Design method of key geometric parameters of trussed arch considering instability timing of member and structure

Abstract

The application relates to the technical field of bridge engineering, in particular to a truss arch key geometric parameter design method considering the time sequence of component and structure instability, which comprises the following steps: S1. Designing the slenderness ratio of a main arch structure; S2. Calculating the section rotation radius and the slenderness ratio of a web member; S3. Carrying out slenderness ratio constraint on the main arch structure and the web member; and S4. According to the slenderness ratio constraint, the interval limit value of the web member is calculated and obtained, and through construction requirements, the final value of the key geometric parameter of the web member is obtained. The application can reasonably control the time sequence relationship between component instability and structure overall instability, avoid brittle failure, and improve the safety of the structure.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, and in particular to a design method for key geometric parameters of truss arches that takes into account the instability sequence of components and structures. Background Technology

[0002] Steel-concrete composite truss arch bridges have become the mainstream structural form in the construction of long-span bridges due to their excellent span capacity, ease of construction, and architectural aesthetics. However, the stability control of the main arch structure during construction and operation, especially the coordinated issue of the instability sequence of local components and the overall structure, has long constrained the balance between design safety and economy.

[0003] In current engineering practice, the determination of the spacing between web members often relies on empirical formulas or simplified calculation models, failing to establish a dynamic correlation mechanism between the stability performance of local components and the elastic stability response of the overall structure. According to Article 5.9.1 of the "Design Code for Steel-Concrete Composite Arch Bridges on Highways" (JTG / T D65-06-2015), the overall elastic stability coefficient of the main arch should not be lower than 4.0, and the stability coefficient of local components should not be lower than this value. However, in actual design, due to the lack of systematic control methods, excessively large web member spacing often leads to local buckling of web members or chords before overall instability, resulting in brittle failure; or overly conservative values ​​lead to material redundancy, complex node structures, and increased welding costs.

[0004] Furthermore, existing analytical methods are mostly limited to linear elastic stability calculations, failing to fully consider the coupling effects of geometric nonlinearity and material nonlinearity. This leads to overestimation of stability coefficients and inflated safety margins. According to engineering measurement data, linear analysis results overestimate the stable bearing capacity by 56% to 71% compared to nonlinear analysis, severely weakening design reliability. Meanwhile, traditional wind bracing systems often employ a single-strut arrangement, resulting in insufficient out-of-plane restraint and difficulty in effectively delaying local buckling development.

[0005] Currently, there are no unified design guidelines to guide the coordinated optimization of web member geometric parameters and overall structural parameters. This makes it difficult to avoid the risk of "local instability preceding overall instability," and also makes it impossible to achieve the optimal match between material efficiency and structural safety. Therefore, it is urgent to construct a systematic design method based on the coordinated control of load-bearing capacity at both the "local-overall" level to meet the mandatory requirements of the code and promote the transformation of steel-concrete composite truss arch bridges from experience-based design to theory-driven design. Summary of the Invention

[0006] To address the aforementioned issues, this invention provides a design method for key geometric parameters of truss arches that considers the timing of component and structural instability. This method can reasonably control the timing relationship between component instability and overall structural instability, avoid brittle failure, and improve structural safety.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] The design method for key geometric parameters of truss arches considering the instability sequence of components and structures includes the following steps:

[0009] S1. Slenderness ratio of the main arch structure:

[0010] S2. Calculate the radius of gyration and slenderness ratio of the cross section of the web member;

[0011] S3. Apply slenderness ratio constraints to the main arch structure and the web members;

[0012] S4. Based on the slenderness ratio constraint, calculate the spacing limit of the web members, and obtain the final values ​​of the key geometric parameters of the web members according to the construction requirements.

[0013] Further, in step S1, the slenderness ratio of the main arch structure is calculated based on the equivalent calculated length of the main arch and the equivalent cross-sectional radius of gyration.

[0014] Further, in step S1, the slenderness ratio of the main arch structure is calculated as follows:

[0015] Formula (1)

[0016] in, The equivalent calculation length of the main arch; The equivalent section radius of gyration; for a hingeless arch, the equivalent calculated length is: , The length of the main arch axis.

[0017] Furthermore, the method for calculating the equivalent cross-sectional radius of gyration is as follows:

[0018] Formula (2)

[0019] in, The moment of inertia of the equivalent section of the main arch, It is the sum of the cross-sectional areas of all individual components that make up the equivalent cross-section of the main arch.

[0020] Further, in step S2, the radius of gyration of the cross section of the web member is calculated based on the moment of inertia of the steel-concrete composite section of the web member and the cross-sectional area of ​​the steel-concrete composite section of the web member.

[0021] Further, in step S2, the method for calculating the radius of gyration of the cross section of the web member is as follows:

[0022] Formula (3)

[0023] in, The moment of inertia of the concrete-filled steel tube section; The cross-sectional area of ​​the steel-concrete composite tube is given.

[0024] Further, in step S2, the slenderness ratio of the web members is calculated based on the inter-joint distance and the radius of gyration of the web members. For the web members of a four-tube truss arch, the slenderness ratio is corrected by conversion.

[0025] Furthermore, the slenderness ratio of the web member is calculated as follows:

[0026] Formula (4)

[0027] in, This refers to the internode distance of the web members;

[0028] The correction method for the slenderness ratio of the web members of the four-tube truss arch is as follows:

[0029] Formula (5)

[0030] Formula (6)

[0031] in, , Let be the converted slenderness ratio of the four-tube truss arch with respect to the yy and x axes, and let be the slenderness ratio of the web members of the four-tube truss arch. ; , The slenderness ratio of the main tube of a four-tube truss arch; The slenderness ratio of a single segment of a single-limb steel-concrete composite column; , The calculation is performed using formula (4).

[0032] Furthermore, in step S3, the slenderness ratio of the main arch structure and the web members is constrained by design criteria, wherein the slenderness ratio of the web members is not less than the slenderness ratio of the main arch structure. ,in The length of the web member is slender. Let be the slenderness ratio of the main arch structure, and have .

[0033] Furthermore, in step S4, the final values ​​of the key geometric parameters of the web member are:

[0034] When the cross-sectional dimensions of the web members are fixed, the maximum spacing between web member nodes is:

[0035] Formula (7)

[0036] in, This is the maximum permissible inter-segment distance during construction;

[0037] When the spacing between the web member nodes is fixed, the minimum radius of gyration of the web member is taken as follows:

[0038] Formula (8)

[0039] in, This is the minimum permissible turning radius during construction.

[0040] The beneficial effects of this invention are:

[0041] By constraining the slenderness ratio of the main arch structure and the web members according to design criteria, this invention ensures that local components do not fail before the overall structure becomes unstable. It rationally controls the temporal relationship between component instability and overall structural instability, avoiding brittle failure modes and improving structural safety. Furthermore, this invention transforms the design criteria into a method for minimizing web member spacing. By controlling the slenderness ratio of local and overall components, the order of instability can be forcibly adjusted, thereby transforming brittle failure modes into ductile failure modes. This aligns with structural mechanics principles and directly guides engineering practice, avoiding safety hazards caused by uncontrolled temporal progression in traditional designs. The slenderness ratio of the main arch structure is calculated according to the "Design Code for Highway Steel-Concrete Composite Arch Bridges" JTG / T D65-06-2015, meeting the requirement that the stability coefficient of local components should not be less than the elastic overall stability coefficient of the main arch. This provides a clear quantitative calculation basis for truss arch bridge design. This invention, while meeting stability requirements, avoids material waste caused by overly conservative design, achieving a reasonable balance between safety and economy, and reducing project costs by approximately 10% to 20%. Attached Figure Description

[0042] Figure 1 This is a flowchart of the first embodiment of the present invention.

[0043] Figure 2 This is a front view of the four-limbed CFST truss arch according to the second embodiment of the present invention.

[0044] Figure 3 This is a schematic diagram of the finite element model of the four-limbed CFST truss arch according to the second embodiment of the present invention.

[0045] Figure 4 This is a schematic diagram illustrating the influence of the cross-sectional dimensions of the web members of the four-limbed CFST truss arch in the second embodiment of the present invention on the bearing capacity. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0048] Example 1

[0049] Please see Figure 1 The preferred embodiment of the present invention provides a method for designing key geometric parameters of a truss arch that considers the instability sequence of components and structures, comprising the following steps:

[0050] S1. Design the slenderness ratio of the main arch structure.

[0051] In step S1, the slenderness ratio of the main arch structure is calculated based on the equivalent calculated length and the equivalent cross-sectional radius of gyration of the main arch.

[0052] In step S1, the slenderness ratio of the main arch structure is calculated as follows:

[0053] Formula (1)

[0054] in, The equivalent calculation length of the main arch; The equivalent section radius of gyration; for a hingeless arch, the equivalent calculated length is: , The length of the main arch axis.

[0055] The method for calculating the equivalent cross-sectional radius of gyration is as follows:

[0056] Formula (2)

[0057] in, The moment of inertia of the equivalent section of the main arch, It is the sum of the cross-sectional areas of all individual components that make up the equivalent cross-section of the main arch.

[0058] In this embodiment, the equivalent calculated length and equivalent section radius of gyration of the main arch are calculated according to the "Design Specification for Steel-Concrete Composite Arch Bridges for Highways" JTG / T D65-06-2015, thus obtaining the slenderness ratio of the main arch structure. The slenderness ratio of the main arch structure in this embodiment reflects the flexibility of the main arch structure.

[0059] S2. Calculate the radius of gyration and slenderness ratio of the cross section of the web member.

[0060] In step S2, the radius of gyration of the web member is calculated based on the moment of inertia of the concrete-filled steel tube section and the area of ​​the concrete-filled steel tube section of the web member.

[0061] In step S2, the method for calculating the radius of gyration of the web member section is as follows:

[0062] Formula (3)

[0063] in, The moment of inertia of the concrete-filled steel tube section; The cross-sectional area of ​​the steel-concrete composite tube is given.

[0064] In step S2, the slenderness ratio of the web members is calculated based on the inter-joint distance and the radius of gyration of the web members. For the web members of a four-tube truss arch, the slenderness ratio is corrected by converting the slenderness ratio.

[0065] The method for calculating the slenderness ratio of the web members is as follows:

[0066] Formula (4)

[0067] in, This refers to the internode distance of the web members;

[0068] The correction method for the slenderness ratio of the web members in a four-tube truss arch is as follows:

[0069] Formula (5)

[0070] Formula (6)

[0071] in, , Let be the equivalent slenderness ratio of a four-tube truss arch with respect to the y-axis and x-axis, and let be the slenderness ratio of the web members of the four-tube truss arch. ; , The slenderness ratio of the main tube of a four-tube truss arch; The slenderness ratio of a single segment of a single-limb steel-concrete composite column; , The calculation is performed using formula (4).

[0072] By correcting the slenderness ratio of the web members in a four-tube truss arch through a conversion of the slenderness ratio, the influence of the web member flexibility is superimposed on the overall calculation. If the web members are designed to be relatively slender, the corrected overall slenderness ratio will increase significantly. This also increases the safety margin, allowing for the use of more rigid web members or a reduction in spacing during design, thus ensuring that the entire truss functions as a tightly integrated whole. This embodiment addresses the impact of composite effects on stability calculations in four-tube truss arch structures, ensuring that the calculation results more closely match actual physical characteristics and preventing overestimation of the overall stability of the main arch due to neglecting structural details. This ensures that the web member spacing design is both scientific and safe.

[0073] S3. Slenderness ratio constraints are imposed on the main arch structure and the web members.

[0074] In step S3, the slenderness ratio of the main arch structure and the web members is constrained by design criteria, wherein the slenderness ratio of the web members is not greater than that of the main arch structure. ,in The length and slenderness of the web members The slenderness ratio of the main arch structure, and has .

[0075] The design criteria constrain the slenderness ratio of the main arch structure and the web members, ensuring that the stability coefficient of the web members is not less than that of the main arch as a whole. This guarantees that under stress, local web members will not buckle before the overall structure, thus avoiding brittle failure and allowing the structure to enter the plastic stage with warning. When the design criteria are met, the main arch will undergo overall elastic deformation under load, while the web members remain stable; if not met, the web members may buckle prematurely, leading to sudden structural collapse. This ensures that the structure exhibits a progressive failure mode of overall instability followed by local instability under ultimate limits, rather than a brittle failure mode where local instability leads to instantaneous overall collapse.

[0076] S4. Based on the slenderness ratio constraint, calculate the spacing limit of the web members, and obtain the final values ​​of the key geometric parameters of the web members according to the construction requirements.

[0077] In step S4, the key geometric parameters of the web member are finally determined as follows:

[0078] When the cross-sectional dimensions of the web members are fixed, the maximum spacing between web member nodes is:

[0079] Formula (7)

[0080] in, To determine the maximum permissible inter-segment distance during construction, a value no greater than [value missing] should be selected in the final calculation. And the spacing of the web members meets the structural requirements.

[0081] When the spacing between the web member nodes is fixed, the minimum radius of gyration of the web member is taken as follows:

[0082] Formula (8)

[0083] in, This is the minimum permissible turning radius during construction.

[0084] In this embodiment, the final values ​​of the key geometric parameters of the web members are calculated by formula (7), which forcibly controls the instability sequence of the structure, changes the failure mode of the structure from dangerous brittle failure to safe ductile failure, and significantly reduces the construction cost.

[0085] Example 2

[0086] like Figures 2 to 4 As shown in the figure, the key geometric parameter design method for truss arches that considers the instability sequence of components and structures in this embodiment is used to analyze a four-limb CFST truss arch. The calculation model is as follows. Figure 2 and Figure 3 As shown, Figure 2 This is a front view of a four-limbed CFST truss arch; Figure 3 This is a finite element model of a four-limbed CFST truss arch. The arch axis is a quadratic parabola. A pair of concentrated loads act at the arch crown. The calculated span is L = 9.0m, the rise is f = 1.8m, the rise-to-span ratio is 0.2, the truss arch cross-section width is B = 0.4m, the height is H = 0.4m, and the dimensions of the upper and lower chords are as follows. 89×4.0mm, web members and connecting tubes are... 48×2.0mm, steel yield strength f y =260MPa, elastic modulus E s =2.1×10 5 MPa, compressive strength of concrete cube f cu,k =31.6MPa.

[0087] S1. Calculate the slenderness ratio of the main arch structure.

[0088] Calculate the arc length of the arch axis of the quadratic parabola. :

[0089] 9.87m

[0090] Calculate the equivalent arc length For hingeless arches, according to JTG / T D65-06-2015 standard:

[0091] 3.55 m

[0092] Calculate the elastic modulus ratio n:

[0093] 0.126

[0094] Calculate the sum of the equivalent areas of all individual members of the main arch's equivalent cross-section. :

[0095] Area of ​​a single chord steel tube 1068.14mm 2

[0096] Concrete area of ​​a single chord 5153.00 mm 2

[0097] Calculate the converted area of ​​a single chord :

[0098] 1716.44mm 2

[0099] Calculate the total converted area of ​​the limbs :

[0100] 6865.75 mm 2

[0101] Calculate the equivalent cross section radius of gyration according to equation (2). :

[0102] Equivalent moment of inertia for a single CFST tube: 1.23×10 6 mm 4

[0103] 2.80×10 8 mm 4

[0104] 201.79mm

[0105] Calculate the slenderness ratio of the main arch according to formula (1). :

[0106] 17.60

[0107] S2. Calculation and verification of the slenderness ratio of the web members.

[0108] Calculate the equivalent radius of gyration of the original web member according to formula (3). :

[0109] 289.03 mm 2

[0110] 7.66×10 4 mm4

[0111] 16.28 mm

[0112] The truss height is determined by the inter-joint distance of the web members. m, calculate the slenderness ratio of the web member according to formula (4):

[0113] 24.57

[0114] Design guidelines not met:

[0115] S3. Slenderness ratio constraint of the web members.

[0116] Since the inter-joint spacing of the web members is given in this example, the influence of changing the geometry of the web members and ductwork on the stiffness ratio of the web members to the chord members on the bearing capacity of the truss arch is studied. The chord member dimensions of the original design model are... 89×4.0mm, web members and connecting tubes are sized as follows: 48×2.0mm, therefore, the six sizes of web members and connecting tubes shown in Table 1 are analyzed, and the calculation results are as follows. Figure 4 As shown.

[0117] Table 1. Dimensions of Web Members and Connecting Tubes

[0118]

[0119] Depend on Figure 4 It can be seen that the dimensions of the web members and tie rods have a significant impact on the load-bearing capacity. When the dimensions are smaller than... When the dimensions are 64×3.0mm, the bearing capacity of the truss arch approximately increases linearly with the increase of the web member size. When the dimensions of the web members and tie rods are... When the dimensions are 64×3.0mm, the load-bearing capacity is very close to the maximum value, and the dimensions are greater than or equal to... It has completely stabilized and stopped growing at 72×3.5mm.

[0120] According to the design principle that the slenderness ratio of the web members should not be greater than that of the main arch structure: Given the spacing between the web member nodes, the minimum radius of gyration of the web member section can be calculated by back-calculating:

[0121] =22.73mm

[0122] The study found that the specifications of the web members were taken as follows: 40×1.5mm~ When the diameter is 64×3.0mm, the radius of gyration i is less than 1. The design criteria are not met, and the corresponding load-bearing capacity increases with the increase of the web member radius, but does not reach the maximum value, showing that the web member instability occurs before the main arch; the web member specifications are greater than or equal to When the radius of gyration is 72×3.5mm, the gyration radius meets the design criteria, and the corresponding bearing capacity is stable at the maximum value, not changing with the radius of the web members. This shows that the instability of the main arch takes precedence over that of the web members.

[0123] S4. Based on the slenderness ratio constraint, the web member specifications are recommended.

[0124] The experimental results in step S3 fully validate the correctness of the design criteria presented in this paper. Based on the slenderness ratio constraint of the design criteria and taking into account economic efficiency, the recommended method is [the appropriate design criteria]. 72×3.5mm web member specifications, or other specifications not listed in the text, but with a slewing radius greater than [specified value]. The specifications of the web members, such as 70×3.0mm, etc.

Claims

1. A design method for key geometric parameters of a truss arch considering the instability sequence of components and structure, characterized in that, Includes the following steps: S1. Slenderness ratio of the main arch structure: S2. Calculate the radius of gyration and slenderness ratio of the cross section of the web member; S3. Apply slenderness ratio constraints to the main arch structure and the web members; S4. Based on the slenderness ratio constraint, calculate the spacing limit of the web members, and obtain the final values ​​of the key geometric parameters of the web members according to the construction requirements.

2. The method for designing key geometric parameters of a truss arch considering the instability sequence of components and structure according to claim 1, characterized in that: In step S1, the slenderness ratio of the main arch structure is calculated based on the equivalent calculated length of the main arch and the equivalent cross-sectional radius of gyration.

3. The method for designing key geometric parameters of a truss arch considering the instability sequence of components and structure according to claim 2, characterized in that: In step S1, the slenderness ratio of the main arch structure is calculated as follows: Official (1) in, The equivalent calculation length of the main arch; The equivalent section radius of gyration; for a hingeless arch, the equivalent calculated length is: , The length of the main arch axis.

4. The method for designing key geometric parameters of a truss arch considering the instability sequence of components and structure according to claim 3, characterized in that: The method for calculating the equivalent cross-sectional radius of gyration is as follows: Official (2) in, The moment of inertia of the equivalent section of the main arch, It is the sum of the cross-sectional areas of all individual components that make up the equivalent cross-section of the main arch.

5. The method for designing key geometric parameters of a truss arch considering the instability sequence of components and structure according to claim 1, characterized in that: In step S2, the radius of gyration of the web member is calculated based on the moment of inertia of the steel-concrete composite section and the cross-sectional area of ​​the web member.

6. The method for designing key geometric parameters of a truss arch considering the instability sequence of components and structure according to claim 1, characterized in that: In step S2, the method for calculating the radius of gyration of the cross section of the web member is as follows: Official (3) in, The moment of inertia of the concrete-filled steel tube section; The cross-sectional area of ​​the steel-concrete composite tube is given.

7. The method for designing key geometric parameters of a truss arch considering the instability sequence of components and structure according to claim 6, characterized in that: In step S2, the slenderness ratio of the web members is calculated based on the inter-joint distance and the radius of gyration of the web members. For the web members of a four-tube truss arch, the slenderness ratio is corrected by conversion.

8. The method for designing key geometric parameters of a truss arch considering the instability sequence of components and structure according to claim 7, characterized in that: The slenderness ratio of the web member is calculated as follows: Official (4) in, This refers to the internode distance of the web members; The correction method for the slenderness ratio of the web members of the four-tube truss arch is as follows: Official (5) Official (6) in, , Let be the converted slenderness ratio of the four-tube truss arch with respect to the yy and x axes, and let be the slenderness ratio of the web members of the four-tube truss arch. ; , The slenderness ratio of the main tube of a four-tube truss arch; The slenderness ratio of a single segment of a single-limb steel-concrete composite column; , The calculation is performed using formula (4).

9. The method for designing key geometric parameters of a truss arch considering the instability sequence of components and structure according to claim 8, characterized in that: In step S3, the slenderness ratio of the main arch structure and the web members is constrained by design criteria, wherein the slenderness ratio of the web members is not greater than that of the main arch structure. ,in The length of the web member is slender. Let be the slenderness ratio of the main arch structure, and have .

10. The method for designing key geometric parameters of a truss arch considering the instability sequence of components and structure according to claim 9, characterized in that: In step S4, the key geometric parameters of the web member are finally determined as follows: When the cross-sectional dimensions of the web members are fixed, the maximum spacing between web member nodes is: Official (7) in, This is the maximum permissible inter-segment distance during construction; When the spacing between the web member nodes is fixed, the minimum radius of gyration of the web member is taken as follows: Official (8) in, This is the minimum permissible turning radius during construction.

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