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Cable Tension using Natural Frequency of Each Cable Formula

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Cable Tension is the tension on the cable or the structure at a particular point. (if any random points are considered). Check FAQs

T = ({(ω n \cdot \frac{L span}{n} \cdot π)}^{2}) \cdot \frac{q}{[g]}

T - Cable Tension?ω_n - Natural Frequency?L_span - Cable Span?n - Fundamental Vibration Mode?q - Uniformly Distributed Load?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Cable Tension using Natural Frequency of Each Cable Example

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Here is how the Cable Tension using Natural Frequency of Each Cable equation looks like with Values.

Here is how the Cable Tension using Natural Frequency of Each Cable equation looks like with Units.

Here is how the Cable Tension using Natural Frequency of Each Cable equation looks like.

600.9406 = ({(5.1 \cdot \frac{15}{9.9} \cdot 3.1416)}^{2}) \cdot \frac{10}{9.8066}

600.9406kN = ({(5.1Hz \cdot \frac{15m}{9.9} \cdot 3.1416)}^{2}) \cdot \frac{10kN/m}{9.8066m/s²}

600.9406 = ({(5.1 \cdot \frac{15}{9.9} \cdot 3.1416)}^{2}) \cdot \frac{10}{9.8066}

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Cable Tension using Natural Frequency of Each Cable Solution

Follow our step by step solution on how to calculate Cable Tension using Natural Frequency of Each Cable?

FIRST Step Consider the formula

T = ({(ω n \cdot \frac{L span}{n} \cdot π)}^{2}) \cdot \frac{q}{[g]}

Next Step Substitute values of Variables

∴

T = ({(5.1Hz \cdot \frac{15m}{9.9} \cdot π)}^{2}) \cdot \frac{10kN/m}{[g]}

Next Step Substitute values of Constants

∴

T = ({(5.1Hz \cdot \frac{15m}{9.9} \cdot 3.1416)}^{2}) \cdot \frac{10kN/m}{9.8066m/s²}

Next Step Convert Units

∴

T = ({(5.1Hz \cdot \frac{15m}{9.9} \cdot 3.1416)}^{2}) \cdot \frac{10000N/m}{9.8066m/s²}

Next Step Prepare to Evaluate

∴

T = ({(5.1 \cdot \frac{15}{9.9} \cdot 3.1416)}^{2}) \cdot \frac{10000}{9.8066}

Next Step Evaluate

∴

T = 600940.606442682N

Next Step Convert to Output's Unit

∴

T = 600.940606442682kN

LAST Step Rounding Answer

∴

T = 600.9406kN

Cable Tension using Natural Frequency of Each Cable Formula Elements

Variables

Constants

Cable Tension

Cable Tension is the tension on the cable or the structure at a particular point. (if any random points are considered).

Symbol: T

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Cable Tension

Natural Frequency

Natural Frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force.

Symbol: ω_n

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Natural Frequency

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

Fundamental Vibration Mode

Fundamental Vibration Mode is integral value denoting the mode of vibration.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Fundamental Vibration Mode

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

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Cable Systems category

Go Natural Frequency of Each Cable

ω n = (\frac{n}{π \cdot L span}) \cdot \sqrt{T \cdot \frac{[g]}{q}}

Go Span of Cable given Natural Frequency of Each Cable

L span = (\frac{n}{π \cdot ω n}) \cdot \sqrt{T \cdot (\frac{[g]}{q})}

Go Fundamental Vibration Mode given Natural Frequency of Each Cable

n = \frac{ω n \cdot π \cdot L span}{\sqrt{T}} \cdot \sqrt{\frac{q}{[g]}}

How to Evaluate Cable Tension using Natural Frequency of Each Cable?

Cable Tension using Natural Frequency of Each Cable evaluator uses Cable Tension = ((Natural Frequency*Cable Span/Fundamental Vibration Mode*pi)^2)*Uniformly Distributed Load/[g] to evaluate the Cable Tension, The Cable Tension using Natural Frequency of Each Cable formula is defined as tension acting in the cable due to dynamic loading at any point. Cable Tension is denoted by T symbol.

How to evaluate Cable Tension using Natural Frequency of Each Cable using this online evaluator? To use this online evaluator for Cable Tension using Natural Frequency of Each Cable, enter Natural Frequency (ω_n), Cable Span (L_span), Fundamental Vibration Mode (n) & Uniformly Distributed Load (q) and hit the calculate button.

FAQs on Cable Tension using Natural Frequency of Each Cable

What is the formula to find Cable Tension using Natural Frequency of Each Cable?

The formula of Cable Tension using Natural Frequency of Each Cable is expressed as Cable Tension = ((Natural Frequency*Cable Span/Fundamental Vibration Mode*pi)^2)*Uniformly Distributed Load/[g]. Here is an example- 0.600941 = ((5.1*15/9.9*pi)^2)*10000/[g].

How to calculate Cable Tension using Natural Frequency of Each Cable?

With Natural Frequency (ω_n), Cable Span (L_span), Fundamental Vibration Mode (n) & Uniformly Distributed Load (q) we can find Cable Tension using Natural Frequency of Each Cable using the formula - Cable Tension = ((Natural Frequency*Cable Span/Fundamental Vibration Mode*pi)^2)*Uniformly Distributed Load/[g]. This formula also uses Gravitational acceleration on Earth, Archimedes' constant .

Can the Cable Tension using Natural Frequency of Each Cable be negative?

Yes, the Cable Tension using Natural Frequency of Each Cable, measured in Force can be negative.

Which unit is used to measure Cable Tension using Natural Frequency of Each Cable?

Cable Tension using Natural Frequency of Each Cable is usually measured using the Kilonewton[kN] for Force. Newton[kN], Exanewton[kN], Meganewton[kN] are the few other units in which Cable Tension using Natural Frequency of Each Cable can be measured.

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Cable Tension using Natural Frequency of Each Cable Formula

Cable Tension using Natural Frequency of Each Cable Example

Cable Tension using Natural Frequency of Each Cable Solution

Cable Tension using Natural Frequency of Each Cable Formula Elements

Other formulas in Cable Systems category

How to Evaluate Cable Tension using Natural Frequency of Each Cable?

FAQs on Cable Tension using Natural Frequency of Each Cable

Variable Name