Centroid Axle Distance Optimization Method for Steel-Concrete Composite Structure Bridges and Computer Program Product

Abstract

The present invention relates to the technical field of steel-concrete double-deck rotating bridges, and more specifically, to a method and computer program product for optimizing the centroidal wheelbase of a steel-concrete composite structure bridge. The method comprises: constructing a first constraint based on the centroidal axis of the cross section of the upper chord, the centroidal axis of the cross section of the longitudinal concrete beam, and the centroidal axis of the combined cross section of the upper chord and longitudinal concrete beam cross sections; constructing a second constraint based on the flexural stiffness of the upper chord and the flexural stiffness of the longitudinal concrete beam; constructing a characterization model between the centroidal wheelbase of the centroidal axis of the upper chord cross section and the centroidal axis of the longitudinal concrete beam cross section and the steel consumption per unit length of the truss in the longitudinal direction based on the area of the upper chord cross section, the area of the longitudinal concrete beam cross section, and the steel consumption of the truss; and obtaining the optimal centroidal wheelbase. The present invention can achieve economically optimized structural optimization of the upper steel structure bridge body and the lower concrete structure bridge body.

Description

Technical Field

[0001] The present invention relates to the technical field of steel-concrete double-deck rotating bridges, and in particular to a centroidal wheelbase optimization method and a computer program product for a steel-concrete composite structure bridge. Background Art

[0002] Compared to traditional double-deck steel truss bridges, steel-concrete double-deck rotating bridges use a lower concrete structure instead of a steel bottom chord and orthotropic steel deck. This design firstly aligns with the stress conditions encountered during rotation construction, fully leveraging the superior compressive strength of concrete and avoiding the need for thicker lower steel structures near the fulcrums, saving steel. Secondly, the lower concrete beams require minimal maintenance, meeting the requirements for structural durability and minimal subsequent maintenance and repair. The technical challenges of steel-concrete double-deck rotating bridges lie in their strong spatial constraints and complex stresses; the numerous system transitions, from a T-shaped structure during rotation to a continuous beam system upon completion; the complex stresses at the steel-concrete joints, the stringent steel structure positioning accuracy requirements, and the high concrete pouring quality requirements.

[0003] For steel-concrete double-deck rotating bridges, it is necessary to analyze and study their overall bending stiffness, but there is no relevant research in the existing technology. Summary of the Invention

[0004] In order to analyze and study the flexural stiffness of the upper steel structure bridge body and the lower concrete structure bridge body in a steel-concrete double-deck rotating bridge, the present invention provides a centroidal wheelbase optimization method and computer program product for a steel-concrete composite structure bridge. The method can use the minimum amount of steel as the optimization condition and use the flexural stiffness as a constraint to achieve economic structural optimization of the upper steel structure bridge body and the lower concrete structure bridge body.

[0005] One of the objectives of the present invention is to provide a centroidal wheelbase optimization method for a steel-concrete composite structure bridge based on flexural stiffness matching, wherein the steel-concrete composite structure bridge includes a steel structure bridge body located on an upper layer and a concrete structure bridge body located on a lower layer, the steel structure bridge body and the concrete structure bridge body being connected by a truss; the truss includes an upper chord, a web member, and a lower chord, and the lower chord is located at the longitudinal concrete beam of the concrete structure bridge body;

[0006] It includes:

[0007] A first constraint condition is established based on the centroidal axis of the cross section of the top chord, the centroidal axis of the cross section of the longitudinal concrete beam, and the centroidal axis of the combined cross section of the top chord and the longitudinal concrete beam; wherein the first constraint condition is used to constrain the centroidal axis of the combined cross section to be located within the concrete beam;

[0008] A second constraint condition is established based on the bending stiffness of the top chord and the bending stiffness of the longitudinal concrete beam; wherein the second constraint condition is used to constrain the ratio of the bending stiffness of the top chord to the bending stiffness of the longitudinal concrete beam to be no less than a set threshold;

[0009] Based on the cross-sectional area of the top chord, the cross-sectional area of the longitudinal concrete beam, and the steel consumption of the truss, a model is constructed to characterize the distance between the centroidal axis of the top chord cross-sectional area and the centroidal axis of the longitudinal concrete beam cross-sectional area and the steel consumption per unit length of the truss in the longitudinal direction.

[0010] Obtaining an optimal centroidal wheelbase; wherein the optimal centroidal wheelbase satisfies both the first constraint and the second constraint and minimizes the amount of steel used per unit length of the truss in the longitudinal direction in the characterization model.

[0011] Preferably, the expression of the first constraint condition is:

[0012] ;

[0013] in, is the centroidal distance between the centroidal axis of the cross section of the top chord and the centroidal axis of the cross section of the longitudinal concrete beam; It is the vertical distance between the centroid axis of the combined cross section and the lower edge of the longitudinal concrete beam; is the ratio of the elastic modulus of the material of the top chord to that of the longitudinal concrete beam; It is the ratio of the cross-sectional area of the upper chord to the cross-sectional area of the longitudinal concrete beam.

[0014] Preferably, the expression of the second constraint is:

[0015] ;

[0016] Where h is the equivalent height of the longitudinal concrete beam.

[0017] As a preferred method, based on the matching of bending stiffness, a corresponding relationship between centroidal wheelbase and cross-sectional ratio is constructed;

[0018] Based on the truss structure, the corresponding relationship between the cross-section ratio and the amount of steel used in the truss is obtained.

[0019] Preferably, the construction of the corresponding relationship between the centroidal wheelbase and the cross-sectional ratio based on the bending stiffness matching includes:

[0020] Based on the theoretical stress value of the upper edge of the longitudinal concrete beam, the allowable compressive stress value of the material of the longitudinal concrete beam, the theoretical stress value of the top chord, and the allowable compressive stress value of the material of the top chord, a stress ratio relationship between the longitudinal concrete beam and the top chord is constructed;

[0021] Based on the stress ratio relationship, the centroidal axis distance, and the distance between the centroidal axis of the top chord cross section and the centroidal axis of the combined cross section, the corresponding relationship between the centroidal axis distance and the cross-sectional ratio is obtained.

[0022] Preferably, the theoretical stress value of the upper edge of the longitudinal concrete beam and the theoretical stress value of the upper chord are determined based on their respective cross-sectional axial forces and cross-sectional bending moments.

[0023] Preferably, based on the sectional axial force, sectional bending moment and sectional shear force at the combined cross section, the sectional axial force and sectional bending moment at the combined cross section are distributed according to the ratio of the bending stiffness of the upper chord and the bending stiffness of the longitudinal concrete beam to obtain the sectional axial force and sectional bending moment of the longitudinal concrete beam and the upper chord respectively.

[0024] Preferably, the sectional axial force and the sectional bending moment at the combined cross section are jointly determined based on the sectional axial force, the sectional bending moment and the sectional shear force at the combined cross section.

[0025] As a preferred embodiment, the expression for the corresponding relationship between the centroidal wheelbase and the cross-sectional ratio is:

[0026] ;

[0027] in,

[0028] ;

[0029] ;

[0030] ;

[0031] in,

[0032] N is the axial force at the combined cross section, M is the bending moment at the combined cross section, T is the shear force at the combined cross section, α is the angle between the web and the horizontal direction, is the distance in height between the centroid axis of the combined cross section and the upper edge of the longitudinal concrete beam, and h is the equivalent beam height when the longitudinal concrete beam is equivalent to a rectangular cross section.

[0033] Another object of the present invention is a computer program product, comprising a computer program, which, when executed by a processor, implements any of the above-mentioned centroidal wheelbase optimization methods for steel-concrete composite structure bridges based on bending stiffness matching.

[0034] The present invention has the following beneficial effects:

[0035] The first constraint condition can be used to limit the position of the centroid of the composite cross-section, and the second constraint condition can be used to limit the bending stiffness that the upper chord and the longitudinal concrete beam need to bear. Based on the characterization model, the amount of steel used can be used as an optimization condition to minimize the overall steel usage in the steel-concrete composite structure bridge, thereby reducing manufacturing costs and improving economic performance. In addition, the introduction of the first and second constraints can comprehensively consider the differences between actual construction parameters and theoretical parameters. By solving the characterization model based on the first and second constraints, it can better fit the actual construction situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a schematic cross-sectional view of a steel-concrete composite structure bridge in a specific embodiment of the present invention;

[0037] Figure 2 It is a schematic diagram of a characterization model in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0038] In order to further understand the content of the present invention, the present invention is described in detail with reference to the embodiments. It should be understood that the embodiments are merely for explanation of the present invention and are not intended to limit the present invention.

[0039] Seen in Figure 1 This embodiment provides a centroidal wheelbase optimization method for a steel-concrete composite structure bridge based on bending stiffness matching, wherein the steel-concrete composite structure bridge includes a steel structure bridge body located on an upper layer and a concrete structure bridge body located on a lower layer, and the steel structure bridge body and the concrete structure bridge body are connected by a truss; the truss includes an upper chord, a web member, and a lower chord, and the lower chord is located at the longitudinal concrete beam of the concrete structure bridge body;

[0040] It includes:

[0041] A first constraint condition is established based on the centroidal axis of the cross section of the top chord, the centroidal axis of the cross section of the longitudinal concrete beam, and the centroidal axis of the combined cross section of the top chord and the longitudinal concrete beam; wherein the first constraint condition is used to constrain the centroidal axis of the combined cross section to be located within the concrete beam;

[0042] A second constraint condition is established based on the bending stiffness of the top chord and the bending stiffness of the longitudinal concrete beam. The second constraint condition is used to constrain the ratio of the bending stiffness of the top chord to the bending stiffness of the longitudinal concrete beam to be no less than a set threshold (e.g., 4).

[0043] Based on the cross-sectional area of the top chord, the cross-sectional area of the longitudinal concrete beam, and the steel consumption of the truss, a model is constructed to characterize the distance between the centroidal axis of the top chord cross-sectional area and the centroidal axis of the longitudinal concrete beam cross-sectional area and the steel consumption per unit length of the truss in the longitudinal direction.

[0044] Obtaining an optimal centroidal wheelbase; wherein the optimal centroidal wheelbase satisfies both the first constraint and the second constraint and minimizes the amount of steel used per unit length of the truss in the longitudinal direction in the characterization model.

[0045] Based on the above, the first constraint condition can be used to limit the position of the centroidal axis of the composite cross-section, and the second constraint condition can be used to limit the bending stiffness that the upper chord and the longitudinal concrete beam need to bear respectively. Based on the characterization model, the amount of steel used can be used as an optimization condition to minimize the overall steel usage in the steel-concrete composite structure bridge, thereby reducing manufacturing costs and improving economic performance.

[0046] In addition, the introduction of the first and second constraints can comprehensively consider the differences between actual construction parameters and theoretical parameters. By solving the characterization model based on the first and second constraints, it can better fit the actual construction situation.

[0047] exist Figure 1 In the figure, the centroidal axis of the cross section of the upper chord is P1, the centroidal axis of the cross section of the longitudinal concrete beam is P3, and the centroidal axis of the combined cross section of the upper chord and the longitudinal concrete beam is P2.

[0048] Among them, the expression of the first constraint is,

[0049] ;

[0050] in, is the centroidal distance between the centroidal axis of the cross section of the top chord and the centroidal axis of the cross section of the longitudinal concrete beam; It is the vertical distance between the centroid axis of the combined cross section and the lower edge of the longitudinal concrete beam; is the ratio of the elastic modulus of the material of the top chord to that of the longitudinal concrete beam; It is the ratio of the cross-sectional area of the upper chord to the cross-sectional area of the longitudinal concrete beam.

[0051] By introducing the parameter combination in the first constraint condition, the vertical distance between the centroid axis of the cross section and the lower edge of the longitudinal concrete beam is , which can constrain the centroid axis of the composite section to be located inside the longitudinal concrete beam and as close to the longitudinal concrete beam as possible, thereby effectively realizing the constraint of structural parameters in the actual construction process.

[0052] Among them, the expression of the second constraint is,

[0053] ;

[0054] Where h is the equivalent height of the longitudinal concrete beam.

[0055] The second constraint condition can constrain the bending contribution of the upper chord so that the bending moment of inertia provided by the upper chord accounts for no less than 80%.

[0056] The construction of the representation model includes:

[0057] Based on the matching of bending stiffness, the corresponding relationship between centroidal wheelbase and cross-section ratio is constructed;

[0058] Based on the truss structure, the corresponding relationship between the cross-section ratio and the amount of steel used in the truss is obtained.

[0059] The construction of the corresponding relationship between the centroidal wheelbase and the cross-sectional ratio based on the bending stiffness matching includes:

[0060] Based on the theoretical stress value of the upper edge of the longitudinal concrete beam, the allowable compressive stress value of the material of the longitudinal concrete beam, the theoretical stress value of the top chord, and the allowable compressive stress value of the material of the top chord, a stress ratio relationship between the longitudinal concrete beam and the top chord is constructed;

[0061] Based on the stress ratio relationship, the centroidal axis distance, and the distance between the centroidal axis of the top chord cross section and the centroidal axis of the combined cross section, the corresponding relationship between the centroidal axis distance and the cross-sectional ratio is obtained.

[0062] In this embodiment, taking C60 concrete and Q345qD steel as an example, the allowable compressive stress value of the material of the longitudinal concrete beam is 20 MPa, and the allowable compressive stress value of the material of the upper chord is 200 MPa.

[0063] Among them, the theoretical stress value of the upper edge of the longitudinal concrete beam and the theoretical stress value of the upper chord are determined based on their respective section axial forces and section bending moments.

[0064] Among them, based on the sectional axial force, sectional bending moment and sectional shear force at the combined cross section, the sectional axial force and sectional bending moment at the combined cross section are distributed according to the ratio of the flexural stiffness of the upper chord and the flexural stiffness of the longitudinal concrete beam, and the sectional axial force and sectional bending moment of the longitudinal concrete beam and the upper chord are obtained.

[0065] Among them, the sectional axial force and sectional bending moment at the combined cross section are determined based on the sectional axial force, sectional bending moment and sectional shear force at the combined cross section.

[0066] Combined with the structural characteristics of steel-concrete composite bridges, the cross-sectional axial force, cross-sectional bending moment and cross-sectional shear force at the combined cross section can be N, M and T respectively; the cross-sectional axial force of the longitudinal concrete beam is and the cross-sectional axial force of the upper chord They are,

[0067] ;

[0068] ;

[0069] in, is the elastic modulus of the longitudinal concrete beam, is the elastic modulus of the upper chord, is the cross-sectional area of the longitudinal concrete beam, is the cross-sectional area of the upper chord, is the bending stiffness of the combined cross section, ;

[0070] Sectional bending moment of longitudinal concrete beam and the bending moment of the top chord They are,

[0071] ;

[0072] ;

[0073] in, is the distance between the centroidal axis of the top chord and the centroidal axis of the built-up section; where,

[0074] .

[0075] Among them, the expression of the corresponding relationship between the centroid axis distance and the cross-sectional ratio is:

[0076] ;

[0077] in,

[0078] ;

[0079] ;

[0080] ;

[0081] in,

[0082] N is the axial force at the combined cross section, M is the bending moment at the combined cross section, T is the shear force at the combined cross section, α is the angle between the web and the horizontal direction, is the distance in height between the centroid axis of the combined cross section and the upper edge of the longitudinal concrete beam, and h is the equivalent beam height when the longitudinal concrete beam is equivalent to a rectangular cross section.

[0083] Seen in Figure 2 , which is a schematic diagram representing the model, where the solid line is the corresponding relationship between the centroid wheelbase and the cross-sectional ratio, and the dotted line is the corresponding relationship between the centroid wheelbase and the amount of steel used.

[0084] In addition, a specific embodiment of the present invention further provides an electronic device, comprising:

[0085] at least one processor; and

[0086] a memory communicatively connected to the at least one processor; wherein,

[0087] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the centroidal wheelbase optimization method of the steel-concrete composite structure bridge based on bending stiffness matching of the present invention.

[0088] In addition, a specific embodiment of the present invention further provides a computer program product, including a computer program, which, when executed by a processor, implements the centroidal wheelbase optimization method of the steel-concrete composite structure bridge based on bending stiffness matching of the present invention.

[0089] It is easy to understand that those skilled in the art can combine, split, reorganize, etc. the embodiments of the present application based on one or several embodiments provided in the present application to obtain other embodiments, and these embodiments do not exceed the scope of protection of the present application.

[0090] The above is a schematic description of the present invention and its embodiments, which is not restrictive. The embodiments shown in the embodiments are only part of the embodiments of the present invention, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by the above and, without departing from the purpose of the present invention, designs a structure and embodiment similar to the technical solution without creatively designing, they shall fall within the scope of protection of the present invention.

Claims

1. A centroidal wheelbase optimization method for steel-concrete composite structure bridges based on flexural stiffness matching, where: A steel-concrete composite bridge structure includes a steel structure bridge body located on the upper level and a concrete structure bridge body located on the lower level. The steel structure bridge body and the concrete structure bridge body are connected by a truss. The truss has an upper chord, a web member, and a lower chord. The lower chord is located at the longitudinal concrete beam of the concrete structure bridge body. The invention is characterized by comprising: A first constraint condition is established based on the centroidal axis of the cross section of the top chord, the centroidal axis of the cross section of the longitudinal concrete beam, and the centroidal axis of the combined cross section of the top chord and the longitudinal concrete beam; wherein the first constraint condition is used to constrain the centroidal axis of the combined cross section to be located within the concrete beam; A second constraint condition is established based on the bending stiffness of the top chord and the bending stiffness of the longitudinal concrete beam; wherein the second constraint condition is used to constrain the ratio of the bending stiffness of the top chord to the bending stiffness of the longitudinal concrete beam to be no less than a set threshold; Based on the cross-sectional area of the top chord, the cross-sectional area of the longitudinal concrete beam, and the steel consumption of the truss, a model is constructed to characterize the distance between the centroidal axis of the top chord cross-sectional area and the centroidal axis of the longitudinal concrete beam cross-sectional area and the steel consumption per unit length of the truss in the longitudinal direction. Obtaining an optimal centroidal wheelbase; wherein the optimal centroidal wheelbase satisfies both the first constraint and the second constraint and minimizes the amount of steel used per unit length of the truss in the longitudinal direction in the characterization model.

2. The centroidal wheelbase optimization method for a steel-concrete composite structure bridge based on flexural stiffness matching according to claim 1 is characterized in that: The expression of the first constraint is, ； in, is the centroidal distance between the centroidal axis of the cross section of the top chord and the centroidal axis of the cross section of the longitudinal concrete beam; It is the vertical distance between the centroid axis of the combined cross section and the lower edge of the longitudinal concrete beam; is the ratio of the elastic modulus of the material of the top chord to that of the longitudinal concrete beam; It is the ratio of the cross-sectional area of the upper chord to the cross-sectional area of the longitudinal concrete beam.

3. The centroidal wheelbase optimization method for a steel-concrete composite structure bridge based on flexural stiffness matching according to claim 2 is characterized in that: The expression of the second constraint is, ； Where h is the equivalent height of the longitudinal concrete beam.

4. The centroidal wheelbase optimization method for a steel-concrete composite structure bridge based on flexural stiffness matching according to claim 2 is characterized in that: The construction of the representation model includes: Based on the matching of bending stiffness, the corresponding relationship between centroidal wheelbase and cross-section ratio is constructed; Based on the truss structure, the corresponding relationship between the cross-section ratio and the amount of steel used in the truss is obtained.

5. The centroidal wheelbase optimization method for a steel-concrete composite structure bridge based on flexural stiffness matching according to claim 4 is characterized in that: The corresponding relationship between the centroidal wheelbase and the cross-sectional ratio is constructed based on the bending stiffness matching, including: Based on the theoretical stress value of the upper edge of the longitudinal concrete beam, the allowable compressive stress value of the material of the longitudinal concrete beam, the theoretical stress value of the top chord, and the allowable compressive stress value of the material of the top chord, a stress ratio relationship between the longitudinal concrete beam and the top chord is constructed; Based on the stress ratio relationship, the centroidal axis distance, and the distance between the centroidal axis of the top chord cross section and the centroidal axis of the combined cross section, the corresponding relationship between the centroidal axis distance and the cross-sectional ratio is obtained.

6. The centroidal wheelbase optimization method for a steel-concrete composite structure bridge based on flexural stiffness matching according to claim 5 is characterized in that: The theoretical stress values of the upper edge of the longitudinal concrete beam and the theoretical stress values of the upper chord are determined based on their respective section axial forces and section bending moments.

7. The centroidal wheelbase optimization method for a steel-concrete composite structure bridge based on flexural stiffness matching according to claim 6 is characterized in that: Based on the sectional axial force, sectional bending moment and sectional shear force at the combined cross section, the sectional axial force and sectional bending moment at the combined cross section are distributed according to the ratio of the flexural stiffness of the upper chord and the flexural stiffness of the longitudinal concrete beam, and the sectional axial force and sectional bending moment of the longitudinal concrete beam and the upper chord are obtained.

8. The centroidal wheelbase optimization method for a steel-concrete composite structure bridge based on flexural stiffness matching according to claim 6 is characterized in that: The sectional axial force and sectional bending moment at the combined cross section are determined based on the sectional axial force, sectional bending moment and sectional shear force at the combined cross section.

9. The centroidal wheelbase optimization method for a steel-concrete composite structure bridge based on flexural stiffness matching according to claim 8 is characterized in that: The expression for the correspondence between the centroidal wheelbase and the cross-sectional ratio is: ； in, ； ； ； in, N is the axial force at the combined cross section, M is the bending moment at the combined cross section, T is the shear force at the combined cross section, α is the angle between the web and the horizontal direction, is the distance in height between the centroid axis of the combined cross section and the upper edge of the longitudinal concrete beam, and h is the equivalent beam height when the longitudinal concrete beam is equivalent to a rectangular cross section.

10. A computer program product, characterized in that The invention comprises a computer program, which, when executed by a processor, implements the centroidal wheelbase optimization method of a steel-concrete composite structure bridge based on bending stiffness matching according to any one of claims 1 to 9.

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