Method for predicting elasticity modulus of main cable strand of large-span suspension bridge

Abstract

The invention relates to a method for predicting the elasticity modulus of a main cable strand of a large-span suspension bridge, and relates to the field of main cable strands of bridges. The main cable strand is of a parallel structure composed of n parallel steel wires, and the method comprises the steps that firstly, the diameter of the head and the diameter of the tail of each steel wire forming the main cable strand are measured, and the average value is taken as the calculated diameter of the steel wire; 2, measuring the elastic modulus of the head and the elastic modulus of the tail of each steel wire forming the main cable strand, and averaging the elastic modulus as the calculation elastic modulus of the steel wire; and 3, calculating the elastic modulus of the main cable strand composed of the steel wires according to a prediction formula. The technical problem that the line shape control difficulty of the main cable is increased due to the dispersion of the elastic modulus of the main cable strand of the oversized-span suspension bridge is solved.

Description

Technical Field

[0001] The present invention relates to a method for calculating the elastic modulus of bridge cables. Background Art

[0002] The main cable strands, as the core components of a suspension bridge and its main load-bearing members, the alignment of the main cable directly affects the structural stress and shape state of the entire bridge. High-strength steel wires are usually used as the main cable material. Since the number of steel wires can be set according to actual needs, this can not only save materials and improve the utilization value, but also maximize the unique tensile properties of the steel wire material. Both the geometric deformation and elastic deformation of the main cable have a significant impact on the balance of the entire system, which reflects the mechanical characteristics of large displacement and nonlinearity, and is also the characteristic of a suspension bridge. Therefore, the determination of the main cable alignment is very important. The alignment of the main cable determines the stress and force distribution of the overall structure of the bridge in the completed bridge state, and also affects the determination of the position of the cable clamp in the suspension bridge, the calculation of the stress-free length, the state of the suspender, and the pre-offset of the saddle during the empty cable. The elastic modulus of the main cable strands is an important factor affecting the main cable alignment. High-strength and high-performance steel wires are mostly used as the material for the main cable of long-span suspension bridges. The more such high-performance steel wires, the greater the difficulty in process control during production. It is difficult to absolutely unify the elastic modulus of steel wires in different production batches, resulting in the inability to accurately determine the elastic modulus of the main cable strands. The main cable alignment calculation method determines that different elastic moduli directly correspond to different stress-free lengths, and at the same time has different degrees of influence on the calculation of the elevation of the empty cable node, the pre-offset of the saddle, etc. At present, a segment model about 3 meters long is generally used to test the elastic modulus of the main cable strands in the laboratory, but this test is affected by load errors, length errors, steel wire diameter errors, etc., and there is a large difference between the test results and the elastic modulus of the actual bridge strands.

[0003] For ultra-long-span suspension bridges, the discreteness of the elastic modulus of the main cable strands becomes the most important and difficult problem among the factors affecting the main cable alignment. Summary of the Invention

[0004] The object of the present invention is to propose a prediction method for the elastic modulus of the main cable strands of a long-span suspension bridge with relatively high accuracy.

[0005] The technical solution adopted by the present invention to solve the above problems is as follows: A prediction method for the elastic modulus of the main cable strands of a long-span suspension bridge, where the main cable strands are a parallel structure composed of n mutually parallel steel wires, and the method includes:

[0006] Step 1: Measure the head and tail diameters of each steel wire constituting the main cable strands, and take the average value as the calculated diameter of the steel wire.

[0007] Step 2: Measure the elastic modulus of the head and tail of each steel wire constituting the main cable strands, and take the average value as the calculated elastic modulus of the steel wire.

[0008] Step 3: Calculate the elastic modulus of the main cable strands composed of the above steel wires according to the following formula:

[0009]

[0010] In the formula, E is the elastic modulus of the main cable strands, En is the calculated elastic modulus of the nth steel wire, and dn is the calculated diameter of the nth steel wire. Description of the Drawings

[0011] Figure 1 It is a schematic structural diagram of the main cable strands of the suspension bridge in the embodiment of the present invention. Detailed Embodiment

[0012] The following further describes the present invention in detail with reference to the embodiments. The embodiments are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0013] The main cable strands of the long-span suspension bridge are a parallel structure composed of 127 mutually parallel steel wires. Since the main cable only bears axial tension, under the action of tensile stress, the properties and diameters of the steel wires are basically uniform and continuous, and all are mutually parallel. There is no slippage between the steel wires. Since the ends of the 127 steel wires are integrally anchored, the longitudinal deformation of the cable strands is considered to be basically the same.

[0014] The axial deformation of the cable strands under the action of tension is as follows:

[0015] ε = ε1 = ε2 = …… = ε 127 (Formula 1)[[ID= thirty-one ]]

[0016] In the formula: ε is the axial deformation of the cable strands;

[0017] ε1 is the deformation of the first steel wire;

[0018] ε 127 is the deformation of the 127th steel wire;

[0019] Since the 127 steel wires are all elastic materials, the axial stresses they bear can be calculated by Formulas 2 and 3:

[0020] σ1 = E1ε1 (Formula 2)

[0021] ……

[0022] σ 127 = E1ε 127 (Formula 3)

[0023] In the formula: σ^1 is the stress of the No. 1 steel wire;

[0024] E^1 is the elastic modulus of the No. 1 steel wire;

[0025] σ 127 is the stress of the wire No. 127;

[0026] E 127 is the elastic modulus of the wire No. 127

[0027] Since the tensile force borne by the cable strand is jointly borne by 127 wires, the relationship between the force borne by each wire and the tensile force borne by the cable strand is shown in Formula 4.

[0028] F = F1 + F2……F 127 (Formula 4)

[0029] In the formula: F is the total tensile force borne by the cable strand;

[0030] F1 is the tensile force borne by the No. 1 wire;

[0031] F 127 is the tensile force borne by the wire No. 127;

[0032] The above formula can be changed to Formula 5,

[0033] σA = σ1A1 + σ2A2……σ 127 A 127 (Formula 5)

[0034] In the formula: σ is the stress of the cable strand;

[0035] A is the total area of the wires in the cable strand;

[0036] A1 is the area of the tensile force borne by the No. 1 wire;

[0037] A 127 is the area of the tensile force borne by the wire No. 127;

[0038] Express the above area as the wire diameter, such as Formula 6.

[0039]

[0040] Among them:

[0041] The above formula is changed, such as Formula 7.

[0042]

[0043] And the relationship between the stress of the cable strand, the elastic modulus and the strain is shown in Formulas 8 - 10.

[0044] σ = E ε (Formula 8)

[0045] σ1 = E1ε1 (Formula 9)

[0046] σ127 = E 127 ε 127 (Equation 10)

[0047] Combining Equation 1, Equation 7, Equation 8, Equation 9, and Equation 10 gives Equation 11

[0048]

[0049] Equation 11 is further simplified to obtain Equation 12

[0050]

[0051] Based on Equation 12, the elastic modulus of the prefabricated parallel wire strand can be predicted on the basis of measuring the diameter and elastic modulus of a single wire

[0052] Specifically as follows:

[0053] Step 1: Measure the head and tail diameters of a single coil of wire that makes up the strand, and take the average as the calculated diameter of this wire

[0054] Step 2: Measure the elastic moduli of the head and tail of a single coil of wire that makes up the strand, and take the average as the calculated elastic modulus of this wire

[0055] Step 3: Calculate the elastic modulus of the strand composed of the above wires according to Equation 12

[0056] The main cable strand of a suspension bridge has a specification of 127-Ф5.6mm. The nominal diameter of the wire is 5.60mm, the diameter allowable deviation is ±0.06mm, the nominal elastic modulus of the wire is 200GPa, and the elastic modulus allowable deviation is ±10GPa. The head and tail diameters and elastic moduli of each coil of wire are detected, and the measurement data is as shown in the following table. According to Equation 12, the elastic modulus E of this strand is predicted to be 228GPa

[0057]

[0058]

[0059]

[0060]

[0061] In addition to the above embodiments, the present invention also includes other embodiments. All technical solutions formed by equivalent transformation or equivalent substitution shall fall within the protection scope of the claims of the present invention

Claims

1. A method for predicting the elastic modulus of main cable strands of a long-span suspension bridge, characterized in that: The main cable wire strands are a parallel structure composed of n mutually parallel steel wires. The method includes: Step 1: Measure the head and tail diameters of each steel wire that makes up the main cable wire strands, and take the average value as the calculated diameter of this steel wire; Step 2: Measure the elastic moduli of the heads and tails of each steel wire that makes up the main cable wire strands, and take the average value as the calculated elastic modulus of this steel wire; Step 3: Calculate the elastic modulus of the main cable wire strands composed of the above steel wires according to the following formula: In the formula, E is the elastic modulus of the main cable wire strands, En is the calculated elastic modulus of the nth steel wire, and dn is the calculated diameter of the nth steel wire.

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