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Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load 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

✖Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.ⓘ Load per unit length [w]			+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%
✖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%

✖Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.ⓘ Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load [δ]

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Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Load per unit length: 3 --> No Conversion Required
Length of Shaft: 3.5 Meter --> 3.5 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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = (5*w*L_shaft^4)/(384*E*I_shaft) --> (5*3*3.5^4)/(384*15*1.085522)

Evaluating ... ...

δ = 0.359999852989314

STEP 3: Convert Result to Output's Unit

0.359999852989314 Meter --> No Conversion Required

FINAL ANSWER

0.359999852989314 ≈ 0.36 Meter <-- Static Deflection

(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Length of Shaft given Static Deflection

LaTeX 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

LaTeX 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

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

Natural Frequency given Static Deflection

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

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load Formula

LaTeX Go

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

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 Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load?

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load calculator uses Static Deflection = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft) to calculate the Static Deflection, Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load formula is defined as the maximum displacement of a shaft under a uniformly distributed load, providing a measure of the shaft's flexibility and ability to withstand external forces without deforming excessively. Static Deflection is denoted by δ symbol.

How to calculate Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load using this online calculator? To use this online calculator for Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load, enter Load per unit length (w), Length of Shaft (L_shaft), Young's Modulus (E) & Moment of inertia of shaft (I_shaft) and hit the calculate button. Here is how the Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load calculation can be explained with given input values -> 0.36 = (5*3*3.5^4)/(384*15*1.085522).

FAQ

What is Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load?

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load formula is defined as the maximum displacement of a shaft under a uniformly distributed load, providing a measure of the shaft's flexibility and ability to withstand external forces without deforming excessively and is represented as δ = (5*w*L_shaft^4)/(384*E*I_shaft) or Static Deflection = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft). Load per unit length is the force per unit length applied to a system, affecting its 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, 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.

How to calculate Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load?

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load formula is defined as the maximum displacement of a shaft under a uniformly distributed load, providing a measure of the shaft's flexibility and ability to withstand external forces without deforming excessively is calculated using Static Deflection = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft). To calculate Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load, you need Load per unit length (w), Length of Shaft (L_shaft), Young's Modulus (E) & Moment of inertia of shaft (I_shaft). With our tool, you need to enter the respective value for Load per unit length, Length of Shaft, Young's Modulus & Moment of inertia 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 Static Deflection?

In this formula, Static Deflection uses Load per unit length, Length of Shaft, Young's Modulus & Moment of inertia of shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

Static Deflection = (0.5615/Frequency)^2

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