Question

If the length of the span between two level supports is increased by \(20\%\), the sag will increase by approximately

• A. \(20\%\)
• B. \(40\%\)
• C. \(44\%\)
• D. \(50\%\)

Hint:

Sag is proportional to the square of span length. If span becomes \(1.2\) times, sag becomes \(1.44\) times.

Answer 1

The Correct Option is C

Concept: For a transmission line conductor between level supports, sag is approximately: \[ S=\frac{wL^2}{8T} \] where \(L\) is span length.

Step 1: From the sag formula: \[ S\propto L^2 \]

Step 2: If span length is increased by \(20\%\), then: \[ L'=1.2L \]

Step 3: New sag: \[ S'\propto (L')^2 \] \[ S'\propto (1.2L)^2 \] \[ S'=1.44S \]

Step 4: Increase in sag: \[ S'-S=1.44S-S=0.44S \] \[ \text{Percentage increase}=44\% \] Therefore: \[ \boxed{44\%} \]