Moment of Inertia of Section about Neutral Axis Calculator

✖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.ⓘ Shear Force at Section [V]			+10% -10%
✖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.ⓘ Area of Section above Considered Level [A_above]			+10% -10%
✖Distance to CG of Area from NA is a distance helps in determining the distribution of stresses within a beam or any structural element.ⓘ Distance to CG of Area from NA [ȳ]			+10% -10%
✖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.ⓘ Shear Stress at Section [𝜏]			+10% -10%
✖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.ⓘ Beam Width at Considered Level [w]			+10% -10%

✖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.ⓘ Moment of Inertia of Section about Neutral Axis [I]

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Moment of Inertia of Section about Neutral Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
I = (V*A_above*ȳ)/(𝜏*w)
This formula uses 6 Variables

Variables Used

Moment of Inertia of Area of Section - (Measured in Meter⁴) - 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.
Shear Force at Section - (Measured in Newton) - 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.
Area of Section above Considered Level - (Measured in Square Meter) - 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.
Distance to CG of Area from NA - (Measured in Meter) - Distance to CG of Area from NA is a distance helps in determining the distribution of stresses within a beam or any structural element.
Shear Stress at Section - (Measured in Pascal) - 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.
Beam Width at Considered Level - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Shear Force at Section: 4.9 Kilonewton --> 4900 Newton (Check conversion here)
Area of Section above Considered Level: 1986.063 Square Millimeter --> 0.001986063 Square Meter (Check conversion here)
Distance to CG of Area from NA: 82 Millimeter --> 0.082 Meter (Check conversion here)
Shear Stress at Section: 0.005 Megapascal --> 5000 Pascal (Check conversion here)
Beam Width at Considered Level: 95 Millimeter --> 0.095 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (V*A_above*ȳ)/(𝜏*w) --> (4900*0.001986063*0.082)/(5000*0.095)

Evaluating ... ...

I = 0.00168000023873684

STEP 3: Convert Result to Output's Unit

0.00168000023873684 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.00168000023873684 ≈ 0.00168 Meter⁴ <-- Moment of Inertia of Area of Section

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Shear Stress at a Section Calculators

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

LaTeX Go Distance to CG of Area from NA = (Shear Stress at Section*Moment of Inertia of Area of Section*Beam Width at Considered Level)/(Shear Force at Section*Area of Section above Considered Level)

Moment of Inertia of Section about Neutral Axis

LaTeX Go 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)

Width of Beam at Considered Level

LaTeX Go Beam Width at Considered Level = (Shear Force at Section*Area of Section above Considered Level*Distance to CG of Area from NA)/(Moment of Inertia of Area of Section*Shear Stress at Section)

Shear Force at Section given Shear Area

LaTeX Go Shear Force at Section = Shear Stress at Section*Shear Area of Beam

Moment of Inertia of Section about Neutral Axis Formula

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What is shear stress and strain?

Shear strain is the deformation of an object or medium under shear stress. The shear modulus is the elastic modulus in this case. Shear stress is caused by forces acting along the object's two parallel surfaces.

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

Moment of Inertia of Section about Neutral Axis calculator 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 calculate 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 calculate Moment of Inertia of Section about Neutral Axis using this online calculator? To use this online calculator 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. Here is how the Moment of Inertia of Section about Neutral Axis calculation can be explained with given input values -> 0.005414 = (4900*0.001986063*0.082)/(5000*0.095).

FAQ

What is Moment of Inertia of Section about Neutral Axis?

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 and is represented as I = (V*A_above*ȳ)/(𝜏*w) or 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). 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, 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, Distance to CG of Area from NA is a distance helps in determining the distribution of stresses within a beam or any structural element, 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 & 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.

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

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 is calculated using 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 calculate Moment of Inertia of Section about Neutral Axis, you need 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). With our tool, you need to enter the respective value for 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 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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