Tension At Midspan Given Tension At Supports For Udl On Parabolic Cable Calculator

Formula Used:

\[ T_{mid} = \sqrt{(T_s^2) - \left(\left(\frac{q \cdot L_{span}}{2}\right)^2\right)} \]

Tension at Midspan (Tmid):

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1. What is Tension at Midspan?

Tension at midspan refers to the total tension acting in a cable at its midpoint. For a parabolic cable under uniformly distributed load, this tension is calculated based on the tension at supports, distributed load, and cable span.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_{mid} = \sqrt{(T_s^2) - \left(\left(\frac{q \cdot L_{span}}{2}\right)^2\right)} \]

Where:

\( T_{mid} \) — Tension at midspan (N)
\( T_s \) — Tension at supports (N)
\( q \) — Uniformly distributed load (N/m)
\( L_{span} \) — Cable span (m)

Explanation: This formula calculates the tension at the midpoint of a parabolic cable by considering the equilibrium of forces and the geometric properties of the cable under uniform loading.

3. Importance of Tension Calculation

Details: Accurate tension calculation is crucial for cable structure design, ensuring structural integrity, determining appropriate cable specifications, and preventing failure due to overloading.

4. Using the Calculator

Tips: Enter tension at supports in Newtons, uniformly distributed load in N/m, and cable span in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a parabolic cable?
A: A parabolic cable is a cable that takes the shape of a parabola under uniformly distributed load, commonly used in suspension bridges and cable-supported structures.

Q2: Why is tension different at midspan than at supports?
A: The tension varies along the cable due to the vertical component of force caused by the distributed load, with maximum tension typically occurring at the supports.

Q3: What assumptions are made in this calculation?
A: This calculation assumes ideal parabolic shape, uniform load distribution, perfectly flexible cable, and negligible cable weight compared to the applied load.

Q4: Can this formula be used for non-uniform loads?
A: No, this specific formula is derived for uniformly distributed loads only. Different formulas apply for concentrated or varying loads.

Q5: How does cable sag affect the tension?
A: Cable sag is inherently considered in the parabolic shape assumption. Greater sag typically results in lower tension at midspan for the same span and load conditions.