Cable unstressed length calculation method

Abstract

The application relates to a method for calculating the unstressed length of a cable, which comprises the following steps: S1, dividing the cable into segments and determining the target value of the iterative calculation of the unstressed length of the cable; S2, determining the initial cable force value of the cable; S3, determining the initial unstressed length of the cable and the strain proportionality factor of each segment; S4, finite element analysis of the stress state of the cable; S5, calculating the strain increment of each segment of the cable, and taking the strain increment as the iterative variable of the cyclic iterative calculation; and S6, iterative calculation of the unstressed length of the cable. The design linear shape of the cable under the working state is taken as the target value, the stress state of the cable is simplified into a beam model, the relationship between the unstressed length of the cable and the linear shape of the cable is established, the iterative variable of the calculation of the unstressed length of the cable is determined, and the unstressed length of the cable is calculated through cyclic iterative calculation, so that the cable can reach the ideal design linear shape under the working state.

Description

Technical Field

[0001] This invention belongs to the field of load calculation technology for cable net or suspension structures in building engineering, and specifically relates to a method for calculating the stress-free length of cables. Background Technology

[0002] For cable-net structures or suspension structures in building engineering, the cable alignment given in the design is generally the alignment under load. However, during cable fabrication and installation, the cables are in a stress-free state or the load conditions differ from the final design state. Therefore, the stress-free length or cutting length of the cable does not match the length calculated from the design-provided alignment under stress. It is necessary to reverse-calculate the stress-free length of the cable before installation (before being loaded) based on the design-provided cable stress state. This stress-free length is then used as the cutting length for cable fabrication and installation, ultimately ensuring that the cable achieves the design alignment after being loaded.

[0003] Therefore, how to provide a method for calculating the stress-free length of cables is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] This invention provides a method for calculating the stress-free length of a cable. Taking the design alignment of the cable under working conditions as the target value, the stress state of the cable is simplified into a beam model. The relationship between the stress-free length of the cable and the cable alignment is established, the iterative variables for calculating the stress-free length of the cable are determined, and the stress-free length of the cable is calculated through iterative loops, so that the cable achieves the ideal design alignment under working conditions.

[0005] To solve the above technical problems, the present invention includes the following technical solutions:

[0006] A method for calculating the stress-free length of a cable includes the following steps:

[0007] Step S1: Divide the cable into segments and determine the target value for the stress-free length of the cable in iterative calculation;

[0008] Step S2: Determine the initial cable force value;

[0009] Step S3: Determine the initial stress-free length of the cable and the strain scaling factor for each segment;

[0010] Step S4: Finite element analysis of the stress state of the cable;

[0011] Step S5: Calculate the strain increment of each segment of the cable and use the strain increment as the iteration variable for the iterative calculation.

[0012] Step S6: Iterative calculation of the stress-free length of the cable.

[0013] Further, step S1 includes:

[0014] Divide a cable into n segments and n+1 nodes, where n is an even number. Assume the design geometry H of the cable under load. 0 = [h1,h2,h3……h n+1 ], where h1 represents the coordinates (x1, y1) of node 1, and so on, h n+1 The coordinates (x) of node n+1 n+1 ,y n+1 ), with the longitudinal coordinate y of the center node of the cable. n / 2+1 As the target value;

[0015] Further, step S2 includes: simplifying the stress state of the cable into a beam model, with cable nodes 1 and n+1 as hinged constraint boundaries, assuming that the remaining nodes (2,3,4...n) are all subjected to a vertically downward load F; assuming that the initial cable force of each segment under the load is...

[0016] f = [f1, f2, f3 ... f n The designed angle between each cable segment and the horizontal direction is θ = [θ1, θ2, θ3…θ]. n Based on the nodal force balance calculation formulas, i.e., Equations 1-2, the initial cable force values ​​for each segment of the cable can be obtained, i.e., Equations 3-5:

[0017] f i-1 sinθ i-1 =f i sinθ i +F Formula 1

[0018] f i-1 cosθ i-1 =f i cosθ i Formula 2

[0019]

[0020]

[0021]

[0022] Further, step S3 includes: calculating the initial cable force values ​​of each cable segment obtained through step S2 above, and calculating the initial stress-free length of each cable segment according to Equation 6.

[0023] L 0 =[l 0 1,l 0 2,l 0 3,……l 0 nAccording to equations 7-8, the scaling factor B of each cable segment is calculated by using the ratio of the initial strain of each segment to the initial strain of segment 1. n+1 ],

[0024]

[0025]

[0026]

[0027] In the formula: l 0 i —The initial stress-free length of the i-th segment of the cable; x i —The x-coordinate of the i-th segment of the cable;

[0028] y i —The ordinate of the i-th segment of the cable; f i —The initial cable force value of the i-th segment of the cable;

[0029] E—elastic modulus of the cable; A—cross-sectional area of ​​the cable;

[0030] ε1—Initial strain of cable segment 1; ε i —The initial strain of the i-th segment of the cable;

[0031] b i —The strain factor of the i-th segment of the cable, b1=1.

[0032] Further, step S4 includes: establishing a finite element model and inputting the initial strain parameters of each segment of the cable. Finite element analysis was used to calculate the linear H-shape of the cable under load. k =[h k 1,h k 2,h k 3……h k n+1 ], where k represents the k-th analysis, k = 1, 2, 3, ..., h k 1 represents the coordinates (x, y) of node 1 after the k-th finite element analysis. k 1,y k 1), and so on, h k n+1 The coordinates (x, y) of node n+1 after the k-th finite element analysis are represented by... k n+1 ,y k n+1 The ordinate y of node n / 2+1 after the k-th finite element analysis. k n / 2+1 With the target value y n / 2+1Subtracting the values, we obtain the residual Δy from the k-th finite element analysis. k =y k n / 2+1 -y n / 2+1 Through the k-th finite element analysis, the strain ε of each segment of the cable is obtained. k =[ε k 1,ε k 2,ε k 3……ε k n ].

[0033] Further, step S5 includes: when the k-th...

[0034] When the residuals of the second finite element analysis exceed the set limit, adjust the initial strain parameters Φ of each cable segment in the finite element model. k That is, the strain ε of each segment after the k-th finite element analysis k Based on the superimposed strain increment Δε k =[Δε k 1,Δε k 2,Δε k 3……Δε k n Establish the initial strain parameters required for the (k+1)th finite element analysis. And input it into the finite element model for the (k+1)th finite element analysis; where Δε k =B·Δε k 1, i.e., Δε k i =b i Δε k 1; By equating the strain increment of each cable segment to the cable force, the deformation of each node of the cable under the aforementioned cable force can be calculated using a beam model. This allows the establishment of a relationship between the deformation of node n / 2+1 and the strain increment of each cable segment. Using the residual of the k-th finite element analysis as the target value of the deformation of node n / 2+1, the strain increment of each segment can be obtained through this relationship. The strain increment Δε k and initial strain parameter Φ k Calculate according to formulas 9-14:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] Where: D—horizontal distance between cable endpoints; I—moment of inertia of cable cross section;

[0042] i—the cable segment number, i = 1, 2, 3...n;

[0043] α k i —The horizontal angle of segment i after the kth finite element analysis.

[0044] Further, step S6 includes:

[0045] Set the residual limit R for finite element analysis, when |Δy k If | > R, then repeat steps S4 to S5 until |Δy k The iteration stops when | < R, and the initial strain parameter Φ input into the finite element model is used. k and the initial stress-free length L of the cable 0 The final stress-free length L of the cable is calculated according to Equation 15:

[0046]

[0047] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0048] This invention provides a method for calculating the stress-free length of a cable. Using the designed alignment of the cable under working conditions as the target value, the stress state of the cable is simplified to a beam model. The relationship between the stress-free length and the cable alignment is established, and the iterative variables for calculating the stress-free length are determined. Through iterative calculation, the stress-free length of the cable is achieved, enabling the cable to reach the ideal design alignment under working conditions. In this invention, the initial stress-free length of each cable segment is determined using a simplified beam model. This initial stress-free length is then input as an initial strain parameter into the finite element model for iterative calculation, which improves the convergence efficiency of the iterative calculation. Furthermore, this invention utilizes the relationship between cable deformation and the strain increment of each cable segment, using the iterative residual as the target value and the strain increment as the iterative variable, to derive the calculation formula for the iterative variable. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the cable design profile in a method for calculating the stress-free length of a cable according to an embodiment of the present invention.

[0050] Figure 2 This is a schematic diagram of the cable profile after the k-th finite element analysis in the cable stress-free length calculation method of an embodiment of the present invention. Detailed Implementation

[0051] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a more detailed explanation of the method for calculating the stress-free length of a cable provided by the present invention. The advantages and features of the present invention will become clearer from the following description. It should be noted that the accompanying drawings are all in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the illustration of the embodiments of the present invention. For ease of description, the terms "upper" and "lower" used below are consistent with the upper and lower directions in the accompanying drawings, but this should not be construed as a limitation of the technical solution of the present invention.

[0052] Example 1

[0053] The following is combined with Figure 1 and Figure 2 The present invention provides a detailed description of the method for calculating the stress-free length of cables.

[0054] Please continue to refer to this. Figure 1 and Figure 2 The embodiments of the present invention include the following steps:

[0055] (1) Divide the cable into segments and determine the target value for the stress-free length of the cable in iterative calculations. Divide one cable into n segments and n+1 nodes, where n is an even number. Assume the design alignment H of the cable under load. 0 = [h1,h2,h3……h n+1 ], where h1 represents the coordinates (x1, y1) of node 1, and so on, h n+1 The coordinates (x) of node n+1 n+1 ,y n+1 Generally, under load, a cable exhibits a catenary shape, with the greatest vertical deformation at the cable's center. In engineering applications, the center (or the point of greatest deformation) is often used as the design control point for the cable's alignment. Therefore, the longitudinal (vertical) coordinate y of the cable's center node n / 2+1 is used... n / 2+1 As the target value.

[0056] (2) Determine the initial cable force values. Simplify the cable's stress state as a beam model. Cable nodes 1 and n+1 are hinged constraint boundaries. Assume that the remaining nodes (2, 3, 4…n) are subjected to a downward vertical load F. Assume the initial cable force values ​​for each segment under the load are f = [f1, f2, f3…f…]. n The design angle between each cable segment and the transverse (horizontal) direction is θ = [θ1, θ2, θ3...θ]. n Based on the force balance at the nodes (Equations 1-2), the initial cable force values ​​for each segment of the cable are shown in Equations 3-5 below:

[0057] f i-1 sinθ i-1 =f i sinθ i+F Formula 1

[0058] f i-1 cosθ i-1 =f i cosθ i Formula 2

[0059]

[0060]

[0061]

[0062] (3) Determine the initial stress-free length of the cable and the strain ratio factor for each segment. Calculate the initial cable force values ​​for each segment using the steps in (2) above, and then calculate the initial stress-free length L of each segment according to Equation 6. 0 =[l 0 1,l 0 2,l 0 3,……l 0 n According to equations 7-8, the scaling factor B of each cable segment is calculated by using the ratio of the initial strain of each segment to the initial strain of segment 1. n+1 ].

[0063]

[0064]

[0065]

[0066] In the formula: l 0 i —The initial stress-free length of the i-th segment of the cable; x i —The x-coordinate of the i-th segment of the cable;

[0067] y i —The ordinate of the i-th segment of the cable; f i —The initial cable force value of the i-th segment of the cable;

[0068] E—elastic modulus of the cable; A—cross-sectional area of ​​the cable;

[0069] ε1—Initial strain of cable segment 1; ε i —The initial strain of the i-th segment of the cable;

[0070] b i —The strain factor of the i-th segment of the cable, b1=1.

[0071] (4) Finite element analysis of the cable stress state. A finite element model is established, and the initial strain parameters of each cable segment are input. Finite element analysis was used to calculate the linear H-shape of the cable under load. k =[h k 1,h k 2,h k 3……h k n+1 (where k represents the k-th analysis, k = 1, 2, 3...), h k 1 represents the coordinates (x, y) of node 1 after the k-th finite element analysis. k 1,y k 1), and so on, h k n+1 The coordinates (x, y) of node n+1 after the k-th finite element analysis are represented by... k n+1 ,y k n+1 The y-coordinate of node (n / 2+1) after the k-th finite element analysis. k n / 2+1 With the target value y n / 2+1 Subtracting the values, we obtain the residual Δy from the k-th finite element analysis. k =y k n / 2+1 -y n / 2+1 Through the k-th finite element analysis, the strain ε of each segment of the cable is obtained. k =[ε k 1,ε k 2,ε k 3……ε k n ].

[0072] (5) Calculate the strain increment of each cable segment and use the strain increment as the iterative variable for the iterative calculation. When the residual of the k-th finite element analysis exceeds the set limit, adjust the initial strain parameter Φ of each cable segment in the finite element model. k That is, the strain ε of each segment after the k-th finite element analysis k Based on the superimposed strain increment Δε k =[Δε k 1,Δε k 2,Δε k 3……Δε k n Establish the initial strain parameters required for the (k+1)th finite element analysis. And input it into the finite element model for the (k+1)th finite element analysis. Where, Δε k =B·Δε k 1, i.e., Δε k i =b i Δε k1. By equating the strain increment of each cable segment to the cable force, the deformation of each node of the cable under the aforementioned cable force can be calculated using a beam model. A relationship can be established between the deformation of node n / 2+1 and the strain increment of each cable segment. Using the residual of the k-th finite element analysis as the target value of the deformation of node n / 2+1, the strain increment of each segment can be obtained through this relationship. The strain increment Δε k and initial strain parameter Φ k Calculate according to formulas 9-14:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] Where: D—horizontal distance between cable endpoints; I—moment of inertia of cable cross section;

[0080] i—the cable segment number, i = 1, 2, 3...n;

[0081] α k i —The horizontal angle of segment i after the kth finite element analysis.

[0082] (6) Iterative calculation of the stress-free length of the cable. Set the residual limit R for the finite element analysis, when |Δy k When |>R, repeat steps (4)~(5) until |Δy k The iteration stops when | < R, and the initial strain parameter Φ input into the finite element model is used. k and the initial stress-free length L of the cable 0 The final stress-free length L of the cable is calculated using Equation 15.

[0083]

[0084] The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples. The above embodiments only illustrate several implementations of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A method for calculating the stress-free length of a cable, characterized in that, include: Step S1: Divide the cable into segments and determine the target value for the stress-free length of the cable in iterative calculation; Step S2: Determine the initial cable force value; Step S3: Determine the initial stress-free length of the cable and the strain scaling factor for each segment; Step S4: Finite element analysis of the stress state of the cable; Step S5: Calculate the strain increment of each segment of the cable and use the strain increment as the iteration variable for the iterative calculation. Step S6: Iterative calculation of the stress-free length of the cable; Step S1 includes: Divide one cable into n Duan He n +1 node, of which n If the number is even, assume the design geometry H of the cable under load is... 0 =[h1,h2,h3… …h n+1 ], where h1 represents the coordinates of node 1 ( x 1, y 1), and so on, h n+1 Represents the coordinates of node n+1 ( x n+1 , y n+1 ), with the longitudinal coordinate of the cable center node y n / 2+1 As the target value; Step S2 includes: simplifying the stress state of the cable into a beam model, cable node 1 and node... n +1 represents a hinged constraint boundary, assuming the remaining nodes (2,3,4… … n All cables are subjected to a downward vertical load F; assuming the initial cable force in each segment under the load is f = [ f 1, f 2, f 3… … f n The design angle between each cable segment and the horizontal direction is θ = [ θ 1, θ 2, θ 3… θ n Based on the nodal force balance calculation formulas, i.e., equations 1 and 2, the initial cable force values ​​for each segment of the cable can be obtained, i.e., equations 3 and 5: Formula 1 Formula 2 , i =2,3,4… … n -1 Formula 3 Formula 4 Formula 5.

2. The calculation method according to claim 1, characterized in that, Step S3 includes: calculating the initial cable force values ​​of each cable segment obtained through step S2 above, and calculating the initial stress-free length L of each cable segment according to Equation 6. 0 =[ l 0 1, l 0 2, l 0 3,… … l 0 n According to equations 7-8, the scaling factor B of each cable segment is calculated by using the ratio of the initial strain of each segment to the initial strain of segment 1. b 1, b 2, b 3… … b n+1 ], , i =1,2,3… … n Formula 6 , i =1,2,3… … n Formula 7 , i =1,2,3… … n Formula 8 In the formula: l 0 i —Lassotti i The initial stress-free length of the segment; x i —Lassotti i The x-coordinate of the segment; y i —Lassotti i The vertical coordinate of the segment; f i —Lassotti i The initial cable force value of the segment; E —The elastic modulus of the cable; A —The cross-sectional area of ​​the cable; ε 1—Initial strain of cable segment 1; ε i —Lassotti i The initial strain of the segment; b i —Lassotti i The strain factor of the segment b 1 = 1.

3. The calculation method according to claim 2, characterized in that, Step S4 includes: establishing a finite element model and inputting the initial strain parameters Φ of each segment of the cable. k =[ φ k 1, φ k 2, φ k 3… … φ k n Through finite element analysis, the linear H-shape of the cable under load was calculated. k =[h k 1,h k 2,h k 3… …h k n+1 ],in k Representing the k Second analysis, k =1,2,3… …,h k 1 represents the first k The coordinates of node 1 after the second finite element analysis ( x k 1, y k 1), and so on, h k n+1 Representing the k Nodes after sub-finite element analysis n +1 coordinates ( x k n+1 , y k n+1 ); through the first k Nodes after sub-finite element analysis n / 2+1 ordinate y k n / 2+1 With target value y n / 2+1 Subtracting them, we get the first... k The residual Δ of the second finite element analysis y k = y k n / 2+1 - y n / 2+1 ;through the first k Finite element analysis was performed to obtain the strain ε of each section of the cable. k =[ ε k 1, ε k 2, ε k 3… … ε k n ]。 4. The calculation method according to claim 3, characterized in that, Step S5 includes: when the first k When the residuals of the second finite element analysis exceed the set limit, adjust the initial strain parameters Φ of each cable segment in the finite element model. k That is, the strain ε of each segment after the k-th finite element analysis k Based on the superimposed strain increment Δε k =[△ ε k 1,△ ε k 2,△ ε k 3… …△ ε k n ], establish the first k The initial strain parameter Φ required for +1 finite element analysis k+1 =[ φ k+1 1, φ k+1 2, φ k+1 3… … φ k+1 n ], and input them into the finite element model for the first time. k +1 finite element analysis; where Δε k =B·△ ε k 1, i.e., △ ε k i = b i △ ε k 1; By equating the strain increment of each cable segment to the cable force, the deformation of each node of the cable under the aforementioned cable force can be calculated using a beam model, and thus the cable node can be established. n The relationship between the deformation of / 2+1 and the strain increment of each segment of the cable is given by the formula for the first segment. k The residuals from the sub-finite element analysis are used as cable nodes. n The target value of the deformation / 2+1 can be used to calculate the strain increment of each segment using the relationship, where the strain increment Δε is... k and initial strain parameter Φ k Calculate according to formulas 9-14: Formula 9 Formula 10 Formula 11 Formula 12 Formula 13 Formula 14 In the formula: D —Horizontal spacing between the ends of the cables; I —Moment of inertia of the cable cross section; i — Cable segment number, i =1,2,3… … n ; α k i —No. k Segment after sub-finite element analysis i The horizontal angle.

5. The calculation method according to claim 4, characterized in that, Step S6 includes: Set the residual limit R for finite element analysis, when |Δ y k If | > R, then repeat steps S4~S5 until |△ y k The iteration stops when | < R, and the initial strain parameter Φ input into the finite element model is used. k and the initial stress-free length L of the cable 0 The final stress-free length L of the cable is calculated according to Equation 15: Formula 15.

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