A calculation method for the torsional stiffness of the main cable of a suspension bridge

Abstract

The present invention discloses a method for calculating the torsional stiffness of a suspension bridge main cable, comprising: determining the parameters of the main cable, the location of the clamps, and the tightening force; dividing the main cable into a clamp area, a clamp influence area, and a free area according to the location of the clamps; calculating the polar moment of inertia of the main cable in the clamp area based on the radial force exerted by the clamps on the main cable and the characteristics of the steel wires; calculating the mutual extrusion force of the steel wires within the main cable in the clamp influence area based on the radial force exerted by the clamps on the main cable, and accordingly calculating the polar moment of inertia of the main cable in the clamp influence area and the length of the influence area; calculating the polar moment of inertia of the main cable in the free area based on the number and characteristics of the steel wires; correcting the polar moments of inertia of the main cable in the clamp area, the clamp influence area, and the free area; and forming the overall polar moment of inertia of the main cable based on the corrected polar moments of inertia of the clamp area, the clamp influence area, and the free area according to the segment length. The present invention solves the problem of the inability to accurately calculate the polar moment of inertia of the main cable of a suspension bridge, and has the advantages of accurate calculation, clear principle, and better reflection of the main cable characteristics.

Description

Technical Field

[0001] The invention relates to a method for calculating the comprehensive stiffness of a steel wire bundle, in particular to a method for finely calculating the polar moment of inertia of a main cable section of a suspension bridge. Background Art

[0002] The main cable is a key component of a suspension bridge, and its performance is crucial to its load-bearing capacity and durability. Main cables are typically composed of numerous steel wires, subject to lateral constraints such as cable clamps and lashings. The complex interactions between the wires within the main cable make it difficult to simply superimpose the lateral properties of the steel wires to obtain the main cable's properties. Consequently, scholars both domestically and internationally have conducted extensive theoretical analysis and experimental research on suspension bridge main cables.

[0003] At present, the polar moment of inertia of the main cable of a suspension bridge is often calculated as the product of the theoretical maximum polar moment of inertia and a coefficient less than 1. The theoretical maximum polar moment of inertia is the polar moment of inertia when the main cable is assumed to be a steel cylinder. The coefficient is determined according to the characteristics of the main cable, has no clear theoretical basis, and its accuracy cannot be guaranteed. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for calculating the torsional stiffness of the main cable of a suspension bridge, which has the advantages of accurate calculation, clear principle, and can better reflect the characteristics of the main cable.

[0005] The technical solution adopted by the present invention to solve this technical problem is: a method for calculating the torsional stiffness of the main cable of a suspension bridge, comprising the following steps:

[0006] Step 1: Determine the number, diameter, and friction coefficient of the main cable wires, as well as the cable clamp placement and tightening force;

[0007] Step 2: Divide the main cable into the cable clamp area L1, the cable clamp influence area L2, and the free area L3 according to the cable clamp arrangement position, where L represents the length;

[0008] Step 3: Based on the radial force exerted by the cable clamp on the main cable and the characteristics of the steel wire, calculate the polar moment of inertia of the main cable in the cable clamp area I 1t ;

[0009] Step 4: Based on the radial force applied by the cable clamp on the main cable, calculate the mutual extrusion force of the steel wires in the main cable in the cable clamp influence area, and calculate the polar moment of inertia I of the main cable in the cable clamp influence area accordingly. 2t and the length of the affected area L2;

[0010] Step 5: Calculate the polar moment of inertia I of the main cable in the free zone based on the number and characteristics of the steel wires 3t ;

[0011] Step 6: Correct the polar inertia moment of the main cable in the cable clamp area, cable clamp influence area, and free area according to the main cable tension;

[0012] Step 7: The overall polar inertia moment It of the main cable is formed by connecting the corrected polar inertia moments of the cable clamp area, the cable clamp influence area and the free area in series according to the section length.

[0013] As a further solution of the present invention, the step 1 further includes determining main cable parameters such as main cable porosity and cable clamp length.

[0014] As a further solution of the present invention, in step 2, the length L1 of the cable clamp area is the cable clamp length.

[0015] As a further solution of the present invention, the step three is specifically as follows: determining the radial stress distribution in the main cable based on the radial force applied by the cable clamp to the main cable, determining the friction force between the steel wires by means of the friction formula, and comparing it with the torsional shear stress between the steel wires; when the shear stress is less than the friction force between the steel wires (i.e., the torque is less than the yield torque), the polar moment of inertia of the main cable in the cable clamp is calculated based on the flat cross-section assumption; when the shear stress is greater than the friction force between the steel wires (i.e., the torque is greater than the yield torque), the shear stress is taken to be equal to the friction force, and then the polar moment of inertia of the main cable is solved.

[0016] As a further solution of the present invention, the step four is specifically as follows: according to the radial force applied by the cable clamp on the main cable, the pressure field of the main cable in the cable clamp influence area is solved, and the friction force between the steel wires in the cable clamp influence area is determined by the friction formula; according to whether the torsional shear stress is greater than the friction force, the main cable section is divided into a steel wire non-slip zone (inside) and a steel wire slip zone (outside), and the polar moments of inertia of the two areas are solved respectively, and the polar moment of inertia I2 of the entire section of the main cable is obtained by adding them; the length L2 of the cable clamp influence area is the length of the main cable pressure field influence area.

[0017] As a further solution of the present invention, the step 5 is specifically as follows: the polar moment of inertia of the steel wire is solved according to the circular cross-section polar moment of inertia formula based on the steel wire characteristics, and the polar moments of inertia of the steel wire are summed to obtain the polar moment of inertia of the main cable in the free zone I 3t .

[0018] As a further solution of the present invention, the step six is ​​specifically as follows: applying a unit torsion angle to the main cable, solving the torque generated by the main cable tension by the torque calculation formula, and calculating the influence of the main cable tension on the torsional stiffness according to the torsion angle calculation formula to complete the correction.

[0019] As a further solution of the present invention, step seven is specifically as follows: applying a unit torque to the main cable, solving the main cable torsion angles in the cable clamp area, the cable clamp influence area, and the free area respectively, and adding the torsion angles of the three sections to obtain the total torsion angle; and determining the overall polar moment of inertia of the main cable according to the torsion angle calculation formula based on the unit torque, the total length of the main cable, and the total torsion angle.

[0020] The present invention has at least the following beneficial effects: a refined calculation method for the polar moment of inertia of a suspension bridge main cable can be used as a method for calculating the main cable's lateral stiffness. This method not only provides accurate calculations, a clear principle, and excellent reflection of the main cable's characteristics, but also resolves the difficulty in determining the polar moment of inertia of a steel wire bundle. This method can also be used to determine the moment of inertia of other fiber bundles.

[0021] Other advantages, objectives and features of the present invention will be reflected in part from the following description and will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a schematic diagram of the segmented calculation of the polar moment of inertia of the main cable of the present invention;

[0023] Figure 2 This is the shear stress distribution diagram of the main cable when the shear stress of the present invention is less than the friction force between the steel wires;

[0024] Figure 3 This is the shear stress distribution diagram of the main cable when the shear stress is greater than the friction force between the steel wires;

[0025] Figure 4 It is an exploded view of the steel wire tension F of the present invention. DETAILED DESCRIPTION

[0026] The present invention is described in detail and completely below with reference to the accompanying drawings. Those skilled in the art will be able to implement the present invention based on this description. Before describing the present invention with reference to the accompanying drawings, it should be noted that the technical solutions and technical features provided in various parts of the present invention, including those described below, may be combined with each other unless they conflict.

[0027] In addition, the embodiments of the present invention described below are generally only part of the embodiments of the present invention, rather than all of the embodiments. Therefore, based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making any creative efforts should fall within the scope of protection of the present invention.

[0028] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The specific implementation process is as follows:

[0029] Example 1

[0030] Calculation example: The main cable consists of 37 strands, each strand consists of 127 steel wires with a diameter of 6 mm (d). The main cable has a porosity of 0.18 (φ), a friction coefficient between the steel wires of 0.15, and a shear stiffness of G. The cable clamp length is 2.85 m (L1), the confining pressure exerted by the clamp on the main cable is 2.5 MPa (P0), the cable clamp spacing is 16 m (L), and the main cable tension is 7971.7 kN (N).

[0031] Number of main cable wires n = 37·127 = 4699

[0032] According to the void ratio formula, the equivalent diameter of the main cable is:

[0033] This embodiment provides a method for calculating the torsional stiffness of the main cable of a suspension bridge. Figure 1 As shown, the following steps are included:

[0034] Step 1: Determine the main cable parameters such as the number, diameter and friction coefficient of the main cable wires, the cable clamp arrangement position and the cable clamp tightening force; in another embodiment, step 1 also includes determining the main cable parameters such as the main cable porosity and cable clamp length.

[0035] Step 2: Divide the main cable into a clamp area L1, a clamp influence area L2, and a free area L3 according to the clamp arrangement positions. L1, L2, and L3 represent the lengths of each area. In this embodiment, L1 is set as the clamp length.

[0036] Step 3: Based on the radial force applied by the cable clamp on the main cable and the characteristics of the steel wire, solve the polar moment of inertia I1 of the main cable in the cable clamp area. Specifically, determine the radial stress distribution in the main cable based on the radial force applied by the cable clamp on the main cable, and determine the friction between the steel wires using the friction formula. When determining the radial shear stress distribution in the main cable and the friction between the steel wires, focus on the entire main cable, mainly in the cable clamp area and the cable clamp influence area. Compare the friction between the steel wires with the torsional shear stress between the steel wires, as shown in the following example: Figure 2 As shown in , when the shear stress is less than the friction between the steel wires (i.e. the torque is less than the yield torque), the polar moment of inertia of the main cable in the cable clamp is calculated based on the plane section assumption; Figure 3 As shown in Figure 1, when the shear stress is greater than the friction between the steel wires (i.e., the torque is greater than the yield torque), the shear stress is taken to be equal to the friction force, and then the polar moment of inertia of the main cable is solved.

[0037] The specific calculation method is as follows:

[0038] 3.1 Calculate the length of the cable clamp area L1: L1 is the length of the cable clamp = 2.85m.

[0039] 3.2 Calculate the torsional stiffness I1 of the main cable in the clamping area:

[0040] The torque (yield torque Tq of the main cable in the cable clamp) when the steel wires in the cable clamp slide relative to each other is determined based on the condition that the shear stress and friction force between the steel wires in the cable clamp are equal.

[0041] When the shear stress of the outermost wire in the clamp is equal to the friction force, the main cable torque is equal to the yield torque. The torque when the steel wires in the clamp slip relatively (the yield torque Tq of the main cable in the clamp) is determined. μ is the friction coefficient between the steel wires, R is the main cable radius, and r is the steel wire radius.

[0042]

[0043] When the main cable is subjected to a torque (T), T < Tq, the torsional stiffness formula is:

[0044]

[0045] When the torque (T) borne by the main cable is T>Tq, the shear stress inside the main cable after yielding is integrated to obtain:

[0046]

[0047] Step 4: Based on the radial force applied by the cable clamp on the main cable, calculate the mutual extrusion force of the steel wires in the main cable in the cable clamp influence area, and calculate the polar moment of inertia I of the main cable in the cable clamp influence area accordingly. 2t Specifically, the pressure field of the main cable in the clamp's influence zone is calculated based on the radial force exerted by the clamp on the main cable, and the friction between the steel wires in the clamp's influence zone is determined using the friction formula. Based on whether the torsional shear stress is greater than the friction force, the main cable section is divided into a non-slip zone (inside) and a slip zone (outside). The polar moments of inertia of the two zones are calculated separately, and the polar moment of inertia of the entire main cable section, I2, is obtained by adding them together. The length of the clamp's influence zone, L2, is the length of the main cable pressure field influence zone, where the radius of the non-slip zone is 0.1 times the radius of the main cable.

[0048] The specific calculation method is as follows:

[0049] Calculate the length L2 of the cable clamp influence zone and the torsional stiffness I of the main cable in the cable clamp influence zone 2t :

[0050] When the torque (T) on the main cable is less than Tq, according to elastic mechanics analysis, the length of the cable clamp influence zone (L2) is:

[0051]

[0052] The torsional stiffness of the main cable in the clamp influence area I is approximately obtained by connecting the stiffness of each section of the main cable in the influence area in series. 2t :

[0053]

[0054] After simplification, it is approximately:

[0055]

[0056] When the torque on the main cable is T > T q When , the steel wires in the cable clamp influence zone shift relative to each other, and the length of the cable clamp influence zone L2 = 0, that is, the cable clamp influence zone is not considered.

[0057] Step 5: Calculate the polar moment of inertia I of the main cable in the free zone based on the number and characteristics of the steel wires 3t Specifically: the polar moment of inertia of the steel wire is solved according to the circular section polar moment of inertia formula based on the steel wire characteristics, and the polar moment of inertia of the steel wire is summed to obtain the polar moment of inertia of the main cable in the free zone I 3t .

[0058] The specific calculation method is as follows:

[0059] 5.1 Calculate the free zone length L3: L3 = L-L1-L2.

[0060] 5.2 Calculation of the torsional stiffness of the main cable in the free zone I 3t :

[0061] Torsional stiffness of main cable in free zone (I 3t ) is obtained by calculating and finding the torsional stiffness of each steel wire:

[0062]

[0063] Step 6: Figure 4 As shown in the figure, the main cable polar inertia moment of the cable clamp area, cable clamp influence area and free area is corrected according to the main cable tension, and the influence of the main cable tension on the torsional stiffness is considered (I tN Specifically, a unit torsion angle is applied to the main cable, and the torque generated by the main cable tension is solved using the torque calculation formula. The influence of the main cable tension on the torsional stiffness is calculated based on the torsion angle calculation formula to complete the correction.

[0064] When a main cable of length L is twisted φ, the wire tension can be decomposed into longitudinal, circumferential, and radial components. Taking the moment of the circumferential component about the cable center yields the cable torque generated by the wire tension. Integrating the torque generated by the tension across all wires in the cable cross-section yields the torque generated by the main cable tension. The effect of the main cable tension on torsional stiffness is then determined using the torsion angle calculation formula.

[0065] Decompose the wire tension F into the axial force F l , hoop force F φ , radial force F R , according to the similarity principle:

[0066]

[0067] After summing the steel wires along the main cable section, we get: T N is the main cable tension, G is the shear stiffness:

[0068]

[0069] The influence of increasing the tension on the torsional stiffness of the main cable in the three sections is investigated.

[0070] Step 7: Based on the corrected polar moments of inertia of the main cable in the clamping area, the clamping influence area, and the free zone, the overall polar moment of inertia of the main cable It is formed by serially combining the segment lengths. Specifically, a unit torque is applied to the main cable, and the torsion angles of the main cable in the clamping area, the clamping influence area, and the free zone are calculated separately. The total torsion angle is then added together to obtain the total torsion angle. The overall polar moment of inertia of the main cable is determined using the unit torque, the total length of the main cable, and the total torsion angle according to the torsion angle calculation formula.

[0071] The torsional stiffness of the main cables in the three sections is connected in series:

[0072]

[0073] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the description and implementation methods. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and embodiments shown and described herein.

Claims

1. A method for calculating the torsional stiffness of the main cable of a suspension bridge, characterized in that: The following steps are involved: Step 1: Determine the number, diameter, and friction coefficient of the main cable wires, as well as the cable clamp placement and tightening force; Step 2: Divide the main cable into the cable clamp area L1, the cable clamp influence area L2, and the free area L3 according to the cable clamp arrangement position; Step 3: Based on the radial force exerted by the cable clamp on the main cable and the characteristics of the steel wire, calculate the polar moment of inertia of the main cable in the cable clamp area I 1t ; Step 4: Based on the radial force applied by the cable clamp on the main cable, calculate the mutual extrusion force of the steel wires in the main cable in the cable clamp influence area, and calculate the polar moment of inertia I of the main cable in the cable clamp influence area accordingly. 2t and the length of the affected area L2; Specifically, the pressure field of the main cable in the area affected by the clamp is calculated based on the radial force applied by the clamp on the main cable. The friction force between the steel wires in the area affected by the clamp is determined using the friction formula. Based on whether the torsional shear stress is greater than the friction force, the main cable section is divided into a non-slip zone and a slip zone. The polar moments of inertia of the two zones are calculated separately and added together to obtain the polar moment of inertia I2 of the entire main cable section. The calculation is as follows: Calculate the length L2 of the cable clamp influence zone and the torsional stiffness I of the main cable in the cable clamp influence zone 2t : When the main cable is subjected to a torque T, T < Tq, Tq is the yield torque of the main cable in the clamp. According to elastic mechanics analysis, the length of the clamp influence zone L2 is: The torsional stiffness of the main cable in the clamp influence area I is approximately obtained by connecting the stiffness of each section of the main cable in the influence area in series. 2t After simplification, it is approximately: When the torque on the main cable is T > T q When , the steel wires in the cable clamp influence zone shift relative to each other, and the length of the cable clamp influence zone L2 = 0, that is, the cable clamp influence zone is not considered; Among them, R is the main cable radius, r is the distance from the main cable section integration point to the section center, φ is the main cable porosity, is the shear stress at the integration point of the cross section; Step 5: Calculate the polar moment of inertia I of the main cable in the free zone based on the number and characteristics of the steel wires 3t ; Step 6: Correct the polar inertia moment of the main cable in the cable clamp area, cable clamp influence area, and free area according to the main cable tension; Step 7: According to the corrected polar inertia moments of the main cable in the cable clamp area, cable clamp influence area and free area, the overall polar inertia moment of the main cable I is formed in series according to the segment length. t .

2. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, wherein: The step 1 also includes determining the main cable porosity and the cable clamp length.

3. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, wherein: In the step 2, the length L1 of the cable clamp area is the cable clamp length.

4. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, wherein: The step three is specifically as follows: determining the radial stress distribution in the main cable based on the radial force applied by the cable clamp to the main cable, determining the friction force between the steel wires using the friction formula, and comparing it with the torsional shear stress between the steel wires; when the shear stress is less than the friction force between the steel wires, the polar moment of inertia of the main cable in the cable clamp is calculated based on the flat section assumption; when the shear stress is greater than the friction force between the steel wires, the shear stress is taken to be equal to the friction force, and then the polar moment of inertia of the main cable is solved.

5. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, wherein: The step four is specifically as follows: according to the radial force exerted by the cable clamp on the main cable, the pressure field of the main cable in the cable clamp influence area is solved, and the friction force between the steel wires in the cable clamp influence area is determined by the friction formula; according to whether the torsional shear stress is greater than the friction force, the main cable section is divided into a steel wire non-slip zone and a steel wire slip zone, and the polar moments of inertia of the two areas are solved respectively, and the polar moment of inertia I2 of the entire section of the main cable is obtained by adding them; the length L2 of the cable clamp influence area is the length of the main cable pressure field influence area.

6. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, wherein: The step 5 is specifically as follows: the polar moment of inertia of the steel wire is solved according to the circular section polar moment of inertia formula based on the steel wire characteristics, and the polar moment of inertia of the steel wire is summed to obtain the polar moment of inertia of the main cable in the free zone I 3t .

7. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, wherein: The step six is ​​specifically as follows: applying a unit torsion angle to the main cable, solving the torque generated by the main cable tension using the torque calculation formula, and calculating the influence of the main cable tension on the torsional stiffness according to the torsion angle calculation formula to complete the correction.

8. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, wherein: The step seven specifically comprises: applying a unit torque to the main cable, solving the main cable torsion angles in the cable clamp area, the cable clamp influence area, and the free area respectively, and adding the torsion angles of the three sections to obtain the total torsion angle; The overall polar moment of inertia of the main cable is determined by the unit torque, the total length of the main cable, and the total torsion angle according to the torsion angle calculation formula.

Images