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

✖Tension at Supports is the tension due to loading on supports.ⓘ Tension at Supports [T_s]			+10% -10%
✖Midspan Tension is the total tension acting in cable at midpoint.ⓘ Midspan Tension [T_m]			+10% -10%
✖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.ⓘ Uniformly Distributed Load [q]			+10% -10%

✖Cable Span is total length of cable in horizontal direction.ⓘ Catenary Length given Tension at any Point of Simple Cable with UDL [L_span]

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Formula

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

Formula

`"L"_{"span"} = sqrt((("T"_{"s"}^2)-("T"_{"m"}^2))/("q"^2))`

Example

`"20.99619m"=sqrt(((("210kN")^2)-(("4kN")^2))/(("10.0kN/m")^2))`

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Download General Relation for Suspension Cables Formulas PDF

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))
L_span = sqrt(((T_s^2)-(T_m^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

L_span = sqrt(((T_s^2)-(T_m^2))/(q^2)) --> sqrt(((210000^2)-(4000^2))/(10000^2))

Evaluating ... ...

L_span = 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)

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< 4 Catenary Calculators

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

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

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

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

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

Cable Span = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Uniformly Distributed Load^2))
L_span = sqrt(((T_s^2)-(T_m^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 L_span 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 (T_s), Midspan Tension (T_m) & 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 L_span = sqrt(((T_s^2)-(T_m^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 (T_s), Midspan Tension (T_m) & 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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