Method for calculating torsional rigidity of main cable of suspension bridge

Abstract

The invention discloses a method for calculating torsional rigidity of a main cable of a suspension bridge. The method comprises the following steps: determining parameters of the main cable, a cable clamp arrangement position and fastening force; the main cable is divided into a cable clamp area, a cable clamp influence area and a free area according to the cable clamp arrangement position; according to the radial force applied to the main cable by the cable clamp and the characteristics of the steel wire, the polar inertia moment of the main cable in the cable clamp area is solved; according to the radial force applied by the cable clamp to the main cable, the mutual extrusion force of steel wires in the main cable in the cable clamp influence area is solved, and the polar inertia moment of the main cable in the cable clamp influence area and the length of the influence area are solved accordingly; solving the polar inertia moment of the main cable in the free area according to the number and characteristics of steel wires; correcting the polar inertia moments of the main cables in the cable clamp area, the cable clamp influence area and the free area; and according to the corrected cable clamp area, the cable clamp influence area and the free area, the main cable polar inertia moments are connected in series according to the section length to form the main cable total polar inertia moment. The method solves the problem that the polar inertia moment of the main cable of the suspension bridge cannot be accurately calculated, and has the advantages of accurate calculation, clear principle, capability of better reflecting the characteristics of the main cable and the like.

Description

Technical Field

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

[0002] The main cable is a key component of a suspension bridge, and its performance is crucial for the load-bearing capacity and durability of the suspension bridge. The main cable is generally composed of numerous steel wires. Affected by transverse constraints such as cable saddles and lashing bands, the interaction between the steel wires in the main cable is complex. It is difficult to simply superimpose the transverse characteristics of the steel wires to obtain the transverse characteristics of the main cable. Therefore, domestic and foreign scholars have conducted a large number of theoretical analyses and experimental studies on the main cable of suspension bridges.

[0003] At present, the calculation of the polar moment of inertia of the main cable of a suspension bridge is often taken 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, without a clear theoretical basis, and the 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, including the following steps: Step 1: Determine the number, diameter, and friction coefficient of the steel wires of the main cable, the arrangement position and fastening force of the cable saddles; Step 2: Divide the main cable into a cable saddle area L1, a cable saddle influence area L2, and a free area L3 according to the arrangement position of the cable saddles, where L represents the length; Step 3: Solve the polar moment of inertia I of the main cable in the cable saddle area according to the radial force applied by the cable saddle to the main cable and the characteristics of the steel wires 1t ; Step 4: Solve the mutual extrusion force between the steel wires in the main cable in the cable saddle influence area according to the radial force applied by the cable saddle to the main cable, and solve the polar moment of inertia I of the main cable in the cable saddle influence area and the influence area length L2 accordingly; 2t and the influence area length L2; Step 5: Solve the polar moment of inertia I of the main cable in the free area according to the number and characteristics of the steel wires 3t ; Step 6: Correct the polar moment of inertia of the main cable in the cable saddle area, the cable saddle influence area, and the free area according to the main cable tension; Step 7: Form the overall polar moment of inertia It of the main cable by connecting in series the corrected polar moments of inertia of the main cable in the cable saddle area, the cable saddle influence area, and the free area according to the section lengths.

[0006] A further solution of the present invention is that in the first step, the main cable parameters such as the void ratio of the main cable and the length of the cable clamp are also determined.

[0007] A further solution of the present invention is that in the second step, the length L1 of the cable clamp area is the length of the cable clamp.

[0008] A further solution of the present invention is that the third step is specifically as follows: determine the radial stress distribution in the main cable according to the radial force applied by the cable clamp to the main cable, determine the friction force between the steel wires through the friction formula, and compare 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 according to the plane 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), take the shear stress equal to the friction force, and then solve the polar moment of inertia of the main cable.

[0009] A further solution of the present invention is that the fourth step is specifically as follows: solve the main cable pressure field in the cable clamp influence area according to the radial force applied by the cable clamp to the main cable, and determine the friction force between the steel wires in the cable clamp influence area through the friction formula; divide the main cable cross-section into a non-slip area (inner side) and a slip area (outer side) of the steel wires according to whether the torsional shear stress is greater than the friction force, solve the polar moment of inertia of the two areas respectively, and add them to obtain the polar moment of inertia I2 of the entire cross-section of the main cable; the length L2 of the cable clamp influence area is the length of the main cable pressure field influence area.

[0010] A further solution of the present invention is that the fifth step is specifically as follows: solve the polar moment of inertia of the steel wire according to the circular cross-section polar moment of inertia formula based on the steel wire characteristics, and sum the polar moments of inertia of the steel wires to obtain the polar moment of inertia I of the main cable in the free area 3t 。

[0011] A further solution of the present invention is that the sixth step is specifically as follows: apply a unit torsional angle to the main cable, solve the torque generated by the main cable tension through the torque calculation formula, and obtain the influence of the main cable tension on the torsional stiffness according to the torsional angle calculation formula to complete the correction.

[0012] A further solution of the present invention is that the seventh step is specifically as follows: apply a unit torque to the main cable, solve the torsional angles of the main cable in the cable clamp area, the cable clamp influence area, and the free area respectively, and add the torsional angles of the three sections to obtain the total torsional angle; determine the overall polar moment of inertia of the main cable according to the unit torque, the total length of the main cable, and the total torsional angle according to the torsional angle calculation formula.

[0013] The present invention has at least the following beneficial effects: The refined calculation method of the polar moment of inertia of the main cable of a suspension bridge can be used as a calculation method for the lateral stiffness of the main cable. This method not only has accurate calculations and clear principles, can better reflect the characteristics of the main cable, but also solves the problem of difficult determination of the polar moment of inertia of the steel wire bundle. This method can also be used to determine the moment of inertia of other fiber bundles.

[0014] Other advantages, objects and features of the present invention will be partly reflected by the following description, and partly will be understood by those skilled in the art through the research and practice of the present invention. Description of the Drawings

[0015] Figure 1 It is a schematic diagram of the sectional calculation of the polar moment of inertia of the main cable of the present invention; Figure 2 It is a distribution diagram of the shear stress of the main cable when the shear stress of the present invention is less than the frictional force between steel wires; Figure 3 It is a distribution diagram of the shear stress of the main cable when the shear stress of the present invention is greater than the frictional force between steel wires; Figure 4 It is a decomposition diagram of the steel wire tension F of the present invention. Detailed Embodiment

[0016] The present invention will be described in detail and completely below with reference to the accompanying drawings. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it should be particularly noted that: the technical solutions and technical features provided in each part including the following description of the present invention can be combined with each other without conflict.

[0017] In addition, the embodiments of the present invention involved in the following description are usually only part of the embodiments of the present invention, rather than all of the embodiments. Therefore, all other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative work should fall within the scope of protection of the present invention.

[0018] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, and the specific implementation process is as follows: Embodiment 1 Calculation example: The main cable consists of 37 wire strands, each wire strand is composed of 127 steel wires with a diameter of 6 mm (d), the void ratio of the main cable is 0.18 (φ), the friction coefficient between steel wires is 0.15, and the shear stiffness of the steel wire is G; the length of the cable clamp is 2.85 m (L1), the confining pressure applied by the cable clamp to the main cable is 2.5 MPa (P0), the distance between cable clamps is 16 m (L), and the tension of the main cable is 7971.7 kN (N).

[0019] The number of main cable steel wires n = 37·127 = 4699 From the void ratio formula, the equivalent diameter of the main cable: This embodiment provides a method for calculating the torsional stiffness of the main cable of a suspension bridge, as Figure 1 shown, including the following steps: Step 1: Determine the main cable parameters such as the number of steel wires, diameter, friction coefficient, the arrangement position of the cable clamp, and the tightening force of the cable clamp; in another embodiment, Step 1 further includes determining the main cable void ratio, cable clamp length and other main cable parameters.

[0020] Step 2: Divide the main cable into a cable clamp area L1, a cable clamp influence area L2, and a free area L3 according to the arrangement position of the cable clamp, where L1, L2, and L3 represent the lengths of each area; in this embodiment, L1 is set to the cable clamp length.

[0021] Step 3: Solve the polar moment of inertia I1 of the main cable in the cable clamp area according to the radial force exerted by the cable clamp on the main cable and the wire characteristics; specifically: determine the radial stress distribution in the main cable according to the radial force exerted by the cable clamp on the main cable, determine the friction force between the steel wires through the friction formula, and when determining the radial shear stress distribution in the main cable and the friction force between the steel wires, it is for the entire main cable, mainly applied to the cable clamp area and the cable clamp influence area. Compare the friction force between the steel wires with the torsional shear stress between the steel wires. As Figure 2 shown, 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 according to the plane section assumption; as Figure 3 shown, when the shear stress is greater than the friction force between the steel wires (i.e., the torque is greater than the yield torque), take the shear stress equal to the friction force, and then solve the polar moment of inertia of the main cable.

[0022] The specific calculation method is as follows: 3.1 Calculate the length L1 of the cable clamp area: L1 is the cable clamp length = 2.85m.

[0023] 3.2 Calculate the torsional stiffness I1 of the main cable in the cable clamp area: Determine the torque (yield torque Tq of the main cable in the cable clamp) when the steel wires in the cable clamp slip relative to each other according to the condition that the shear stress between the steel wires in the cable clamp is equal to the friction force Determine the torque (yield torque Tq of the main cable in the cable clamp) when the shear stress of the outermost steel wire in the cable clamp is equal to the friction force, and the torque of the main cable is equal to the yield torque. μ is the friction coefficient between the steel wires, R is the radius of the main cable, and r is the radius of the steel wire.

[0024] When the torque (T) borne by the main cable, T < Tq, according to the torsional stiffness formula: When the torque (T) borne by the main cable, T > Tq, according to the integration of the shear stress in the main cable after yielding: Step 4: Solve the extrusion force between the steel wires in the main cable in the cable clamp influence area according to the radial force exerted by the cable clamp on the main cable, and solve the polar moment of inertia I of the main cable in the cable clamp influence area accordingly 2tand the length L2 of the influence area. Specifically: According to the radial force exerted by the cable clamp on the main cable, solve the pressure field of the main cable in the influence area of the cable clamp, and determine the friction force between the steel wires in the influence area of the cable clamp through the friction formula; divide the cross-section of the main cable into a non-slip area (inner side) and a slip area (outer side) of the steel wires according to whether the torsional shear stress is greater than the friction force, solve the polar moment of inertia of the two areas respectively, and add them to obtain the polar moment of inertia I2 of the entire cross-section of the main cable; the length L2 of the influence area of the cable clamp is the length of the influence area of the main cable pressure field, where the radius of the non-slip area is 0.1 times the radius of the main cable.

[0025] The specific calculation method is as follows: Calculate the length L2 of the influence area of the cable clamp and the torsional stiffness I of the main cable in the influence area of the cable clamp 2t : When the torque (T) borne by the main cable, T < Tq, according to the analysis of elasticity mechanics, the length (L2) of the influence area of the cable clamp is: Approximate the torsional stiffness I of the main cable in the influence area of the cable clamp by connecting the main cable stiffness of each cross-section in the influence area in series 2t : After simplification, it is approximately: When the torque T borne by the main cable > T q At this time, the steel wires in the influence area of the cable clamp move relative to each other, and the length L2 of the influence area of the cable clamp = 0, that is, the influence area of the cable clamp is not considered.

[0026] Step Five: Solve the polar moment of inertia I of the main cable in the free area according to the number and characteristics of the steel wires 3t . Specifically: Solve the polar moment of inertia of the steel wires according to the circular cross-section polar moment of inertia formula based on the characteristics of the steel wires, and sum the polar moments of inertia of the steel wires to obtain the polar moment of inertia I of the main cable in the free area 3t .

[0027] The specific calculation method is as follows: 5.1 Calculate the length L3 of the free area: L3 = L - L1 - L2.

[0028] 5.2 Calculate the torsional stiffness I of the main cable in the free area 3t : The torsional stiffness (I 3t ) of the main cable in the free area is obtained by calculating and summing the torsional stiffnesses of each steel wire: Step Six: As Figure 4 shown, correct the polar moment of inertia of the main cable in the cable clamp area, the influence area of the cable clamp, and the free area according to the main cable tension, and consider the influence of the main cable tension on the torsional stiffness (I tNSpecifically, apply a unit torsional angle to the main cable, solve the torque generated by the main cable tension through the torque calculation formula, and obtain the influence of the main cable tension on the torsional stiffness according to the torsional angle calculation formula to complete the correction.

[0029] When the main cable of length L is twisted by φ, the wire tension can be decomposed into longitudinal, circumferential, and radial components. Taking the moment of the circumferential component about the center of the main cable, the torque of the main cable generated by the wire tension can be obtained. Integrating the torques generated by the tensions of all wires in the main cable cross-section, the torque generated by the main cable tension can be obtained, and the influence of the main cable tension on the torsional stiffness can be obtained according to the torsional angle calculation formula.

[0030] Decompose the wire tension F into axial component F l , circumferential component F φ , and radial component F R . According to the similarity principle: After summing the wires along the cross-section of the main cable, T N is substituted as the main cable tension, and G is the shear stiffness: Increase the torsional stiffness of the main cable in the three sections by the influence of the tension on the torsional stiffness of the main cable respectively.

[0031] Step 7: According to the corrected polar moments of inertia of the main cable in the clamp area, clamp influence area, and free area, form the overall polar moment of inertia It of the main cable in series according to the section lengths. Specifically, apply a unit torque to the main cable, solve the torsional angles of the main cable in the clamp area, clamp influence area, and free area respectively, and add the torsional angles of the three sections to obtain the total torsional angle; determine the overall polar moment of inertia of the main cable according to the unit torque, the total length of the main cable, and the total torsional angle according to the torsional angle calculation formula.

[0032] After connecting the torsional stiffnesses of the main cable in the three sections in series, we get: Although the embodiments of the present invention have been disclosed as above, it is not limited to the applications listed in the specification and embodiments. It can be fully applied to various fields suitable for the present invention. For those familiar with the field, additional modifications can be easily made. Therefore, without departing from the general concept defined by the claims and the equivalent scope, the present invention is not limited to the specific details and the 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 It includes the following steps: Step 1: Determine the number of wires, diameter, and friction coefficient of the main cable, the arrangement positions of the cable clips, and the fastening force; Step 2: Divide the main cable into a cable clip area L1, a cable clip influence area L2, and a free area L3 according to the arrangement positions of the cable clips; Step 3: Solve the polar moment of inertia I of the main cable in the clip area according to the radial force exerted by the clip on the main cable and the properties of the steel wires 1t ; Step 4: According to the radial force exerted by the cable clip on the main cable, solve the mutual extrusion force of the steel wires in the main cable within the influence area of the cable clip, and based on this, solve the polar moment of inertia I of the main cable within the influence area of the cable clip 2t and the length L2 of the influence area; Step 5. Solve the polar moment of inertia I of the main cable in the free zone according to the number and characteristics of the steel wires 3t ; Step 6: Correct the polar moment of inertia of the main cable in the cable clip area, the cable clip influence area, and the free area according to the main cable tension; Step 7: Form the overall polar moment of inertia I of the main cable by connecting in series the polar moments of inertia of the main cable in the clip area, the clip influence area, and the free area according to the corrected values and the section lengths t .

2. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, characterized in that, In Step 1, it also includes determining the void ratio of the main cable and the length of the cable clip.

3. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, characterized in that, In Step 2, the length L1 of the cable clip area is the length of the cable clip.

4. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, characterized in that, Step 3 is specifically as follows: Determine the radial stress distribution in the main cable according to the radial force exerted by the cable clip on the main cable, determine the friction force between the wires through the friction formula, and compare it with the torsional shear stress between the wires. When the shear stress is less than the friction force between the wires, the polar moment of inertia of the main cable in the cable clip is calculated according to the plane section assumption; when the shear stress is greater than the friction force between the wires, take the shear stress equal to the friction force, and then solve the polar moment of inertia of the main cable.

5. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, characterized in that, Step 4 is specifically as follows: Solve the pressure field of the main cable in the cable clip influence area according to the radial force exerted by the cable clip on the main cable, and determine the friction force between the wires in the cable clip influence area through the friction formula; divide the main cable cross-section into a non-slip area of the wires and a slip area of the wires according to whether the torsional shear stress is greater than the friction force, solve the polar moment of inertia of the two areas respectively, and add them to obtain the polar moment of inertia I2 of the entire cross-section of the main cable; the length L2 of the cable clip influence area is the length of the pressure field influence area of the main cable.

6. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, wherein The specific content of the fifth step is as follows: Solve the polar moment of inertia of the steel wire according to the formula of the polar moment of inertia of a circular cross-section based on the characteristics of the steel wire, sum up the polar moments of inertia of the steel wires, and obtain the polar moment of inertia I of the main cable in the free zone 3t .

7. The method for calculating the torsional stiffness of the main cable of a suspension bridge according to claim 1, characterized in that, Step 6 is specifically as follows: Apply a unit torsional angle to the main cable, solve the torque generated by the main cable tension through the torque calculation formula, and obtain the influence of the main cable tension on the torsional stiffness according to the torsional 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 Step 7 is specifically as follows: Apply a unit torque to the main cable, solve the torsional angles of the main cable in the cable clip area, the cable clip influence area, and the free area respectively, and add the torsional angles of the three sections to obtain the total torsional angle; Determine the overall polar moment of inertia of the main cable according to the unit torque, the total length of the main cable, and the total torsional angle according to the torsional angle calculation formula.

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