Sag & Tension

Sag and tension calculations for conductor earth wire are done for the river crossing by following steps :

1. Determination of Equivalent Span :Based on anchor spans L₁ & L₃ and crossing span L₂, the equivalent span for river crossing portion is determined by the following formula :
   Eq. Span = ÖL₁³ + L₂³ + L₃³ / L₁   + L₂   + L₃ (Refer Figure 10-II)
    
2. Sag and tension calculation for conductor/earth wire for above equivalent span is done from the following formula :T² (T - K + aEa (q₂-q₁)) = W² L² aE / 24 x q²where,
   T = Tension at temperature q₂ (kg)
   K= Constant
   a = Area of conductor/Earth wire (mm²)
   E = Modulus of Elasticity kg/mm²a = Linear Coeft. of expansion (per degree celcius)
   W = weight of conductor (kg/m)
   L = Equivalent span (m)
   q = Wind load factor = P² + W² / W² = 1 (At no wind condition)
   q₁ = Initial condition temperature
   
   
3. Calculation for conductor

1. Initial condition for conductor is taken as 32°C and No wind and T₀ tension under these conditions is taken as 22% of ultimate tensile strength of conductor.
2. From the above value of T₀, we calculate the constant 'K which is fixed for all further sag-tension calculations.
3. Considering the calculated value of K, the tension at 0°C under No-wind & full wind and 32°C full wind and 75°C No-wind is determined from the above formula by hit & trial method.
4. Sag at various tension :
   = WL_A² / 8T  where L_A is actual span

4. Calculation for Earth wire

1. The earth wire sag at 0°C and no-wind should be 90% of the Conductor sag at 0°C and No-wind. Value of tension at 0° and no wind is determined by the following formula
   T = {WL² / 0.9 x Sag of Conductor at 0⁰N/W}
   for equivalent span
   where L = Equivalent span in meters.
2. As in the case of conductor, the tensions at 0°C (No-wind & full wind Condition), 32"C full wind conditions and 75°C no-wind condition are determined.
3. Sag = [WL_A² / 8T_A] where L_A = Actual span.

Ruling Span

The Ruling Span is defined as the assumed uniform span that most likely represents actual spans that are in any particular section of the line. In the absence of finite element analysis tools or software (ex. PLS CADD), the ruling span is used to calculate sag and clearances on the plan profile drawing, and it is necessary in structure spotting.

Ruling Span Tip: When stringing the line, the general rule is that the spans in the line should not be more than twice the ruling span, or less than half of the ruling span.

Ruling Span is one of the most used yet misunderstood and misused terms in the design, staking, and construction of overhead lines. “Ruling span” is loosely used with several different meanings.

Theoretical Ruling Span: It is the equation derived from the conductor length equation and by making certain assumptions, approximations, and formula substitutions. This formula must be used if the actual spans are already known.

 

The theoretical ruling span equation is not exact because of the assumptions made. Since

its accuracy is sufficient for most line designs, it is the equation used most often to calculate the ruling span for new overhead distribution lines.

Estimated Ruling Span: If the actual spans are not yet determined but knowledge gained from a reconnaissance and previous surveys of the proposed line are known, it is possible to estimate a ruling span. A traditional “rule of thumb” equation that may be helpful in the estimation of a ruling span is:

Se = Average Span + 2/3 (Maximum Span – Average Span)

Use this rule for estimating the ruling span with caution.  Use only this formula if the actual spans are not yet known.

What would happen if my ruling span is different from the actual design?

• If the design sag is greater than the theoretical sag, then the actual sag of the installed conductors will be less than the predicted sag. This condition will lead to increased conductor tensions, which may exceed the permitted loads of support structures and guying assemblies.

• If the design sag is less than the theoretical sag, then the actual sag of the installed conductors will be greater than the predicted sag. This condition may result in inadequate ground clearances.