Span of Cable given Tension at Supports for UDL on Parabolic Cable Calculator

Formula Used:

\[ \text{Length of Cable Span} = \frac{2 \times \sqrt{(Tension\ at\ Supports)^2 - (Midspan\ Tension)^2}}{Total\ UDL} \]

Length of Cable Span:

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1. What is the Span of Cable given Tension at Supports for UDL on Parabolic Cable?

The Span of Cable given Tension at Supports for UDL on Parabolic Cable is a calculation used in structural engineering to determine the horizontal length of a cable span when subjected to a uniformly distributed load (UDL), forming a parabolic shape. This calculation is essential for designing cable-supported structures like suspension bridges and overhead power lines.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Length of Cable Span} = \frac{2 \times \sqrt{(Tension\ at\ Supports)^2 - (Midspan\ Tension)^2}}{Total\ UDL} \]

Where:

\( Tension\ at\ Supports \) — The tension due to loading on supports (Newton)
\( Midspan\ Tension \) — The total tension acting in cable at midpoint (Newton)
\( Total\ UDL \) — A load that is distributed or spread across the whole region (Newton)

Explanation: This formula calculates the cable span length by considering the difference in tension between the supports and the midspan, divided by the total uniformly distributed load.

3. Importance of Cable Span Calculation

Details: Accurate cable span calculation is crucial for ensuring structural stability, proper load distribution, and safety in cable-supported structures. It helps engineers design systems that can withstand expected loads without failure.

4. Using the Calculator

Tips: Enter tension at supports and midspan tension in Newtons, and total UDL in Newtons. All values must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a uniformly distributed load (UDL)?
A: A UDL is a load that is evenly distributed across the entire length of a structural element, such as a cable or beam.

Q2: Why does the cable form a parabolic shape under UDL?
A: A cable subjected to a uniformly distributed load naturally assumes a parabolic shape due to the equal distribution of weight along its length.

Q3: What are typical applications of this calculation?
A: This calculation is commonly used in the design of suspension bridges, overhead transmission lines, and cable-supported roofs.

Q4: How does tension vary along the cable length?
A: Tension is highest at the supports and lowest at the midspan in a parabolic cable under UDL.

Q5: What factors can affect the accuracy of this calculation?
A: Factors include cable elasticity, temperature changes, wind loads, and the accuracy of tension measurements.