indeterminacy of continuous rigid frame bridges. In view of the low efficiency of bridge construction, the influence of concrete shrinkage and creep caused by non-synchronous closure, the influence of temperature changes on measured values, and changes in temporary loads and other complex internal forces, a construction plan for synchronous closure of multi-span continuous systems is proposed. The influence of the sequence of gradual closure and synchronous closure after bridge completion and after ten years of shrinkage and creep, main beam stress, main beam line shape and pier top displacement are analyzed, and a construction plan with correct line shape, reasonable force and fast bridge completion is provided for continuous rigid frame bridges. Summary of the Invention

[0005] In order to overcome the above-mentioned shortcomings of the prior art, the present invention proposes a method for synchronous closure of multi-span continuous rigid frame bridges. The influence of the sequence of gradual closure and synchronous closure after completion of the bridge and after ten years of shrinkage and creep is analyzed, and a construction scheme with correct alignment, reasonable stress and fast completion is provided for continuous rigid frame bridges.

[0006] The technical solution adopted by the present invention to solve the technical problem is: a method for synchronous closure of a multi-span continuous rigid frame bridge, comprising the following steps:

[0007] (1) Theoretical analysis of deflection calculation under non-synchronous closure includes the following sub-steps:

[0008] 1.1 The proportional coefficient ν formed at point K in stage J is a time function related to the loading age ψ;

[0009] 1.2 Unify the loading time and the actual time coordinates on site;

[0010] 1.3 Calculation of deflection under deadweight, calculation of deflection caused by prestressing;

[0011] 1.4 Calculate the deflection of point K after tensioning of section J under non-synchronous closure;

[0012] (2) Theoretical analysis of deflection calculation under synchronous closure: Theoretical analysis of deflection calculation under synchronous closure of bridges mainly considers the structural stress and deformation. The finite element method is used to discretize the bridge into multiple units and solve the mechanical equilibrium equation to calculate the deflection. The specific steps include the following:

[0013] 2.1 Based on the unit beam analysis, the rotation angle of the cantilever beam of the continuous rigid frame bridge is obtained;

[0014] 2.2 Calculate the deflection of point K in the synchronous closure process;

[0015] 2.3 Use step function to represent the moment of elastic deformation;

[0016] 2.4 After the completion of Section J, calculate the height of point K under the action of the pier under the girder and the centerline;

[0017] 2.5 After the completion of Section J, the height of point K at the bottom of the joint after simultaneous prestressing is applied;

[0018] Combining steps 2.4 and 2.5, we can get the deflection at the current stage by taking the elevation difference of point K after the J-th segment is completed and the prestressing is synchronized and the joint is synchronized.

[0019] (3) Based on the finite element analysis platform, a comparative model of span-by-span closure and synchronous closure processes was established: During the bridge completion stage, the two different closure sequences of asynchronous closure and synchronous closure have a significant impact on the main beam line shape. Therefore, the difference in the installation elevation of the construction segment formwork will directly lead to the accumulation of formwork positioning deviations. It is necessary to implement precise dynamic regulation in the construction process control, and finally form a closed-loop construction control system of "analysis-optimization-control-verification".

[0020] Furthermore, the proportional coefficient ν formed at point K in stage J is a time function related to the loading age ψ as follows:

[0021]

[0022] In formula (1), t j Indicates the pouring time of the Jth section; t0 indicates the beginning of pouring.

[0023] Furthermore, the loading moment and the actual time coordinates on site are unified by using the following formula:

[0024]

[0025] In formula (2), H0 represents the relative height; ΔT represents the temperature difference between the two measurements before and after tensioning; E and B0 represent the elastic modulus and cross-sectional area of ​​the pier, respectively; Q i represents the deadweight of the i-th section beam; t i Indicates the time when the i-th section is completed; the ζ(t,T) function represents the unification of the loading time and the actual time coordinate on site.

[0026] Furthermore, the deflection β under the action of deadweight kj (t) is calculated as follows:

[0027]

[0028] In formula (3): l Li represents the equivalent force arm from segment i to the center of segment L; t L Indicates the pouring time of the Lth section; x k represents the horizontal coordinate of point K; λ L Indicates the midpoint coordinates of segment L (1≤L≤K); E, I L Respectively represent the elastic modulus and moment of inertia of the L segment; G, A L They represent the shear modulus and cross-sectional area of ​​the L segment respectively; dL represents the length of the L segment;

[0029] Deflection caused by prestressing for:

[0030]

[0031] In formula (4): P Li represents the tension of the i-th steel cable on the L section; t i ' represents the tensioning moment of the i-th segment, e L Indicates the eccentricity in the L segment.

[0032] Calculate the deflection of point K after tensioning of section J under non-synchronous closure Specifically:

[0033]

[0034] Where, is the deflection caused by prestressing, is the deflection under deadweight; Unified deflection is made for the loading moment and the actual time coordinate on site.

[0035] Furthermore, according to the unit beam analysis, the rotation angle of the cantilever beam of the continuous rigid frame bridge is:

[0036]

[0037] Furthermore, the deflection of point K in the synchronous closure process is:

[0038]

[0039] In formula (7): M(λ L ) represents the bending moment at the midpoint of section L after section J is completed; T(λ L ) represents the torque applied to the midpoint of section L after section J is completed; where,

[0040]

[0041] Furthermore, the moment of elastic deformation is represented by a step function, specifically:

[0042]

[0043] Furthermore, in step 2.4, after segment J is built, the height of point K is:

[0044]

[0045] In formula (11): t i represents the time when the i-th section is completed; t i ' represents the tensioning moment of the i-th section; E, B0 represent the elastic modulus and cross-sectional area of ​​the pier respectively.

[0046] Furthermore, in step 2.5, the height of the K point under the synchronous closure is:

[0047]

[0048] Combining equations (11) and (12) we can obtain equation (13):

[0049]

[0050] The above derivation is based on the assumption that the elastic modulus and section moment of inertia of each segment are different under synchronous closure construction and do not change with time.

[0051] The asynchronous closure process involves complex internal force variations, and deflection is affected by varying measurement times and environments. Concrete shrinkage and creep are particularly significant, causing the main beam to gradually deflect downward, affecting the bridge's long-term alignment. Furthermore, temperature fluctuations cause the main beam to expand and contract, interfering with the accuracy of deflection measurements. Furthermore, changes in temporary loads during construction can also affect the distribution of internal forces. These intertwined factors complicate deflection calculation and measurement, requiring comprehensive consideration to ensure the structural safety and performance of the bridge.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] (1) The present invention uses multi-span synchronous closure to shorten the construction period of the entire closure project and make the process more compact. In addition, the multi-span continuous system is closed at one time, so that the load of the closure section acts on the final structure at the same time, which can make the change of internal force more uniform. This is much simpler than the complex internal force calculation caused by the continuous change of the secondary internal force generated by the closure of each span as the number of statically indeterminate times increases.

[0054] (2) Structural closure is the most critical process in construction. During the bridge construction stage, the two different closure sequences, asynchronous closure and synchronous closure, have a significant impact on the main beam line shape, which reached 54.74% for this bridge. Therefore, the difference in the installation elevation of the construction segment formwork will directly lead to the accumulation of formwork positioning deviations, and precise dynamic regulation must be implemented in the construction process control.

[0055] (3) The secondary internal forces caused by the construction of multi-span continuous rigid frame bridges are positively correlated with the indeterminate order of the structure. The current non-synchronous closure construction method is complex in terms of structural system conversion. This invention studies the effects of different closure schemes on the stress and linear shape of the main beam, and ultimately forms a closed-loop construction control system of "analysis-optimization-control-verification". Not only has the feasibility of the new method been verified in theory, but in practice, a shorter construction period and higher economic efficiency have been achieved, providing a new process option for the construction of three-span rigid frame bridges under special circumstances. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments.

[0057] Figure 1 The present invention provides a flowchart of a method for synchronous closure of a multi-span continuous rigid frame bridge according to an embodiment of the present invention.

[0058] Figure 2 This is a discrete diagram of the bridge structure according to an embodiment of the present invention.

[0059] Figure 3 These are the stress diagrams of the main beams at the bridge completion stage under different closure sequences according to the embodiments of the present invention, where (a) is a stress comparison diagram of the upper edge of the main beam, and (b) is a stress comparison diagram of the lower edge of the main beam.

[0060] Figure 4 Figure 1 shows the stress diagrams of the main beam during the ten-year shrinkage creep stage under different closure sequences in an embodiment of the present invention, where (a) is a stress comparison diagram of the upper edge of the main beam, and (b) is a stress comparison diagram of the lower edge of the main beam.

[0061] Figure 5 The vertical displacement diagrams of the main beams under different closure sequences of the embodiments of the present invention are shown in FIG. (a) is the vertical displacement diagram of the main beams during the completion stage, and (b) is the vertical displacement diagram of the main beams after ten years of shrinkage creep.

[0062] Figure 6 These are comparison diagrams of the main beam line shape and stress after closure of an embodiment of the present invention, where (a) is the main beam stress diagram and (b) is the main beam vertical displacement diagram. DETAILED DESCRIPTION

[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0064] In the description of the present invention, it should be noted that the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside", etc., indicating directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction. Therefore, they cannot be understood as limiting the present invention.

[0065] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be internal communication between two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances. In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0066] like Figure 1 As shown, a method for synchronous closure of a multi-span continuous rigid frame bridge according to an embodiment of the present invention includes the following steps:

[0067] (1) Theoretical analysis of deflection calculation under non-synchronous closure includes the following sub-steps:

[0068] 1.1 The proportional coefficient ν formed at point K in stage J is a time function related to the loading age ψ as follows:

[0069]

[0070] In formula (1), t j Indicates the pouring time of the Jth section; t0 indicates the beginning of pouring.

[0071] 1.2 Unify the loading time and the actual time coordinates on site; specifically, use the following formula:

[0072]

[0073] In formula (2), H0 represents the relative height; ΔT represents the temperature difference between the two measurements before and after tensioning; E and B0 represent the elastic modulus and cross-sectional area of ​​the pier, respectively; Q i represents the deadweight of the i-th section beam; t i Indicates the time when the i-th section is completed; the ζ(t,T) function represents the unification of the loading time and the actual time coordinate on site.

[0074] 1.3 Calculation of deflection under self-weight, calculation of deflection caused by prestressing; deflection under self-weight β kj (t) is calculated as follows:

[0075]

[0076] In formula (3): l Li represents the equivalent force arm from segment i to the center of segment L; t L Indicates the pouring time of the Lth section; x krepresents the horizontal coordinate of point K; λ L Indicates the midpoint coordinates of segment L (1≤L≤K); E, I L Respectively represent the elastic modulus and moment of inertia of the L segment; G, A L They represent the shear modulus and cross-sectional area of ​​the L segment respectively; dL represents the length of the L segment;

[0077] Deflection caused by prestressing for:

[0078]

[0079] In formula (4): P Li represents the tension of the i-th steel cable on the L section; t i ' represents the tensioning moment of the i-th segment, e L Indicates the eccentricity in the L segment.

[0080] 1.4 Calculate the deflection of point K after tensioning of section J under non-synchronous closure; Calculate the deflection of point K after tensioning of section J under non-synchronous closure Specifically:

[0081]

[0082] Where, is the deflection caused by prestressing, is the deflection under deadweight; Unified deflection is made for the loading moment and the actual time coordinate on site.

[0083] (2) Theoretical analysis of deflection calculation under synchronous closure: Theoretical analysis of deflection calculation under synchronous closure of bridges mainly considers the structural stress and deformation. The finite element method is used to discretize the bridge into multiple units and solve the mechanical equilibrium equation to calculate the deflection. The specific steps include the following:

[0084] 2.1 According to the unit beam analysis, the rotation angle of the cantilever beam of the continuous rigid frame bridge is obtained as:

[0085]

[0086] 2.2 Calculation of the deflection of point K using the synchronous closure process:

[0087]

[0088] In formula (7): M(λ L ) represents the bending moment at the midpoint of section L after section J is completed; T(λ L ) represents the torque applied to the midpoint of section L after section J is completed; where,

[0089]

[0090] 2.3 The moment of elastic deformation is represented by a step function, specifically:

[0091]

[0092] 2.4 After the completion of Section J, calculate the height of point K under the action of the pier under the action of the beam and the center:

[0093]

[0094] In formula (11): t i represents the time when the i-th section is completed; t i ' represents the tensioning moment of the i-th section; E, B0 represent the elastic modulus and cross-sectional area of ​​the pier respectively.

[0095] 2.5 After the completion of Section J, the height of point K under the simultaneous closure after simultaneous prestressing is:

[0096]

[0097] Combining equations (11) and (12) we can obtain equation (13):

[0098]

[0099] The above derivation is based on the assumption that the elastic modulus and section moment of inertia of each segment are different under synchronous closure construction and do not change with time.

[0100] Combining steps 2.4 and 2.5, we can get the deflection at the current stage by taking the elevation difference of point K after the J-th segment is completed and the prestressing is synchronized and the joint is synchronized.

[0101] (3) Based on the finite element analysis platform, a comparative model of span-by-span closure and synchronous closure processes was established: During the bridge completion stage, the two different closure sequences of asynchronous closure and synchronous closure have a significant impact on the main beam line shape. Therefore, the difference in the installation elevation of the construction segment formwork will directly lead to the accumulation of formwork positioning deviations. It is necessary to implement precise dynamic regulation in the construction process control, and finally form a closed-loop construction control system of "analysis-optimization-control-verification".

[0102] Taking a large bridge as an example, the bridge is designed to be 627.00 meters long, with spans of 5x40 mm + (77 mm + 145 mm + 77 mm) + 3x40 mm on both sides. The bridge superstructure is a prestressed continuous rigid frame. The main span is 299 meters long and is arranged as a double-span bridge, with a single span deck width of 12.75 meters. The lower pier structure is arranged in sections, using hollow, thin-walled rectangular piers. The pier columns are chamfered in the direction of the water flow, and the maximum pier height is 74.132 meters. The bridge is constructed in sections, with four main piers on the left and right sections, located at P6# and P7# respectively. The 0# block segment is 11m long, with a beam height of 8.7m (beam height is the height at the center of the box girder). The upper portion of the bottom pier is 8m wide, with a cantilever width of 7m. The wing plates on both sides are 2.875m long, with straight outer webs, a top plate width of 12.75m, and a bottom plate thickness of 1.26m. The two sides cantilever out 2.5m along the length of the bridge. The main bridge superstructure was constructed using a cantilevered casting method using a hanging basket. There are four cast-in-place side span sections, four side span closure sections, and two mid-span closure sections.

[0103] Based on the plane bar theory, the bridge analysis software MIDAS Civil was used to model and analyze the two closure sequences according to the design drawings. The structural calculation model and boundary conditions must be consistent with the actual structure. The entire bridge is divided into 123 nodes and 120 units, of which the superstructure has 95 nodes and 94 units, and the substructure has 28 nodes and 26 units. The discrete diagram of the bridge structure is shown in Figure 2 shown.

[0104] The stress calculation results of the upper and lower edges of the typical main beam sections under the two processes of non-synchronous closure and synchronous closure are shown in Tables 1 and 2 below. The stress calculation results of the entire main beam section are as follows Figures 3 and 4 shown.

[0105] Table 1 Stress on the upper edge of the main beam under different closure sequences

[0106]

[0107] Note: ① in the table is non-synchronous closure, ② is synchronous closure

[0108] Table 2 Stress on the lower edge of the main beam under different closure sequences

[0109]

[0110]

[0111] Note: ① in the table is non-synchronous closure, ② is synchronous closure

[0112] As shown in Tables 1 to 2 above and Figures 3 and 4As shown in Figure 2 , during the completion phase, the maximum stress at the upper edge of the main girder of this three-span rigid frame bridge was -10.8 MPa during the span-by-span closure sequence, and -11.0 MPa during the simultaneous closure sequence. The difference between the two was 0.2 MPa, with the former being 1.85% greater than the latter. The maximum stress at the lower edge of the main girder was -8.18 MPa during the span-by-span closure sequence, and -8.06 MPa during the simultaneous closure sequence. The difference between the two was 0.12 MPa, with the former being 1.47% greater than the latter. Furthermore, the main girder cross-section exhibited no tensile stress. Numerical analysis results indicate that the stress distribution of the main girder in the completed state is not significantly sensitive to variations in the closure process. Further comparison with stress monitoring data from a decade of operation reveals that the stress variation in key sections remains within 3%, confirming that the mechanism by which the time-varying effects of shrinkage and creep affect the mechanical behavior of the main girder is not significantly correlated with the closure scheme selection. This mechanical property provides important theoretical support for optimizing the closure process for multi-span continuous rigid frame bridges.

[0113] A comparative analysis of the vertical displacement of the main beam was conducted for two different processes: asynchronous closure and synchronous closure. The results of the typical cross-section of the main beam are shown in Table 3. The vertical displacement of the entire cross-section of the main beam is as follows: Figure 5 shown.

[0114] Table 3 Main beam line shape under different closure sequences

[0115]

[0116] Note: ① in the table is non-synchronous closure, ② is synchronous closure

[0117] From the above table 3 and Figure 5 As shown, during the construction phase, the maximum vertical displacement of this three-span rigid frame bridge during span-by-span closure was 11.23mm, and during simultaneous closure, 8.53mm. Both occurred at the mid-span closure. The former was 24.05% greater than the latter, or 2.70mm. Furthermore, after using two different closure sequences, the calculation results show that the positions of some main girder nodes varied significantly. For example, at the quarter-span side span, the vertical displacement during span-by-span closure was 39.51mm downward, while during simultaneous closure, it was 61.14mm downward. The former was -54.74% less than the latter, or 21.63mm. The above analysis shows that the two different closure sequences during the construction phase (span-by-span closure and simultaneous closure) have a significant impact on the main girder alignment. Differences in the installation elevations of construction segment formwork will directly lead to cumulative formwork positioning deviations, necessitating precise dynamic control during construction process control. The study further showed that the cumulative vertical displacement of key monitoring sections remained stable within the 1.5mm threshold during the ten-year operation period. The measured data verified that the structural deformation characteristics caused by the time-varying effect of concrete shrinkage and creep showed no significant correlation with the choice of joint closure process path.

[0118] Based on the structural stress characteristics of the bridge in the embodiment, the key to its construction control is the linear and stress control of the structure. The progressive forming of the mechanical system of the continuous rigid frame bridge is essentially reflected in the process of structural system reconstruction under the coupling of multi-stage construction. The stress and vertical linear shape of the main beam are very sensitive to factors such as prestressing tensioning accuracy, beam cross-sectional dimensions, concrete material properties and pouring weight, construction period, and temperature of the structure, and should be the focus of precision control. The entire process of joint closure construction is tracked in real time under the synchronous joint closure sequence, and the stress and linear results of the synchronous joint closure are monitored. The main beam stress monitoring results are shown in Table 4 and below. Figure 6 -(a), the main beam linear monitoring results are shown in Table 5 and below Figure 6 -(b) shows:

[0119] Table 4 Main beam stress after closure under synchronous closure sequence

[0120]

[0121] Table 5 Main beam alignment after closure under synchronous closure sequence

[0122] Serial number Node location Measured vertical displacement (mm) Theoretical vertical displacement (mm) Vertical displacement difference (mm) 1 left pivot 3.00 0.00 3.00 2 1 / 4 of the side span 5.00 3.88 1.12 3 Side span and mid span 3.00 0.65 2.35 4 3 / 4 of the side span 1.00 0.50 0.50 5 1 / 4 of the middle span 8.00 9.01 -1.01 6 mid-span mid-span 36.00 31.00 5.00 7 3 / 4 of the middle span 10.00 9.00 1.00 8 right fulcrum 3.00 0.00 3.00

[0123] From Table 4 to Table 5 above and Figure 6 As shown in the figure, after the synchronous closure, the measured values ​​of the cross-sectional stress and vertical displacement of each main beam of the three-span rigid frame bridge are basically consistent with the theoretical values, and the error is within the allowable range. Among them, the maximum difference in the main beam stress is only -0.51Mpa, which occurs at 1 / 4 of the left span. The measured values ​​of the vertical displacement of the main beam cross-sectional area are basically consistent with the theoretical values, and the maximum difference is only 5mm, which occurs in the middle of the middle span.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for synchronous closure of a multi-span continuous rigid frame bridge, characterized in that: The following steps are involved: (1) Theoretical analysis of deflection calculation under non-synchronous closure includes the following sub-steps: 1.1 The proportional coefficient ν formed at point K in stage J is a time function related to the loading age ψ; 1.2 Unify the loading time and the actual time coordinates on site; 1.3 Calculation of deflection under deadweight, calculation of deflection caused by prestressing; 1.4 Calculate the deflection of point K after tensioning of section J under non-synchronous closure; (2) Theoretical analysis of deflection calculation under synchronous closure: Theoretical analysis of deflection calculation under synchronous closure of bridges mainly considers the structural stress and deformation. The finite element method is used to discretize the bridge into multiple units and solve the mechanical equilibrium equation to calculate the deflection. The specific steps include the following: 2.1 Based on the unit beam analysis, the rotation angle of the cantilever beam of the continuous rigid frame bridge is obtained; 2.2 Calculate the deflection of point K in the synchronous closure process; 2.3 Use step function to represent the moment of elastic deformation; 2.4 After the completion of Section J, calculate the height of point K under the action of the pier under the girder and the centerline; 2.5 After the completion of Section J, the height of point K at the bottom of the joint after simultaneous prestressing is applied; Combining steps 2.4 and 2.5, we can get the deflection at the current stage by taking the elevation difference of point K after the J-th segment is completed and the prestressing is synchronized and the joint is synchronized. (3) Based on the finite element analysis platform, a comparative model of span-by-span closure and synchronous closure processes was established: During the bridge completion stage, the two different closure sequences, asynchronous closure and synchronous closure, have a significant impact on the main beam line shape. Therefore, the difference in the installation elevation of the construction segment formwork will directly lead to the accumulation of formwork positioning deviations. It is necessary to implement precise dynamic control in the construction process control, and finally form a closed-loop construction control system of "analysis-optimization-control-verification".

2. The method for synchronous closure of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: The proportional coefficient ν formed at point K in stage J is a time function related to the loading age ψ as follows: In formula (1), t j Indicates the pouring time of the Jth section; t0 indicates the beginning of pouring.

3. The method for synchronous closure of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: The specific method to unify the loading time and the actual time coordinates on site is to use the following formula: In formula (2): H0 represents the relative height; ΔT represents the temperature difference between the two measurements before and after tensioning; E and B0 represent the elastic modulus and cross-sectional area of ​​the pier, respectively; Q i represents the deadweight of the i-th section beam; t i Indicates the time when the i-th section is completed; the ζ(t,T) function represents the unification of the loading time and the actual time coordinate on site.

4. The method for synchronous closure of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: Deflection β under deadweight kj (t) is calculated as follows: In formula (3): l Li represents the equivalent force arm from segment i to the center of segment L; t L Indicates the pouring time of the Lth section; x k represents the horizontal coordinate of point K; λ L Indicates the midpoint coordinates of segment L (1≤L≤K); E, I L Respectively represent the elastic modulus and moment of inertia of the L segment; G, A L They represent the shear modulus and cross-sectional area of ​​the L segment respectively; dL represents the length of the L segment; Deflection caused by prestressing for: In formula (4): P Li represents the tension of the i-th steel cable on the L section; t' i represents the tensioning moment of the i-th segment, e L Indicates the eccentricity in the L segment.

5. The method for synchronous closure of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: Calculate the deflection of point K after tensioning of section J under non-synchronous closure, specifically: Where, is the deflection caused by prestressing, is the deflection under deadweight; Unified deflection is made for the loading moment and the actual time coordinate on site.

6. The method for synchronous closure of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: According to the unit beam analysis, the rotation angle of the cantilever beam of the continuous rigid frame bridge is:

7. The method for synchronous closure of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: Deflection of point K using the synchronous closure process: In formula (7): M(λ L ) represents the bending moment at the midpoint of section L after section J is completed; T(λ L ) represents the torque applied to the midpoint of section L after section J is completed; where, 8. The method for synchronous closure of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: The moment of elastic deformation is represented by a step function, specifically:

9. The method for synchronous closure of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: Using a step function to represent the moment of elastic deformation, in step 2.4, after segment J is built, the height of point K is: In formula (11): t i represents the time when the i-th section is completed; t i ' represents the tensioning moment of the i-th section; E, B0 represent the elastic modulus and cross-sectional area of ​​the pier respectively.

10. The method for synchronous closure of a multi-span continuous rigid frame bridge according to claim 1, characterized in that: The moment of elastic deformation is represented by a step function. In step 2.5, the height of point K under synchronous closure is:

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