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Moment of Inertia of Section about Neutral Axis Formula

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Moment of inertia of area of section is a geometric property that measures how a cross-section’s area is distributed relative to an axis for predicting a beam’s resistance to bending and deflection. Check FAQs

I = \frac{V \cdot A above \cdot ȳ}{𝜏 \cdot w}

I - Moment of Inertia of Area of Section?V - Shear Force at Section?A_above - Area of Section above Considered Level?ȳ - Distance to CG of Area from NA?𝜏 - Shear Stress at Section?w - Beam Width at Considered Level?

Moment of Inertia of Section about Neutral Axis Example

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Here is how the Moment of Inertia of Section about Neutral Axis equation looks like with Values.

Here is how the Moment of Inertia of Section about Neutral Axis equation looks like with Units.

Here is how the Moment of Inertia of Section about Neutral Axis equation looks like.

0.0017 = \frac{4.9 \cdot 1986.063 \cdot 82}{0.005 \cdot 95}

0.0017m⁴ = \frac{4.9kN \cdot 1986.063mm² \cdot 82mm}{0.005MPa \cdot 95mm}

0.0017 = \frac{4.9 \cdot 1986.063 \cdot 82}{0.005 \cdot 95}

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Moment of Inertia of Section about Neutral Axis Solution

Follow our step by step solution on how to calculate Moment of Inertia of Section about Neutral Axis?

FIRST Step Consider the formula

I = \frac{V \cdot A above \cdot ȳ}{𝜏 \cdot w}

Next Step Substitute values of Variables

∴

I = \frac{4.9kN \cdot 1986.063mm² \cdot 82mm}{0.005MPa \cdot 95mm}

Next Step Convert Units

∴

I = \frac{4900N \cdot 0.002m² \cdot 0.082m}{5000Pa \cdot 0.095m}

Next Step Prepare to Evaluate

∴

I = \frac{4900 \cdot 0.002 \cdot 0.082}{5000 \cdot 0.095}

Next Step Evaluate

∴

I = 0.00168000023873684m⁴

LAST Step Rounding Answer

∴

I = 0.0017m⁴

Moment of Inertia of Section about Neutral Axis Formula Elements

Variables

Moment of Inertia of Area of Section

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

Shear Force at Section

Shear force at section is the algebraic sum of all the vertical forces acting on one side of the section representing the internal force that acts parallel to the cross-section of the beam.

Symbol: V

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Shear Force at Section

Area of Section above Considered Level

Area of section above considered level is the area of a section of a beam or other structural member that is above a certain reference level, used in calculations of shear stress and bending moments.

Symbol: A_above

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Section above Considered Level

Distance to CG of Area from NA

Distance to CG of Area from NA is a distance helps in determining the distribution of stresses within a beam or any structural element.

Symbol: ȳ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance to CG of Area from NA

Shear Stress at Section

Shear stress at section is the internal force per unit area acting parallel to the cross-section of a material arises from shear forces, that act along the plane of the section.

Symbol: 𝜏

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress at Section

Beam Width at Considered Level

Beam width at considered level is the width of a beam at a specific height or section along its length analyzed for the load distribution, shear forces, and bending moments within the beam.

Symbol: w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Beam Width at Considered Level

Other formulas in Shear Stress at a Section category

Go Shear Force at Section given Shear Area

V = 𝜏 \cdot A v

Go Width of Beam at Considered Level

w = \frac{V \cdot A above \cdot ȳ}{I \cdot 𝜏}

Go Distance of Center of Gravity of Area (above Considered Level) from Neutral Axis

ȳ = \frac{𝜏 \cdot I \cdot w}{V \cdot A above}

Go Area of Section above Considered Level

A above = \frac{𝜏 \cdot I \cdot w}{V \cdot ȳ}

How to Evaluate Moment of Inertia of Section about Neutral Axis?

Moment of Inertia of Section about Neutral Axis evaluator uses Moment of Inertia of Area of Section = (Shear Force at Section*Area of Section above Considered Level*Distance to CG of Area from NA)/(Shear Stress at Section*Beam Width at Considered Level) to evaluate the Moment of Inertia of Area of Section, Moment of Inertia of Section about Neutral Axis formula is defined as a measure of the tendency of an object to resist changes in its rotation, providing a way to calculate the rotational inertia of a section around its neutral axis, which is essential in structural analysis and design. Moment of Inertia of Area of Section is denoted by I symbol.

How to evaluate Moment of Inertia of Section about Neutral Axis using this online evaluator? To use this online evaluator for Moment of Inertia of Section about Neutral Axis, enter Shear Force at Section (V), Area of Section above Considered Level (A_above), Distance to CG of Area from NA (ȳ), Shear Stress at Section (𝜏) & Beam Width at Considered Level (w) and hit the calculate button.

FAQs on Moment of Inertia of Section about Neutral Axis

What is the formula to find Moment of Inertia of Section about Neutral Axis?

The formula of Moment of Inertia of Section about Neutral Axis is expressed as Moment of Inertia of Area of Section = (Shear Force at Section*Area of Section above Considered Level*Distance to CG of Area from NA)/(Shear Stress at Section*Beam Width at Considered Level). Here is an example- 0.005414 = (4900*0.001986063*0.082)/(5000*0.095).

How to calculate Moment of Inertia of Section about Neutral Axis?

With Shear Force at Section (V), Area of Section above Considered Level (A_above), Distance to CG of Area from NA (ȳ), Shear Stress at Section (𝜏) & Beam Width at Considered Level (w) we can find Moment of Inertia of Section about Neutral Axis using the formula - Moment of Inertia of Area of Section = (Shear Force at Section*Area of Section above Considered Level*Distance to CG of Area from NA)/(Shear Stress at Section*Beam Width at Considered Level).

Can the Moment of Inertia of Section about Neutral Axis be negative?

No, the Moment of Inertia of Section about Neutral Axis, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia of Section about Neutral Axis?

Moment of Inertia of Section about Neutral Axis 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 Section about Neutral Axis can be measured.

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Moment of Inertia of Section about Neutral Axis Formula

Moment of Inertia of Section about Neutral Axis Example

Moment of Inertia of Section about Neutral Axis Solution

Moment of Inertia of Section about Neutral Axis Formula Elements

Other formulas in Shear Stress at a Section category

How to Evaluate Moment of Inertia of Section about Neutral Axis?

FAQs on Moment of Inertia of Section about Neutral Axis

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