A power transmission line engineering tower design method based on multi-target cooperation

Abstract

The application discloses a kind of transmission line engineering tower design methods based on multi-objective cooperation, it is related to overhead transmission line tower structure design technical field.The method includes the following steps: calculating tower head contour control point coordinates to generate the preliminary modeling scheme of transmission line engineering tower;Three-dimensional electrical clearance constraint modeling and automatic checking are carried out, then finite element model is established, and load calculation and multi-condition analysis are carried out, to obtain the modeling scheme of transmission line engineering tower optimization component section;Key node optimization is carried out using the first constraint condition and the second constraint condition, to obtain the candidate scheme of transmission line engineering tower;The design result of transmission line engineering tower is output using comprehensive evaluation system.The application organically fuses Gangba sheep culture image, electrical constraint, structure optimization and economic evaluation, realizes the high landscape of landscape tower under the premise of safety and economy, with the advantages of design process systematization, electrical checking automation and scheme comparison quantification.

Description

Technical Field

[0001] The present invention relates to the technical field of structural design of overhead transmission line towers, and in particular to a multi-objective collaboration-based design method for transmission line engineering towers. Background Art

[0002] With the advancement of power infrastructure construction, transmission line engineering towers are not only required to meet structural safety and electrical performance requirements, but also need to take into account environmental coordination and regional cultural expression. Traditional pole and tower design is mostly experience-based, such as "I-shaped", "wine-cup-shaped" and other shapes, which have single shapes and are difficult to meet the requirements of complex projects. In recent years, a small number of landscape tower design methods with other shapes have emerged. Among them, an existing method discloses a yak-shaped transmission pole and tower structural design method, which establishes a pole and tower model based on the head characteristics of yaks, and realizes the structural design of the yak-shaped pole and tower through load calculation, Eiffel effect analysis and node optimization.

[0003] However, this method still has the following deficiencies: the design process lacks systematicness, the mapping from cultural images to structural dimensions relies on experience, and no quantitative relationship has been established; electrical clearance verification is mostly post-check, which is not integrated into the shape generation process, easily leading to repeated modifications; usually only a single feasible solution is output, and no multi-dimensional comprehensive evaluation system including tower weight, construction cost, landscape coordination and other indicators has been established for scheme comparison and selection, making it difficult to achieve balanced optimization of landscape performance, economy and structural efficiency.

[0004] Therefore, there is an urgent need in the art for a transmission line engineering tower design method that can realize the collaborative optimization of cultural image, electrical function, structural safety and economy. Summary of the Invention

[0005] Aiming at the above deficiencies in the prior art, the present invention provides a multi-objective collaboration-based design method for transmission line engineering towers.

[0006] In order to achieve the above object of the invention, the technical solution adopted by the present invention is: A multi-objective collaboration-based design method for transmission line engineering towers, comprising the following steps: abstracting the geometric features of Gangba sheep into parameterizable control elements, establishing a system of equations for solving the coordinates of control points of tower head contour based on the parameterizable control elements and electrical constraints, and calculating the coordinates of control points of tower head contour based on the system of equations for solving the coordinates of control points of tower head contour and electrical parameters, so as to generate a preliminary shape scheme of the transmission line engineering tower; performing three-dimensional electrical clearance constraint modeling and automatic verification on the preliminary shape scheme of the transmission line engineering tower to generate a modified shape scheme of the transmission line engineering tower, establishing a finite element model based on the modified shape scheme of the transmission line engineering tower, and performing load calculation and multi-working-condition analysis thereon to obtain a shape scheme of the transmission line engineering tower with optimized component sections; The first constraint condition is constructed based on the scaling ratio between the tower head outline size and the size of the Gamba sheep horn, and the second constraint condition is constructed based on the stress stability requirements of key nodes. The first and second constraints are used to optimize the shape scheme of the cross section of the transmission line engineering tower to obtain candidate schemes for the transmission line engineering tower. A comprehensive evaluation system including technical and landscape indicators is constructed, and the candidate schemes for transmission line engineering towers are quantitatively evaluated using the comprehensive evaluation system to output the design results of transmission line engineering towers.

[0007] Furthermore, the parameterizable control elements include the horizontal distance between the outer tower hanging point of the side conductor and the side conductor hanging point, the horizontal distance between the inner tower hanging point of the side conductor and the side conductor hanging point, the horizontal distance between the inner tower hanging point of the side conductor and the middle conductor tower hanging point, the horizontal distance between the middle conductor tower hanging point and the middle conductor hanging point, the vertical distance between the outer tower hanging point of the side conductor and the side conductor hanging point, the vertical distance between the ground wire hanging point and the outer tower hanging point, the horizontal distance between the outer tower hanging point of the side conductor and the ground wire hanging point, and the vertical distance between the middle conductor hanging point and the middle crossarm.

[0008] Furthermore, the coordinates of the control points of the tower head profile are solved using the following equation system: , , , , , , in: This refers to the horizontal distance between the outer tower suspension point and the outer conductor suspension point. This refers to the horizontal distance between the inner tower suspension point and the outer conductor suspension point. Let the length of the edge be the length of the string. It is a sine function. The angle between the V-shaped phases is... The horizontal distance between the inner tower suspension point of the side conductor and the middle conductor tower suspension point. For tower type coefficient, This refers to the horizontal distance between the suspension points on the center conductor tower and the suspension points on the center conductor. For the middle phase V string length, The angle between the middle phase V series, This is the vertical distance between the suspension point of the side conductor tower and the suspension point of the side conductor. It is a cosine function. This is the vertical distance between the ground wire suspension point and the side conductor tower suspension point. This is the minimum offset angle of the conductor. It is the tangent function. This is the protection angle between the ground wire and the side conductor. This refers to the horizontal distance between the suspension point on the side conductor tower and the suspension point on the ground wire. This is the vertical distance between the center conductor suspension point and the center crossarm. This refers to the clearance margin angle between the middle phase gap and the crossarm of the tower. is the thickness constant of the middle phase crossarm.

[0009] Furthermore, a three-dimensional electrical clearance constraint model and automatic verification are performed on the preliminary design scheme of the transmission line tower to generate a revised design scheme. The specific process is as follows: In a three-dimensional digital environment, a parametric model including conductors, insulator strings, and the tower body is constructed based on the preliminary design scheme of the transmission line tower. Based on the parametric model, according to the clearance circle data provided by the electrical engineering professionals and the wind deflection envelope under different working conditions, the clearance index, namely the minimum electrical distance between the conductor and the tower body components, is automatically calculated and verified. When a part that does not meet the safety specifications is detected, the coordinates of the tower head contour control points are dynamically adjusted through a closed-loop feedback mechanism until all clearance indices meet the design requirements, thereby generating a revised design scheme for the transmission line tower.

[0010] Furthermore, a finite element model is established based on the modified design scheme of the transmission line tower, and load calculations and multi-condition analyses are performed on it to obtain the design scheme of the optimized component cross-section of the transmission line tower. The specific process is as follows: Based on the modified design scheme of the transmission line tower, a finite element model coupled with the whole is established. By applying load combinations of multiple conditions, including strong winds, icing, wire breakage, installation, and uneven ice, to the conductor suspension point and ground wire suspension point, linear static analysis, modal analysis, dynamic analysis, and buckling analysis are performed to calculate the internal forces and structural deformation of the members. The component cross-section is iteratively optimized to achieve full stress design, thereby obtaining the design scheme of the optimized component cross-section of the transmission line tower.

[0011] Furthermore, the second constraint includes: Under long-term combined loads, the calculated deflection of the transmission line tower is less than or equal to , This refers to the total vertical distance between the top surface of the foundation and the highest point of the tower in a power transmission line project. The compression members of the tower body and tower head are less than or equal to 150, the diagonal bracing inside the crossarm, the cross diagonal members inside the tower window and all compression members on the ground wire support are less than or equal to 200, and the tension members of the tower body and tower head are less than or equal to 400. The ratio of the bearing capacity of the diagonal member at the intersection of the upper and lower curved arms to the internal force of the supported main member is greater than or equal to 3%. The ratio of the supporting force provided by the auxiliary materials of the tower body and tower head to the maximum axial compressive force of the materials they support. Greater than or equal to 1.5 and less than or equal to 3, The slenderness ratio of the supported material.

[0012] Furthermore, key nodes include the intersection of the crossarm root and the upper curved arm, the chord turning point of the crossarm, the intersection of the upper curved arm and the lower curved arm, and the intersection of the lower curved arm and the tower body.

[0013] The beneficial effects of this invention are as follows: (1) This invention differs from the traditional experience model of “modeling first and then verifying” for landscape towers. This invention abstracts the geometric features of the Gamba sheep into parameterizable control elements, establishes a set of equations for solving the control point coordinates of the tower head outline based on the parameterizable control elements and electrical constraints, and directly converts the electrical parameters into the control point coordinates of the tower head outline by combining the set of equations for solving the control point coordinates of the tower head outline. This process realizes the leap from qualitative imitation to quantitative generation of cultural expression, ensuring that the final tower shape accurately presents the external features of the Gamba sheep and meets the electrical functional requirements. (2) After generating the preliminary shape scheme of the transmission line engineering tower, the present invention generates a modified shape scheme of the transmission line engineering tower by performing three-dimensional electrical clearance constraint modeling and automatic verification on the preliminary shape scheme of the transmission line engineering tower. Based on the modified shape scheme of the transmission line engineering tower, a finite element model is established, and load calculation and multi-condition analysis are performed on it to obtain the shape scheme of the optimized component section of the transmission line engineering tower. This process transforms the traditional design of "post-verification and passive modification" into "process control and active optimization", avoiding repeated iterations caused by shape adjustment and significantly shortening the design cycle. (3) This invention constructs a first constraint condition based on the scaling ratio between the tower head outline size and the horn size of the Gamba sheep, and constructs a second constraint condition based on the stress stability requirements of key nodes. The first and second constraint conditions are used to optimize the shape scheme of the cross section of the transmission line engineering tower to obtain candidate schemes for the transmission line engineering tower. This process ensures that the long-term load deflection of the node is less than or equal to 3h / 1000 and that the slenderness ratio and bearing capacity ratio of the component meet the specifications. Through smoothing treatment and structural optimization, the problem of stiff nodes of conventional iron towers is solved, and the coordination of structural efficiency and visual smoothness is achieved. (4) This invention constructs a comprehensive evaluation system that includes technical indicators and landscape indicators, and uses the comprehensive evaluation system to quantitatively evaluate the candidate schemes of transmission line engineering towers, so as to output the design results of transmission line engineering towers. This process incorporates the landscape effect into a quantifiable and comparable decision-making framework, avoids the one-sidedness of pursuing economy or shape, and provides a scientific basis for engineering selection. Attached Figure Description

[0014] Figure 1This is a schematic diagram of a transmission line tower design method based on multi-objective collaboration. Figure 2 A schematic diagram of parameterizable control elements; Figure 3 This is a schematic diagram of key nodes. Detailed Implementation

[0015] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0016] like Figure 1 As shown, a method for designing transmission line towers based on multi-objective collaboration includes steps S1-S4, as detailed below: S1. The geometric features of the Gamba sheep are abstracted into parameterizable control elements. Based on the parameterizable control elements and electrical constraints, a set of equations for solving the control point coordinates of the tower head contour is established. Based on the control point coordinates of the tower head contour and the electrical parameters, the coordinates of the control point of the tower head contour are calculated to generate a preliminary shape scheme for the transmission line engineering tower.

[0017] In an optional embodiment of the present invention, the parameterizable control element includes the horizontal distance between the outer tower suspension point and the outer conductor suspension point. Horizontal distance between the inner tower suspension point and the outer conductor suspension point Horizontal distance between the inner tower hanging point of the side conductor and the middle conductor tower hanging point Horizontal distance between the suspension points of the middle conductor tower and the suspension points of the middle conductor tower Vertical distance between the suspension point of the side conductor tower and the suspension point of the side conductor Vertical distance between the ground wire suspension point and the side conductor tower suspension point Horizontal distance between the suspension point of the side conductor tower and the suspension point of the ground wire Vertical distance between the center conductor suspension point and the center crossarm ,like Figure 2 As shown.

[0018] Solving the system of equations for the coordinates of the control points of the tower head profile, the expression is as follows: , , , , , , in: This refers to the horizontal distance between the outer tower suspension point and the outer conductor suspension point. This refers to the horizontal distance between the inner tower suspension point and the outer conductor suspension point. Let the length of the edge be the length of the string. It is a sine function. The angle between the V-shaped phases is... The horizontal distance between the inner tower suspension point of the side conductor and the middle conductor tower suspension point. For tower type coefficient, The value range is 1.05-1.15. This refers to the horizontal distance between the suspension points on the center conductor tower and the suspension points on the center conductor. For the middle phase V string length, The angle between the middle phase V series, This is the vertical distance between the suspension point of the side conductor tower and the suspension point of the side conductor. It is a cosine function. This is the vertical distance between the ground wire suspension point and the side conductor tower suspension point. This is the minimum offset angle of the conductor. It is the tangent function. This is the protection angle between the ground wire and the side conductor. This refers to the horizontal distance between the suspension point on the side conductor tower and the suspension point on the ground wire. This is the vertical distance between the center conductor suspension point and the center crossarm. This refers to the clearance margin angle between the middle phase gap and the crossarm of the tower. The value range is 5-15. The thickness constant of the middle phase crossarm. The value range is 1 / 2 to 2 / 3.

[0019] Electrical parameters include minimum conductor offset angle, side phase string length, middle phase V string length, side phase V string angle, and middle phase V string angle.

[0020] S2. Perform three-dimensional electrical clearance constraint modeling and automatic verification on the preliminary shape scheme of the transmission line engineering tower to generate a modified shape scheme of the transmission line engineering tower. Based on the modified shape scheme of the transmission line engineering tower, establish a finite element model and perform load calculation and multi-condition analysis on it to obtain the shape scheme of the optimized component section of the transmission line engineering tower.

[0021] In an optional embodiment of the present invention, the present invention performs three-dimensional electrical clearance constraint modeling and automatic verification on the preliminary design scheme of the transmission line engineering tower to generate a modified design scheme for the transmission line engineering tower. The specific process is as follows: In a three-dimensional digital environment, a parametric model including conductors, insulator strings and tower body is constructed on the preliminary design scheme of the transmission line engineering tower. Based on the parametric model, according to the clearance circle data provided by the electrical profession and the wind deflection envelope under different working conditions, the clearance index, i.e., the minimum electrical distance between the conductor and the tower body components, is automatically calculated and verified. When a part that does not meet the safety specifications is detected, the coordinates of the tower head contour control point are dynamically adjusted through a closed-loop feedback mechanism until all clearance indexes meet the design requirements, so as to generate a modified design scheme for the transmission line engineering tower.

[0022] This invention establishes a finite element model based on a modified design scheme for transmission line engineering towers, and performs load calculations and multi-condition analysis on it to obtain a design scheme for the optimized component cross-section of the transmission line engineering tower. The specific process is as follows: Based on the modified design scheme of the transmission line engineering tower, a finite element model coupled with the whole is established. By applying load combinations of multiple conditions, including strong winds, icing, wire breakage, installation, and uneven ice, to the conductor suspension point and ground wire suspension point, linear static analysis, modal analysis, dynamic analysis, and buckling analysis are performed to calculate the internal forces and structural deformation of the members. The component cross-section is iteratively optimized to achieve full stress design, thereby obtaining a design scheme for the optimized component cross-section of the transmission line engineering tower.

[0023] S3. Based on the scaling ratio between the tower head outline size and the Gamba sheep horn size, a first constraint condition is constructed, and based on the stress stability requirements of key nodes, a second constraint condition is constructed. Using the first and second constraint conditions, the key node optimization of the shape scheme of the cross section of the transmission line engineering tower is carried out to obtain candidate schemes for the transmission line engineering tower.

[0024] In an optional embodiment of the present invention, the second constraint condition includes: under long-term combined load action, the calculated deflection of the transmission line tower is less than or equal to... , The total vertical distance from the top surface of the foundation to the highest point of the tower head in a transmission line project; the compressive strength of the tower body and tower head is less than or equal to 150, the compressive strength of the diagonal braces inside the crossarms, the cross braces inside the tower windows, and all compressive members on the ground wire supports is less than or equal to 200, and the tensile strength of the tower body and tower head is less than or equal to 400; the ratio of the bearing capacity of the diagonal braces at the intersection of the upper and lower curved arms to the internal force of the supported main material is greater than or equal to 3%; the ratio of the supporting force provided by the auxiliary materials of the tower body and tower head to the maximum axial compressive force of the supported material. Greater than or equal to 1.5 and less than or equal to 3, The slenderness ratio of the supported material.

[0025] like Figure 3 As shown, key nodes include the intersection of the crossarm root and the upper curved arm, the chord turning point of the crossarm, the intersection of the upper curved arm and the lower curved arm, and the intersection of the lower curved arm and the tower body.

[0026] Specifically, the scaled-down ratio between the tower head outline dimensions and the horn dimensions of the Gamba sheep refers to: based on precise measurements of the biological characteristics of the Gamba sheep's head, extracting key visual proportion parameters between the horns and the sheep's face (including the ratio of the width of the horn base to the width of the face, the height ratio of the sheep's eyes relative to the face, the upward angle of the horns, and the outward flare of the horn tips), and transforming them into a set of quantitative aesthetic constraints; this relationship is not simply a proportional enlargement of the biological dimensions, but rather, based on the initial tower head dimensions generated by electrical functions, adjusting the crossarm length, tower window height, and hanging point positions to make the outline proportion of the transmission line engineering tower approximate the actual physical characteristics of the Gamba sheep, thereby achieving a unity of cultural imagery and engineering entity form while ensuring electrical safety and structural stress.

[0027] S4. Construct a comprehensive evaluation system that includes technical and landscape indicators, and use the comprehensive evaluation system to quantitatively evaluate the candidate schemes for transmission line engineering towers, so as to output the design results of transmission line engineering towers.

[0028] In an optional embodiment of the present invention, the present invention constructs a comprehensive evaluation system including technical indicators and landscape indicators. The technical indicators are determined based on engineering quotas and include quantitative data such as tower weight, cost, corridor width, and construction difficulty. The landscape indicators are determined through expert scoring and social surveys and include ecological sensitivity, morphological coordination, landscape suitability, and social acceptance. Then, the present invention uses a weighted scoring method (45% weight for technical indicators, 55% weight for landscape indicators, and a maximum score of 10 points for each individual indicator) to quantitatively evaluate and rank the candidate schemes for transmission line engineering towers. Finally, the scheme with the highest comprehensive score is the design result of the transmission line engineering tower.

[0029] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for designing transmission line towers based on multi-objective collaboration, characterized in that, Includes the following steps: The geometric features of the Gamba sheep are abstracted into parameterizable control elements. Based on the parameterizable control elements and electrical constraints, a set of equations is established to solve the control point coordinates of the tower head contour. Based on the control point coordinates of the tower head contour and the electrical parameters, the coordinates of the control point of the tower head contour are calculated to generate a preliminary shape scheme for the tower of the transmission line project. The preliminary design scheme of the transmission line tower is modeled and automatically verified using three-dimensional electrical clearance constraints to generate a modified design scheme. Based on the modified design scheme, a finite element model is established, and load calculations and multi-condition analyses are performed to obtain the design scheme of the optimized component cross-section of the transmission line tower. The first constraint condition is constructed based on the scaling ratio between the tower head outline size and the size of the Gamba sheep horn, and the second constraint condition is constructed based on the stress stability requirements of key nodes. The first and second constraints are used to optimize the shape scheme of the cross section of the transmission line engineering tower to obtain candidate schemes for the transmission line engineering tower. A comprehensive evaluation system including technical and landscape indicators is constructed, and the candidate schemes for transmission line engineering towers are quantitatively evaluated using the comprehensive evaluation system to output the design results of transmission line engineering towers.

2. The transmission line tower design method based on multi-objective collaboration according to claim 1, characterized in that, The parameterizable control elements include the horizontal distance between the outer tower hanging point and the outer conductor hanging point, the horizontal distance between the inner tower hanging point and the outer conductor hanging point, the horizontal distance between the inner tower hanging point and the middle conductor hanging point, the horizontal distance between the middle conductor hanging point and the middle conductor hanging point, the vertical distance between the outer conductor hanging point and the outer conductor hanging point, the vertical distance between the ground wire hanging point and the outer conductor hanging point, the horizontal distance between the outer conductor hanging point and the ground wire hanging point, and the vertical distance between the middle conductor hanging point and the middle crossarm.

3. The transmission line tower design method based on multi-objective collaboration according to claim 1, characterized in that, Solving the system of equations for the coordinates of the control points of the tower head profile, the expression is as follows: ， ， ， ， ， ， in: This refers to the horizontal distance between the outer tower suspension point and the outer conductor suspension point. This refers to the horizontal distance between the inner tower suspension point and the outer conductor suspension point. Let the length of the edge be the length of the string. It is a sine function. The angle between the V-shaped phases is... The horizontal distance between the inner tower suspension point of the side conductor and the middle conductor tower suspension point. For tower type coefficient, This refers to the horizontal distance between the suspension points on the center conductor tower and the suspension points on the center conductor. For the middle phase V string length, The angle between the middle phase V series, This is the vertical distance between the suspension point of the side conductor tower and the suspension point of the side conductor. It is a cosine function. This is the vertical distance between the ground wire suspension point and the side conductor tower suspension point. This is the minimum offset angle of the conductor. It is the tangent function. This is the protection angle between the ground wire and the side conductor. This refers to the horizontal distance between the suspension point on the side conductor tower and the suspension point on the ground wire. This is the vertical distance between the center conductor suspension point and the center crossarm. This refers to the clearance margin angle between the middle phase gap and the crossarm of the tower. is the thickness constant of the middle phase crossarm.

4. The transmission line tower design method based on multi-objective collaboration according to claim 1, characterized in that, The preliminary design of the transmission line tower is modeled and automatically verified using 3D electrical clearance constraints to generate a revised design. The specific process involves: constructing a parametric model of the preliminary design, including conductors, insulator strings, and the tower body, in a 3D digital environment; automatically calculating and verifying clearance parameters, i.e., the minimum electrical distance between the conductor and the tower body components, based on the clearance circle data provided by the electrical engineering department and the wind deflection envelope under different operating conditions, using a closed-loop feedback mechanism when any parts do not meet safety specifications; and finally, generating a revised design for the transmission line tower by dynamically adjusting the coordinates of the tower head contour control points through a closed-loop feedback mechanism until all clearance parameters meet design requirements.

5. The method for designing transmission line towers based on multi-objective collaboration according to claim 1, characterized in that, A finite element model is established based on the modified design scheme of the transmission line tower, and load calculations and multi-condition analyses are performed on it to obtain the design scheme of the optimized component cross-section of the transmission line tower. The specific process is as follows: Based on the modified design scheme of the transmission line tower, a finite element model coupled with the whole is established. By applying load combinations of multiple conditions including strong wind, icing, wire breakage, installation, and uneven ice to the conductor suspension point and ground wire suspension point, linear static analysis, modal analysis, dynamic analysis, and buckling analysis are performed to calculate the internal forces and structural deformation of the members. The component cross-section is iteratively optimized to achieve full stress design, thereby obtaining the design scheme of the optimized component cross-section of the transmission line tower.

6. The method for designing transmission line towers based on multi-objective collaboration according to claim 1, characterized in that, The second constraint includes: Under long-term combined loads, the calculated deflection of the transmission line tower is less than or equal to , This refers to the total vertical distance between the top surface of the foundation and the highest point of the tower in a power transmission line project. The compression members of the tower body and tower head are less than or equal to 150, the diagonal bracing inside the crossarm, the cross diagonal members inside the tower window and all compression members on the ground wire support are less than or equal to 200, and the tension members of the tower body and tower head are less than or equal to 400. The ratio of the bearing capacity of the diagonal member at the intersection of the upper and lower curved arms to the internal force of the supported main member is greater than or equal to 3%. The ratio of the supporting force provided by the auxiliary materials of the tower body and tower head to the maximum axial compressive force of the materials they support. Greater than or equal to 1.5 and less than or equal to 3, The slenderness ratio of the supported material.

7. The method for designing transmission line towers based on multi-objective collaboration according to claim 1, characterized in that, Key nodes include the intersection of the crossarm root and the upper curved arm, the chord turning point of the crossarm, the intersection of the upper curved arm and the lower curved arm, and the intersection of the lower curved arm and the tower body.

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