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.