Span of Cable given Natural Frequency of Each Cable Calculator

✖Fundamental Vibration Mode is integral value denoting the mode of vibration.ⓘ Fundamental Vibration Mode [n]			+10% -10%
✖Natural Frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force.ⓘ Natural Frequency [ω_n]			+10% -10%
✖Cable Tension is the tension on the cable or the structure at a particular point. (if any random points are considered).ⓘ Cable Tension [T]			+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.ⓘ Span of Cable given Natural Frequency of Each Cable [L_span]

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Span of Cable given Natural Frequency of Each Cable Solution

STEP 0: Pre-Calculation Summary

Formula Used

Cable Span = (Fundamental Vibration Mode/(pi*Natural Frequency))*sqrt(Cable Tension*([g]/Uniformly Distributed Load))
L_span = (n/(pi*ω_n))*sqrt(T*([g]/q))
This formula uses 2 Constants, 1 Functions, 5 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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.
Fundamental Vibration Mode - Fundamental Vibration Mode is integral value denoting the mode of vibration.
Natural Frequency - (Measured in Hertz) - Natural Frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force.
Cable Tension - (Measured in Newton) - Cable Tension is the tension on the cable or the structure at a particular point. (if any random points are considered).
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

Fundamental Vibration Mode: 9.9 --> No Conversion Required
Natural Frequency: 5.1 Hertz --> 5.1 Hertz No Conversion Required
Cable Tension: 600 Kilonewton --> 600000 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 = (n/(pi*ω_n))*sqrt(T*([g]/q)) --> (9.9/(pi*5.1))*sqrt(600000*([g]/10000))

Evaluating ... ...

L_span = 14.9882562255015

STEP 3: Convert Result to Output's Unit

14.9882562255015 Meter --> No Conversion Required

FINAL ANSWER

14.9882562255015 ≈ 14.98826 Meter <-- Cable Span

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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National Institute of Technology (NIT), Warangal

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< Cable Systems Calculators

Fundamental Vibration Mode given Natural Frequency of Each Cable

LaTeX Go Fundamental Vibration Mode = (Natural Frequency*pi*Cable Span)/sqrt(Cable Tension)*sqrt(Uniformly Distributed Load/[g])

Span of Cable given Natural Frequency of Each Cable

LaTeX Go Cable Span = (Fundamental Vibration Mode/(pi*Natural Frequency))*sqrt(Cable Tension*([g]/Uniformly Distributed Load))

Natural Frequency of Each Cable

LaTeX Go Natural Frequency = (Fundamental Vibration Mode/(pi*Cable Span))*sqrt(Cable Tension*[g]/Uniformly Distributed Load)

Cable Tension using Natural Frequency of Each Cable

LaTeX Go Cable Tension = ((Natural Frequency*Cable Span/Fundamental Vibration Mode*pi)^2)*Uniformly Distributed Load/[g]

Span of Cable given Natural Frequency of Each Cable Formula

LaTeX Go

Cable Span = (Fundamental Vibration Mode/(pi*Natural Frequency))*sqrt(Cable Tension*([g]/Uniformly Distributed Load))
L_span = (n/(pi*ω_n))*sqrt(T*([g]/q))

What is Cable?

Cables are flexible structures that support the applied transverse loads by the tensile resistance developed in its members. Cables are used in suspension bridges, tension leg offshore platforms, transmission lines, and several other engineering applications.

How to Calculate Span of Cable given Natural Frequency of Each Cable?

Span of Cable given Natural Frequency of Each Cable calculator uses Cable Span = (Fundamental Vibration Mode/(pi*Natural Frequency))*sqrt(Cable Tension*([g]/Uniformly Distributed Load)) to calculate the Cable Span, The Span of Cable given Natural Frequency of Each Cable formula is defined as the total length in the horizontal direction. Cable Span is denoted by L_span symbol.

How to calculate Span of Cable given Natural Frequency of Each Cable using this online calculator? To use this online calculator for Span of Cable given Natural Frequency of Each Cable, enter Fundamental Vibration Mode (n), Natural Frequency (ω_n), Cable Tension (T) & Uniformly Distributed Load (q) and hit the calculate button. Here is how the Span of Cable given Natural Frequency of Each Cable calculation can be explained with given input values -> 14.98826 = (9.9/(pi*5.1))*sqrt(600000*([g]/10000)).

FAQ

What is Span of Cable given Natural Frequency of Each Cable?

The Span of Cable given Natural Frequency of Each Cable formula is defined as the total length in the horizontal direction and is represented as L_span = (n/(pi*ω_n))*sqrt(T*([g]/q)) or Cable Span = (Fundamental Vibration Mode/(pi*Natural Frequency))*sqrt(Cable Tension*([g]/Uniformly Distributed Load)). Fundamental Vibration Mode is integral value denoting the mode of vibration, Natural Frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force, Cable Tension is the tension on the cable or the structure at a particular point. (if any random points are considered) & 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 Span of Cable given Natural Frequency of Each Cable?

The Span of Cable given Natural Frequency of Each Cable formula is defined as the total length in the horizontal direction is calculated using Cable Span = (Fundamental Vibration Mode/(pi*Natural Frequency))*sqrt(Cable Tension*([g]/Uniformly Distributed Load)). To calculate Span of Cable given Natural Frequency of Each Cable, you need Fundamental Vibration Mode (n), Natural Frequency (ω_n), Cable Tension (T) & Uniformly Distributed Load (q). With our tool, you need to enter the respective value for Fundamental Vibration Mode, Natural Frequency, Cable 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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