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Moment of Inertia of Rectangular 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}{2 \cdot 𝜏} \cdot (\frac{d^{2}}{4} - σ^{2})

I - Moment of Inertia of Area of Section?V - Shear Force on Beam?𝜏 - Shear Stress in Beam?d - Depth of Rectangular Section?σ - Distance from Neutral Axis?

Moment of Inertia of Rectangular Section about Neutral Axis Example

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

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

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

8.1E-6 = \frac{4.8}{2 \cdot 6} \cdot (\frac{285^{2}}{4} - 5^{2})

8.1E-6m⁴ = \frac{4.8kN}{2 \cdot 6MPa} \cdot (\frac{{285mm}^{2}}{4} - {5mm}^{2})

8.1E-6 = \frac{4.8}{2 \cdot 6} \cdot (\frac{285^{2}}{4} - 5^{2})

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Moment of Inertia of Rectangular Section about Neutral Axis Solution

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

FIRST Step Consider the formula

I = \frac{V}{2 \cdot 𝜏} \cdot (\frac{d^{2}}{4} - σ^{2})

Next Step Substitute values of Variables

∴

I = \frac{4.8kN}{2 \cdot 6MPa} \cdot (\frac{{285mm}^{2}}{4} - {5mm}^{2})

Next Step Convert Units

∴

I = \frac{4800N}{2 \cdot 6E+6Pa} \cdot (\frac{{0.285m}^{2}}{4} - {0.005m}^{2})

Next Step Prepare to Evaluate

∴

I = \frac{4800}{2 \cdot 6E+6} \cdot (\frac{{0.285}^{2}}{4} - {0.005}^{2})

Next Step Evaluate

∴

I = 8.1125E-06m⁴

LAST Step Rounding Answer

∴

I = 8.1E-6m⁴

Moment of Inertia of Rectangular 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 on Beam

Shear Force on Beam refers to the internal force that acts parallel to the cross-section of the beam is the result of external loads, reactions at supports, and the beam’s own weight.

Symbol: V

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Shear Force on Beam

Shear Stress in Beam

Shear stress in beam is the internal stress that arises from the application of shear force and acts parallel to the cross-section of the beam.

Symbol: 𝜏

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress in Beam

Depth of Rectangular Section

Depth of rectangular section is the vertical dimension of the cross-section of the beam helps in calculating various stresses and ensuring the structural integrity of the beam.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Rectangular Section

Distance from Neutral Axis

Distance from neutral axis in a beam is the perpendicular distance from the neutral axis to a specific point within the beam’s cross-section. It is an imaginary line where the bending stress is zero.

Symbol: σ

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Distance from Neutral Axis

Other formulas in Shear Stress in Rectangular Section category

Go Distance of C.G of Area (above Considered Level) from Neutral Axis for Rectangular Section

ȳ = \frac{1}{2} \cdot (σ + \frac{d}{2})

Go Distance of Considered Level from Neutral Axis for Rectangular Section

σ = 2 \cdot (ȳ - \frac{d}{4})

Go Shear Stress for Rectangular Section

𝜏 = \frac{V}{2 \cdot I} \cdot (\frac{d^{2}}{4} - σ^{2})

Go Shear Force for Rectangular Section

V = \frac{2 \cdot I \cdot 𝜏}{\frac{d^{2}}{4} - σ^{2}}

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

Moment of Inertia of Rectangular Section about Neutral Axis evaluator uses Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2) to evaluate the Moment of Inertia of Area of Section, Moment of Inertia of Rectangular Section about Neutral Axis formula is defined as a measure of the resistance of a rectangular section to bending or twisting, which is crucial in determining the shear stress and deformation of the section under various loads. Moment of Inertia of Area of Section is denoted by I symbol.

How to evaluate Moment of Inertia of Rectangular Section about Neutral Axis using this online evaluator? To use this online evaluator for Moment of Inertia of Rectangular Section about Neutral Axis, enter Shear Force on Beam (V), Shear Stress in Beam (𝜏), Depth of Rectangular Section (d) & Distance from Neutral Axis (σ) and hit the calculate button.

FAQs on Moment of Inertia of Rectangular Section about Neutral Axis

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

The formula of Moment of Inertia of Rectangular Section about Neutral Axis is expressed as Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2). Here is an example- 8.1E-6 = 4800/(2*6000000)*(0.285^2/4-0.005^2).

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

With Shear Force on Beam (V), Shear Stress in Beam (𝜏), Depth of Rectangular Section (d) & Distance from Neutral Axis (σ) we can find Moment of Inertia of Rectangular Section about Neutral Axis using the formula - Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*(Depth of Rectangular Section^2/4-Distance from Neutral Axis^2).

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

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

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

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

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Moment of Inertia of Rectangular Section about Neutral Axis Formula

Moment of Inertia of Rectangular Section about Neutral Axis Example

Moment of Inertia of Rectangular Section about Neutral Axis Solution

Moment of Inertia of Rectangular Section about Neutral Axis Formula Elements

Other formulas in Shear Stress in Rectangular Section category

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

FAQs on Moment of Inertia of Rectangular Section about Neutral Axis

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