# Basic data on mechanical calculation of wires

### Source conditions for mechanical calculation of wires

The Rules state three permissible values for tension (at average annual conditions, for maximum loads and for lowest temperature).

The maximum tension could appear either at low temperatures or at maximum loads. They do not coincide in time. Average annual loads (vibration) are essential as well. They do not coincide in time either.

We can solve the question of which one of these values for tension is the reference value based on the notion of critical span.

The notion of critical span could be illustrated by the example of the lowest temperatures and maximum load (combination of these conditions, when the maximum tension could be observed).

Based on the equation of the wire state, the biggest change of tension in the wire material is influenced by the length of the span. (approaches zero, small span).

Let is insert the value of the span length in the equation of the wire state Thus, the tension is defined by the temperature and the maximum tension in the wire will be observed at lowest temperatures. (approaches infinity, large span).

Let us divide all the members of the wire state equation by . So, we have: Thus the maximum tension in the wire material is observed at maximum loads.

It is obvious, that between small spans and large spans there will be some average span, that will be simultaneously defined by maximum loads and lowest temperatures.

This would be a critical span (second critical span)

The critical span should be compared to an actual span.

If , the reference value for tension will be the permissible tension for maximum load conditions (ice accumulation). .

If , the reference values for tension will be the tension at lowest temperatures.

The reference permissible tension could be sorted out from EIR or Technical Conditions for wires, and from reference catalogs.

The right part of the equation for the wire state will be defined and the reference conditions will be sorted out.

The Rules state the reference permissible tension at average annual conditions.

The span in which the maximum tension in the wire material will be observed at low temperatures and average annual temperatures is known as the first critical span .

The span in which the maximum tension will be observed ant average annual conditions and maximum loads is called the third critical span .

Thus, we should define the three critical spans. We could comprise the following table:

 n m         н – lowest temperature, г – maximum load (ice), с – average annual conditions.

The expression for defining the critical span could be deduced from the equation of the wire state: . СWhich is fair both for mono metal wires and for composite wires (which means that the calculation is applicable for self-supporting insulated wires as well as for self-supporting fiber optic communication cables)

All the three critical spans are defined based on this expression.

Let us consider the physical sense of the critical spans and their co-relation based on dependencies between average annual conditions and the span length at lowest temperatures and in case of ice accumulation. Based on the equation of the wire state:   - the right part is known at the lowest - the right part is known in case of ice accumulation;

At the same time, the span length is changes. The critical spans are obvious.

The operating zone is cross-hatched.

If the span length is changed from 0 to the reference conditions will be the lowest temperatures; from to - average annual conditions; from to - ice accumulation.

For such conditions span will not have physical sense (one could do without it). The curves’ positioning could be different depending on particular combinations of climatic conditions.  - co-relation between the spans. The second critical span  will be the reference span . ( and will not have physical sense in this case). - reference conditions are lowest temperatures; - reference conditions are conditions of ice accumulation (maximum loads).

Critical spans could not have physical sense as virtual values.  - virtual critical span; - does not have physical sense; - reference critical span. - reference conditions – average annual conditions; - reference conditions – ice accumulation.  - virtual critical span; - does not have physical sense; - reference critical span. - reference conditions – average annual conditions; - reference conditions – ice accumulation.  and - virtual critical spans; - does not have physical sense.

In this case, the reference conditions will be average annual conditions for all span lengths.

- These are all the possible combinations of critical spans.

It often happens that there is no need to calculate all the three critical spans. The calculation is usually started from the second critical span ( ).

1.      If , should be calculated .

If , the reference conditions will be the lowest temperatures.

If , the reference conditions will be ice accumulation.

2.      If , one needs to calculate and draw conclusions.

WARNING! The last combination of critical spans is not entirely useless, as some consider at times excluding it from the methodology. Of course, it takes time and pains to calculate it “manually”, but it’s a shame not to calculated it on computer, especially as it turns out to be quite a necessary correlation.

That is all! See an example of manual calculation!