Tension At Any Point Given Catenary Length Of Simple Cable With UDL Calculator

Formula Used:

\[ Tension\ at\ Supports = \sqrt{(Midspan\ Tension^2)+(Uniformly\ Distributed\ Load \times Cable\ Span)^2} \] \[ T_s = \sqrt{(T_m^2)+(q \times L_{span})^2} \]

Tension at Supports (T_s):

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1. What is Tension at Supports?

Tension at Supports refers to the total tension force acting on the cable supports due to the combined effects of midspan tension and the uniformly distributed load along the cable span. It is a critical parameter in cable structure design and analysis.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ T_s = \sqrt{(T_m^2)+(q \times L_{span})^2} \]

Where:

\( T_s \) — Tension at Supports (N)
\( T_m \) — Midspan Tension (N)
\( q \) — Uniformly Distributed Load (N/m)
\( L_{span} \) — Cable Span (m)

Explanation: The formula calculates the resultant tension at supports by considering both the midspan tension and the effect of uniformly distributed load over the cable span.

3. Importance of Tension Calculation

Details: Accurate tension calculation is crucial for structural design, ensuring cable systems can withstand applied loads, determining support requirements, and maintaining structural integrity and safety.

4. Using the Calculator

Tips: Enter midspan tension in Newtons, uniformly distributed load in Newtons per meter, and cable span in meters. All values must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between midspan tension and tension at supports?
A: Midspan tension is the tension at the center of the cable, while tension at supports includes the additional component from the uniformly distributed load acting along the cable span.

Q2: When is this formula applicable?
A: This formula is applicable for simple cables with uniformly distributed loads where the cable forms a catenary shape and the supports are at the same elevation.

Q3: What units should be used for input values?
A: Use Newtons (N) for tension, Newtons per meter (N/m) for distributed load, and meters (m) for cable span length.

Q4: Are there limitations to this calculation?
A: This calculation assumes ideal conditions with uniformly distributed load, flexible cable, and supports at the same level. It may not account for additional factors like wind loads, temperature effects, or support flexibility.

Q5: How accurate is this calculation for real-world applications?
A: While this provides a good theoretical estimate, real-world applications may require additional safety factors and consideration of environmental conditions for precise engineering design.