# Analytical Investigation of the Effects of Secondary Structural Members on the Structural Behaviors of Transmission Towers

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. General Configuration and Design Load Combinations for Transmission Towers

#### 2.1. Description and Characteristics of Structures

#### 2.1.1. Model Details

^{3}, 210 GPa, and 0.3, respectively. We summarize the section properties of the 765 kV transmission tower in Table 1. The horizontal angle of the wire was 30°, and the wind span and weight span were 450 and 800 m, respectively. For the conductors, we applied the cardinal aluminum conductor steel-reinforced model that is primarily used in 765 kV lattice transmission towers. The rated tensile strength was 150 kN, and the unit weight was 17.26 N/m. The rated tensile strength of the ground wire (AWS-200) was 126 kN, and the unit weight was 9.42 N/m. We summarize the conductor and ground wire properties in Table 2.

#### 2.1.2. Parametric Variables of Analytical Model

#### 2.2. Analytical Load Combination and Method

#### 2.2.1. Design Load and Load Combination

^{2}) (A).

_{z}K

_{zt}(V

_{100})

^{2}GC

_{f},

#### 2.2.2. Linear Static Analysis

#### 2.2.3. Eigenvalue Analysis

#### 2.2.4. Geometric Nonlinear and Inelastic Analysis

## 3. Contribution of Secondary Members to Structural Behavior and Load-Carrying Capacity

#### 3.1. Comparative Studies of Linear Static Behavior

#### 3.2. Comparative Studies of Eigenvalues and Corresponding Modes

#### 3.3. Effects of Secondary Members on Load-Carrying Capacity

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Descriptions of parametric variables in analytical models: (

**a**) models with five equal braces; (

**b**) models with four equal braces; (

**c**) models with three equal braces; (

**d**) models with two equal braces.

**Figure 9.**Comparison of deformed shapes of transmission towers with X bracing under considered load combinations (scale factor: 10.0): (

**a**) models with five equal spacings and horizontal members; (

**b**) models with five equal spacings without horizontal members; (

**c**) models with two equal spacings and horizontal members; (

**d**) models with two equal spacings without horizontal members.

**Figure 10.**Comparison of deformed shapes of transmission towers with K bracing under considered load combinations (scale factor: 10.0): (

**a**) models with five equal spacings and horizontal members; (

**b**) models with five equal spacings without horizontal members; (

**c**) models with two equal spacings and horizontal members; (

**d**) models with two equal spacings without horizontal members.

**Figure 11.**Comparison of distortion effects of presence or absence of horizontal members in models with X bracing: (

**a**) models with five equal spacings; (

**b**) models with four equal spacings; (

**c**) models with three equal spacings; (

**d**) models with two equal spacings.

**Figure 12.**Comparison of distortion effects of presence or absence of horizontal members in models with K bracing: (

**a**) models with five equal spacings; (

**b**) models with four equal spacings; (

**c**) models with three equal spacings; (

**d**) models with two equal spacings.

**Figure 13.**Changes in eigenvalues and corresponding mode shapes of transmission tower models with five equal braces (scale factor: 5.0): (

**a**) model with X bracing and horizontal members; (

**b**) model with X bracing without horizontal members; (

**c**) model with K bracing and horizontal members; (

**d**) model with K bracing without horizontal members.

**Figure 14.**Changes in eigenvalues and corresponding mode shapes of transmission tower models with four equal braces (scale factor: 5.0): (

**a**) model with X bracing and horizontal members; (

**b**) model with X bracing without horizontal members; (

**c**) model with K bracing and horizontal members; (

**d**) model with K bracing without horizontal members.

**Figure 15.**Changes in eigenvalues and corresponding mode shapes of transmission tower models with three equal braces (scale factor: 5.0): (

**a**) model with X bracing and horizontal members; (

**b**) model with X bracing without horizontal members; (

**c**) model with K bracing and horizontal members; (

**d**) model with K bracing without horizontal members.

**Figure 16.**Changes in eigenvalues and corresponding mode shapes of transmission tower models with two equal braces (scale factor: 5.0): (

**a**) model with X bracing and horizontal members; (

**b**) model with X bracing without horizontal members; (

**c**) model with K bracing and horizontal members; (

**d**) model with K bracing without horizontal members.

**Figure 17.**Comparison of elastic buckling strengths based on effects of braces and horizontal members.

**Figure 18.**Deformation progress of transmission towers with five equally spaced braces (scale factor: 10.0): (

**a**) model with X bracing and horizontal members; (

**b**) model with X bracing without horizontal members; (

**c**) model with K bracing and horizontal members; (

**d**) model with K bracing without horizontal members.

**Figure 19.**Deformation progress of transmission towers with two equally spaced braces (scale factor: 10.0): (

**a**) model with X bracing and horizontal members; (

**b**) model with X bracing without horizontal members; (

**c**) model with K bracing and horizontal members; (

**d**) model with K bracing without horizontal members.

**Figure 20.**Two points to determine load–displacement curves in analytical models: (

**a**) model with X bracing of five equal spacings; (

**b**) model with K bracing of five equal spacings; (

**c**) model with X bracing of two equal spacings; (

**d**) model with K bracing of two equal spacings.

**Figure 21.**Comparison of load–displacement curves in models with five equally spaced X braces with or without horizontal members: (

**a**) topmost section; (

**b**) main post section.

**Figure 22.**Comparison of load–displacement curves in models with five equally spaced K braces with or without horizontal members: (

**a**) topmost section; (

**b**) main post section.

**Figure 23.**Comparison of load–displacement curves in models with two equally spaced X braces with or without horizontal members: (

**a**) topmost section; (

**b**) brace section.

**Figure 24.**Comparison of load–displacement curves in models with two equally spaced K braces with or without horizontal members: (

**a**) topmost section; (

**b**) brace section.

**Figure 25.**Comparison of trends between LPF and brace spacings based on effects of brace and horizontal members: (

**a**) models with X bracing; (

**b**) models with K bracing.

Member Type | Cross Section (mm × mm) |
---|---|

Main Post | Φ 609.6 × 16 Φ 609.6 × 14 Φ 558.8 × 14 Φ 558.8 × 12 Φ 457.0 × 12 Φ 406.0 × 10 Φ 318.5 × 8.0 Φ 216.3 × 7.0 Φ 165.2 × 5.5 |

Brace | Φ 216.3 × 7.0 Φ 190.7 × 5.3 Φ 165.2 × 5.5 Φ 139.8 × 4.5 Φ 101.6 × 3.2 Φ 89.1 × 3.2 |

Horizontal Member | Φ 216.3 × 7.0 Φ 190.7 × 5.3 Φ 165.2 × 5.5 Φ 139.8 × 4.5 Φ 89.1 × 3.2 Φ 76.3 × 2.8 |

Cross Arm | L 600 × 40 L 650 × 60 L 700 × 60 L 750 × 60 L 800 × 60 L 900 × 60 L 900 × 70 L 1000 × 70 L 1200 × 80 L 1300 × 90 L 1300 × 120 L 1500 × 120 L 1750 × 120 L 1750 × 150 L 2000 × 150 L 2000 × 200 |

Parameter | Conductor | Ground Wire |
---|---|---|

Specification | ACSR (cardinal) | AWS-200 |

Rated tension strength (kN) | 150 | 126 |

Unit weight (N/m) | 17.26 | 9.42 |

Outer diameter (m) | 0.03 | 0.018 |

Area (mm^{2}) | 547.3 | 204.3 |

Modulus of elasticity (GPa) | 74.2 | 108.8 |

Thermal expansion coefficient (10–6/°C) | 23 | 15.5 |

Analysis Flow | Analysis Type | Objective | Applied Load Case |
---|---|---|---|

1 | Linear static analysis | To observe the torsional and distortional resistance effect | Broken wire case |

2 | Eigenvalue analysis | To observe the elastic buckling resistance effect | Wind load case |

3 | Geometric nonlinear and inelastic analysis | To observe the load-carrying-capacity effect | Wind load case |

Panel | Height (m) | Kz | Cf | Wind Pressure (N/mm ^{2}) |
---|---|---|---|---|

1 | 16.5 | 1.0 | 1.9 | 1438.1 |

2 | 26.5 | 1.2 | 1.8 | 1679.8 |

3 | 35.5 | 1.3 | 1.7 | 1765.6 |

4 | 42.5 | 1.3 | 1.7 | 1815.8 |

5 | 46 | 1.4 | 1.7 | 1839.1 |

6 | 52 | 1.4 | 1.7 | 1932.5 |

7 | 57.5 | 1.4 | 1.6 | 1862.9 |

8 | 63.5 | 1.5 | 1.6 | 1807.5 |

9 | 67.8 | 1.5 | 1.6 | 1858.6 |

10 | 71.9 | 1.5 | 1.6 | 1935.6 |

11 | 76.0 | 1.5 | 1.7 | 2045.7 |

12 | 80.0 | 1.5 | 1.6 | 1957.7 |

13 | 84.3 | 1.6 | 1.6 | 2002.6 |

14 | 88.4 | 1.6 | 1.7 | 2060.8 |

15 | 92.5 | 1.6 | 1.8 | 2234.7 |

16 | 96.5 | 1.6 | 1.7 | 2154.6 |

17 | 100.8 | 1.6 | 1.7 | 2210.3 |

18 | 103.3 | 1.6 | 1.7 | 2206.2 |

19 | 108.5 | 1.6 | 1.8 | 2349.9 |

Conductor | Ground Wire | |
---|---|---|

V | 47,705 N | 6280 N |

T | 86,827 N | 17,619 N |

L | 324,043 N | 65,753 N |

Spacing | X Brace | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Post 1 | Post 2 | Post 3 | Post 4 | ||||||||||||||

Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | ||

Five | Lv1 | 8.8 | 6.3 | 0.4 | 0.001 | −3.4 | 6.6 | 4.5 | 0.001 | −3.6 | −6.1 | 0.8 | 0.001 | 9.0 | −5.8 | 4.9 | 0.001 |

Lv2 | 13.5 | 9.6 | 0.6 | 0.002 | −0.2 | 10.2 | 6.6 | 0.001 | −0.6 | −4.5 | 1.2 | 0.000 | 14.0 | −3.9 | 7.2 | 0.001 | |

Lv3 | 20.3 | 14.5 | 0.7 | 0.003 | 5.0 | 15.1 | 8.4 | 0.002 | 4.5 | −1.3 | 1.5 | 0.001 | 20.8 | −0.6 | 9.2 | 0.002 | |

Lv4 | 29.8 | 21.5 | 0.7 | 0.005 | 12.1 | 22.1 | 9.8 | 0.003 | 11.6 | 3.2 | 1.8 | 0.002 | 30.4 | 3.9 | 10.8 | 0.004 | |

Lv5 | 43.0 | 31.3 | 0.5 | 0.009 | 21.3 | 31.9 | 10.8 | 0.006 | 20.8 | 9.1 | 1.8 | 0.004 | 43.6 | 9.8 | 12.0 | 0.007 | |

Lv6 | 60.1 | 44.4 | 0.07 | 0.015 | 33.2 | 44.5 | 11.1 | 0.011 | 33.2 | 17.8 | 1.7 | 0.008 | 60.2 | 17.9 | 12.5 | 0.013 | |

Four | Lv1 | 8.7 | 6.2 | 0.4 | 0.001 | −3.3 | 6.6 | 4.5 | 0.001 | −3.6 | −6.2 | 0.8 | 0.001 | 9.1 | −5.7 | 4.9 | 0.001 |

Lv2 | 14.8 | 10.5 | 0.6 | 0.002 | 1.0 | 11.3 | 7.1 | 0.001 | 0.4 | −3.9 | 1.3 | 0.000 | 15.5 | −3.1 | 7.7 | 0.002 | |

Lv3 | 24.2 | 17.3 | 0.7 | 0.004 | 8.4 | 18.2 | 9.0 | 0.002 | 7.7 | 0.7 | 1.7 | 0.001 | 25.0 | 1.7 | 9.9 | 0.003 | |

Lv4 | 39.5 | 28.6 | 0.5 | 0.008 | 18.2 | 29.4 | 10.5 | 0.005 | 17.5 | 6.7 | 1.8 | 0.003 | 40.3 | 7.6 | 11.7 | 0.006 | |

Lv5 | 61.1 | 45.1 | 0.02 | 0.016 | 31.8 | 45.2 | 11.0 | 0.011 | 31.7 | 16.1 | 1.7 | 0.007 | 61.2 | 16.2 | 12.4 | 0.013 | |

Three | Lv1 | 8.6 | 6.1 | 0.4 | 0.001 | −3.3 | 6.7 | 4.5 | 0.001 | −3.7 | −6.3 | 0.8 | 0.001 | 9.1 | −5.6 | 4.9 | 0.001 |

Lv2 | 17.6 | 12.5 | 0.7 | 0.002 | 2.9 | 13.5 | 7.7 | 0.002 | 2.1 | −3.1 | 1.4 | 0.000 | 18.4 | −1.9 | 8.4 | 0.002 | |

Lv3 | 34.2 | 24.6 | 0.6 | 0.006 | 13.7 | 25.7 | 10.0 | 0.004 | 12.9 | 3.3 | 1.7 | 0.002 | 35.1 | 4.4 | 11.0 | 0.005 | |

Lv4 | 63.7 | 47.0 | 0.09 | 0.016 | 28.6 | 47.1 | 10.9 | 0.011 | 28.5 | 12.1 | 1.5 | 0.006 | 63.9 | 12.3 | 12.2 | 0.013 | |

Two | Lv1 | 8.6 | 6.1 | 0.4 | 0.001 | −3.2 | 6.7 | 4.5 | 0.001 | −3.7 | −6.3 | 0.8 | 0.001 | 9.2 | −5.5 | 4.9 | 0.001 |

Lv2 | 25.6 | 18.3 | 0.6 | 0.004 | 6.1 | 19.7 | 8.7 | 0.003 | 5.0 | −2.5 | 1.5 | 0.001 | 26.9 | −0.9 | 9.6 | 0.003 | |

Lv3 | 73.2 | 53.8 | 0.46 | 0.019 | 19.2 | 54.0 | 10.7 | 0.012 | 19.1 | 0.2 | 1.1 | 0.004 | 73.4 | 0.3 | 11.9 | 0.015 |

Spacing | X Brace | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Post 1 | Post 2 | Post 3 | Post 4 | ||||||||||||||

Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | ||

Five | Lv1 | 8.9 | 6.4 | 0.4 | 0.001 | −3.4 | 6.5 | 4.5 | 0.001 | −3.5 | −6.0 | 0.8 | 0.001 | 9.0 | −5.9 | 4.9 | 0.001 |

Lv2 | 13.2 | 9.2 | 0.6 | 0.002 | 0.1 | 10.6 | 6.6 | 0.001 | −0.9 | −5.0 | 1.2 | 0.001 | 14.4 | −3.4 | 7.2 | 0.001 | |

Lv3 | 20.2 | 14.3 | 0.7 | 0.003 | 5.1 | 15.2 | 8.4 | 0.002 | 4.4 | −1.4 | 1.6 | 0.001 | 21.1 | −0.4 | 9.2 | 0.002 | |

Lv4 | 29.8 | 21.2 | 0.7 | 0.005 | 12.2 | 22.4 | 9.8 | 0.003 | 11.4 | 3.1 | 1.8 | 0.002 | 30.8 | 4.4 | 10.9 | 0.004 | |

Lv5 | 42.4 | 30.5 | 0.5 | 0.009 | 22.1 | 32.8 | 10.8 | 0.006 | 20.2 | 8.4 | 1.9 | 0.004 | 44.8 | 11.0 | 12.0 | 0.008 | |

Lv6 | 60.6 | 44.8 | 0.05 | 0.016 | 33.5 | 44.8 | 11.3 | 0.012 | 33.6 | 18.2 | 1.8 | 0.008 | 60.6 | 18.1 | 12.7 | 0.013 | |

Four | Lv1 | 8.9 | 6.4 | 0.4 | 0.001 | −3.4 | 6.5 | 4.5 | 0.001 | −3.5 | −5.9 | 0.8 | 0.001 | 9.0 | −5.9 | 4.9 | 0.001 |

Lv2 | 14.2 | 9.7 | 0.6 | 0.002 | 1.6 | 12.1 | 7.0 | 0.001 | −0.2 | −4.9 | 1.3 | 0.001 | 16.3 | −2.0 | 7.6 | 0.002 | |

Lv3 | 24.4 | 17.4 | 0.7 | 0.004 | 8.4 | 18.2 | 9.2 | 0.002 | 7.8 | 0.9 | 1.7 | 0.001 | 25.2 | 1.9 | 10.1 | 0.003 | |

Lv4 | 38.4 | 27.3 | 0.5 | 0.007 | 19.7 | 31.1 | 10.5 | 0.006 | 16.6 | 5.3 | 1.8 | 0.003 | 42.2 | 9.6 | 11.6 | 0.007 | |

Lv5 | 61.8 | 45.7 | 0.01 | 0.016 | 32.4 | 45.7 | 11.3 | 0.012 | 32.4 | 16.7 | 1.7 | 0.008 | 61.9 | 16.6 | 12.7 | 0.013 | |

Three | Lv1 | 8.8 | 6.3 | 0.4 | 0.001 | −3.4 | 6.5 | 4.5 | 0.001 | −3.6 | −6.0 | 0.8 | 0.001 | 9.0 | −5.8 | 4.9 | 0.001 |

Lv2 | 16.6 | 11.2 | 0.6 | 0.002 | 3.8 | 14.8 | 7.6 | 0.002 | 1.3 | −4.4 | 1.4 | 0.001 | 19.6 | −0.3 | 8.3 | 0.002 | |

Lv3 | 32.8 | 23.1 | 0.6 | 0.006 | 15.6 | 27.7 | 10.0 | 0.005 | 11.7 | 1.6 | 1.8 | 0.002 | 37.5 | 6.9 | 11.0 | 0.005 | |

Lv4 | 64.9 | 47.9 | 0.1 | 0.017 | 29.7 | 48.0 | 11.2 | 0.012 | 29.7 | 13.1 | 1.6 | 0.007 | 65.0 | 13.1 | 12.6 | 0.014 | |

Two | Lv1 | 8.9 | 6.4 | 0.4 | 0.001 | −3.4 | 6.4 | 4.6 | 0.001 | −3.4 | −5.8 | 0.8 | 0.001 | 8.9 | −5.9 | 4.9 | 0.001 |

Lv2 | 21.4 | 13.4 | 0.6 | 0.003 | 10.6 | 25.4 | 8.3 | 0.003 | 1.5 | −8.1 | 1.4 | 0.001 | 32.3 | 5.7 | 9.0 | 0.004 | |

Lv3 | 75.3 | 55.5 | 0.46 | 0.019 | 21.1 | 55.6 | 11.2 | 0.012 | 21.2 | 1.8 | 1.3 | 0.004 | 75.4 | 1.8 | 12.6 | 0.016 |

Spacing | K Brace | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Post 1 | Post 2 | Post 3 | Post 4 | ||||||||||||||

Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | ||

Five | Lv1 | 8.3 | 5.9 | 0.4 | 0.001 | −3.0 | 6.1 | 4.5 | 0.001 | −3.1 | −5.5 | 0.8 | 0.001 | 8.5 | −5.3 | 4.8 | 0.001 |

Lv2 | 13.2 | 9.4 | 0.6 | 0.002 | 0.1 | 9.7 | 6.6 | 0.001 | −0.1 | −3.9 | 1.2 | 0.000 | 13.4 | −3.6 | 7.2 | 0.001 | |

Lv3 | 20.0 | 14.4 | 0.7 | 0.003 | 5.2 | 14.6 | 8.4 | 0.002 | 5.0 | −0.7 | 1.6 | 0.001 | 20.3 | −0.4 | 9.2 | 0.002 | |

Lv4 | 29.7 | 21.4 | 0.7 | 0.005 | 12.2 | 21.8 | 9.8 | 0.003 | 11.9 | 3.6 | 1.8 | 0.002 | 30.0 | 4.0 | 10.9 | 0.004 | |

Lv5 | 43.0 | 31.4 | 0.5 | 0.009 | 21.5 | 31.6 | 10.8 | 0.006 | 21.3 | 9.6 | 1.9 | 0.004 | 43.3 | 9.9 | 12.1 | 0.007 | |

Lv6 | 61.1 | 45.1 | 0.02 | 0.016 | 32.8 | 44.9 | 11.2 | 0.011 | 33.0 | 17.3 | 1.7 | 0.008 | 61.1 | 17.1 | 12.6 | 0.013 | |

Four | Lv1 | 8.3 | 5.9 | 0.4 | 0.001 | −3.0 | 6.1 | 4.5 | 0.001 | −3.1 | −5.5 | 0.8 | 0.001 | 8.5 | −5.3 | 4.8 | 0.001 |

Lv2 | 14.6 | 10.5 | 0.6 | 0.002 | 1.2 | 10.7 | 7.1 | 0.001 | 1.0 | −3.2 | 1.3 | 0.000 | 14.9 | −2.9 | 7.8 | 0.002 | |

Lv3 | 24.3 | 17.4 | 0.7 | 0.004 | 8.5 | 17.7 | 9.1 | 0.002 | 8.3 | 1.4 | 1.7 | 0.001 | 24.5 | 1.8 | 10.0 | 0.003 | |

Lv4 | 39.7 | 28.8 | 0.5 | 0.008 | 18.5 | 29.1 | 10.6 | 0.005 | 18.3 | 7.4 | 1.8 | 0.003 | 39.9 | 7.7 | 11.8 | 0.006 | |

Lv5 | 62.4 | 46.0 | 0.04 | 0.016 | 31.7 | 45.8 | 11.2 | 0.011 | 31.9 | 15.9 | 1.7 | 0.007 | 62.3 | 15.6 | 12.6 | 0.013 | |

Three | Lv1 | 8.3 | 5.9 | 0.4 | 0.001 | −3.0 | 6.1 | 4.5 | 0.001 | −3.1 | −5.5 | 0.8 | 0.001 | 8.4 | −5.3 | 4.8 | 0.001 |

Lv2 | 17.6 | 12.6 | 0.7 | 0.002 | 3.0 | 12.8 | 7.9 | 0.001 | 2.8 | −2.2 | 1.5 | 0.000 | 17.8 | −1.9 | 8.6 | 0.002 | |

Lv3 | 35.0 | 25.3 | 0.6 | 0.006 | 13.8 | 25.5 | 10.2 | 0.004 | 13.6 | 3.9 | 1.8 | 0.002 | 35.2 | 4.1 | 11.3 | 0.005 | |

Lv4 | 66.1 | 48.5 | 0.2 | 0.017 | 28.8 | 48.4 | 11.2 | 0.012 | 28.9 | 11.8 | 1.6 | 0.006 | 66.0 | 11.6 | 12.6 | 0.014 | |

Two | Lv1 | 8.3 | 5.9 | 0.4 | 0.001 | −2.9 | 6.1 | 4.5 | 0.001 | −3.1 | −5.4 | 0.8 | 0.001 | 8.4 | −5.2 | 4.9 | 0.001 |

Lv2 | 26.5 | 19.0 | 0.6 | 0.004 | 6.5 | 19.2 | 9.2 | 0.003 | 6.3 | −1.2 | 1.6 | 0.001 | 26.7 | −1.0 | 10.1 | 0.003 | |

Lv3 | 77.4 | 56.4 | 0.6 | 0.020 | 20.5 | 56.3 | 11.3 | 0.012 | 20.6 | 0.1 | 1.2 | 0.004 | 77.3 | −0.1 | 12.6 | 0.016 |

Spacing | K Brace | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Post 1 | Post 2 | Post 3 | Post 4 | ||||||||||||||

Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | Ux (mm) | Uy (mm) | Uz (mm) | Uθ (rad) | ||

Five | Lv1 | 8.3 | 5.9 | 0.4 | 0.001 | −3.0 | 6.1 | 4.5 | 0.001 | −3.1 | −5.5 | 0.8 | 0.001 | 8.4 | −5.3 | 4.9 | 0.001 |

Lv2 | 12.8 | 8.9 | 0.6 | 0.002 | 0.8 | 10.5 | 6.5 | 0.001 | −0.4 | −4.5 | 1.2 | 0.000 | 14.2 | −2.6 | 7.1 | 0.001 | |

Lv3 | 20.0 | 14.2 | 0.7 | 0.003 | 5.6 | 14.8 | 8.4 | 0.002 | 5.1 | −0.5 | 1.6 | 0.001 | 20.5 | 0.1 | 9.2 | 0.002 | |

Lv4 | 29.3 | 20.8 | 0.7 | 0.005 | 13.0 | 22.5 | 9.7 | 0.004 | 11.7 | 3.2 | 1.8 | 0.002 | 30.8 | 5.1 | 10.7 | 0.004 | |

Lv5 | 42.5 | 30.8 | 0.5 | 0.009 | 22.7 | 32.4 | 10.7 | 0.006 | 21.3 | 9.6 | 1.9 | 0.004 | 44.2 | 11.4 | 11.9 | 0.007 | |

Lv6 | 61.4 | 45.3 | 0.01 | 0.016 | 33.0 | 45.1 | 11.3 | 0.012 | 33.1 | 17.5 | 1.8 | 0.008 | 61.3 | 17.2 | 12.7 | 0.013 | |

Four | Lv1 | 8.3 | 5.9 | 0.4 | 0.001 | −3.0 | 6.1 | 4.5 | 0.001 | −3.1 | −5.5 | 0.8 | 0.001 | 8.4 | −5.3 | 4.9 | 0.001 |

Lv2 | 14.1 | 9.7 | 0.6 | 0.002 | 2.3 | 11.9 | 6.9 | 0.001 | 0.8 | −3.9 | 1.3 | 0.000 | 16.0 | −1.4 | 7.5 | 0.002 | |

Lv3 | 24.4 | 17.3 | 0.7 | 0.004 | 9.1 | 18.6 | 9.0 | 0.003 | 8.0 | 1.0 | 1.7 | 0.001 | 25.6 | 2.5 | 9.9 | 0.003 | |

Lv4 | 38.6 | 27.7 | 0.5 | 0.007 | 20.7 | 30.6 | 10.3 | 0.006 | 18.3 | 7.1 | 1.8 | 0.003 | 41.5 | 10.5 | 11.5 | 0.007 | |

Lv5 | 62.8 | 46.2 | 0.04 | 0.016 | 31.9 | 46.0 | 11.3 | 0.012 | 32.1 | 16.0 | 1.7 | 0.007 | 62.6 | 15.8 | 12.7 | 0.013 | |

Three | Lv1 | 8.3 | 6.0 | 0.4 | 0.001 | −3.0 | 6.1 | 4.5 | 0.001 | −3.1 | −5.4 | 0.8 | 0.001 | 8.4 | −5.3 | 4.9 | 0.001 |

Lv2 | 16.6 | 11.1 | 0.6 | 0.002 | 5.2 | 15.2 | 7.4 | 0.002 | 2.3 | −3.6 | 1.4 | 0.000 | 20.1 | 1.0 | 8.1 | 0.002 | |

Lv3 | 33.3 | 23.6 | 0.6 | 0.006 | 17.1 | 27.4 | 9.8 | 0.005 | 14.0 | 3.8 | 1.7 | 0.002 | 37.0 | 8.2 | 10.8 | 0.005 | |

Lv4 | 66.4 | 48.7 | 0.19 | 0.017 | 28.9 | 48.6 | 11.3 | 0.012 | 29.1 | 11.9 | 1.6 | 0.006 | 66.3 | 11.7 | 12.7 | 0.014 | |

Two | Lv1 | 8.3 | 6.0 | 0.4 | 0.001 | −3.0 | 6.1 | 4.5 | 0.001 | −3.1 | −5.4 | 0.8 | 0.001 | 8.4 | −5.3 | 4.9 | 0.001 |

Lv2 | 23.2 | 14.9 | 0.5 | 0.003 | 14.3 | 25.9 | 7.7 | 0.004 | 5.9 | −3.9 | 1.4 | 0.001 | 33.0 | 8.8 | 8.4 | 0.004 | |

Lv3 | 77.8 | 56.7 | 0.6 | 0.020 | 20.7 | 56.5 | 11.4 | 0.012 | 20.9 | 0.3 | 1.2 | 0.004 | 77.7 | 0.0 | 12.8 | 0.016 |

Details | Models with X Bracing | Models with K Bracing | ||
---|---|---|---|---|

With Horizontal Members | Without Horizontal Members | With Horizontal Members | Without Horizontal Members | |

Five equal brace spacings | 8.51 | 8.21 | 10.31 | 8.08 |

Four equal brace spacings | 6.01 | 5.82 | 8.18 | 5.87 |

Three equal brace spacings | 3.97 | 3.76 | 6.73 | 4.19 |

Two equal brace spacings | 2.29 | 2.27 | 5.08 | 2.85 |

Details | Models with X Bracing | Models with K Bracing | ||
---|---|---|---|---|

With Horizontal Members | Without Horizontal Members | With Horizontal Members | Without Horizontal Members | |

Five equal brace spacings | 2.08 | 2.06 | 2.08 | 2.06 |

Four equal brace spacings | 2.04 | 2.03 | 2.04 | 1.99 |

Three equal brace spacings | 1.93 | 1.92 | 2.01 | 1.80 |

Two equal brace spacings | 1.74 | 1.68 | 1.98 | 1.67 |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kim, P.; Han, W.S.; Kim, J.H.; Lee, J.; Kang, Y.J.; Kim, S.
Analytical Investigation of the Effects of Secondary Structural Members on the Structural Behaviors of Transmission Towers. *Buildings* **2023**, *13*, 223.
https://doi.org/10.3390/buildings13010223

**AMA Style**

Kim P, Han WS, Kim JH, Lee J, Kang YJ, Kim S.
Analytical Investigation of the Effects of Secondary Structural Members on the Structural Behaviors of Transmission Towers. *Buildings*. 2023; 13(1):223.
https://doi.org/10.3390/buildings13010223

**Chicago/Turabian Style**

Kim, Pyounghwa, Whi Seok Han, Jeong Hun Kim, Jeonghwa Lee, Young Jong Kang, and Seungjun Kim.
2023. "Analytical Investigation of the Effects of Secondary Structural Members on the Structural Behaviors of Transmission Towers" *Buildings* 13, no. 1: 223.
https://doi.org/10.3390/buildings13010223