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Area Moment of Inertia of Circular Cross-Section about Diameter Formula

GoArea Moment of Inertia of specimen given bending moment and bending stress Formula

GoArea Moment of inertia of rectangular cross-section along centroidal axis parallel to breadth Formula

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Area Moment of Inertia is a property of a two-dimensional plane shape that characterizes its deflection under loading. Check FAQs

I = π \cdot \frac{{d c}^{4}}{64}

I - Area Moment of Inertia?d_c - Diameter of circular section of shaft?π - Archimedes' constant?

Area Moment of Inertia of Circular Cross-Section about Diameter Example

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Here is how the Area Moment of Inertia of Circular Cross-Section about Diameter equation looks like with Values.

Here is how the Area Moment of Inertia of Circular Cross-Section about Diameter equation looks like with Units.

Here is how the Area Moment of Inertia of Circular Cross-Section about Diameter equation looks like.

65597.24 = 3.1416 \cdot \frac{34^{4}}{64}

65597.24mm⁴ = 3.1416 \cdot \frac{{34mm}^{4}}{64}

65597.24 = 3.1416 \cdot \frac{34^{4}}{64}

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Area Moment of Inertia of Circular Cross-Section about Diameter Solution

Follow our step by step solution on how to calculate Area Moment of Inertia of Circular Cross-Section about Diameter?

FIRST Step Consider the formula

I = π \cdot \frac{{d c}^{4}}{64}

Next Step Substitute values of Variables

∴

I = π \cdot \frac{{34mm}^{4}}{64}

Next Step Substitute values of Constants

∴

I = 3.1416 \cdot \frac{{34mm}^{4}}{64}

Next Step Convert Units

∴

I = 3.1416 \cdot \frac{{0.034m}^{4}}{64}

Next Step Prepare to Evaluate

∴

I = 3.1416 \cdot \frac{{0.034}^{4}}{64}

Next Step Evaluate

∴

I = 6.55972400051183E-08m⁴

Next Step Convert to Output's Unit

∴

I = 65597.2400051183mm⁴

LAST Step Rounding Answer

∴

I = 65597.24mm⁴

Area Moment of Inertia of Circular Cross-Section about Diameter Formula Elements

Variables

Constants

Area Moment of Inertia

Area Moment of Inertia is a property of a two-dimensional plane shape that characterizes its deflection under loading.

Symbol: I

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Diameter of circular section of shaft

Diameter of circular section of shaft is the diameter of the circular cross-section of the specimen.

Symbol: d_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of circular section of shaft

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 Area Moment of Inertia

Go Area Moment of Inertia of specimen given bending moment and bending stress

I = \frac{M b \cdot y}{σ b}

Go Area Moment of inertia of rectangular cross-section along centroidal axis parallel to breadth

I = \frac{b \cdot (L^{3})}{12}

Go Area Moment of inertia of rectangular cross-section along centroidal axis parallel to length

I = \frac{(L^{3}) \cdot b}{12}

Other formulas in Stresses due to Bending Moment category

Go Bending stress in specimen due to bending moment

σ b = \frac{M b \cdot y}{I}

Go Bending moment in specimen given bending stress

M b = \frac{σ b \cdot I}{y}

How to Evaluate Area Moment of Inertia of Circular Cross-Section about Diameter?

Area Moment of Inertia of Circular Cross-Section about Diameter evaluator uses Area Moment of Inertia = pi*(Diameter of circular section of shaft^4)/64 to evaluate the Area Moment of Inertia, The Area Moment of Inertia of Circular Cross-Section about Diameter formula is defined as the quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation. Area Moment of Inertia is denoted by I symbol.

How to evaluate Area Moment of Inertia of Circular Cross-Section about Diameter using this online evaluator? To use this online evaluator for Area Moment of Inertia of Circular Cross-Section about Diameter, enter Diameter of circular section of shaft (d_c) and hit the calculate button.

FAQs on Area Moment of Inertia of Circular Cross-Section about Diameter

What is the formula to find Area Moment of Inertia of Circular Cross-Section about Diameter?

The formula of Area Moment of Inertia of Circular Cross-Section about Diameter is expressed as Area Moment of Inertia = pi*(Diameter of circular section of shaft^4)/64. Here is an example- 6.6E+16 = pi*(0.034^4)/64.

How to calculate Area Moment of Inertia of Circular Cross-Section about Diameter?

With Diameter of circular section of shaft (d_c) we can find Area Moment of Inertia of Circular Cross-Section about Diameter using the formula - Area Moment of Inertia = pi*(Diameter of circular section of shaft^4)/64. This formula also uses Archimedes' constant .

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

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

Area Moment of Inertia=(Bending Moment*Distance from Neutral Axis of Curved Beam)/Bending Stress
Area Moment of Inertia=(Breadth of rectangular section*(Length of rectangular section^3))/12
Area Moment of Inertia=((Length of rectangular section^3)*Breadth of rectangular section)/12

Can the Area Moment of Inertia of Circular Cross-Section about Diameter be negative?

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

Which unit is used to measure Area Moment of Inertia of Circular Cross-Section about Diameter?

Area Moment of Inertia of Circular Cross-Section about Diameter is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Area Moment of Inertia of Circular Cross-Section about Diameter can be measured.

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