The task is to perform mechanical calculation of АС-120 wire with the span of _{}, for an overhead power transmission line of 110 kV in the III area for ice and in the III area for wind with the following temperatures:

_{}

_{}

_{}

The sectional area of aluminum part is, _{}; the sectional area of steel part is, _{}; the overall sectional area of the wire is, _{}; the diameter of the wire is, _{}; the weight of 1km of the wire equals 492 kg (_{}).

Specific loads (1…7):

1. Own-weight load of the wire

_{}

2. Ice-weight load (the ice on the wire is shaped cylindrically).

_{}_{}- unit weight of ice. _{}

_{}- ice thickness (is taken from table 1-5 of Krukov K.P., Novgorodtsev B.P. Constructions and Mechanical Calculation of Power Transmission Line, p. 27, hereinafter Krukov).

3. Wire-and-ice-weight load.

_{}

4. Wind-pressure-no-ice load. The value for _{}(wind pressure)_{}is taken from the table (Krukov, p. 25).

The value for _{} ((coefficient of unevenness) is acquired by interpolation. _{}(Krukov, p. 31).

The value for _{}(aeriodynamic coefficient) is also taken from the table (Krukov, p.30). _{}

Interpolation of _{}: The values of _{} for _{}Based on them we find the actual value of _{}.

_{} - based on wind pressure.

_{} - based on wind velocity _{}

_{}

5. Wind-pressure-with-ice load.

_{} In case of ice accumulation, _{} (Krukov, p.31). _{} remains unxhanged.

_{}

6. Wind-pressure-no-ice load.

_{}

7. Wind – with-ice load.

_{}

Now we can define critical spans.

The source data are taken from tables.

_{}

_{} (Krukov, p.52).

_{}

Permissible tension:

_{}

_{}

_{} (Krukov, p.51).

_{}

The data for “n”- and “m”-conditions are selected from the table given in theoretical part. We also select the loads that should be accounted, based on the task.

_{}

_{}

_{}

As a result, we have a case when _{}.

The second critical span will be the reference value (_{}) (See Theory).

In our case _{}, i.e. _{}.

Thus, the reference conditions will be the ones of maximum loads (ice).

To define the maximum sag of the wire, one needs to define the tension in the wire at different atmospheric conditions.

The calculation is performed based on the equation of the wire state (see Theory).

_{} where:

_{} - tension in the wire material at changing atmospheric conditions (see Theory).

_{} - actual (given) span length.

_{} - the load for each combination of atmospheric conditions (see Theory).

_{} - modulus of elasticity.

_{} - compared tension in the wire material. In this case we have ice accumulation; according to this tension:

_{} - load at compared atmospheric conditions - _{} - in our example.

_{} - correspondingly, in our example – the temperature for ice accumulation (-5ºС).

_{} - the temperature for corresponding combination of atmospheric (climatic) conditions..

We will take each combination of climatic conditions one by one and define the tension in the wire, comparing it to “m”-conditions of ice accumulation.

**I****st combination** (wires are covered with ice; _{} (wind pressure)).

_{}

From our previous calculation, the reference condition – ice accumulation, i.e.

_{}

**II****nd combination **(wires are covered with ice, no wind; _{})

Compare all the combinations with the conditions for ice accumulation (“m”-conditions)

_{}

_{}

_{}

_{}

Solve this cubic equation with the help of slide-rule (Krukov, p.49).

_{} _{}

_{}

_{}

_{} _{}

**III****rd combination **(wind pressure - _{} no ice)

_{}

_{}

_{} (the same).

_{} (the same); _{}

_{} _{}.

**IV**** th combination (no ice, no wind; average annual temperature** -

In our example _{}

_{}

_{}

_{} (the same).

_{}

**V****th combination**** **(_{} no ice or wind).

_{}

_{}

_{} (the same).

_{}

**VI****th combination**** **(_{} - minimum temperature mode; no ice or wind).

_{}

_{}

_{} (the same).

_{}

**VII****th combination**** **(_{} - maximum temperature mode; no ice or wind).

_{}

_{}

_{} (the same).

_{}

Now we are able to define the sag. We are interested in maximum sag (to define the height of supports).

The maximum sag could occur in two possible cases: in case of ice accumulation (maximum load) without wind; in case of lowest tension in the wire at conditions of the first specific load _{}, i.e. at maximum temperatures.

Define the sag in case of ice accumulation without wind (no horizontal deflection of the wire) – possible condition for maximum sag.

1. For our example (from the table, see Theory), define the specific load_{} (2nd combination of climatic conditions).

The tension for the calculation should also be taken from the 2nd combination of climatic conditions from the previous calculation.

_{}

_{} _{}

2. Define the sag at the lowest tension in the wire, maximum temperatures mode – which is also a possible condition of maximum sag.

This would be the 7th combination of climatic conditions.

_{}

_{}

From these two possible values, the bigger sag will occur at the 2nd combination of climatic conditions.

**So**, _{}

The sag will be less at different combinations of conditions.

When we know the sag, we can select a standard-height support.

GOOD LUCK!