Cable Tension using Natural Frequency of Each Cable Calculator

✖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 Span is total length of cable in horizontal direction.ⓘ Cable Span [L_span]			+10% -10%
✖Fundamental Vibration Mode is integral value denoting the mode of vibration.ⓘ Fundamental Vibration Mode [n]			+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 Tension is the tension on the cable or the structure at a particular point. (if any random points are considered).ⓘ Cable Tension using Natural Frequency of Each Cable [T]

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Cable Tension using Natural Frequency of Each Cable Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

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

Variables Used

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).
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 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.
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

Natural Frequency: 5.1 Hertz --> 5.1 Hertz No Conversion Required
Cable Span: 15 Meter --> 15 Meter No Conversion Required
Fundamental Vibration Mode: 9.9 --> No Conversion Required
Uniformly Distributed Load: 10 Kilonewton per Meter --> 10000 Newton per Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = ((ω_n*L_span/n*pi)^2)*q/[g] --> ((5.1*15/9.9*pi)^2)*10000/[g]

Evaluating ... ...

T = 600940.606442682

STEP 3: Convert Result to Output's Unit

600940.606442682 Newton -->600.940606442682 Kilonewton (Check conversion here)

FINAL ANSWER

600.940606442682 ≈ 600.9406 Kilonewton <-- Cable Tension

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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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]

Cable Tension using Natural Frequency of Each Cable Formula

LaTeX Go

Cable Tension = ((Natural Frequency*Cable Span/Fundamental Vibration Mode*pi)^2)*Uniformly Distributed Load/[g]
T = ((ω_n*L_span/n*pi)^2)*q/[g]

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.

What is the natural frequency of a system?

Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving or damping force. The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all parts of the system move sinesuoidally with that same frequency).

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

Cable Tension using Natural Frequency of Each Cable calculator uses Cable Tension = ((Natural Frequency*Cable Span/Fundamental Vibration Mode*pi)^2)*Uniformly Distributed Load/[g] to calculate 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 calculate Cable Tension using Natural Frequency of Each Cable using this online calculator? To use this online calculator 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. Here is how the Cable Tension using Natural Frequency of Each Cable calculation can be explained with given input values -> 0.600941 = ((5.1*15/9.9*pi)^2)*10000/[g].

FAQ

What is Cable Tension using Natural Frequency of Each Cable?

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 and is represented as T = ((ω_n*L_span/n*pi)^2)*q/[g] or Cable Tension = ((Natural Frequency*Cable Span/Fundamental Vibration Mode*pi)^2)*Uniformly Distributed Load/[g]. Natural Frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force, Cable Span is total length of cable in horizontal direction, Fundamental Vibration Mode is integral value denoting the mode of vibration & 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 Cable Tension using Natural Frequency of Each Cable?

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 is calculated using Cable Tension = ((Natural Frequency*Cable Span/Fundamental Vibration Mode*pi)^2)*Uniformly Distributed Load/[g]. To calculate Cable Tension using Natural Frequency of Each Cable, you need Natural Frequency (ω_n), Cable Span (L_span), Fundamental Vibration Mode (n) & Uniformly Distributed Load (q). With our tool, you need to enter the respective value for Natural Frequency, Cable Span, Fundamental Vibration Mode & 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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