Method for calculating tower leg inclined member axial force after displacement of multi-leg foundation of power transmission tower

Abstract

The present application relates to a kind of tower leg inclined material axial force calculation method after the displacement of transmission tower multi-leg foundation, comprising: the axial force of each tower leg inclined material is calculated when tower leg a occurs r, θ direction displacement of tower leg inclined material;Under the condition that tower leg d is fixed, respectively when tower leg b, c respectively occurs displacement, the axial force of each tower leg inclined material is obtained respectively, all axial forces are superimposed, and the axial force of each tower leg inclined material under the condition of foundation multi-leg horizontal displacement is obtained;The maximum inclined material axial force under the special condition that tower leg is perpendicular to ground is obtained;The maximum axial force of bottom inclined material under the condition that multi-leg occurs foundation displacement in general situation is obtained.For different sizes of tower, the present application does not need to establish corresponding tower real model for finite element calculation for different towers, and only needs to know the root opening of cross-shaped connecting leg tower, the material properties of tower leg inclined material and the horizontal displacement of each tower leg, so as to quickly find out the change rule of tower leg inclined material axial force and foundation horizontal displacement.

Description

Technical Field

[0001] This invention relates to the field of power transmission tower calculation technology, and in particular to a method for calculating the axial force of the inclined members of the tower legs after multiple leg foundation displacements occur in a power transmission tower. Background Technology

[0002] When a self-supporting transmission tower is located in an area with unfavorable geological or topographical conditions, its foundation may experience horizontal displacement. This can lead to changes in the relative distance between the tower legs, causing variations in the stress on the steel structural members of the tower. Consequently, the tower members may fail, become unstable, or collapse entirely, affecting the safe and stable operation of the transmission line. However, current foundation design specifications do not provide a specific relationship between foundation displacement and the axial force of the diagonal members. Therefore, deriving an expression for the relationship between the foundation displacement and the maximum axial force of the diagonal members is of great significance for the safety assessment and reinforcement of the transmission tower.

[0003] Qian Jinshu established a finite element analysis model of a 500kV high-voltage transmission tower, simulating and analyzing the tower's failure under single and complex operating conditions. The results showed that tension on the foundation is more dangerous than compression, and horizontal displacement of the foundation is the main factor leading to tower instability. Yuan Guanglin studied the influence of various surface deformations on the internal forces and deformations of the transmission tower, using support displacement at material yield as a standard for judging the safety of the transmission tower. The study showed that the lower members are mainly affected by horizontal surface deformation, while the upper members are mainly affected by vertical deformation, and the axial force variation in the bottom members is greater than that in the upper members. Huang Feilong established a finite element model of the transmission tower, simulating the influence of different displacements of the tower leg foundation supports on tower deformation and material failure. Studies have shown that the upper tower members are minimally affected by foundation support displacement, while the internal force changes are greatest in the bottom tower legs, diagonal members, and transverse diaphragm members on the upper side of the tower legs, leading to failure before the upper tower members. Liu Zhengwei established a pile-soil-transmission tower finite element coupled model, considering four combinations of foundation displacements, and studied the influence of foundation horizontal displacement on the internal force changes of various transmission tower members. Based on the strength and stability requirements of the specifications, he gave the allowable horizontal displacement values ​​for two typical transmission towers.

[0004] As can be seen, the aforementioned studies on the horizontal displacement of transmission tower foundations mostly focus on finite element simulations of specific problems to determine the allowable displacement of the transmission tower foundation under different working conditions. However, this calculation method requires establishing different tower models for different towers, making the calculation process cumbersome. Currently, no literature provides a calculation expression for the relationship between the horizontal displacement of the transmission tower foundation and the axial force of the diagonal members. Therefore, providing the variation law of the axial force of the diagonal members under the action of horizontal displacement of the foundation is of great significance for the safety assessment and reinforcement of transmission towers. Summary of the Invention

[0005] To address the problem that existing technologies require the creation of different tower models for different towers, resulting in cumbersome calculation processes, the present invention aims to provide a method for calculating the axial force of the inclined members of the tower legs after multi-leg foundation displacement of a transmission tower, which eliminates the need for finite element calculations based on corresponding real tower models for different towers.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for calculating the axial force of the inclined members of the tower legs after multi-leg foundation displacement of a transmission tower, the method comprising the following sequential steps:

[0007] (1) Taking the lowest-level transmission tower, considering the special case that the four tower legs are perpendicular to the ground, number the four tower legs a, b, c, d clockwise, and calculate the displacement of the diagonal member of the tower leg in the r direction at tower leg a. At that time, the axial force of the inclined members of each tower leg

[0008] (2) Calculate the displacement of the inclined member of the tower leg in the θ direction at leg a. At that time, the axial force of the inclined members of each tower leg

[0009] (3) Similarly, following the calculation methods in steps (1) and (2), calculate the displacements of tower legs b and c under the condition that tower leg d is fixed. At that time, the axial force of the inclined members of each tower leg is obtained separately, and all the axial forces are superimposed to obtain the axial force of the inclined members of each tower leg under the horizontal displacement of the foundation.

[0010] (4) Compare the magnitudes of the axial forces of each inclined member obtained in step (3) to obtain the maximum axial force N0 of the inclined member under the special case where the tower leg is perpendicular to the ground;

[0011] (5) Consider using polynomial f to fit and correct the maximum axial force N0 of the inclined member obtained in step (4), and obtain the maximum axial force N of the bottom inclined member under the condition of multiple legs undergoing foundation displacement.

[0012] Step (1) specifically refers to: the tower leg a undergoing displacement in the r direction. At that time, the axial forces of each diagonal member are as follows:

[0013]

[0014] In the formula: A2,s are the cross-sectional area of ​​the diagonal member of the tower leg and the base opening of the tower, respectively; E is the elastic modulus of the diagonal member. This represents the axial force on the inclined member a1 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member a2 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member b1 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member b2 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member c1 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member c2 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member d1 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member d1 when the tower leg a undergoes displacement in the direction r; a ray is drawn from the center point O of the tower to each tower leg, and the direction of the ray is the direction of displacement r of each tower leg.

[0015] Step (2) specifically refers to: the tower leg a undergoing a displacement in the θ direction. At that time, the axial force of the inclined members of each tower leg is:

[0016]

[0017] In the formula, This represents the axial force on the inclined member a1 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member a2 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member b1 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member b2 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member c1 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member c2 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member d1 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member d1 when the tower leg a undergoes a displacement in the θ direction; the θ direction refers to a 90° counterclockwise rotation in the r direction.

[0018] Step (3) specifically refers to: shifting the six displacements downwards... The results are summed up, so that The analytical expression for the axial force of the inclined members of each tower leg under the horizontal displacement of the foundation is as follows:

[0019]

[0020]

[0021] In the formula: For the tower leg a to undergo displacement in the r direction, For the tower leg b to undergo displacement in the r direction, Let c be the displacement in the r direction of the tower leg, A2 and s be the cross-sectional area of ​​the inclined member of the tower leg and the base opening of the tower, respectively, and E be the elastic modulus of the inclined member.

[0022] Step (4) specifically refers to: comparing the magnitudes of the axial forces of each diagonal member in step (3) to obtain the maximum axial force of the diagonal member under the special case where the tower leg is perpendicular to the ground:

[0023] N0=max{|N (x) |,x∈[a1,a2,b1,b2,c1,c2,d1,d2]}

[0024] In the formula, a1 and a2 are the diagonal members of the tower leg connected to the foundation of tower leg a, b1 and b2 are the diagonal members of the tower leg connected to the foundation of tower leg b, c1 and c2 are the diagonal members of the tower leg connected to the foundation of tower leg c, and d1 and d2 are the diagonal members of the tower leg connected to the foundation of tower leg d.

[0025] Step (5) specifically includes the following steps:

[0026] (5a) Consider using polynomial f to fit and correct the maximum diagonal axial force N0, and obtain the function f after fitting the diagonal axial force as follows:

[0027] f=3.609+0.0735α-3.825n-0.027αn+1.215n 2

[0028] In the formula: α is the tilt of the transmission tower; η is the ratio of the bottom tower height h1 to the tower root opening s;

[0029] (5b) Based on the maximum axial force N0 of the inclined member and the function f after fitting the axial force of the inclined member, the maximum axial force N of the bottom inclined member under the condition of foundation displacement of multiple legs is obtained:

[0030] N = fN0.

[0031] As can be seen from the above technical solution, the beneficial effects of the present invention are as follows: First, for towers of different sizes, the present invention does not require the establishment of corresponding real tower models for finite element calculations. It only needs to know the material properties of the root opening and the inclined members of the tower legs of the cross-type joint tower, as well as the horizontal displacement of each tower leg, to quickly find the variation law of the axial force of the inclined members of the tower legs and the horizontal displacement of the foundation. Second, since the current foundation design specifications do not have clear provisions on the displacement of the top of the tower foundation column, but obviously the foundation displacement will affect the safety performance of the tower, the present invention can provide an important reference for the safety assessment and reinforcement of the tower after the horizontal displacement of the foundation of the tower legs of the cross-type joint overhead transmission tower. Attached Figure Description

[0032] Figure 1 This is a flowchart of the method of the present invention;

[0033] Figure 2 This is a schematic diagram of the theoretical calculation model for the axial force of the inclined members of the tower leg. Detailed Implementation

[0034] like Figure 1 As shown, a method for calculating the axial force of the inclined members of the tower legs after multi-leg foundation displacement of a power transmission tower is presented. The method includes the following steps in sequence:

[0035] (1) Taking the lowest-level transmission tower, considering the special case that the four tower legs are perpendicular to the ground, number the four tower legs a, b, c, d clockwise, and calculate the displacement of the diagonal member of the tower leg in the r direction at tower leg a. At that time, the axial force of the inclined members of each tower leg

[0036] (2) Calculate the displacement of the inclined member of the tower leg in the θ direction at leg a. At that time, the axial force of the inclined members of each tower leg

[0037] (3) Similarly, following the calculation methods in steps (1) and (2), calculate the displacements of tower legs b and c under the condition that tower leg d is fixed. At that time, the axial force of the inclined members of each tower leg is obtained separately, and all the axial forces are superimposed to obtain the axial force of the inclined members of each tower leg under the horizontal displacement of the foundation.

[0038] (4) Compare the magnitudes of the axial forces of each inclined member obtained in step (3) to obtain the maximum axial force N0 of the inclined member under the special case where the tower leg is perpendicular to the ground;

[0039] (5) Consider using polynomial f to fit and correct the maximum inclined axial force N0 obtained in step (4), and obtain the maximum axial force N of the bottom inclined member under the general case of multiple legs undergoing foundation displacement. Here, "general case" refers to the case other than the special case where the four tower legs are perpendicular to the ground.

[0040] like Figure 2 As shown, step (1) specifically refers to: the tower leg a undergoing displacement in the r direction. At that time, the axial forces of each diagonal member are as follows:

[0041]

[0042] In the formula: A2,s are the cross-sectional area of ​​the diagonal member of the tower leg and the base opening of the tower, respectively; E is the elastic modulus of the diagonal member. This represents the axial force on the inclined member a1 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member a2 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member b1 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member b2 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member c1 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member c2 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member d1 when the tower leg a undergoes displacement in the r direction; This represents the axial force on the inclined member d1 when the tower leg a undergoes displacement in the direction r; a ray is drawn from the center point O of the tower to each tower leg, and the direction of the ray is the direction of displacement r of each tower leg.

[0043] Step (2) specifically refers to: the tower leg a undergoing a displacement in the θ direction. At that time, the axial force of the inclined members of each tower leg is:

[0044]

[0045] In the formula, This represents the axial force on the inclined member a1 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member a2 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member b1 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member b2 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member c1 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member c2 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member d1 when the tower leg a undergoes a displacement in the θ direction; This represents the axial force on the inclined member d1 when the tower leg a undergoes a displacement in the θ direction; the θ direction refers to a 90° counterclockwise rotation in the r direction.

[0046] Step (3) specifically refers to: shifting the six displacements downwards... The results are summed up, so that The analytical expression for the axial force of the inclined members of each tower leg under the horizontal displacement of the foundation is as follows:

[0047]

[0048]

[0049] In the formula: For the tower leg a to undergo displacement in the r direction, For the tower leg b to undergo displacement in the r direction, Let c be the displacement in the r direction of the tower leg, A2 and s be the cross-sectional area of ​​the inclined member of the tower leg and the base opening of the tower, respectively, and E be the elastic modulus of the inclined member.

[0050] Step (4) specifically refers to: comparing the magnitudes of the axial forces of each diagonal member in step (3) to obtain the maximum axial force of the diagonal member under the special case where the tower leg is perpendicular to the ground:

[0051] N0=max{|N (x) |,x∈[a1,a2,b1,b2,c1,c2,d1,d2]}

[0052] In the formula, a1 and a2 are the diagonal members of the tower leg connected to the foundation of tower leg a, b1 and b2 are the diagonal members of the tower leg connected to the foundation of tower leg b, c1 and c2 are the diagonal members of the tower leg connected to the foundation of tower leg c, and d1 and d2 are the diagonal members of the tower leg connected to the foundation of tower leg d.

[0053] Step (5) specifically includes the following steps:

[0054] (5a) Consider using polynomial f to fit and correct the maximum diagonal axial force N0, and obtain the function f after fitting the diagonal axial force as follows:

[0055] f=3.609+0.0735α-3.825n-0.027αn+1.215n 2

[0056] In the formula: α is the tilt of the transmission tower; η is the ratio of the bottom tower height h1 to the tower root opening s;

[0057] (5b) Based on the maximum axial force N0 of the inclined member and the function f after fitting the axial force of the inclined member, the maximum axial force N of the bottom inclined member under the condition of foundation displacement of multiple legs is obtained:

[0058] N = fN0.

[0059] Example 1

[0060] Based on theoretical derivation, a finite element method is used to verify the results, taking a certain ultra-high voltage transmission tower as an example.

[0061] (1) The results of the transmission iron show that as the displacement of the iron tower increases, the calculation expression of the inclined axial force of the present invention always matches the finite element results well.

[0062] Comparison results of this invention with finite element values

[0063] Tower foundation displacement loading conditions: A total of 10 transmission tower cases were calculated. The material parameters of each transmission tower are the same, with an elastic modulus E = 206 GPa and a Poisson's ratio ν = 0.3. The displacement conditions shown in Table 1 were applied to the tower leg supports, and the magnitude of the applied displacement was the same.

[0064] Table 1. Basic Displacement Loading Conditions

[0065]

[0066] (2) The formula of this invention is as follows:

[0067] N = fN0

[0068] (3) Finite element calculation process: The power transmission tower is calculated using finite element simulation. The loads shown in Table 1 are applied and the magnitude of the axial force of the inclined members of the power transmission tower is recorded.

[0069] Compare the results calculated in (2) and (3), N FEM Table 2 shows the results of the maximum resultant bending moment calculated by the finite element method and the axial force calculated by the present invention. Table 2 shows that the greater the horizontal displacement in the r direction, the greater the axial force of the inclined member of the tower leg. Comparing Case 7 and Case 9, it can be found that when leg d is fixed, the axial force of the inclined member of the tower leg decreases when leg b, diagonally opposite leg d, undergoes displacement in the r direction. Column 4 of Table 2 shows the calculation error between the finite element method results and the results of the present invention. The error is very small, demonstrating the feasibility of the results of the present invention.

[0070] Table 2 Comparison of Finite Element Values ​​and Expressions

[0071]

[0072]

[0073] In summary, this invention derives an expression for the axial force of the inclined members of a transmission tower under the condition of horizontal displacement of multiple foundations through theoretical derivation, providing a reference for tower reinforcement measures. Currently, no literature provides a calculation expression for the relationship between the horizontal displacement of the transmission tower foundation and the axial force of the inclined members. Therefore, providing the variation law of the axial force of the inclined members of the transmission tower under the action of horizontal displacement of the foundation is of great significance for the safety assessment and reinforcement of the tower.

Claims

1. A method for calculating the axial force of the inclined members of the tower legs after multi-leg foundation displacement of a power transmission tower, characterized in that: The method includes the following steps in sequence: (1) Take the lowest transmission tower and consider the special case that the four tower legs are perpendicular to the ground. Number the four tower legs clockwise. , , d, calculate the diagonal members of the tower leg in the tower leg Displacement occurs in the r direction At that time, the axial force of the inclined members of each tower leg , , , , , , , ; (2) Calculate the diagonal members of the tower leg at the base of the tower leg. occur Displacement in direction At that time, the axial force of the inclined members of each tower leg , , , , , , , ; (3) Similarly, following the calculation methods in steps (1) and (2), calculate the calculation on the tower legs. Under fixed conditions, tower legs , Displacement occurs respectively At that time, the axial force of the inclined members of each tower leg is obtained separately, and all the axial forces are superimposed to obtain the axial force of the inclined members of each tower leg under the horizontal displacement of the foundation. ; (4) Compare the magnitudes of the axial forces of each inclined member obtained in step (3) to obtain the maximum axial force of the inclined member under the special case where the tower leg is perpendicular to the ground. ; (5) Consider using polynomials The maximum axial force of the diagonal member obtained in the fitting correction step (4) The maximum axial force of the bottom inclined member under normal circumstances when multiple legs experience foundation displacement is obtained. ; Step (1) specifically refers to: tower legs Displacement occurs in the r direction At that time, the axial forces of each diagonal member are as follows: ； In the formula: These are the cross-sectional areas of the inclined members of the tower legs and the base of the iron tower, respectively. Let be the elastic modulus of the diagonal member. Indicates tower legs When the diagonal member undergoes displacement in the r direction The axial force acting on it; Indicates tower legs When the diagonal member undergoes displacement in the r direction The axial force acting on it; Indicates tower legs When the diagonal member undergoes displacement in the r direction The axial force acting on it; Indicates tower legs When the diagonal member undergoes displacement in the r direction The axial force acting on it; Indicates tower legs When the diagonal member undergoes displacement in the r direction The axial force acting on it; Indicates tower legs When the diagonal member undergoes displacement in the r direction The axial force acting on it; Indicates tower legs When the diagonal member undergoes displacement in the r direction The axial force acting on it; Indicates tower legs When the diagonal member undergoes displacement in the r direction The axial force acting on the tower; draw a ray from the center point O of the tower to each leg, the direction of the ray is the displacement of each leg. direction; Step (2) specifically refers to: tower legs occur Displacement in direction At that time, the axial force of the inclined members of each tower leg is: ； In the formula, Indicates tower legs occur Diagonal members during directional displacement The axial force acting on it; Indicates tower legs occur Diagonal members during directional displacement The axial force acting on it; Indicates tower legs occur Diagonal members during directional displacement The axial force acting on it; Indicates tower legs occur Diagonal members during directional displacement The axial force acting on it; Indicates tower legs occur Diagonal members during directional displacement The axial force acting on it; Indicates tower legs occur Diagonal members during directional displacement The axial force acting on it; Indicates tower legs occur Diagonal members during directional displacement The axial force acting on it; Indicates tower legs occur Diagonal members during directional displacement The axial force acting on it; Direction refers to Rotate 90° counterclockwise.

2. The method for calculating the axial force of the inclined members of the tower legs after multi-leg foundation displacement of a transmission tower according to claim 1, characterized in that: Step (3) specifically refers to: shifting the six displacements downwards... , , The results are summed up, so that The analytical expression for the axial force of the inclined members of each tower leg under the horizontal displacement of the foundation is obtained as follows: ； ； In the formula: For tower legs A displacement occurs in the r direction. For tower legs A displacement occurs in the r direction. For tower legs A displacement occurs in the r direction. These are the cross-sectional areas of the inclined members of the tower legs and the base of the iron tower, respectively. This is the elastic modulus of the diagonal member.

3. The method for calculating the axial force of the inclined members of the tower legs after multi-leg foundation displacement of a transmission tower according to claim 1, characterized in that: Step (4) specifically refers to: comparing the magnitudes of the axial forces of each diagonal member in step (3) to obtain the maximum axial force of the diagonal member under the special case where the tower leg is perpendicular to the ground: ； In the formula, To the tower leg The diagonal members of the tower legs connected to the foundation, To the tower leg The diagonal members of the tower legs connected to the foundation, To the tower leg The diagonal members of the tower legs connected to the foundation, To the tower leg The diagonal bracing of the tower legs connected to the foundation.

4. The method for calculating the axial force of the inclined members of the tower legs after multi-leg foundation displacement of a transmission tower according to claim 1, characterized in that: Step (5) specifically includes the following steps: (5a) Consider using polynomials Fitting Correction for Maximum Diagonal Axial Force The function obtained after fitting the axial force of the oblique member is obtained. for: ； In the formula: The tilt angle of the transmission tower; The height of the lowest tower With the Iron Tower Root Open The ratio; (5b) Based on the maximum axial force of the diagonal member The function after fitting the axial force of the diagonal member The maximum axial force N of the bottom inclined member under multi-leg foundation displacement is obtained: 。

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