Span Length Given Vertical Reaction At Supports Calculator

Formula Used:

\[ \text{Cable Span} = \frac{\text{Vertical Reaction at Supports} \times 2}{\text{Uniformly Distributed Load}} \] \[ L_{\text{span}} = \frac{VR \times 2}{q} \]

Cable Span (Lspan):

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1. What is the Cable Span Formula?

The cable span formula calculates the total length of cable in horizontal direction based on the vertical reaction at supports and the uniformly distributed load. This is essential in structural engineering for designing cable-supported structures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_{\text{span}} = \frac{VR \times 2}{q} \]

Where:

\( L_{\text{span}} \) — Cable Span (meters)
\( VR \) — Vertical Reaction at Supports (Newtons)
\( q \) — Uniformly Distributed Load (N/m)

Explanation: The formula calculates the cable span by doubling the vertical reaction at supports and dividing by the uniformly distributed load across the cable.

3. Importance of Cable Span Calculation

Details: Accurate cable span calculation is crucial for designing suspension bridges, cable-stayed structures, overhead power lines, and other cable-supported systems to ensure structural integrity and safety.

4. Using the Calculator

Tips: Enter vertical reaction at supports in Newtons and uniformly distributed load in N/m. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is vertical reaction at supports?
A: Vertical reaction at supports is the total upward force exerted by the supports to balance the downward forces acting on the cable system.

Q2: What is uniformly distributed load?
A: Uniformly distributed load is a load that is evenly distributed along the entire length of the cable, maintaining constant magnitude throughout.

Q3: When is this formula applicable?
A: This formula is applicable for cables with uniformly distributed loads where the cable takes the shape of a parabola and the supports are at the same level.

Q4: Are there limitations to this formula?
A: This formula assumes ideal conditions with perfectly flexible cables, uniform loading, and level supports. It may not account for cable elasticity, temperature effects, or asymmetric loading.

Q5: Can this be used for inclined cables?
A: For inclined cables or supports at different levels, more complex formulas considering the cable's catenary shape may be required.