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Static Deflection given Moment of Inertia of Shaft Formula

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

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

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

Static Deflection given Moment of Inertia of Shaft Example

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Here is how the Static Deflection given Moment of Inertia of Shaft equation looks like with Values.

Here is how the Static Deflection given Moment of Inertia of Shaft equation looks like with Units.

Here is how the Static Deflection given Moment of Inertia of Shaft equation looks like.

0.398 = \frac{0.4534 \cdot {3.5}^{3}}{3 \cdot 15 \cdot 1.0855}

0.398m = \frac{0.4534kg \cdot {3.5m}^{3}}{3 \cdot 15N/m \cdot 1.0855kg·m²}

0.398 = \frac{0.4534 \cdot {3.5}^{3}}{3 \cdot 15 \cdot 1.0855}

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Static Deflection given Moment of Inertia of Shaft Solution

Follow our step by step solution on how to calculate Static Deflection given Moment of Inertia of Shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

δ = \frac{0.4534kg \cdot {3.5m}^{3}}{3 \cdot 15N/m \cdot 1.0855kg·m²}

Next Step Prepare to Evaluate

∴

δ = \frac{0.4534 \cdot {3.5}^{3}}{3 \cdot 15 \cdot 1.0855}

Next Step Evaluate

∴

δ = 0.397965149485685m

LAST Step Rounding Answer

∴

δ = 0.398m

Static Deflection given Moment of Inertia of Shaft Formula Elements

Variables

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

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

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

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

Other formulas in General Shaft category

Go Load at Free End in Free Transverse Vibrations

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

Go Length of Shaft

L shaft = {(\frac{δ \cdot 3 \cdot E \cdot I shaft}{W attached})}^{\frac{1}{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 Static Deflection given Moment of Inertia of Shaft?

Static Deflection given Moment of Inertia of Shaft evaluator uses Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft) to evaluate 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 evaluate Static Deflection given Moment of Inertia of Shaft using this online evaluator? To use this online evaluator 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.

FAQs on Static Deflection given Moment of Inertia of Shaft

What is the formula to find Static Deflection given Moment of Inertia of Shaft?

The formula of Static Deflection given Moment of Inertia of Shaft is expressed as Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft). Here is an example- 0.397965 = (0.453411*3.5^3)/(3*15*1.085522).

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

With 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) we can find Static Deflection given Moment of Inertia of Shaft using the formula - Static Deflection = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Moment of inertia of shaft).

Can the Static Deflection given Moment of Inertia of Shaft be negative?

No, the Static Deflection given Moment of Inertia of Shaft, measured in Length cannot be negative.

Which unit is used to measure Static Deflection given Moment of Inertia of Shaft?

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

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Static Deflection given Moment of Inertia of Shaft Formula

Static Deflection given Moment of Inertia of Shaft Example

Static Deflection given Moment of Inertia of Shaft Solution

Static Deflection given Moment of Inertia of Shaft Formula Elements

Other formulas in General Shaft category

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

FAQs on Static Deflection given Moment of Inertia of Shaft

Variable Name