General Order 64-A
(a) Basis of Curves.
(1) Heavy Loading Areas – Giving minimum sags under normal conditions (60° F., no wind or ice loading) to which conductors may be strung so that when loaded with specified loads (weight of conductor plus layer of ice ½ inch in radial thickness, with horizontal wind pressure of 6 pounds per square foot of projected area, at 0° F.), the total tension will not exceed one-half the assumed ultimate breaking strength of the conductors. (Sec. IV, Rule 43.)
(2) Light Loading Areas – Giving minimum sags under normal conditions (60° F., no wind or ice loading) to which conductors may be strung so that when loaded with specified loads (weight of conductor plus horizontal wind pressure of 8 pounds per square foot of projected area, at 25° F.), the total tension will not exceed one-half the assumed ultimate breaking strength of the conductors.
(b) Sags for Unequal Spans, Level Supports and
When a crossing span and adjoining spans are of different lengths it is not possible to string the conductors so as to make both the normal tension and the loaded tension balance in the several spans. This condition should be met by selecting a sag for the longest span not less than that shown in the accompanying curves.
The sags for the other spans should then be determined as follows: For each span multiply the sag for the longest span by the square of the ration of the length of the span under consideration to that of the longest span. The total normal tension in each of the spans will then balance and the total tension under loaded conditions will be slightly less in the short spans than in the longest span.
A crossing span length of 250 feet – Heavy
Adjoining spans of 3000 feet and 200 feet, respectively.
Conductors No. 0, A.W.G. copper, medium hard drawn stranded, bare.
Sag from curve (Curve 1), for a 300-foot span is 4.90 feet.
Making the sags in the other spans proportional to the squares of their lengths, the sag in the 250-foot span will be,
The sag in the 200-foot span will be,
(c) Sag Correction for Temperature.
The curves (Curves 9 and 10), cover the correction of sags for string temperatures other than that for which the sag curves were calculated. These figures cover the normal range of stringing conditions for temperatures at time of stringing, varying between 0°F. and 130°F., and for spans of from 100 feet to 1000 feet, inclusive, in 100-foot steps, with the exception that the 150-foot span has also been included. They represent average values for each degree F. difference between actual stringing temperature and the temperature for which the curves were calculated; that is 60° F. The corrections for temperatures greater than 60° F. are to be added to the normal sags while the corrections for temperatures less than 60° F. are to be subtracted. The correction for a given difference of temperature from the base value is considered the same whether the stringing temperature is greater or less than the base value.
The use of these correction may be illustrated by assuming a specific case:
A span of 300 feet – Heavy Loading
Conductors No. 0, A.W.G. copper, medium hard drawn, stranded, bare.
Stringing temperature 80° F.
Minimum normal sag, Curve 1, is 4.90 feet.
Difference between stringing temperature and normal temperature is 20° F.
The ration for sag divided by span is 0.0163. From the curve (Curve 9), the correction per degree F. for this ration a span of 300 feet is 0.024 feet.
Then the corrected sag is 4.90+0.48 equals 5.38 feet. If some other span than those covered by specific curves.
(d) Sags for Supports at Different Elevations.
The sag curves have been based on the supports being at the same elevation. This condition is not always possible. The curve (Curve 11) covers the correction of the sag to care for this condition.
The use of this correction may be best illustrated by taking a concrete case:
A span of 300 feet – Heavy Loading
A difference in level of supports 5 feet.
Conductors No. 0 A.W.G copper, medium hard drawn, stranded, bare.
The curve, page xxx, requires a sag of 4.90 feet.
The ratio of difference in level of supports divided by the sag is 5.0 divided by 4.90 equals 1.02 which is the ratio marked h/S on curve, (Curve 1). The multiplier C for this ration is 0.55. Therefore the sag below the lower point of support is,
If the sag
is to be measured from the higher support, the sag below the lower support may
be obtained as above and the difference in elevation of supports added thereto
or the sag below the higher support is 2.70 + 5.00 equals 7.70 feet. The difference of levels may be such that
the resultant pull is upward at the lower support; that is, the lowest point in
the span is at the support. To cover
this condition, and also as an alternative method of solving cases like that just
considered, use may be made of the following approximate rule which is
sufficiently accurate for all ordinary situations:
The apparent sag, or the vertical distance between a straight line joining supports and the tangent to the span, parallel thereto, equals the sag for a normal span of the same length.
(e) Determination of Amount of Sag for Various
Points in a Span.
The sag curves (Curves 1 to 8) show for wires of different sizes and materials the value of the center sag at which these wires should be strung under normal conditions to have the assumed factors of safety under the designated loaded conditions. At times it is desirable to know, not only the amount of sag at the center of the span, but also the amount of sag at some other point in the span.
This is necessary, for example, in obtaining the clearance over other wires where the point of crossing between the crossing span and the wires crossed, occurs, not at the center of the crossing span, but at some other point.
On Curve 12 a curve is given by means of which, given the amount of center sag, the amount of the sag at any other point in the span can be determined. This curve gives the value of the sag at all points on the catenary curve, expressed in percent of the center sag. The used of this curve is shown by the following example:
A span of 300 feet – Heavy Loading
A center sag, determined from the sag curves of 4.90 feet.
The crossing span crosses over a Class “S” line, on which the top wire at the point of this crossing has an elevation of 25 feet.
This point of crossing to be 105 feet from the nearest support of the crossing conductor, and a minimum vertical clearance of 6 feet is required at the point of crossing.
Required - At what height must the crossing conductor
be supported in order that this required vertical clearance shall be obtained?
As the span length is 300 feet, and the distance from the nearest support to the point of crossing is 105 feet, this distance is 35 percent of the span length. From the curve (Curve 12)the value of the sag at this point is 91 percent of the center sag.
Therefore, the required elevation of the crossing conductor at its point of support s equal to the height of the Class “S” wires crossed (25 feet), plus the minimum vertical clearance required (6 feet), plus the sag of the conductor at the point of crossing (4.46 feet).