The N.Z. Journal of Science and Technology. 
100 
[Mar. 
is given on pages 4 and 5 of a pamphlet by Mr. E. Parry, entitled Cable 
Spans 3 T 2 | * Y» 2 A. ) xWk 
‘•+1. | 6T -T-l, r 6 
where x = half the span (variable) ; 
q : ratio of loading, in this case — 2*38 ; 
co : weight per unit length — 2-587 lb. per link for copper ; 
A — elastic modulus of wire ; 
T q = tension under extreme loading = 25,000 lb. per square inch ; 
T 0 = tension in the unloaded wire. 
Values of T 0 for different values of x are shown as lines of datum tempera¬ 
ture in figs. 2 and 3. 
The length of wire in a span is subject to three separate variations, due 
to sag, tension, and temperature. 
By equation (4) we have for a level span (we shall show later that slope 
makes no difference) 
( . X 2 ) X 3 . X 3 
s = x 'i 1 + 6? ) =a: + 6? or ( s — *) = 6^ 
s and x refer to half the span reckoning from the apex, 
span we have ^3 
Sag-extension = 2 (s — x) = . 
OC “ 
For the whole 
.(5). 
These values are shown for various spans in fig. 2, curving upwards from 
right to left. 
Elastic Contraction .—As the tension decreases the wire contracts by 
an amount depending on the elastic modulus of copper, which is taken 
as 16 X 10 6 . This contraction is shown in fig. 2, by straight lines from 
the intersection of sag-lines with the line of datum temperature. Now, 
at datum temperature we have equilibrium, the sag-extension, and elastic 
strain balancing. Then the temperature rises and the wires slacken, sag- 
extension increases, and elastic strain decreases. We must still have 
equilibrium, therefore thermal expansion must make up the difference, or 
St = Se -j- Ss. 
Take, for example, an 8-chain span. The tension at datum tempera¬ 
ture is 13,900. If now the temperature rises 90° F., causing an expansion 
of 90 X 800 X 9 X 10 ~ 6 = 0-648 of a link where the coefficient of thermal 
expansion is taken as 9 X 10~ 6 . Take this distance on the scale and slide 
it along the elastic line of 8 chains till it just fits between the elastic and 
sag lines, and thus determine the tension, 10,760, at which the three 
balance. Other points are obtained in the same way, and isothermal lines 
are drawn for 30°, 60°, 90°, and 120° F. 
Fig. 3 shows sag-deflection in feet as ordinates with tension as abscissae, 
the isothermal lines with respect to tension being transferred from fig. 2. 
In using these diagrams we have to estimate the maximum possible 
range of temperature to which the wires will be subjected. Suppose this 
is 90° : then, following up the 90° line where it intersects the span lines 
we read directly the tension and sag-deflection. 
Where suspension insulators are used and spans are not all of the same 
length, owing to longitudinal movement of the point of support, the tension 
will become approximately uniform between anchorages. Since sag-exten¬ 
sion varies as the cube of the span, the tension will tend to approach that 
of the longer span. 
*E. Parry, Cable Spans, Public Works Department, Wellington, N.Z., 1917. 
