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Length of Shaft Formula

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Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft. Check FAQs

L shaft = {(\frac{δ \cdot 3 \cdot E \cdot I shaft}{W attached})}^{\frac{1}{3}}

L_shaft - Length of Shaft?δ - Static Deflection?E - Young's Modulus?I_shaft - Moment of inertia of shaft?W_attached - Load Attached to Free End of Constraint?

Length of Shaft Example

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Here is how the Length of Shaft equation looks like with Values.

Here is how the Length of Shaft equation looks like with Units.

Here is how the Length of Shaft equation looks like.

1.9795 = {(\frac{0.072 \cdot 3 \cdot 15 \cdot 1.0855}{0.4534})}^{\frac{1}{3}}

1.9795m = {(\frac{0.072m \cdot 3 \cdot 15N/m \cdot 1.0855kg·m²}{0.4534kg})}^{\frac{1}{3}}

1.9795 = {(\frac{0.072 \cdot 3 \cdot 15 \cdot 1.0855}{0.4534})}^{\frac{1}{3}}

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Length of Shaft Solution

Follow our step by step solution on how to calculate Length of Shaft?

FIRST Step Consider the formula

L shaft = {(\frac{δ \cdot 3 \cdot E \cdot I shaft}{W attached})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

L shaft = {(\frac{0.072m \cdot 3 \cdot 15N/m \cdot 1.0855kg·m²}{0.4534kg})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

L shaft = {(\frac{0.072 \cdot 3 \cdot 15 \cdot 1.0855}{0.4534})}^{\frac{1}{3}}

Next Step Evaluate

∴

L shaft = 1.97953808889316m

LAST Step Rounding Answer

∴

L shaft = 1.9795m

Length of Shaft Formula Elements

Variables

Length of Shaft

Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Static Deflection

Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.

Symbol: δ

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Static Deflection

Young's Modulus

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.

Symbol: E

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Moment of inertia of shaft

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.

Symbol: I_shaft

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of inertia of shaft

Load Attached to Free End of Constraint

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.

Symbol: W_attached

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Load Attached to Free End of Constraint

Other formulas in General Shaft category

Go Static Deflection given Moment of Inertia of Shaft

δ = \frac{W attached \cdot {L shaft}^{3}}{3 \cdot E \cdot I shaft}

Go Load at Free End in Free Transverse Vibrations

W attached = \frac{δ \cdot 3 \cdot E \cdot I shaft}{{L shaft}^{3}}

Go Moment of Inertia of Shaft given Static Deflection

I shaft = \frac{W attached \cdot {L shaft}^{3}}{3 \cdot E \cdot δ}

Go Natural Frequency of Free Transverse Vibrations

f = \frac{\sqrt{\frac{s}{W attached}}}{2} \cdot π

How to Evaluate Length of Shaft?

Length of Shaft evaluator uses Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3) to evaluate the Length of Shaft, Length of Shaft formula is defined as the distance between the points of support in a shaft, which is a critical parameter in determining the natural frequency of free transverse vibrations, and is influenced by factors such as the shaft's modulus of elasticity, moment of inertia, and the weight of the attached load. Length of Shaft is denoted by L_shaft symbol.

How to evaluate Length of Shaft using this online evaluator? To use this online evaluator for Length of Shaft, enter Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Load Attached to Free End of Constraint (W_attached) and hit the calculate button.

FAQs on Length of Shaft

What is the formula to find Length of Shaft?

The formula of Length of Shaft is expressed as Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3). Here is an example- 1.979538 = ((0.072*3*15*1.085522)/(0.453411))^(1/3).

How to calculate Length of Shaft?

With Static Deflection (δ), Young's Modulus (E), Moment of inertia of shaft (I_shaft) & Load Attached to Free End of Constraint (W_attached) we can find Length of Shaft using the formula - Length of Shaft = ((Static Deflection*3*Young's Modulus*Moment of inertia of shaft)/(Load Attached to Free End of Constraint))^(1/3).

Can the Length of Shaft be negative?

No, the Length of Shaft, measured in Length cannot be negative.

Which unit is used to measure Length of Shaft?

Length of Shaft is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Length of Shaft can be measured.

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Length of Shaft Formula

Length of Shaft Example

Length of Shaft Solution

Length of Shaft Formula Elements

Other formulas in General Shaft category

How to Evaluate Length of Shaft?

FAQs on Length of Shaft

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