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Moment of Inertia for Hollow Circular Shaft Formula

GoMoment of Inertia about Polar Axis Formula

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The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape. Check FAQs

J = \frac{π}{32} \cdot ({d ho}^{4} - {d hi}^{4})

J - Polar Moment of Inertia?d_ho - Outer Diameter of Hollow Circular Section?d_hi - Inner Diameter of Hollow Circular Section?π - Archimedes' constant?

Moment of Inertia for Hollow Circular Shaft Example

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Here is how the Moment of Inertia for Hollow Circular Shaft equation looks like with Values.

Here is how the Moment of Inertia for Hollow Circular Shaft equation looks like with Units.

Here is how the Moment of Inertia for Hollow Circular Shaft equation looks like.

8.6E-8 = \frac{3.1416}{32} \cdot (40^{4} - 36^{4})

8.6E-8m⁴ = \frac{3.1416}{32} \cdot ({40mm}^{4} - {36mm}^{4})

8.6E-8 = \frac{3.1416}{32} \cdot (40^{4} - 36^{4})

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Moment of Inertia for Hollow Circular Shaft Solution

Follow our step by step solution on how to calculate Moment of Inertia for Hollow Circular Shaft?

FIRST Step Consider the formula

J = \frac{π}{32} \cdot ({d ho}^{4} - {d hi}^{4})

Next Step Substitute values of Variables

∴

J = \frac{π}{32} \cdot ({40mm}^{4} - {36mm}^{4})

Next Step Substitute values of Constants

∴

J = \frac{3.1416}{32} \cdot ({40mm}^{4} - {36mm}^{4})

Next Step Convert Units

∴

J = \frac{3.1416}{32} \cdot ({0.04m}^{4} - {0.036m}^{4})

Next Step Prepare to Evaluate

∴

J = \frac{3.1416}{32} \cdot ({0.04}^{4} - {0.036}^{4})

Next Step Evaluate

∴

J = 8.64314970855624E-08m⁴

LAST Step Rounding Answer

∴

J = 8.6E-8m⁴

Moment of Inertia for Hollow Circular Shaft Formula Elements

Variables

Constants

Polar Moment of Inertia

The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Polar Moment of Inertia

Outer Diameter of Hollow Circular Section

Outer diameter of hollow circular section is the measure of the outermost surface diameter of the 2D concentric circular cross-section.

Symbol: d_ho

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Diameter of Hollow Circular Section

Inner Diameter of Hollow Circular Section

Inner diameter of hollow circular section is the measure of the smallest diameter of the 2D concentric circular cross-section.

Symbol: d_hi

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Inner Diameter of Hollow Circular Section

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Polar Moment of Inertia

Go Moment of Inertia about Polar Axis

J = \frac{π \cdot {d s}^{4}}{32}

Other formulas in Stress and Strain category

Go Elongation Circular Tapered Bar

∆ = \frac{4 \cdot W load \cdot L bar}{π \cdot D 1 \cdot D 2 \cdot e}

Go Elongation of Prismatic Bar due to its Own Weight

∆ = \frac{W load \cdot L bar}{2 \cdot A \cdot e}

Go Deflection of Fixed Beam with Uniformly Distributed Load

δ = \frac{W beam \cdot {L beam}^{4}}{384 \cdot e \cdot I}

Go Deflection of Fixed Beam with Load at Center

δ = \frac{W beam \cdot {L beam}^{3}}{192 \cdot e \cdot I}

How to Evaluate Moment of Inertia for Hollow Circular Shaft?

Moment of Inertia for Hollow Circular Shaft evaluator uses Moment of Inertia for Hollow Circular Shaft = pi/32*(Outer Diameter of Hollow Circular Section^(4)-Inner Diameter of Hollow Circular Section^(4)) to evaluate the Polar Moment of Inertia, The Moment of Inertia for Hollow Circular Shaft formula is defined as a measure of an object's resistance to changes in its rotation, which is a critical concept in the analysis of stress and strain in mechanical systems, particularly in the design of circular shafts with hollow cross-sections. Polar Moment of Inertia is denoted by J symbol.

How to evaluate Moment of Inertia for Hollow Circular Shaft using this online evaluator? To use this online evaluator for Moment of Inertia for Hollow Circular Shaft, enter Outer Diameter of Hollow Circular Section (d_ho) & Inner Diameter of Hollow Circular Section (d_hi) and hit the calculate button.

FAQs on Moment of Inertia for Hollow Circular Shaft

What is the formula to find Moment of Inertia for Hollow Circular Shaft?

The formula of Moment of Inertia for Hollow Circular Shaft is expressed as Moment of Inertia for Hollow Circular Shaft = pi/32*(Outer Diameter of Hollow Circular Section^(4)-Inner Diameter of Hollow Circular Section^(4)). Here is an example- 8.6E-8 = pi/32*(0.04^(4)-0.036^(4)).

How to calculate Moment of Inertia for Hollow Circular Shaft?

With Outer Diameter of Hollow Circular Section (d_ho) & Inner Diameter of Hollow Circular Section (d_hi) we can find Moment of Inertia for Hollow Circular Shaft using the formula - Moment of Inertia for Hollow Circular Shaft = pi/32*(Outer Diameter of Hollow Circular Section^(4)-Inner Diameter of Hollow Circular Section^(4)). This formula also uses Archimedes' constant .

What are the other ways to Calculate Polar Moment of Inertia?

Here are the different ways to Calculate Polar Moment of Inertia-

Polar Moment of Inertia=(pi*Diameter of Shaft^(4))/32

Can the Moment of Inertia for Hollow Circular Shaft be negative?

Yes, the Moment of Inertia for Hollow Circular Shaft, measured in Second Moment of Area can be negative.

Which unit is used to measure Moment of Inertia for Hollow Circular Shaft?

Moment of Inertia for Hollow Circular Shaft is usually measured using the Meter⁴[m⁴] for Second Moment of Area. Centimeter⁴[m⁴], Millimeter⁴[m⁴] are the few other units in which Moment of Inertia for Hollow Circular Shaft can be measured.

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