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Moment of Inertia of Circular Section Formula

GoMoment of Inertia of Circular Section given Maximum Shear Stress Formula

GoMoment of Inertia of Circular Section given Shear Stress Formula

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Moment of Inertia of Area of Section is a geometric property that quantifies how a cross-sectional area is distributed relative to an axis. Check FAQs

I = \frac{π}{4} \cdot r^{4}

I - Moment of Inertia of Area of Section?r - Radius of Circular Section?π - Archimedes' constant?

Moment of Inertia of Circular Section Example

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Here is how the Moment of Inertia of Circular Section equation looks like with Values.

Here is how the Moment of Inertia of Circular Section equation looks like with Units.

Here is how the Moment of Inertia of Circular Section equation looks like.

1.6286 = \frac{3.1416}{4} \cdot 1200^{4}

1.6286m⁴ = \frac{3.1416}{4} \cdot {1200mm}^{4}

1.6286 = \frac{3.1416}{4} \cdot 1200^{4}

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Moment of Inertia of Circular Section Solution

Follow our step by step solution on how to calculate Moment of Inertia of Circular Section?

FIRST Step Consider the formula

I = \frac{π}{4} \cdot r^{4}

Next Step Substitute values of Variables

∴

I = \frac{π}{4} \cdot {1200mm}^{4}

Next Step Substitute values of Constants

∴

I = \frac{3.1416}{4} \cdot {1200mm}^{4}

Next Step Convert Units

∴

I = \frac{3.1416}{4} \cdot {1.2m}^{4}

Next Step Prepare to Evaluate

∴

I = \frac{3.1416}{4} \cdot {1.2}^{4}

Next Step Evaluate

∴

I = 1.62860163162095m⁴

LAST Step Rounding Answer

∴

I = 1.6286m⁴

Moment of Inertia of Circular Section Formula Elements

Variables

Constants

Moment of Inertia of Area of Section

Moment of Inertia of Area of Section is a geometric property that quantifies how a cross-sectional area is distributed relative to an axis.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia of Area of Section

Radius of Circular Section

Radius of Circular Section is the distance from the center of a circle to any point on its boundary, it represent the characteristic size of a circular cross-section in various applications.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of 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 Moment of Inertia of Area of Section

Go Moment of Inertia of Circular Section given Maximum Shear Stress

I = \frac{F s}{3 \cdot 𝜏 max} \cdot r^{2}

Go Moment of Inertia of Circular Section given Shear Stress

I = \frac{F s \cdot \frac{2}{3} \cdot {(r^{2} - y^{2})}^{\frac{3}{2}}}{𝜏 beam \cdot B}

Other formulas in Moment of Inertia category

Go Area Moment of Considered Area about Neutral Axis

A y = \frac{2}{3} \cdot {(r^{2} - y^{2})}^{\frac{3}{2}}

How to Evaluate Moment of Inertia of Circular Section?

Moment of Inertia of Circular Section evaluator uses Moment of Inertia of Area of Section = pi/4*Radius of Circular Section^4 to evaluate the Moment of Inertia of Area of Section, The Moment of Inertia of Circular Section formula is defined as a measure of the tendency of an object to resist changes in its rotation, which is essential in calculating the shear stress in circular sections, particularly in mechanical and structural engineering applications. Moment of Inertia of Area of Section is denoted by I symbol.

How to evaluate Moment of Inertia of Circular Section using this online evaluator? To use this online evaluator for Moment of Inertia of Circular Section, enter Radius of Circular Section (r) and hit the calculate button.

FAQs on Moment of Inertia of Circular Section

What is the formula to find Moment of Inertia of Circular Section?

The formula of Moment of Inertia of Circular Section is expressed as Moment of Inertia of Area of Section = pi/4*Radius of Circular Section^4. Here is an example- 1.628602 = pi/4*1.2^4.

How to calculate Moment of Inertia of Circular Section?

With Radius of Circular Section (r) we can find Moment of Inertia of Circular Section using the formula - Moment of Inertia of Area of Section = pi/4*Radius of Circular Section^4. This formula also uses Archimedes' constant .

What are the other ways to Calculate Moment of Inertia of Area of Section?

Here are the different ways to Calculate Moment of Inertia of Area of Section-

Moment of Inertia of Area of Section=Shear Force on Beam/(3*Maximum Shear Stress on Beam)*Radius of Circular Section^2
Moment of Inertia of Area of Section=(Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Shear Stress in Beam*Width of Beam Section)

Can the Moment of Inertia of Circular Section be negative?

No, the Moment of Inertia of Circular Section, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia of Circular Section?

Moment of Inertia of Circular Section 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 of Circular Section can be measured.

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