LCM calculator

Uniformly Distributed Load Unit Length given Static Deflection Calculator

Physics Chemistry Engineering Financial More >>

↳

Mechanical Aerospace Basic Physics Others and Extra

⤿

Theory of Machine Automobile Design of Automobile Elements Design of Machine Elements More >>

⤿

Vibrations Balancing of Rotating Masses Belt, Rope and Chain Drives Brakes and Dynamometers More >>

⤿

Longitudinal and Transverse Vibrations Torsional Vibrations

⤿

Natural Frequency of Free Transverse Vibrations Load for Various Types of Beams and Load Conditions Critical or Whirling Speed of Shaft Effect of Inertia of Constraint in Longitudinal and Transverse Vibrations More >>

⤿

Uniformly Distributed Load Acting Over a Simply Supported Shaft General Shaft Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Shaft Subjected to a Number of Point Loads

✖Static deflection is the extension or compression of the constraint.ⓘ Static Deflection [δ]			+10% -10%
✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.ⓘ Moment of inertia of shaft [I_shaft]			+10% -10%
✖Length of shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%

✖Load per unit length is the distributed load which is spread over a surface or line.ⓘ Uniformly Distributed Load Unit Length given Static Deflection [w]

⎘ Copy

👎

Formula

Reset

👍

Download Longitudinal and Transverse Vibrations Formula PDF PDF Image

Uniformly Distributed Load Unit Length given Static Deflection Solution

STEP 0: Pre-Calculation Summary

Formula Used

Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4)
w = (δ*384*E*I_shaft)/(5*L_shaft^4)
This formula uses 5 Variables

Variables Used

Load per unit length - Load per unit length is the distributed load which is spread over a surface or line.
Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Moment of inertia of shaft - (Measured in Kilogram Square Meter) - Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.
Length of Shaft - (Measured in Meter) - Length of shaft is the distance between two ends of shaft.

STEP 1: Convert Input(s) to Base Unit

Static Deflection: 0.072 Meter --> 0.072 Meter No Conversion Required
Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Moment of inertia of shaft: 6 Kilogram Square Meter --> 6 Kilogram Square Meter No Conversion Required
Length of Shaft: 4500 Millimeter --> 4.5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w = (δ*384*E*I_shaft)/(5*L_shaft^4) --> (0.072*384*15*6)/(5*4.5^4)

Evaluating ... ...

w = 1.21362962962963

STEP 3: Convert Result to Output's Unit

1.21362962962963 --> No Conversion Required

FINAL ANSWER

1.21362962962963 ≈ 1.21363 <-- Load per unit length

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Mechanical » Uniformly Distributed Load Acting Over a Simply Supported Shaft » Uniformly Distributed Load Unit Length given Static Deflection

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

Dipto Mandal has verified this Calculator and 400+ more calculators!

< Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Length of Shaft given Static Deflection

Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)

Uniformly Distributed Load Unit Length given Static Deflection

Go Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4)

Circular Frequency given Static Deflection

Go Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))

Natural Frequency given Static Deflection

Go Frequency = 0.5615/(sqrt(Static Deflection))

Uniformly Distributed Load Unit Length given Static Deflection Formula

Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4)
w = (δ*384*E*I_shaft)/(5*L_shaft^4)

What is transverse and longitudinal vibration?

The difference between transverse and longitudinal waves is the direction in which the waves shake. If the wave shakes perpendicular to the movement direction, it's a transverse wave, if it shakes in the movement direction, then it's a longitudinal wave.

How to Calculate Uniformly Distributed Load Unit Length given Static Deflection?

Uniformly Distributed Load Unit Length given Static Deflection calculator uses Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4) to calculate the Load per unit length, Uniformly Distributed Load Unit Length given Static Deflection formula is defined as a measure of the load per unit length of a shaft in terms of its static deflection, modulus of elasticity, and moment of inertia, providing a crucial parameter in the analysis of transverse vibrations in mechanical systems. Load per unit length is denoted by w symbol.

How to calculate Uniformly Distributed Load Unit Length given Static Deflection using this online calculator? To use this online calculator for Uniformly Distributed Load Unit Length given Static Deflection, enter Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Length of Shaft (L_shaft) and hit the calculate button. Here is how the Uniformly Distributed Load Unit Length given Static Deflection calculation can be explained with given input values -> 1.21363 = (0.072*384*15*6)/(5*4.5^4).

FAQ

What is Uniformly Distributed Load Unit Length given Static Deflection?

Uniformly Distributed Load Unit Length given Static Deflection formula is defined as a measure of the load per unit length of a shaft in terms of its static deflection, modulus of elasticity, and moment of inertia, providing a crucial parameter in the analysis of transverse vibrations in mechanical systems and is represented as w = (δ*384*E*I_shaft)/(5*L_shaft^4) or Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4). Static deflection is the extension or compression of the constraint, Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation & Length of shaft is the distance between two ends of shaft.

How to calculate Uniformly Distributed Load Unit Length given Static Deflection?

Uniformly Distributed Load Unit Length given Static Deflection formula is defined as a measure of the load per unit length of a shaft in terms of its static deflection, modulus of elasticity, and moment of inertia, providing a crucial parameter in the analysis of transverse vibrations in mechanical systems is calculated using Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4). To calculate Uniformly Distributed Load Unit Length given Static Deflection, you need Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Length of Shaft (L_shaft). With our tool, you need to enter the respective value for Static Deflection, Young's Modulus, Moment of inertia of shaft & Length of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Load per unit length?

In this formula, Load per unit length uses Static Deflection, Young's Modulus, Moment of inertia of shaft & Length of Shaft. We can use 2 other way(s) to calculate the same, which is/are as follows -

Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)
Load per unit length = (pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)

Home

FREE PDFs

🔍 Search