Sags & Tensions of Span Attachments

Determining the loads and clearances of the wire and cable attachments on a pole or other structure, is the most important feature to the analysis of any pole or pole line. The tensions, along with the associated wind and ice loads, determine the loads to be applied to the structure and the sags of the attachment. Knowing the sag of the wire or cable will determine ground clearances and mid-span clearances. It is well established and provable that tension and the amount of sag that results are inversely related. As the tension in the wire/cable increases, the amount of sag created is reduced. The reverse is also true. A very approximate relationship has been used for years for a quick estimate of sag or tension, if you know one of the values already:

Where:
W = weight per unit length
L = Span length
T = Tension
D = Sag

Failure to calculate the Sag and Tension accurately is the leading cause of differences in the Analysis Results of Pole Line Design software tools. If you have these values wrong or too far off from being accurate, the loading on the structure will not represent reality. These inaccuracies can lead to undetected overloaded conditions or upgrade recommendations which are simply not necessary. There are considerable differences in how different software tools approach this requirement. Some tools expose to users how they calculate Sags & Tensions, while others provide very little insight (Black Box). Of the tools in use in the Marketplace today, many create inaccurate predictions through the use of the following practices:

1. Ruling Spans. If a tool calculates an average or Ruling Span and applies it to one or more pole spans, it is not calculating exactly what is required. It is making assumptions about how the structures behave in response to unequal span lengths along a pole line under different loading conditions. These assumptions may not be valid. In the case of Joint Use Distribution Pole Lines, this assumption is almost certainly to be inaccurate. More on this later.
2. Pole Elevations. If a tool does not take differences in attachment height elevations into account, the tensions and sags calculated will be inaccurate, period. Elevation differences change the effective span length for the calculations, which changes the tension and sag values that should be used. This will be shown in detail later.
3. Constant Modulus of Elasticity. Several tools in the Marketplace use one value for the major parameter of wires or cables – Modulus of Elasticity. This parameter is similar to a spring constant in the way it relates the amount it stretches with the amount of tension. The reality is that no wire or cable that exists has a purely constant modulus. The modulus (slope of the stress-strain curve) changes as more tension is applied. Failure to recognize this will result in inaccurate results, or the correct result by pure luck. Slack Tension situations would be an exception to this as the tensions are very low on the Stress/Strain curve.
4. Wire Creep ignored. All wires and self-supporting cables in the Marketplace today will permanently stretch when exposed to constant everyday tensions over a long period of time, or as a result of being exposed to extreme loads. In response to this permanent stretching, the tension in the wire or cable will reduce and the sags will increase. This phenomenon has been well-known for several decades and can result in very different results than if it was not considered at all. Failure to consider this effect can lead to significantly inaccurate results. For wires with more than one type of material (Outer/Core) the effects of Creep must be taken into account separately in order to determine the net impact to the wire.
5. Using constant tension values. Some tools require that tensions be pre-determined and entered into a data file for their use. Different tension values are specified for different span lengths and loading criteria for the Loading Analysis stage of their software tool. While there is usually some adjustment to better relate these values to the actual span lengths of the pole line, these can never be as accurate as calculating the Sags & Tensions directly, for the following reasons:
1. The amount of permanent stretch (creep) experienced by the wire/cable is dependent on the actual span length. As mentioned above, this has a significant impact on sag & tension. It is unlikely that a simple interpolation of values between the provided span lengths will produce accurate results.
2. The amount of wind and ice load that must be extracted from the provided span and tension values for proper application to the pole structure for support must be estimated. This can be difficult, especially when the wind is applied at angles different than 90 degrees to the wire or cable.

Whether you are an experienced Pole Line Designer, a Professional Engineer taking responsibility for the work, or someone new to this field, it is important to understand and become completely comfortable with the concepts. With this knowledge you can critique the value of any Sag & Tension result generated by any means.