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

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Cable Span is total length of cable in horizontal direction. Check FAQs

L span = \sqrt{\frac{({T s}^{2}) - ({T m}^{2})}{q^{2}}}

L_span - Cable Span?T_s - Tension at Supports?T_m - Midspan Tension?q - Uniformly Distributed Load?

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

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Here is how the Catenary Length given Tension at any Point of Simple Cable with UDL equation looks like with Values.

Here is how the Catenary Length given Tension at any Point of Simple Cable with UDL equation looks like with Units.

Here is how the Catenary Length given Tension at any Point of Simple Cable with UDL equation looks like.

20.9962 = \sqrt{\frac{(210^{2}) - (4^{2})}{10^{2}}}

20.9962m = \sqrt{\frac{({210kN}^{2}) - ({4kN}^{2})}{{10kN/m}^{2}}}

20.9962 = \sqrt{\frac{(210^{2}) - (4^{2})}{10^{2}}}

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

Follow our step by step solution on how to calculate Catenary Length given Tension at any Point of Simple Cable with UDL?

FIRST Step Consider the formula

L span = \sqrt{\frac{({T s}^{2}) - ({T m}^{2})}{q^{2}}}

Next Step Substitute values of Variables

∴

L span = \sqrt{\frac{({210kN}^{2}) - ({4kN}^{2})}{{10kN/m}^{2}}}

Next Step Convert Units

∴

L span = \sqrt{\frac{({210000N}^{2}) - ({4000N}^{2})}{{10000N/m}^{2}}}

Next Step Prepare to Evaluate

∴

L span = \sqrt{\frac{(210000^{2}) - (4000^{2})}{10000^{2}}}

Next Step Evaluate

∴

L span = 20.9961901305927m

LAST Step Rounding Answer

∴

L span = 20.9962m

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

Variables

Functions

Cable Span

Cable Span is total length of cable in horizontal direction.

Symbol: L_span

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Cable Span

Tension at Supports

Tension at Supports is the tension due to loading on supports.

Symbol: T_s

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Tension at Supports

Midspan Tension

Midspan Tension is the total tension acting in cable at midpoint.

Symbol: T_m

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Midspan Tension

Uniformly Distributed Load

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.

Symbol: q

Measurement: Surface TensionUnit: kN/m

Note: Value can be positive or negative.

Formulas to find Uniformly Distributed Load

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.

Syntax: sqrt(Number)

Other formulas in Catenary category

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

T s = \sqrt{({T m}^{2}) + {(q \cdot L span)}^{2}}

Go Horizontal Component given Tension at any Point of Simple Cable with UDL

H = \sqrt{(T^{2}) - ({(W' \cdot s)}^{2})}

Go UDL given Tension at any Point of Simple Cable with UDL

q = \sqrt{\frac{({T s}^{2}) - ({T m}^{2})}{{L span}^{2}}}

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

Catenary Length given Tension at any Point of Simple Cable with UDL evaluator uses Cable Span = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Uniformly Distributed Load^2)) to evaluate 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 evaluate Catenary Length given Tension at any Point of Simple Cable with UDL using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Catenary Length given Tension at any Point of Simple Cable with UDL?

The formula of Catenary Length given Tension at any Point of Simple Cable with UDL is expressed as Cable Span = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Uniformly Distributed Load^2)). Here is an example- 20.99619 = sqrt(((210000^2)-(4000^2))/(10000^2)).

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

With Tension at Supports (T_s), Midspan Tension (T_m) & Uniformly Distributed Load (q) we can find Catenary Length given Tension at any Point of Simple Cable with UDL using the formula - Cable Span = sqrt(((Tension at Supports^2)-(Midspan Tension^2))/(Uniformly Distributed Load^2)). This formula also uses Square Root (sqrt) function(s).

Can the Catenary Length given Tension at any Point of Simple Cable with UDL be negative?

No, the Catenary Length given Tension at any Point of Simple Cable with UDL, measured in Length cannot be negative.

Which unit is used to measure Catenary Length given Tension at any Point of Simple Cable with UDL?

Catenary Length given Tension at any Point of Simple Cable with UDL is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Catenary Length given Tension at any Point of Simple Cable with UDL can be measured.

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

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

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

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

Other formulas in Catenary category

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

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

Variable Name