Transmission line sag and slack

Thread Starter

Kayne

Joined Mar 19, 2009
105
Hi all,

I am haven trouble with a question to do with solving the Sag and Slack of a transmission line, I have been starting at this for a while now without any luck.The question is

Using a level-span catenary model, calculate the sag and slack for a 335-m span of ACSR cable having a cable mass per unit length of 1.63 kg / m and a diameter of 2.86 cm.
The load on the cable consists of (i) ice with a uniformly distributed radial thickness of 0.965 cm and (ii) a constant horizontal wind pressure of 383 Pa of total projected area. Take the breaking tension for the cable as 133 kN and use a safety factor of 3.
Take the density of ice as \(915 kg.m^-3\) and gravitational acceleration constant as \(9.81 m.s^-2\)
Neglect thermal and elongation effects.


Span \(S = 335m\)
Mass \(M = 1.63 kg/m\)
diameter \(d = 2.86cm\)
ice radius thickness \(irt = 0.965 cm \)
horizontal wind pressure \(hwp = 383Pa\)
breaking tension \(br = 133kN \)
density of ice \( id = 915 kg.m^-3\)
gravity \(g = 9.81 m.s^-2\)

So I have found that the effects of Ice and Wind loading is

Xsectional area of ice
\(Ai = pi*irt(d+irt) = 1.16*10^-3 m^3\)

Weight of ice per unit lenght of cable
\(Wi = Ai*id*g =10.409 kg\)

projected area per unit lenght of ice covered cable
\(ai=d+2*irt=0.048\)

Horizontal wind force of ice covered cable
\(Fw = hwp*ai=18.346 \)

Resultant force due to wind and ice
\( Fwi = (\sqrt(Fw^2)+\sqrt(M*g+Wi)^2)=32.148\)

Now this is where I am stuck as I need to calculate Sag and slack. Am I on the right path or is there another way I should be solving this??

Any guidance would be a great help

 

t_n_k

Joined Mar 6, 2009
5,455
The effective deflection would presumably be determined from the catenary relationship:

\(D=\frac{T_h}{W} \[ \cosh{\( \frac{SW}{2T_h} \)}-1 \]\)

Where:

\(T_h=\frac{133 \ kN}{3} = 44.333 \ kN \)

Applying a loading safety factor of 3

\(W=32.148 \ N \)

as you have calculated as the effective per meter loading

\(S=335 \ m\)

being the cable span

This effective deflection D may then be resolved into its vertical and horizontal components per the relationship of vertical [ice + cable weight] and horizontal [wind load] force components.
 
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