Transmission Line Failure Due To Increase In Conductor Tension

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This article is a primer to Example 2: Pole Loading Analysis of the Angled Structure based on NESC 2017. Also, this is a supplement of the previous post: Loading Analysis of Transmission and Distribution Structures based on NESC 2017.

Angled Structures are greatly affected by the transverse load imposed by the 1) wind on the structure itself, 2) initial conductor tension, and 3) wind load on the conductor. However, as a Transmission Line Designer, you must take into account also the possible increase in conductor tension due to wind with/without ice loads. In order to do that, you must be knowledgeable in performing sag-and-tension calculations.

A note on NESC 2017 pp 481 states the following:

Rule 252B3 details the requirement at angles in the line. As written, it requires the vector sum of the transverse wind load and the resultant load imposed by the wires due to their change in direction. The latter is required to include the effects of wind on the wire tension.”

Related: You may review my extensive articles regarding sag and tension here.

Formulas

Transmission lines typically contain a majority of tangent (no line angle) structures. However, it is common for the installed locations of tangent structures to vary from design and thus have a small line angle. This can be caused by construction considerations, subsoil issues, right-of-way limitations, etc. Consequently, it is common to design some small angle loading into most tangent structures to provide a bit of excess capacity to allow for these circumstances.

The drawing above shows an angled structure with line angle θ. By trigonometry, we can solve the resultant force due to wire tension as the following:

\begin{align} F_{tension} = 2*Tension*\sin(\frac{\theta}{2})\\ \end{align}

Example with Increase in Conductor Tension

We will use the data in the previous example to illustrate the effect of wind on the conductor tension. Let us assume that we have a line angle of 15 degrees and consider only the Phase A conductor.

The initial conditions are the following:

Initial Conditions:
Initial Horizontal Tension25% RTSNewton
Initial Conductor Temperature15deg C

The Phase A conductor has the following properties.

Code WordCondor
Size795 MCM ACSR
Stranding54/7
Rated Tensile Strength (RTS)12954.5 kg
Unit Weight1.527 kg/m
Cross-sectional Area0.0004548 m^2
Diameter0.0278 m
Final Modulus of Elasticity59 GPa
Coefficient of Thermal Expansion0.0000193 / deg C

For Rule250B (Light Loading District)

It must withstand the following loads:

Rule 250B (Light Loading District)
Radial Ice Thickness (Table 250-1)0 mm0 inches
Wind Pressure (Table 250-1)430 Pa9 lb/ft^2
Temperature (Table 250-1)-1 deg C30 deg F

The result of the sag-tension calculation showed that the horizontal conductor tension was significantly increased by 8,987.5 N. See the full result here.

Sag and Tension Result for Rule 250B (Light Loading District)
Initial ConditionFinal Condition
Horizontal Tension31,771 N40,758.5 N
Resultant Transverse Load8,294 N10,640 N

For Rule 250C (Extreme Wind)

For Rule 250C, we need to calculate first the wind pressure while taking into account the Kz, GRF, Cf, and Importance Factor. These parameters were already found in the previous post. Hence,

Calculation of Wind Pressure for Phase A Conductor
Height Above GLKzGRFICfVWind Pressure (Pa)
ftm/s=0.613*Kz*GRF*I*Cf*V^2
Phase A65.51.20.751.01.0632,189.7

Hence, the final loading for this load case is the following:

Rule 250C (Extreme Wind)
Radial Ice Thickness (Table 250-1)0 mm0 inches
Wind Pressure (Calculated Above)2,189.7 Pa45.7 lb/ft^2
Temperature (Table 250-1)15 deg C60 deg F

The result of the sag-tension calculation showed that the horizontal conductor tension was significantly increased by 32,496.5 N. See the full result here.

Sag and Tension Result for Rule 250C (Extreme Wind)
Initial ConditionFinal Condition
Horizontal Tension31,771 N64,267.5 N
Resultant Transverse Load8,294 N16,777 N

For Rule 250D (Extreme Ice with Concurrent Wind)

Again, using the loading found in the previous post we have the following:

Rule 250D (Extreme Ice with Concurrent Wind)
Radial Ice Thickness (Figure 250-3)0 mm0 inches
Wind Pressure (Figure 250-3)110 Pa2.3 lb/ft^2
Temperature (Table 250-1)-10 deg C15 deg F

The result of the sag-tension calculation showed that the horizontal conductor tension was significantly increased by 9,223.8 N. See the full result here.

Sag and Tension Result for Rule 250D (Extreme Ice with Concurrent Wind)
Initial ConditionFinal Condition
Horizontal Tension31,771 N40,994.8 N
Resultant Transverse Load8,294 N10,701.8 N

In Conclusion,

The following table summarizes the effect on conductor tension with respect to the four load cases. Extreme wind load case has the highest effect on the resultant transverse load due to the increase in conductor tension.Hence, this highest value must be used for the loading analysis of the structure.

Summary of Different Load Cases Effect on Conductor Tension
InitialRule 250BRule 250CRule 250D
Horizontal Tension31,771 N40,758.5 N64,267.5 N40,994.8 N
Resultant Transverse Load8,294 N10,640 N16,777 N10,701.8 N

In this article we had laid out the foundation for the next example.

2 comments

  1. HELLO,Sir dear
    We know that the initial tension can be calculated by the cubic equation,how can we calculate tension after loading & after creep ?
    note: i have IEEE Std 80- 2013

    1. Hi Sir, including plastic deformations (after load/creep) is quite complex because you need to factor in the conductor stress-strain-creep curves. I haven’t figured it out yet. Rest assured, I will share it on this blog once I have the spreadsheet.

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