Study on Wind Resistance Performance of Transmission Tower Using Fixture-Type Reinforcement Device

Abstract

Transmission towers are an important component of the electric system, and their tall structural characteristics make them susceptible to failure under strong winds. Therefore, it is crucial to enhance the wind resistance of the transmission tower structures. This paper uses the finite element method to investigate the influence of a fixture-type reinforcement device (FRD) on the load-bearing performance of the transmission tower structure and explores the effects of different numbers of fixture pairs on the reinforcement. Based on this, the paper further analyzes the stress characteristics and failure modes of a typical tower structure under wind loads in two directions and investigates the influence of different reinforcement lengths on the wind resistance performance of the tower structure. The research results indicate that the FRD can effectively improve the deformation mode and failure characteristics of steel components under axial load. At the same time, using the FRD can effectively reduce the deformation of tower structures under strong wind, and only reinforcing three angled steel components can reduce the tower top displacement by about 55% and more.

1. Background

The construction of China’s power system has developed rapidly with the economic boom, and the safety issues of the massive transmission structure systems directly affect the development of society and the economy. Taking Jiangsu Province as an example, there are currently more than 2300 transmission lines of 220 kV and above, with a total length of over 47,000 km and a total number of transmission towers approaching 87,000. As an important role in the power transmission system, the structure of the transmission tower is a typical high-rise, wind-sensitive structure. Therefore, extreme climatic effects, such as heavy snows and strong winds, can easily cause local damage to the tower structures, and even lead to the complete collapse of the entire structure, which seriously threatens the operational stability of the power system [1,2,3].

Strong wind is one of the most destructive and frequent natural disasters that could destroy the transmission tower structures, which are the key component of the electric power system. Okamura et al. analyzed the wind properties in a mountainous area and the wind-induced responses of a transmission tower based on on-site monitoring, and also conducted the wind tunnel test on a simulated mountain [4]. Based on the findings, a wind response analysis was performed on a transmission tower. Deng et al. conducted the wind tunnel test on a 1/80-scale model of a lattice tower and found that the conductors play a significant role in the wind-induced responses of the tower [5]. Yang et al. also conducted the wind tunnel test on an angled steel triangular transmission tower so as to derive its drag coefficients [6]. Additionally, the experimental results are verified by the computational fluid dynamic analysis.

Apart from the field tests and the wind tunnel experiments, many researchers have also conducted numerical analyses on the wind-induced responses of transmission towers. Battista et al. used the finite element model to analyze the structural behavior of the transmission line towers under the action of winds and proposed an analytical framework to assess their stability in the design stage [7]. Based on the results, a simplified model with two degrees of freedom was proposed to derive the dynamic properties of the tower. Du and Hajjar proposed to utilize the incremental dynamic analysis method to assess the collapse fragility curve of transmission towers when attacked by hurricanes, and the results can be used to quantify the uncertainty and evaluate the economic loss of the power system [8]. Cai et al. proposed a modelling framework to evaluate the fragility of the transmission towers under strong winds, in which the wind loads exerted on the structure can be represented by the combination of two orthogonal loads on the tower and a load on the transmission wires [9]. Additionally, the effects of wind directionality [10], fatigue damage [11], the component-system level of fragility [12] were also considered. Furthermore, downburst wind, as a typical local highly intensive wind type, has attracted the attention of researchers, and the fragility of the transmission tower under such winds has been studied [13,14]. Khalil et al. also investigated the fragility problems of similar steel structures, in which the different failure modes are considered [15].

To enhance the wind resistance performance of transmission towers, some reinforcing schemes have been proposed and validated by researchers. These reinforcing schemes include the bolted splices [16,17], steel casings [18], and clamps [19,20]. Xie et al. conducted experiments on the retrofitted diagonal braces to derive their failure mode and the enhancement of the loading-carrying capacity, and the results show that the most vulnerable member in the retrofitted model is the leg member instead of the diagonal braces in the original model [21,22]. To increase the strength and the stiffness of the aged transmission towers, Lu et al. proposed to use the bolted cruciform and splice connectors to retrofit the tower leg and the effectiveness of this reinforcing scheme was verified by the cyclic experiment [23]. Bilionis et al. [24] investigated the risk and losses of the steel lattice telecommunication towers under extreme wind load and studied the influence of different rehabilitation schemes.

In this paper, the fixture-type reinforcement device (FRD) is used to enhance the wind resistance performance of the transmission tower, and the effectiveness is checked by numerical analysis. At first, the configuration of the device is introduced, and the finite element analysis of the main angled steel component is conducted. Secondly, the analytical model of the transmission tower is established, and the wind load is applied in two directions. Lastly, the reinforcing effect of the FRD is verified through the simulation of the tower model under different cases.

2. Fixture-Type Reinforcement Device (FRD)

2.1. Configuration of the FRD

The configuration of the fixture-type reinforcement device is shown in Figure 1. It can be seen that the FRD consists of a reinforcing component, several L-type and crossed steel plates connected by the bolts. The main component, which is the reinforcing target, is set between the crossed steel plates and the L-type steel plates, and the normal pressure is exerted on the main component by the bolts. The L-type steel plate and crossed steel plate in Figure 1 are connected by bolts and are like fixtures or clamps to make the reinforcing component and the original component work together to resist the wind load. It should be noted that the bolts do not pass directly through the main component, which means there is no need to drill holes in it so as to prevent local weakness of its mechanical properties. However, there are some holes on the reinforcing component, and the bolts are used to firmly attach it to the crossed steel plates. Therefore, when the main component is subjected to a large load and deforms, the reinforcing component can work simultaneously with the main component, increasing its strength and stiffness. The combination of an L-type steel plate, a crossed steel plate, and several bolts is termed a fixture pair in the following context. Therefore, the FRD can be simply regarded as a main component reinforced by the reinforcing component with several fixture pairs. This configuration of the FRD forms a stable and reliable connection with the main component through these fixture pairs.

2.2. Finite Element Simulation of the FRD

To analyze the enhancement effect of the FRD on the mechanical properties of the main component, a typical angled steel component was selected as the prototype, and the finite element models are built based on the Abaqus platform. The length of the angled steel component is 1.5 m; the thickness and the width of the L-shaped section are, respectively, 5 mm and 75 mm. The finite element models of the main component and the reinforced one are established as shown in Figure 2.

The eight-node solid elements are used to simulate all the parts of the model. The material of the two models is Q235, and its mechanical properties are listed in

Table 1. Mechanical properties of the material.

Type	Density (kg/m3)	Elastic Modulus (MPa)	Poisson Ratio	Yield Stress (MPa)
Q235	7850	2.06 × 105	0.31	235

. The reinforcing component shares the same sectional dimensions as the main component, but its length is only 1 m. The height of the L-type steel plate and the crossed steel plate is 100 mm, while their thickness is 5 mm, which is identical to that of the main component. The effect of the bolts connecting different parts of the model are simulated by the pressure directly exerted on the surfaces of them, including the L-type steel plate, the crossed steel plate, and the reinforcing component. Two steel plates are set on both ends of the main component so as to act as the loading plates. The vertical load is applied directly in the form of displacement to the top plate of the two models, and the bottom plates of them are constrained. In this way, the load–displacement relationship can be derived to assess the enhancement effect of the FRD. It can be seen in Figure 2b that three fixture pairs are used as the illustration example. Actually, the number of the fixture pairs is a key factor that could influence the enhancement effect of the FRD, and therefore different numbers, namely 2 to 4, of the fixture pairs are investigated in this section.

The failure mode of the original model is given in Figure 3a. As can be seen from the figure, when not reinforced, the main angled steel component will undergo plastic deformation and buckling failure at the middle part due to axial displacement loading. When it is reinforced by the FRD with different numbers of fixture pairs, the failure modes are represented in Figure 3b. It can be seen that the failure mode of the reinforced model with two fixture pairs is nearly identical to that of the original model, which indicates the number of the fixture pairs is not sufficient to avoid the buckling failure of the entire component. However, when three or four fixture pairs are used in the reinforcement, the failure mode of the model switches to the local buckling near the top and/or the bottom fixture pair. That is to say, using three or more fixtures can change the loading and deformation patterns of the reinforced models so as to prevent the buckling failure of the entire component.

The load–displacement curves derived from these models are plotted in Figure 4. It can be seen that these four curves share a similar varying trend such that they get their peak values of load at the displacement of around 2 mm. The initial stiffness values of these models are very close because only the main component participates in taking the vertical load at the beginning. With the increase in the loading displacement, the reinforcing device gradually takes part in working with the main component, and therefore the peak load of the reinforced models becomes larger than the original model. However, when four fixture pairs are used, the load–displacement curve shows a rapid decline after the peak load is achieved, which indicates a sudden failure of the model. Meanwhile, the peak loads of the reinforced models with three or four fixture pairs have close peak load values. Therefore, it can be deduced that the appropriate number of the fixture pairs for this main component is three, since the addition of the extra fixture pairs has little effect on increasing the peak load of the main componet but could cause its sudden failure.

The peak load of the main componennt is a key parameter that can affect the wind resistance performance of a transmission tower; therefore they are listed in

Table 2. Peak loads of different models.

Model	Original	Reinforced
		2 Fixture Pairs	3 Fixture Pairs	4 Fixture Pairs
Peak Load (kN)	69.2	87.3	95	95.4
Changing Ratio	/	26%	37%	38%

for a detailed comparison. The peak load of the original model is 69.2 kN, while with the addition of two, three, and four fixture pairs in the reinforced models, the peak loads change to 87.3 kN, 95.0 kN, and 95.4 kN. The increasing ratios of the three models with FRD are, respectively, 26%, 37%, and 38%, which represents great growth for the peak load of the main component and verifies the effectiveness of the FRD in enhancing the wind resistance performance of the main angled steel component.

3. Transmission Tower and Wind Load

3.1. Transmission Tower and Its Analytical Model

To investigate the wind resistance performance of typical towers and the reinforcement effect of using FRD, the transmission tower shown in Figure 5a is selected as the research prototype. For simplicity, this transmission tower is considered a structured body, and the welded connections between the components are not included. This type of transmission tower has been widely constructed in the rural areas of China. The overall height of this tower is 36.3 m, and the transmission cables are about 30 m above the ground. All the components of this transmission tower are L-shaped angled steel, but different components have different sectional dimensions and materials.

Figure 5b demonstrates the two types of steel used in the construction of the transmission tower. The steel type of the green components is Q235, whose mechanical properties are the same as those in Table 1, while the blue components are made of Q345 with their mechanical properties given in

Table 3. Mechanical properties of the Q345 steel.

Type	Density (kg/m3)	Elastic Modulus (MPa)	Poisson Ratio	Yield Stress (MPa)
Q345	7850	2.06 × 105	0.31	345

. It can be seen from the comparison between the mechanical properties of the two types of steel that the only difference is the yield stress. In Figure 5c, the components with different sectional dimensions are labeled with different colors. The detailed information of the sectional dimensions of them are listed in

Table 4. Dimensional data for angled steel components of the transmission tower.

No.	Shape	Specification	Length of Wing (mm)	Thickness of Wing (mm)
1	L	50 × 5	50	5
2	L	50 × 4	50	4
3	L	45 × 4	45	4
4	L	80 × 6	80	6
5	L	63 × 5	63	5
6	L	40 × 3	40	3
7	L	75 × 5	75	5
8	L	70 × 5	70	5
9	L	56 × 5	56	5

. It can be seen that nine types of L-shaped angled steel components are used to construct the transmission tower, and the largest section of these components has a length of 80 mm and a thickness of 6 mm. In the transmission tower, the vertical component in the lower half of the height has sectional dimensions of 75 mm × 5 mm and is exactly the main component investigated in Figure 2. Based on these geometrical dimensions of the components and the mechanical properties of the material, the finite element model of the transmission tower is built on the Abaqus platform. The components are simulated utilizing a two-node Euler beam element. The bottom of the tower is completely constrained, and for simplicity the soil–pile interaction is not considered in this study.

The first 5 vibration modes and frequencies of this transmission tower are given in Figure 6 and

Table 5. First five vibration modes and frequencies of the tower structure.

Order	Vibration Mode	Frequency (Hz)
1	Bending around y-axis	1.575
2	Bending around x-axis	1.577
3	Bending around y-axis	6.832
4	Bending around x-axis	6.983
5	Torsion around z-axis	8.711

by conducting the dynamic property analysis. It can be seen that the first vibration mode is the tower bending with respect to the Y-axis in Figure 6a, and the vibration frequency is 1.575 Hz, which corresponds to a period of 0.635 s. The second vibration mode is the tower bending with respect to the X-axis, as shown in Figure 6b, and the vibration frequency is 1.577 Hz. The vibration periods of these two modes are very close because the vertical components of the tower are symmetrical in the two horizontal directions. The third and fourth vibration modes are also the bending deformation, and their frequencies are around 6.9 Hz. The first torsional vibration mode appears in the fifth order, as presented in Figure 6e, and the corresponding vibration frequency is 8.711 Hz.

3.2. Wind Load

The Chinese standard load code for the design of overhead transmission Lines [25] gives specifications on how to calculate the wind load taken by the tower structure and grounding cables. The wind load on the transmission tower structure can be calculated by the following equation:

$$W_s=W_0·{\mu }_z·{\mu }_s·{\beta }_z·B_2·A_s$$

(1)

where $W_s$ is the wind pressure taken by the component of the transmission tower structure; $W_0$ is the reference wind pressure of a certain area, and can be derived from appendix; ${\mu }_z$ is the height variation coefficient of wind pressure, which accounts for the influence of elevation; ${\mu }_s$ is the shape coefficient of the component; ${\beta }_z$ is the wind fluttering coefficient at the height of z; $B_2$ is the amplification coefficient of the component when it is covered by ice; and $A_s$ is the projected area of the component.

The wind pressure exerted on the transmission cables and grounding cables can be calculated by Equation (2)

$$W_x={\beta }_c·{\alpha }_L·W_0·{\mu }_z·{\mu }_{\mathit{sc}}·d·L_p·B_1·{\sin }^2\theta$$

(2)

where ${\beta }_c$ is the gustiness factor of the transmission or grounding cable; ${\alpha }_L$ is the span reduction factor; ${\mu }_{sc}$ is the shape coefficient of the cable; $d$ is the outer diameter of the cable; $L_p$ is the horizontal span between towers; $B_1$ is the amplification coefficient of the cable when covered by ice; and $\theta$ is the angle between the direction of the wind and that of the cable.

Considering the velocity of the wind, the wind load of the tower and the cables can be derived based on Equations (1) and (2), and they are directly applied to the finite element model as the static loads. Two directions of the wind load are taken in the analysis: (1) along the direction of the transmission cables and (2) perpendicular to the direction of the transmission cables. Here, it should be noted that the two directions can form the plane parallel to the horizontal plane, as illustrated in Figure 7.

4. Results and Discussion

4.1. Wind Resistance Performance of the Original Tower

To assess the wind resistance performance of the original transmission tower, the wind loads are applied directly to the components of the tower, as mentioned above. Since the wind load derived from Equations (1) and (2) are dependent on the wind speed, the gradually increasing values of the wind speed are taken. The wind speed is increased from 1 m/s to the speed that can cause the failure of the whole tower. To check whether the transmission tower reaches its ultimate state, the displacement of the top component of the tower is used. It is defined herein that the ultimate state is reached when the displacement of the top component increases rapidly.

Figure 8 presents the displacement of the top of the tower with respect to the speed of the wind. It can be seen that when the wind speed in the direction perpendicular to the transmission cables reaches around 38.1 m/s, the displacement of the top component of the tower begins to sharply increase. Therefore, at this wind speed, the tower reaches its ultimate state, and the stress distribution of the tower is presented in Figure 9. It can be seen that the maximum stress occurs in the vertical component where the steel of the components changes, as given in Figure 5b. The failure mode in this case is the buckle of the component, which can be attributed to the instability of structural components under such circumstance. When the wind load is applied along the direction of the transmission cable, the failure component is the same one as in the perpendicular direction. However, under this circumstance, the ultimate wind speed increases to about 44.7 m/s, as shown in Figure 8, which can be attributed to the smaller value of the wind load applied along the cable taken by the transmission and grounding cables, as calculated by Equation (2).

4.2. Enhancement Effect of the FRD

In order to investigate the enhancement effect of wind resistance performance of the transmission tower with the installation of the FRD, the first reinforcement scheme is to only add FRD to the failure component shown in Figure 9. To accurately analyze the behavior of this component when enhanced by the FRD, the solid element is used to build this component while the other components are still modeled by the beam element. The four feet of the tower are set to be totally constrained to the ground. This multi-scale finite element model is presented in Figure 10. At the connection points of different elements, the six freedoms of the node of the beam element are completely constrained to the adjacent surface of the solid element, and therefore the force can be transferred among these components. It should be noted that the FRD used here has three fixture pairs, as analyzed in Section 2.

In Figure 10, the length of the reinforced component is 1.5 m, which is identical to the case analyzed in Section 2. To assess the necessity of reinforcing more components of the tower, three more reinforcement schemes are also analyzed here, namely reinforcing the components with the respective lengths of 3 m, 4.5 m, and 6 m, as shown in Figure 11.

To better compare with the original model, the wind loads are applied to the tower when the wind speeds are respectively set as 38.1 m/s along the direction of the cable and as 44.7 m/s perpendicular to the direction of the cable. Figure 12 presents the displacement of the top component of the tower when different reinforcing lengths of the component are selected. It can be seen in Figure 12a that when the wind load is applied along the direction of the cable, the displacement of the top of the tower gradually decreases with the increase in the reinforcing length, which means the more components above the failure one are reinforced, the better the performance of the tower under the wind load. When the tower is not reinforced, the top displacement reaches 1455 mm, and it gets smaller until it reaches 977 mm, when the failure components are reinforced by the FRD. When the reinforcing length is 3 m, which corresponds to the case that two adjacent components in the vertical column are reinforced, the top displacement reduces to 658 mm and remains steady when the reinforcing length is enlarged. That is to say, the installation of the FRD can reduce the top displacement of the tower by 55%.

Figure 12b demonstrates the results of the tower when the wind load is applied in the direction perpendicular to the cable. The varying trend of the results is similar to that in Figure 12a. When the tower is not reinforced, the displacement of the top of the tower is about 2047 mm, and it decreases to 1493 mm when the reinforcing length is 1.5 m. When the reinforcing length reaches around 4.5 m, the top displacement of the tower becomes stable and is around 670 mm, which is about a reduction of 67% of that of the original model.

5. Conclusions

To investigate the wind resistance performance of a transmission tower, the fixture-type reinforcement device was used. The configuration of the device was first introduced, and then the finite element analysis of the main angled steel component was conducted. Then, the complete model of the transmission tower was established, and a wind load was applied in two directions. Lastly, the reinforcing effect of the FRD was verified through the simulation of the tower model under different cases. The main conclusions can be drawn as follows:

(1)

The FRD can effectively improve the deformation characteristics and failure modes of angled steel components under axial loads. The FRD with three fixture pairs shows great influence since it can increase the peak load of the angled steel component by 37%.

(2)

The tower structure is prone to integral structural collapse due to local component failure under wind loads and the failure occurring at the connection between two different steel materials. The ultimate state of the tower is derived when the wind speeds are, respectively, 44.7 m/s in the direction of the cable and 38.1 m/s in the direction perpendicular to the cable.

(3)

The use of the FRD can effectively reduce the deformation of the tower structure under strong winds. Only reinforcing three angled steel components (4.5 m) above the vulnerable component can achieve good results. The top displacements of the tower can be reduced by 55% and 67% in, and perpendicular to, the direction of the cable, respectively.

(4)

FRD is easy to install in an existing transmission tower; therefore, it is a low-cost option to improve its wind resistance performance and keep its deformation within a safe operational zone under strong wind conditions.

The FRD is utilized in this study to enhance the wind resistance performance of the transmission tower when subjected to wind load. However, the selection of the strengthening zones is another important factor that could influence the effectiveness of the strengthening scheme, which will be investigated in the next step. Additionally, the authors will conduct an optimization study of different strengthening devices to find optimal strengthening schemes for various types of transmission towers.