Prestressed steel strand deformation calculation method considering structural bending rigidity

Abstract

The invention discloses a prestressed steel strand deformation calculation method considering structural bending rigidity, which belongs to the technical field of bridge engineering, and comprises the following steps: constructing a finite element model of a prestressed seven-wire steel strand; performing a three-point bending test on the finite element model of the prestressed seven-wire steel strand to obtain a three-point bending test result; based on the three-point bending test result, obtaining the equivalent bending rigidity of the finite element model by adopting a structural bending rigidity calculation method; constructing a deflection control equation of the prestressed seven-wire steel strand considering the self-weight and prestress effects at the same time; based on the deflection control equation and the equivalent bending rigidity, the deflection and the rotation angle of the finite element model structure are obtained through calculation, and then the deformation result of the prestressed seven-wire steel strand is obtained. The calculation method provided by the invention has more accurate calculation precision and wider engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology, and in particular relates to a method for calculating the deformation of prestressed steel strands that takes into account the bending stiffness of the structure. Background Technology

[0002] Cable-stayed bridges are crucial load-bearing components in highway and railway cable-stayed bridges. Their operating costs, especially replacement costs, are high, making their durability an increasingly important concern for engineers. Many factors influence the durability of cable-stayed bridges, with the installation quality during construction having a significant impact. If the pre-embedded cable guide tube is installed at an improper angle, resulting in the cable being too close to the tube, friction between the cable and the tube wall is highly likely during use, causing mechanical damage and affecting the cable's service life and even the operational safety of the cable-stayed bridge. Therefore, calculating the cable's deflection and end rotation angle under its own weight and correcting the cable guide tube angle during the design phase is of great importance.

[0003] Current calculation methods often neglect the bending resistance of the cables, treating them as completely flexible, and then derive the corresponding calculation methods. Existing technologies have three major drawbacks: ① they do not consider the strengthening effect of prestress on bending stiffness; ② they ignore the shear force transfer characteristics of the seven-wire twisted structure; ③ they lack a collaborative solution framework combining finite element and analytical methods.

[0004] Secondly, stay cables are usually made up of multiple strands of steel wire. The length of the steel wire test sample is generally a unit lay length. Most tests use Euler beam theory when processing and analyzing data, ignoring the effect of shear force, which affects the accuracy of calculation.

[0005] To address the aforementioned problems in existing technologies, there is an urgent need to propose a method for calculating the deformation of prestressed steel strands that takes into account the structural bending stiffness. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method for calculating the deformation of prestressed steel strands that considers the structural bending stiffness. This method corrects the angle of the cable guide tube by using equivalent bending stiffness, thus solving the cable-tube friction problem caused by neglecting bending stiffness in short and thick cable stays. It is particularly suitable for the construction design of cable guide tubes in low-tower cable-stayed bridges.

[0007] This invention proposes a method for calculating the deformation of prestressed steel strands considering structural bending stiffness, comprising the following steps:

[0008] Construct a finite element model of a prestressed seven-wire steel strand;

[0009] A three-point bending test was conducted on the finite element model of the prestressed seven-wire steel strand to obtain the test results.

[0010] Based on the results of the three-point bending test, the equivalent bending stiffness of the finite element model is obtained by using the structural bending stiffness calculation method.

[0011] Construct the deflection control equation for a prestressed seven-wire steel strand that simultaneously considers its own weight and prestressing effect;

[0012] Based on the aforementioned deflection control equation and equivalent bending stiffness, the deflection and rotation angle of the finite element model structure are calculated, thereby obtaining the deformation results of the prestressed seven-wire steel strand.

[0013] Optionally, a three-point bending test is conducted on the finite element model of the prestressed seven-wire steel strand. The process of obtaining the three-point bending test results includes:

[0014] Binding constraints are established between adjacent wires of the prestressed seven-strand steel strand. Reference points and reference point sets are established at both ends of the finite element model to couple the binding constraints, and prestress is applied to output the warping height. A mid-span top node set is established at the top of the mid-span of the finite element model to apply displacement loads to output support reactions. A mid-span middle node set is established at the middle node to output displacement. A bottom node set is established at the bottom position half a lay length from the mid-span to apply hinged constraints.

[0015] Optionally, before obtaining the equivalent bending stiffness of the finite element model based on the three-point bending test results, the method for calculating the structural bending stiffness also includes selecting a method for calculating the structural bending stiffness:

[0016] A preset slenderness ratio threshold is set. When the slenderness ratio of the finite element model is less than the preset threshold, the structural bending stiffness is calculated using Timoshenko beam theory. When the slenderness ratio of the finite element model is greater than the preset threshold, the structural bending stiffness is calculated using Euler beam theory.

[0017] Optionally, the equivalent bending stiffness obtained based on Euler beam theory is calculated using the following formula:

[0018]

[0019] Where F is the applied load, L is the beam span, T is the prestressed axial force, d is the height of the beam's two ends overhang, f is the mid-span deflection, and EI is the load. eff This is the equivalent bending stiffness.

[0020] Optionally, the equivalent bending stiffness obtained based on Timoshenko beam theory is calculated using the following formula:

[0021]

[0022] Where A is the cross-sectional area, I is the moment of inertia of the cross section, K is the shear force coefficient, and ν is Poisson's ratio.

[0023] Optionally, the deflection control equation for the prestressed seven-wire steel strand is calculated as follows:

[0024]

[0025] Among them, EI eff The equivalent bending stiffness is given by T, where T is the prestressed axial force, q is the cable self-weight intensity, and N is the vertical support reaction force of the cable self-weight at the anchorage end of the cable beam. L is the original length of the stay cable, and θ is the design value of the cable-beam angle.

[0026] Optionally, the process of constructing the finite element model of the prestressed seven-wire steel strand also includes:

[0027] The geometric dimensions, prestress magnitude, and elastic properties of the finite element model are determined by parameters.

[0028] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0029] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

[0030] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method.

[0031] Compared with the prior art, the present invention has the following advantages and technical effects:

[0032] This invention proposes a method for calculating the deformation of prestressed steel strands that considers the bending stiffness of the structure. Instead of simply treating the stay cable as a flexible hinge for analysis, it simplifies the finite element model to consider the equivalent bending stiffness of the structure. The method uses the governing equations to solve for the expression of the steel strand deflection as a function of space, and by differentiating this expression, the rotation angle of the steel strand at different positions can be obtained. This method considers more comprehensive factors, has more accurate calculation precision, and has wider engineering application value. Attached Figure Description

[0033] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0034] Figure 1 This is a schematic diagram of the cable guide tube according to an embodiment of the present invention;

[0035] Figure 2 This is a schematic diagram of the cross-section of the cable guide tube according to an embodiment of the present invention;

[0036] Figure 3 This is a flowchart of a method according to an embodiment of the present invention;

[0037] Figure 4 This is a schematic diagram of a cable-stayed bridge model according to an embodiment of the present invention;

[0038] Figure 5 This is a schematic diagram of the deflection curve of the steel strand in an embodiment of the present invention. Detailed Implementation

[0039] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0040] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0041] Example 1

[0042] like Figure 3 As shown, this embodiment provides a method for calculating the deformation of prestressed steel strands considering structural bending stiffness, applicable to, for example... Figure 1 In the angle correction of the cable-stayed bridge duct shown, its cross-section is as follows: Figure 2 As shown, the method includes the following steps:

[0043] Construct a finite element model of a prestressed seven-wire steel strand;

[0044] A three-point bending test was conducted on the finite element model of the prestressed seven-wire steel strand to obtain the test results.

[0045] Based on the results of the three-point bending test, the equivalent bending stiffness of the finite element model is obtained by using the structural bending stiffness calculation method.

[0046] Construct the deflection control equation for a prestressed seven-wire steel strand that simultaneously considers its own weight and prestressing effect;

[0047] Based on the aforementioned deflection control equation and equivalent bending stiffness, the deflection and rotation angle of the finite element model structure are calculated, thereby obtaining the deformation results of the prestressed seven-wire steel strand.

[0048] As a specific implementation method, the following steps are included:

[0049] S1: The bending deformation of cables under prestress is complex and cannot be calculated using simple material mechanics formulas. Some cable bending tests also show that the equivalent bending stiffness of the cable is not constant, but gradually decreases with loading. To obtain accurate equivalent bending stiffness, a three-point bending test of the cable is required.

[0050] This embodiment uses a simplified finite element model of a prestressed seven-wire steel strand to conduct a three-point bending test. The finite element model only considers a prestressed seven-wire steel strand with a single twist length. Based on literature and the actual situation of the cable-stayed bridge project, the friction between the steel wires and the deformation of the cable cross section are ignored. Prestress is applied at both ends of the model to obtain the force-displacement curve of the structure.

[0051] Implementable, step S1 includes the following steps:

[0052] For prestressed seven-wire steel strands of different specifications, the geometric dimensions, prestress magnitude, and elastic properties in the finite element model are determined.

[0053] As one feasible approach, the geometric and material parameters of the finite element model in this embodiment are shown in Table 1.

[0054] Table 1

[0055]

[0056] It is feasible that in step S1:

[0057] The finite element model ignores the friction between steel wires and the deformation of the cable cross section, so binding constraints need to be established between adjacent steel wires.

[0058] It is feasible that in step S1:

[0059] The finite element model has prestressed axial forces applied at both ends. It is necessary to establish point-to-surface coupling constraints at both ends of the model through reference points to apply the prestress.

[0060] It is feasible that in step S1:

[0061] The finite element model outputs data such as loaded load, mid-span deflection, and uplift height. It is necessary to establish a corresponding set and set field output variables, and then extract these data in post-processing.

[0062] As an feasible approach, such as Figure 4As shown, bonding constraints are established between adjacent steel wires. Reference points “RP1” and “RP2” are established at both ends of the finite element model, and sets “set-rp1” and “set-rp2” are established to couple constraints, apply prestress, and output the warping height. A node set “set-load” is established at the top of the mid-span to apply displacement load and output support reaction force. The mid-span node is established as a set “set-displacement” to output displacement. A node set “set-support” is established at the bottom of the position half a lay length away from the mid-span to apply hinged support constraints.

[0063] S2: A structural bending stiffness calculation method based on finite element model data and materials mechanics. This method considers the warping height at both ends of the steel strand during loading and eliminates the additional bending moment caused by prestress. The equivalent bending stiffness calculation formula is as follows:

[0064]

[0065] Where F is the applied load, L is the beam span, T is the prestressed axial force (internal force of steel strands), d is the height of the beam's two ends, and f is the mid-span deflection.

[0066] The above calculation formula is applied to Euler beams. If the slenderness ratio of the model is very small, the Timoshenko beam theory should be considered, and the formula for calculating the equivalent bending stiffness is as follows:

[0067]

[0068] Where A is the cross-sectional area, I is the moment of inertia of the cross section, K is the shear force coefficient, and ν is Poisson's ratio.

[0069] Implementable, the steps preceding S2 include:

[0070] The suitability of the model for Euler beam or Timoshenko beam theory is determined based on the slenderness ratio of the structure. In this embodiment, if the slenderness ratio of the model is 15, the simpler Euler beam theory can be applied.

[0071] Implementable, the steps preceding S2 include:

[0072] The formula for calculating the equivalent stiffness of the Timoshenko beam requires determining the shear force coefficient K, which is related to the cross-sectional dimensions. For a cross-section such as... Figure 2 The placed seven-strand steel wire has a shear force coefficient of 1.0931, which is independent of the wire radius R.

[0073] Implementable, in step S2:

[0074] The equivalent bending stiffness is calculated using the data in S1. Since the deflection of steel strands in actual engineering is very small, the equivalent bending stiffness corresponding to a smaller mid-span deflection is often used. For example, the equivalent bending stiffness calculated from this model is 5.4526 × 10⁻⁶. 9 N·mm 2 .

[0075] S3: Based on the deflection control equation of the prestressed seven-wire steel strand considering both self-weight and prestressing, the deflection and rotation angle of the structure are obtained according to the equivalent bending stiffness solution equation calculated in S2. For Figure 1 The governing equations for the cable structure shown are as follows:

[0076]

[0077] Where q is the self-weight intensity of the cable, L is the original length of the cable, and N is the vertical support reaction force of the cable at the anchorage end of the cable beam. θ is the design value of the cable-beam angle.

[0078] Implementable, step S3 includes the following steps:

[0079] For prestressed seven-wire steel strands of different specifications, the parameters of self-weight intensity, original length and cable-beam angle design values ​​in the finite element model are determined.

[0080] As an feasible approach, this embodiment uses a steel strand self-weight intensity of 0.1837 kg / m for calculation. Steel strands with different original lengths and cable-beam angle design values ​​are selected for calculation, and the parameters are shown in Table 2.

[0081] Table 2

[0082]

[0083] Implementable, in step S3:

[0084] Substituting the equivalent bending stiffness and other geometric and physical parameters obtained in S2 into the governing equations, the expression for the spatial variation curve of the steel strand deflection, which simultaneously considers the bending stiffness and self-weight, is obtained. Differentiating this expression yields the rotation angle of the steel strand at different positions. In engineering, the angle of the steel strand at the beam end and tower end is of particular concern, and this angle can be used to correct the cable-beam angle and tower angle.

[0085] As one feasible approach, this embodiment plots the deflection curves of the S1-S4 steel strands as follows: Figure 5 As shown in the figure, the correction value of the beam end rotation angle is calculated as shown in Table 3. After correction, the installation angle of the cable guide is more accurate, which is of great significance for structural safety and service life improvement.

[0086] Table 3

[0087]

[0088] This embodiment proposes a method for calculating the deflection and rotation angle of prestressed seven-wire steel strands that considers the structural bending stiffness. Instead of simply treating the stay cable as a flexible hinge for analysis, it calculates the equivalent bending stiffness by simplifying the finite element model, solves the expression for the steel strand deflection as a function of space using the governing equations, and obtains the rotation angle of the steel strand at different positions by differentiating this expression. This method considers more comprehensive factors, has more accurate calculation precision, and has wider engineering application value.

[0089] Example 2

[0090] This embodiment also discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in Embodiment 1.

[0091] Example 3

[0092] This embodiment also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0093] Example 4

[0094] This embodiment also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0095] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for calculating the deformation of prestressed steel strands considering structural bending stiffness, characterized in that, Includes the following steps: Construct a finite element model of a prestressed seven-wire steel strand; A three-point bending test was conducted on the finite element model of the prestressed seven-wire steel strand to obtain the test results. Based on the results of the three-point bending test, the equivalent bending stiffness of the finite element model is obtained by using the structural bending stiffness calculation method. Construct the deflection control equation for a prestressed seven-wire steel strand that simultaneously considers its own weight and prestressing effect; Based on the aforementioned deflection control equation and equivalent bending stiffness, the deflection and rotation angle of the finite element model structure are calculated, thereby obtaining the deformation results of the prestressed seven-wire steel strand.

2. The method according to claim 1, characterized in that, The process of conducting a three-point bending test on a finite element model of a prestressed seven-wire steel strand and obtaining the test results includes: Binding constraints are established between adjacent wires of the prestressed seven-strand steel strand. Reference points and reference point sets are established at both ends of the finite element model to couple the binding constraints, and prestress is applied to output the warping height. A mid-span top node set is established at the top of the mid-span of the finite element model to apply displacement loads to output support reactions. A mid-span middle node set is established at the middle node to output displacement. A bottom node set is established at the bottom position half a lay length from the mid-span to apply hinged constraints.

3. The method according to claim 1, characterized in that, Based on the results of the three-point bending test, before obtaining the equivalent bending stiffness of the finite element model using the structural bending stiffness calculation method, the following steps are also taken: Select a structural bending stiffness calculation method. A preset slenderness ratio threshold is set. When the slenderness ratio of the finite element model is less than the preset threshold, the structural bending stiffness is calculated using Timoshenko beam theory. When the slenderness ratio of the finite element model is greater than the preset threshold, the structural bending stiffness is calculated using Euler beam theory.

4. The method according to claim 3, characterized in that, The equivalent bending stiffness obtained based on Euler beam theory is calculated using the following formula: Where F is the applied load, L is the beam span, T is the prestressed axial force, d is the height of the beam's two ends overhang, f is the mid-span deflection, and EI is the load. eff This is the equivalent bending stiffness.

5. The method according to claim 4, characterized in that, The equivalent bending stiffness obtained based on Timoshenko beam theory is calculated using the following formula: Where A is the cross-sectional area, I is the moment of inertia of the cross section, K is the shear force coefficient, and ν is Poisson's ratio.

6. The method according to claim 1, characterized in that, The deflection control equation and calculation formula for prestressed seven-wire steel strand are as follows: Among them, EI eff The equivalent bending stiffness is given by T, where T is the prestressed axial force, q is the cable self-weight intensity, and N is the vertical support reaction force of the cable self-weight at the anchorage end of the cable beam. L is the original length of the stay cable, and θ is the design value of the cable-beam angle.

7. The method according to claim 1, characterized in that, The process of constructing a finite element model of a prestressed seven-wire steel strand also includes: The geometric dimensions, prestress magnitude, and elastic properties of the finite element model are determined by parameters.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-7.

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