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Uniformly Distributed Load Unit Length given Static Deflection Calculator

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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 maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.ⓘ Static Deflection [δ]			+10% -10%
✖Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.ⓘ Moment of inertia of shaft [I_shaft]			+10% -10%
✖Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%

✖Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.ⓘ Uniformly Distributed Load Unit Length given Static Deflection [w]

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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 force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.
Static Deflection - (Measured in Meter) - Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.
Moment of inertia of shaft - (Measured in Kilogram Square Meter) - Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.
Length of Shaft - (Measured in Meter) - Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating 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: 1.085522 Kilogram Square Meter --> 1.085522 Kilogram Square Meter No Conversion Required
Length of Shaft: 3.5 Meter --> 3.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

w = (δ*384*E*I_shaft)/(5*L_shaft^4) --> (0.072*384*15*1.085522)/(5*3.5^4)

Evaluating ... ...

w = 0.600000245017909

STEP 3: Convert Result to Output's Unit

0.600000245017909 --> No Conversion Required

FINAL ANSWER

0.600000245017909 ≈ 0.6 <-- Load per unit length

(Calculation completed in 00.020 seconds)

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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

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< 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 -> 0.6 = (0.072*384*15*1.085522)/(5*3.5^4).

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 maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness, Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations, Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations & Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating 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)

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