Structural design method of wide integral multi-arch tied-arch bridge based on internal force comprehensive regulation and control

Abstract

The invention relates to the field of arch bridge design, and particularly discloses a wide integral multi-arch tied-arch bridge structure design method based on internal force comprehensive regulation and control, and the method comprises the steps: firstly, according to the dead load of a bridge floor, initially simulating the suspender force and the size of main components; establishing a finite element model, and calculating the rigidity of the lower rod end of the suspender under the combined action of arch rib-wind bracing-suspender by stripping longitudinal and transverse beams of the main beam; the rigidity serves as an elastic support, the cross beam is simply designed, and prestress configuration of the cross beam is determined; a design result is substituted into the overall model for finished bridge analysis, the suspender cable force is finely adjusted with the aim that the tie bar beam reaches the flat beam state, and internal force comprehensive regulation and control are achieved; and finally checking and iteratively optimizing until all the components meet specifications. According to the method, the problems that an internal force coupling mechanism of a wide-width multi-arch-rib structure is complex and the design efficiency is low are effectively solved, and a set of clear, efficient and reliable design process is provided.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of arch bridge design, in particular to a structure design method for wide integral multi-arch tied arch bridge based on internal force comprehensive regulation. BACKGROUND

[0002] With the increasing construction of eight-lane expressways and wide municipal roads, tied arch bridges with a span of 80-200 meters gradually develop in the direction of wide and multi-arch rib due to their competitive advantages. Compared with the traditional double-width separated structure, the integral three-rib or multi-rib structure has more advantages in space saving and landscape improvement, and is considered more economical and reasonable.

[0003] However, the structural degree of static indeterminacy of wide integral multi-arch tied arch bridge is high, and the internal force coupling effect between the main girder, arch rib and suspender is significant. The proportion of each arch rib sharing the load of the bridge deck is complexly affected by various factors such as the stiffness of the cross beam and the prestress configuration. This leads to large errors when the traditional simplified design method based on two arch ribs is applied to such bridges, making it difficult to accurately determine the cross-sectional size of the components.

[0004] In addition, there are numerous prestressed steel strands in the longitudinal and transverse beams in the wide bridge deck system, and the secondary internal force generated by the prestress will cause redistribution of the suspender force, and its mechanism is not clear. Different steel strand arrangements have a significant impact on the suspender force, making the process of adjusting the cable force and optimizing the prestress in the completed bridge state tedious and the target ambiguous. The existing technology lacks an effective comprehensive analysis process, resulting in high design difficulty and high dependence on personnel experience, which restricts the promotion and application of this bridge type. SUMMARY

[0005] In order to improve the problem of high structural design difficulty and poor applicability of conventional analysis methods for wide integral multi-arch tied arch bridges, the present application provides a structure design method for wide integral multi-arch tied arch bridge based on internal force comprehensive regulation.

[0006] The structure design method for wide integral multi-arch tied arch bridge based on internal force comprehensive regulation provided by the present application adopts the following technical solution: A structure design method for wide integral multi-arch tied arch bridge based on internal force comprehensive regulation, comprising the following steps: S1, based on the dead load of the bridge deck system standard segment and assuming that the load is evenly distributed among the multi-arch ribs, initially determine the suspender force and specifications; S2, according to the initially determined suspender force, calculate the arch top horizontal thrust and tied beam tension, and determine the preliminary cross-sectional size of the arch rib and tied beam and the number of prestressed strands in the tied beam; S3, establish a global spatial finite element truss model of the structure; S4, separate the main girder longitudinal and transverse beams, and calculate the lower end stiffness of each suspender under the combined action of the arch rib, wind brace and suspender; S5, simplify the cross beam as a continuous beam with the lower rod end stiffness as elastic support, preliminarily determine the cross beam structure size and prestressed steel beam arrangement; S6, substitute the determined cross beam prestressed steel beam into the whole space finite element truss model for bridge completion analysis, fine-tune the suspender cable force, so that the tied arch bridge under the dead load reaches the basic beam flat state; S7, according to the optimized suspender force, check the internal force of the main component, and adjust the cross section size and prestressed arrangement thereof; repeat steps S1 to S7 for iteration until all components meet the specification requirements.

[0007] Further, in step S1, the dead load includes the second phase dead load composed of bridge pavement and auxiliary facilities.

[0008] Further, in step S1, the multiple arch ribs are three arch ribs.

[0009] Further, in step S2, the arch top horizontal thrust and tied arch beam tension are obtained by selecting a half-arch beam cantilever structure for calculation.

[0010] Further, in step S3, the arch rib and main beam in the whole space finite element truss model are simulated by beam elements, and the suspender is simulated by truss elements.

[0011] Further, in step S4, the method for calculating the lower rod end stiffness is: a unit vertical load F0 is applied at the lower rod end of the suspender, and the displacement x thereof is calculated ij , then the lower rod end stiffness Kij of the suspender is F0 / x ij , wherein i represents the i-th longitudinal suspender, and j represents the j-th transverse suspender.

[0012] Further, in step S5, the cross beam includes a middle cross beam and an end cross beam.

[0013] Further, in step S6, the basic beam flat state refers to that the vertical displacement of the tied arch beam is not greater than 1 cm and the bending moment value is not greater than 2000 kN·m.

[0014] Further, the method is suitable for wide-span whole three-arch tied arch bridges.

[0015] The application also provides a structure design system for wide-span whole multiple-arch tied arch bridges based on internal force comprehensive regulation and control, for realizing the above method, the system comprising: a data processing and initialization module: for inputting bridge basic parameters, and according to the assumption of bridge deck standard segment dead load and multiple arch rib load sharing, preliminarily determining suspender force and specifications, preliminary cross section size of arch rib and tied arch beam, and number of tied arch beam internal prestressed beam; Finite element analysis module: used for establishing and calculating the overall spatial finite element truss model of the structure, and the combined action model of the arch rib, wind brace and suspender after the longitudinal and transverse beams of the main beam are stripped; Stiffness calculation module: coupled with the finite element analysis module, used for calculating the lower end stiffness of each suspender; Transverse beam design and analysis module: used for simplifying the transverse beam into a continuous beam model with the following rod end stiffness as elastic support, and performing preliminary design and analysis of the transverse beam structure size and prestressed steel strand arrangement; Internal force regulation and iterative optimization module: used for substituting the transverse beam design parameters into the overall finite element model to perform bridge completion analysis, fine-tuning the suspender cable force to make the tied arch beam reach the basic beam flat state, and performing iterative optimization on the component cross-sectional size and prestressed configuration according to the checking results until all designs meet the specification requirements.

[0016] In summary, the present application includes the following beneficial technical effects: Firstly, by introducing the transverse beam simplified design method based on the vertical combined stiffness of the arch rib and suspender (i.e. the lower end stiffness of the suspender), the present application can clearly separate the mutual influence of the arch rib-wind brace-suspender combined action system and the main beam longitudinal and transverse beam system. This effectively solves the core problem of unclear internal force coupling mechanism caused by high degree of static indeterminacy of wide multi-arch rib structure, provides a clear analysis path for designers, and can quickly and efficiently determine the main beam longitudinal and transverse beam steel strand and suspender tension force parameters.

[0017] Secondly, the present application establishes a set of suspender cable force and prestress comprehensive regulation process with the clear goal of "realizing the basic beam flat state of the tied arch beam under dead load". This goal is clear and quantifiable, guiding designers to fine-tune and iteratively optimize through finite element models, improving the complex regulation process and ambiguous target dilemma caused by the influence of prestress secondary internal force in traditional methods, and improving design efficiency and accuracy.

[0018] The combination of the above technical means forms a systematic, efficient and reliable design process. It not only ensures the rationality of the internal force distribution of the main components in the bridge completion state and the safety of the structure, but also reduces the excessive dependence on personal experience of designers, providing strong technical support for the large-scale popularization and application of wide overall multi-arch tied arch bridges. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 is the elevation view of the wide overall multi-arch tied arch bridge in the embodiment of the present application; Figure 2 is the transverse section view of the wide overall multi-arch tied arch bridge in the embodiment of the present application; Figure 3 is a schematic view of the arch top horizontal thrust H and the tied arch beam tension T in step S2 in the embodiment of the present application; Figure 4 is a structural schematic diagram of the beam disengaging body in step S4 of the embodiment of the present application; Figure 5 is a vertical plane calculation schematic diagram of the end stiffness of the lower boom of the beam disengaging body in step S4 of the embodiment of the present application; Figure 6 is a horizontal cross-section calculation schematic diagram of the end stiffness of the lower boom of the beam disengaging body in step S4 of the embodiment of the present application; Figure 7 is a schematic diagram of a simplified model of the beam in step S5 of the embodiment of the present application; Figure 8 is a schematic diagram of the structural size and steel beam arrangement of the beam in step S5 of the embodiment of the present application.

[0020] Reference signs, 1, tie beam, 1-1, side tie beam, 1-2, middle tie beam, 2, middle cross beam, 3, end cross beam, 4, arch rib, 4-1, side arch rib, 4-2, middle arch rib, 5, wind brace, 6, suspender, 6-1, side suspender, 6-2, middle suspender. DETAILED DESCRIPTION

[0021] The following will be described in detail with reference to the accompanying drawings. Figures 1-8 The present application will be further described in detail.

[0022] The present embodiment takes a through-type three-arch-rib steel pipe concrete tie beam arch bridge with a span L = 103 m and a bridge width B = 46.9 m on a certain expressway as an example, and designs the bridge by applying the structural design method of the wide-width integral multi-arch tie beam arch bridge based on internal force comprehensive regulation and control provided by the present application.

[0023] Referring to Figure 1 and Figure 2 The main structure of the bridge includes a tie beam 1 (including a side tie beam 1-1 and a middle tie beam 1-2), a middle cross beam 2, an end cross beam 3, an arch rib 4 (including a side arch rib 4-1 and a middle arch rib 4-2), a wind brace 5, and a suspender 6 (including a side suspender 6-1 and a middle suspender 6-2).

[0024] Specifically, as Figure 1 and Figure 2As shown, the middle cross beam 2 is vertically erected and fixed between the side tie beam 1-1 and the middle tie beam 1-2, connecting the tie beams in each piece into an integral bridge deck system to jointly bear the deck load; the end cross beam 3 is located at the two ends of the bridge and is also fixed with the end portions of the side tie beam 1-1 and the middle tie beam 1-2. The two ends (arch feet) of the side arch rib 4-1 and the middle arch rib 4-2 are fixed with the end portions of the side tie beam 1-1 and the middle tie beam 1-2. The upper ends of all the suspenders 6 are hingedly connected to the lower edges of the arch ribs 4 through anchorage devices; the side suspenders 6-1 connect the side arch rib 4-1, and the middle suspenders 6-2 connect the middle arch rib 4-2; the lower ends of all the suspenders 6 pass through the middle cross beam 2 and are finally anchored on the cross beams; the deck load is transmitted to the suspenders 6 through the cross beams, and then the load is lifted and transmitted to the arch ribs 4 by the suspenders 6. The wind brace 5 is transversely arranged between adjacent arch ribs 4, and the two ends thereof are fixed with the side arch rib 4-1 and the middle arch rib 4-2 respectively to enhance the transverse connection between the arch ribs 4.

[0025] The specific design steps are as follows: Step S1, preliminary parameters are determined: referring to the results of similar projects, the structural size of the bridge is initially determined. According to the principle that the suspender force and the structural dead load in the standard section range are basically balanced, the dead load (including the secondary dead load such as bridge deck pavement) of one standard section (the length is equal to the suspender spacing 5m) of the bridge deck system is calculated to be 5515 kN. Assuming that the three arch ribs evenly share the load, the suspender force corresponding to each arch rib is 5515 / 3≈1838 kN. According to this, the suspender specification is initially selected as LZM7-151, the design breaking force of which is 9705 kN, and the design cable force safety factor K under the dead load is about 5.0, which meets the specification requirements.

[0026] Step S2, the size of the main load-bearing member is determined: the half-arch beam cantilever structure is selected as the calculation model, the arch top horizontal thrust H is calculated according to the suspender force initially determined in step S1, and the tie beam tension T is obtained according to the static equilibrium principle, as shown in the formula: Figure 3 Based on the internal force, the tie beam cross section size is selected as 150cm×260cm (width×height), and the total amount of longitudinal prestressed steel strand required to be arranged in the tie beam is determined to be 48 strands, each of which is composed of 12 Φ12.5mm steel strands.

[0027] Step S3, the overall finite element model is established: the bridge analysis software is used to establish the overall spatial finite element truss model of the whole bridge, in which the arch rib and the main beam (tie beam, middle cross beam and end cross beam) are simulated by beam elements, and the suspender is simulated by truss elements.

[0028] Step S4, the stiffness of the lower end of the suspender is calculated: in the overall spatial finite element truss model, the longitudinal and transverse beam structures (tie beam, middle cross beam and end cross beam) of the main beam are stripped off, and only the jointly acting system (cross beam detached body) composed of arch rib, wind brace and suspender is retained, as shown in the formula: Figure 4The vertical displacement x of the lower end of each hanger is calculated by applying a unit vertical load F0 to the lower end of each hanger in the system ij , and the stiffness K of the lower end of each hanger is obtained ij =F0 / x ij , as shown in Figure 5 and Figure 6 , where i represents the i-th hanger in the longitudinal direction, and j represents the j-th hanger in the transverse direction. This process determines the actual elastic support effect of the hangers on the cross beam.

[0029] Step S5, designing the cross beam: the middle cross beam and the end cross beam are simplified as continuous beams supported on elastic supports with stiffness K ij , as shown in Figure 7 . The load on the cross beam is the constant load of the bridge deck system and the live load such as automobiles within the range of the distance between adjacent cross beams. Under the premise of meeting the bearing capacity and stress requirements of the specification, the cross-sectional size of the cross beam and the arrangement form of the prestressed steel strands are preliminarily determined, as shown in Figure 8 .

[0030] Step S6, overall analysis and internal force regulation: the prestressed steel strand arrangement of the cross beam determined in step S5 is substituted into the overall spatial finite element truss model established in step S3 to perform the analysis of the completed bridge state. The internal forces of the structure are comprehensively regulated by fine-tuning the cable forces of each hanger, and the goal is to make the truss girder basically in the "beam flat" state under the action of the constant load, i.e., the vertical displacement of the truss girder is not greater than 1 cm and the truss girder is basically free of bending moment (for example, the bending moment value is not greater than 2000 kN·m). In this embodiment, after regulation, the vertical displacements of the side truss girder and the middle truss girder under the constant load state of the completed bridge are only 13.9 mm and 10.4 mm, respectively, and the bending moment is significantly reduced, and the preset goal is successfully achieved.

[0031] Step S7, checking and iterative optimization: according to the optimized hanger force in step S6, the final internal force values of the arch rib, truss girder and hanger in the overall model are read, and the relevant bridge design specification is checked. The checking result confirms that the initially proposed component size, prestress configuration and hanger selection can meet the specification requirements. If the checking does not meet the requirements, return to step S1 to perform iterative analysis with the current results (current arch rib and truss girder cross-sectional size, number of truss girder internal prestressed strands and hanger specification selection) as new initial values, until the checking results of all components such as arch rib, truss girder and hanger meet the specification requirements, and the bridge structure calculation is completed.

[0032] The above are preferred embodiments of the present application, and do not limit the protection scope of the present application, so: any equivalent changes made according to the structure, shape, principle of the present application should be covered within the protection scope of the present application.

Claims

1. A structural design method for a wide-span integral multi-arch tied arch bridge based on comprehensive internal force control, characterized in that: Includes the following steps: S1. Based on the dead load of the standard segment of the bridge deck system and assuming that the load is evenly distributed among the multiple arch ribs, the initial calculation of the hanger force and specifications is made. S2. Based on the initial simulated hanger force, calculate the horizontal thrust at the arch crown and the tension of the tie beam, and determine the preliminary cross-sectional dimensions of the arch rib and tie beam and the number of prestressed tendons in the tie beam accordingly. S3. Establish the overall spatial finite element model of the structure; S4. Strip the longitudinal and transverse beams of the main beam and calculate the stiffness of the lower end of each hanger under the combined action of the arch rib, wind brace and hanger. S5. Simplify the crossbeam into a continuous beam with the lower rod end stiffness as the elastic support, and preliminarily determine the crossbeam structural dimensions and the arrangement of prestressed steel strands; S6. Substitute the determined prestressed steel strands of the crossbeam into the overall spatial finite element model of the bridge system for bridge analysis, and fine-tune the cable force of the suspenders so that the tie beam reaches the basic beam flat state under dead load. S7. Calculate the internal forces of the main components based on the optimized hanger force, and adjust their cross-sectional dimensions and prestress configuration; repeat steps S1 to S7 iteratively until all components meet the specification requirements.

2. The structural design method for a wide-span integral multi-arch tied arch bridge based on comprehensive internal force control according to claim 1, characterized in that: In step S1, the dead load includes the second-phase dead load consisting of the bridge deck pavement and ancillary facilities.

3. The structural design method for a wide-span integral multi-arch tied arch bridge based on comprehensive internal force control according to claim 1, characterized in that: In step S1, the multi-arch rib consists of three arch ribs.

4. The structural design method for a wide-span integral multi-arch tied arch bridge based on comprehensive internal force control according to claim 1, characterized in that: In step S2, the horizontal thrust at the top of the arch and the tension of the tie beam are calculated by selecting a semi-arch cantilever structure.

5. The structural design method for a wide-span integral multi-arch tied arch bridge based on comprehensive internal force control according to claim 1, characterized in that: In step S3, the arch ribs and main beams in the overall spatial finite element rod system model are simulated using beam elements, and the hangers are simulated using truss elements.

6. The structural design method for a wide-span integral multi-arch tied arch bridge based on comprehensive internal force control according to claim 1, characterized in that: In step S4, the method for calculating the stiffness of the lower rod end is as follows: apply a unit vertical load F0 to the lower rod end of the suspension rod, and calculate the displacement x generated at that point. ij Then the stiffness K of the lower end of the boom is... ij =F0 / x ij , where i represents the i-th longitudinal hanger and j represents the j-th transverse hanger.

7. The structural design method for a wide-span integral multi-arch tied arch bridge based on comprehensive internal force control according to claim 1, characterized in that: In step S5, the crossbeam includes a middle crossbeam and an end crossbeam.

8. The structural design method for a wide-span integral multi-arch tied arch bridge based on comprehensive internal force control according to claim 1, characterized in that: In step S6, the basic beam flat state refers to the vertical displacement of the tie beam not exceeding 1 cm and the bending moment value not exceeding 2000 kN·m.

9. The structural design method for a wide-span integral multi-arch tied arch bridge based on comprehensive internal force control according to claim 1, characterized in that: The method is applicable to wide, integral, three-arch tied arch bridges.

10. A structural design system for a wide-span integral multi-arch tied arch bridge based on comprehensive internal force control, used to implement the structural design method described in any one of claims 1-9, characterized in that: include: Data processing and initialization module: used to input basic bridge parameters, and based on the assumptions of dead load of standard segments of bridge deck system and load sharing of multiple arch ribs, to initially calculate the hanger force and specifications, the preliminary cross-sectional dimensions of arch ribs and tie beams, and the number of prestressed tendons in tie beams. Finite Element Analysis Module: Used to establish and calculate the overall spatial finite element truss model of the structure, as well as the combined action model of the arch ribs, wind braces and hangers after stripping the main beams, longitudinal and transverse beams; Stiffness calculation module: Coupled with the finite element analysis module, it is used to calculate the stiffness of the lower end of each rod; Beam Design and Analysis Module: This module simplifies the beam into a continuous beam model with elastic support at the lower end stiffness, and performs preliminary design and analysis of the beam structure dimensions and prestressed steel strand arrangement. Internal force control and iterative optimization module: It is used to substitute the crossbeam design parameters into the overall finite element model for bridge analysis, fine-tune the suspender cable force to make the tie beam reach the basic beam flat state, and iteratively optimize the component cross-sectional dimensions and prestress configuration based on the verification results until all designs meet the specifications.

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