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Nth Moment of Inertia Formula

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Nth Moment of Inertia is a measure of the distribution of the beam's mass around its axis of rotation, used in bending beam analysis. Check FAQs

I n = \frac{b \cdot d^{n + 2}}{(n + 2) \cdot 2^{n + 1}}

I_n - Nth Moment of Inertia?b - Breadth of Rectangular Beam?d - Depth of Rectangular Beam?n - Material Constant?

Nth Moment of Inertia Example

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

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

Here is how the Nth Moment of Inertia equation looks like.

1.3E+10 = \frac{80 \cdot 20^{0.25 + 2}}{(0.25 + 2) \cdot 2^{0.25 + 1}}

1.3E+10kg*mm² = \frac{80mm \cdot {20mm}^{0.25 + 2}}{(0.25 + 2) \cdot 2^{0.25 + 1}}

1.3E+10 = \frac{80 \cdot 20^{0.25 + 2}}{(0.25 + 2) \cdot 2^{0.25 + 1}}

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Nth Moment of Inertia Solution

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

FIRST Step Consider the formula

I n = \frac{b \cdot d^{n + 2}}{(n + 2) \cdot 2^{n + 1}}

Next Step Substitute values of Variables

∴

I n = \frac{80mm \cdot {20mm}^{0.25 + 2}}{(0.25 + 2) \cdot 2^{0.25 + 1}}

Next Step Prepare to Evaluate

∴

I n = \frac{80 \cdot 20^{0.25 + 2}}{(0.25 + 2) \cdot 2^{0.25 + 1}}

Next Step Evaluate

∴

I n = 12645.5424713879kg·m²

Next Step Convert to Output's Unit

∴

I n = 12645542471.3879kg*mm²

LAST Step Rounding Answer

∴

I n = 1.3E+10kg*mm²

Nth Moment of Inertia Formula Elements

Variables

Nth Moment of Inertia

Nth Moment of Inertia is a measure of the distribution of the beam's mass around its axis of rotation, used in bending beam analysis.

Symbol: I_n

Measurement: Moment of InertiaUnit: kg*mm²

Note: Value should be greater than 0.

Formulas to find Nth Moment of Inertia

Breadth of Rectangular Beam

Breadth of Rectangular Beam is the horizontal distance of a rectangular beam's cross-section, perpendicular to its length, in bending beam applications.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Breadth of Rectangular Beam

Depth of Rectangular Beam

Depth of Rectangular Beam is the vertical distance from the neutral axis to the bottom of the beam, used to calculate bending stresses and moments.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Rectangular Beam

Material Constant

Material Constant is a measure of the stiffness of a material, used to calculate the bending stress and deflection of beams under various loads.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Material Constant

Other formulas in Nonlinear Behavior of Beams category

Go Maximum Bending Stress in Plastic State

σ = \frac{M \cdot y^{n}}{I n}

Go Radius of Curvature given Bending Stress

R = {(\frac{H \cdot y^{n}}{σ})}^{\frac{1}{n}}

Go Radius of Curvature given Bending Moment

R = {(\frac{H \cdot I n}{M})}^{\frac{1}{n}}

How to Evaluate Nth Moment of Inertia?

Nth Moment of Inertia evaluator uses Nth Moment of Inertia = (Breadth of Rectangular Beam*Depth of Rectangular Beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1)) to evaluate the Nth Moment of Inertia, Nth Moment of Inertia formula is defined as a measure of the distribution of the beam's section modulus around its neutral axis, providing a way to calculate the beam's resistance to bending and deformation under various loads and stresses in structural analysis. Nth Moment of Inertia is denoted by I_n symbol.

How to evaluate Nth Moment of Inertia using this online evaluator? To use this online evaluator for Nth Moment of Inertia, enter Breadth of Rectangular Beam (b), Depth of Rectangular Beam (d) & Material Constant (n) and hit the calculate button.

FAQs on Nth Moment of Inertia

What is the formula to find Nth Moment of Inertia?

The formula of Nth Moment of Inertia is expressed as Nth Moment of Inertia = (Breadth of Rectangular Beam*Depth of Rectangular Beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1)). Here is an example- 1.3E+16 = (0.08*0.02^(0.25+2))/((0.25+2)*2^(0.25+1)).

How to calculate Nth Moment of Inertia?

With Breadth of Rectangular Beam (b), Depth of Rectangular Beam (d) & Material Constant (n) we can find Nth Moment of Inertia using the formula - Nth Moment of Inertia = (Breadth of Rectangular Beam*Depth of Rectangular Beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1)).

Can the Nth Moment of Inertia be negative?

No, the Nth Moment of Inertia, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Nth Moment of Inertia?

Nth Moment of Inertia is usually measured using the Kilogram Square Millimeter[kg*mm²] for Moment of Inertia. Kilogram Square Meter[kg*mm²], Kilogram Square Centimeter[kg*mm²], Gram Square Centimeter[kg*mm²] are the few other units in which Nth Moment of Inertia can be measured.

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Nth Moment of Inertia Formula

Nth Moment of Inertia Example

Nth Moment of Inertia Solution

Nth Moment of Inertia Formula Elements

Other formulas in Nonlinear Behavior of Beams category

How to Evaluate Nth Moment of Inertia?

FAQs on Nth Moment of Inertia

Variable Name