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Catenary Definition
Updated over 8 months ago

Here the user may choose from various ways to define the stringing of the conductor and the resulting tension and sag. In each case a certain property of the conductor is specified to hold at a defined temperature, and from this property the other properties are derived. For example, the tension, sag, length, etc may be specified.

In all cases, PLP assumes that horizontal tensions will equalise throughout the conductor, between the first and final strain endpoints, using the ruling span method.

A catenary curve is mathematically defined by the catenary constant: C = H/W, and PLP will ultimately use these properties to derive the uniform horizontal tension (and catenary constant) for the conductor.

For conductors with multiple cables (phases), it is possible to define the property to hold across all cables, or to define the property on each cable individually.

It is possible to switch between these methods without affecting the catenary, as PLP will automatically work out the equivalent properties. However, if other changes are made (e.g. changing the design geometry), then the specific property will be held constant, yielding different results depending on what property is being defined.

See below for descriptions of each type of constraint property that may be specified.

HT - Horizontal Tension

This is the simplest constraint. As mentioned above, the horizontal tension is assumed to be constant throughout the conductor at a given temperature, and here the user can specify what that tension is, either directly or as a percentage of the cable’s maximum load.

Example use cases:

  • The user knows or wants to specify the horizontal load that is being applied to a structure, instead of having to work backwards to a tangential tension

  • The user can use this method to validate simple hand tipload calculations. Hand calculation methods typically simplify the cable tension forces on a pole to being just the horizontal component.

MT - Max Tension

This property sets the maximum tangential (axial) tension that will occur anywhere in the conductor (at the defined temperature).

PLP will examine all span endpoints in all cables to find the place where the maximum tension would occur, and sets it to this value. From this, the equivalent horizontal tension is derived.

By definition, as the specified tension is the maximum axial tension on the cable, this method of deriving the catenary curves will be slightly more conservative compared to the HT method. For most cases where the cable does not have a significant sag (i.e. a large vertical component in the tangential tension), HT and MT settings will produce very similar curves, as the horizontal tension is the dominant component of the axial tension.

Example use case:

Most use cases should use the Max Tension property.

S% - ratio of sag to ruling span

This property constrains the vertical sag to be a certain fraction of the horizontal span length. If the span length is changed, the sag fraction will be held constant. For example, setting the sag ratio to 2% will yield a 2m sag for a 100m span, which will grow to 3m if the span is lengthened to 150m.

In these cases, unlike with the tension constraints (HT and MT), the tension may be significantly different for different span lengths.

Given the assumption of equalising tensions, in the case where a conductor has multiple spans of uneven length, it is not possible to constrain them all to the same sag/span ratio. Instead, PLP derives the tension for a hypothetical level span with length equal to the ruling span, as a best-effort compromise. In practice this means:

  • For lengths shorter than the ruling span, the resulting sag to span ratio will be slightly smaller than the specified sag to ruling span ratio.

  • For lengths longer than the ruling span, the resulting sag to span ratio will be slightly larger than the specified sag to ruling span ratio.

If the user needs each span to reflect the sag to span ratio exactly, the conductor should be broken up into individual spans, each strained separately. This can be accomplished with the split tool. This allows the horizontal tensions to be treated as unbalanced under temperature change.

Example use case:

Telecommunications companies typically require stringing to be done in terms of sag/span ratio, instead of a fixed tension.

Len - lock length at horizontal tension

The length of the cable can be fixed. Where a construction has multiple cables, each length of cable must be fixed in accordance to all the available caternery definitions, at the temperature specified.

Because the calculations are highly sensitive to the length, it must be specified for each cable separately. For example, the outer cable on a crossarm with a deviation angle will be longer than the inner cable.

Important caveats:

  • The horizontal tensions are still assumed to equalise, meaning that any structural changes are assumed to be done by putting all conductors on rollers, equalising tensions, and replacing them in their new positions.

  • Pole deflection is not accounted for. As sag is very sensitive to length, this could have a significant impact on the validity of the results. Please consider whether or not the calculation would be conservative in your case.

  • Insulator swing is directly calculated as per AS 7000, but it may be slightly inaccurate for shorter spans. As this could affect the lengths, again it could cause a significant impact. Please consider whether or not the calculation would be conservative in your case.

Stretch in the conductor due to varying tensions is accounted for, so in fact the constrained length may vary slightly as the cable is “stretched” more.

Example use cases

This setting can be used to examine effect on an existing line given various changes, without having to replace the line. For example:

  • Lifting an existing pole top construction on the pole and seeing the effect of this on the cable tension, pole tip load etc.

  • Adding an intermediate pole to a existing span and seeing the effect of this on the cable tension, tip load etc.

Please also see the attachment lift validation report, which provides similar information by simulating lifts on all attachments during construction.

FET- First End-point Tension

The specified tension is the axial/tangential cable tension at the first dead end attached point of the conductor run. This is more conservative than HT, but it could be less conservative than MT if subsequent attach points are at higher angles and thus larger axial/tangential tensions.

Input Field Data

When inputting data from field measurements, the tension derived from the field data is by default defined as the FET.

Tension in Environments

Tensions reported are the maximum tangential tension in any of the cables in the conductor.

Env - each environment case

Nominal - conductor tension with no factors applied

Factored - conductor tension with factors applied. The factors applied are Ft, Fc and Gc.

Env Max - conductor strength derating factor applicable to the environment case, in percentage format

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