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Static Deflection given Moment of Inertia of Shaft Calculator

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

✖Load Attached to Free End of Constraint is the force applied to the free end of a constraint in a system undergoing free transverse vibrations.ⓘ Load Attached to Free End of Constraint [W_attached]			+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 given Moment of Inertia of Shaft [δ]

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Static Deflection given Moment of Inertia of Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft)
δ = (W_attached*L_shaft^3)/(3*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 Attached to Free End of Constraint - (Measured in Kilogram) - Load Attached to Free End of Constraint is the force applied to the free end of a constraint in a system undergoing 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 Attached to Free End of Constraint: 0.453411 Kilogram --> 0.453411 Kilogram 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 = (W_attached*L_shaft^3)/(3*E*I_shaft) --> (0.453411*3.5^3)/(3*15*1.085522)

Evaluating ... ...

δ = 0.397965149485685

STEP 3: Convert Result to Output's Unit

0.397965149485685 Meter --> No Conversion Required

FINAL ANSWER

0.397965149485685 ≈ 0.397965 Meter <-- Static Deflection

(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 » General Shaft » Static Deflection given Moment of Inertia of Shaft

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< General Shaft Calculators

Length of Shaft

LaTeX Go Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3)

Static Deflection given Moment of Inertia of Shaft

LaTeX Go Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft)

Moment of Inertia of Shaft given Static Deflection

LaTeX Go Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection)

Load at Free End in Free Transverse Vibrations

LaTeX Go Load Attached to Free End of Constraint = (Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Length of Shaft^3)

Static Deflection given Moment of Inertia of Shaft Formula

LaTeX Go

Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft)
δ = (W_attached*L_shaft^3)/(3*E*I_shaft)

What are Transverse Vibrations?

A vibration in which the element moves to and fro in a direction perpendicular to the direction of the advance of the wave.

How to Calculate Static Deflection given Moment of Inertia of Shaft?

Static Deflection given Moment of Inertia of Shaft calculator uses Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft) to calculate the Static Deflection, Static Deflection given Moment of Inertia of Shaft formula is defined as a measure of the maximum displacement of a shaft from its original position when a load is applied, taking into account the shaft's moment of inertia, modulus of elasticity, and the weight and length of the attached load. Static Deflection is denoted by δ symbol.

How to calculate Static Deflection given Moment of Inertia of Shaft using this online calculator? To use this online calculator for Static Deflection given Moment of Inertia of Shaft, enter Load Attached to Free End of Constraint (W_attached), 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 given Moment of Inertia of Shaft calculation can be explained with given input values -> 0.397965 = (0.453411*3.5^3)/(3*15*1.085522).

FAQ

What is Static Deflection given Moment of Inertia of Shaft?

Static Deflection given Moment of Inertia of Shaft formula is defined as a measure of the maximum displacement of a shaft from its original position when a load is applied, taking into account the shaft's moment of inertia, modulus of elasticity, and the weight and length of the attached load and is represented as δ = (W_attached*L_shaft^3)/(3*E*I_shaft) or Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft). Load Attached to Free End of Constraint is the force applied to the free end of a constraint in a system undergoing 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 given Moment of Inertia of Shaft?

Static Deflection given Moment of Inertia of Shaft formula is defined as a measure of the maximum displacement of a shaft from its original position when a load is applied, taking into account the shaft's moment of inertia, modulus of elasticity, and the weight and length of the attached load is calculated using Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft). To calculate Static Deflection given Moment of Inertia of Shaft, you need Load Attached to Free End of Constraint (W_attached), 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 Attached to Free End of Constraint, 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.

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