Catenary Length given Tension at any Point of Simple Cable with UDL Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cable Span = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Uniformly Distributed Load^2))
Lspan = sqrt(((Ts^2)-(Tm^2))/(q^2))
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Cable Span - (Measured in Meter) - Cable Span is total length of cable in horizontal direction.
Tension at Supports - (Measured in Newton) - Tension at Supports is the tension due to loading on supports.
Midspan Tension - (Measured in Newton) - Midspan Tension is the total tension acting in cable at midpoint.
Uniformly Distributed Load - (Measured in Newton per Meter) - Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element.
STEP 1: Convert Input(s) to Base Unit
Tension at Supports: 210 Kilonewton --> 210000 Newton (Check conversion ​here)
Midspan Tension: 4 Kilonewton --> 4000 Newton (Check conversion ​here)
Uniformly Distributed Load: 10 Kilonewton per Meter --> 10000 Newton per Meter (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Lspan = sqrt(((Ts^2)-(Tm^2))/(q^2)) --> sqrt(((210000^2)-(4000^2))/(10000^2))
Evaluating ... ...
Lspan = 20.9961901305927
STEP 3: Convert Result to Output's Unit
20.9961901305927 Meter --> No Conversion Required
FINAL ANSWER
20.9961901305927 20.99619 Meter <-- Cable Span
(Calculation completed in 00.004 seconds)

Credits

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Created by Rithik Agrawal
National Institute of Technology Karnataka (NITK), Surathkal
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NSS College of Engineering (NSSCE), Palakkad
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Catenary Calculators

Catenary Length given Tension at any Point of Simple Cable with UDL
​ LaTeX ​ Go Cable Span = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Uniformly Distributed Load^2))
UDL given Tension at any Point of Simple Cable with UDL
​ LaTeX ​ Go Uniformly Distributed Load = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Cable Span^2))
Horizontal Component given Tension at any Point of Simple Cable with UDL
​ LaTeX ​ Go Horizontal Tension = sqrt((Cable Tension^2)-((Total Load per Unit Length*Catenary Length)^2))
Tension at any Point given Catenary Length of Simple Cable with UDL
​ LaTeX ​ Go Tension at Supports = sqrt((Midspan Tension^2)+(Uniformly Distributed Load*Cable Span)^2)

Catenary Length given Tension at any Point of Simple Cable with UDL Formula

​LaTeX ​Go
Cable Span = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Uniformly Distributed Load^2))
Lspan = sqrt(((Ts^2)-(Tm^2))/(q^2))

What is Cable Span?

Cable Span is the aerial distance between two poles or towers, meaning the physical resistance of the jacket to support its own weight.

How to Calculate Catenary Length given Tension at any Point of Simple Cable with UDL?

Catenary Length given Tension at any Point of Simple Cable with UDL calculator uses Cable Span = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Uniformly Distributed Load^2)) to calculate the Cable Span, The Catenary Length given Tension at any Point of Simple Cable with UDL formula is defined as the total projected horizontal length of the cable. Cable Span is denoted by Lspan symbol.

How to calculate Catenary Length given Tension at any Point of Simple Cable with UDL using this online calculator? To use this online calculator for Catenary Length given Tension at any Point of Simple Cable with UDL, enter Tension at Supports (Ts), Midspan Tension (Tm) & Uniformly Distributed Load (q) and hit the calculate button. Here is how the Catenary Length given Tension at any Point of Simple Cable with UDL calculation can be explained with given input values -> 20.99619 = sqrt(((210000^2)-(4000^2))/(10000^2)).

FAQ

What is Catenary Length given Tension at any Point of Simple Cable with UDL?
The Catenary Length given Tension at any Point of Simple Cable with UDL formula is defined as the total projected horizontal length of the cable and is represented as Lspan = sqrt(((Ts^2)-(Tm^2))/(q^2)) or Cable Span = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Uniformly Distributed Load^2)). Tension at Supports is the tension due to loading on supports, Midspan Tension is the total tension acting in cable at midpoint & Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element.
How to calculate Catenary Length given Tension at any Point of Simple Cable with UDL?
The Catenary Length given Tension at any Point of Simple Cable with UDL formula is defined as the total projected horizontal length of the cable is calculated using Cable Span = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Uniformly Distributed Load^2)). To calculate Catenary Length given Tension at any Point of Simple Cable with UDL, you need Tension at Supports (Ts), Midspan Tension (Tm) & Uniformly Distributed Load (q). With our tool, you need to enter the respective value for Tension at Supports, Midspan Tension & Uniformly Distributed Load and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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