Moment of Inertia of Section about Neutral Axis Calculator

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Shear Stress In Beam

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Shear Stress at a Section

Shear Stress Distribution for Different Sections

✖Shear Force at Section is the force that causes shear deformation to occur in the shear plane.ⓘ Shear Force at Section [S]			+10% -10%
✖Area of Section above Considered Level can be defined as the space occupied by a flat shape or the surface of an object.ⓘ Area of Section above Considered Level [A_abv]			+10% -10%
✖Distance of CG of area from NA is a numerical measurement of how far apart objects or points are.ⓘ Distance of CG of Area from NA [ȳ]			+10% -10%
✖Shear stress at section is a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear stress at section [𝜏_section]			+10% -10%
✖Beam Width at Considered Level is the description of how wide the beam is at that level.ⓘ Beam Width at Considered Level [w]			+10% -10%

✖Moment of Inertia of Area of Section is the second moment of the area of the section about the neutral axis.ⓘ Moment of Inertia of Section about Neutral Axis [I]

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Formula

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Moment of Inertia of Section about Neutral Axis

Formula

`"I" = ("S"*"A"_{"abv"}*"ȳ")/("𝜏"_{"section"}*"w")`

Example

`"0.005414m⁴"=("4.9kN"*"6400mm²"*"82mm")/("0.005MPa"*"95mm")`

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Download Shear Stress In Beam Formula PDF

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 of CG of Area from NA)/(Shear stress at section*Beam Width at Considered Level)
I = (S*A_abv*ȳ)/(𝜏_section*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 the second moment of the area of the section about the neutral axis.
Shear Force at Section - (Measured in Newton) - Shear Force at Section is the force that causes shear deformation to occur in the shear plane.
Area of Section above Considered Level - (Measured in Square Meter) - Area of Section above Considered Level can be defined as the space occupied by a flat shape or the surface of an object.
Distance of CG of Area from NA - (Measured in Meter) - Distance of CG of area from NA is a numerical measurement of how far apart objects or points are.
Shear stress at section - (Measured in Pascal) - Shear stress at section is a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Beam Width at Considered Level - (Measured in Meter) - Beam Width at Considered Level is the description of how wide the beam is at that level.

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: 6400 Square Millimeter --> 0.0064 Square Meter (Check conversion here)
Distance of 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 = (S*A_abv*ȳ)/(𝜏_section*w) --> (4900*0.0064*0.082)/(5000*0.095)

Evaluating ... ...

I = 0.00541372631578948

STEP 3: Convert Result to Output's Unit

0.00541372631578948 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.00541372631578948 ≈ 0.005414 Meter⁴ <-- Moment of Inertia of Area of Section

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Shear Stress In Beam » Shear Stress at a Section » Moment of Inertia of Section about Neutral Axis

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National Institute Of Technology (NIT), Hamirpur

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< 7 Shear Stress at a Section Calculators

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

Go Distance of 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

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

Area of Section above Considered Level

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

Width of Beam at Considered Level

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

Shear Stress at Section

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

Shear Force at Section

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

Shear Force at Section given Shear Area

Go Shear Force at Section = Shear stress at section*Shear Area of beam

Moment of Inertia of Section about Neutral Axis Formula

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 of CG of Area from NA)/(Shear stress at section*Beam Width at Considered Level) to calculate the Moment of Inertia of Area of Section, The Moment of inertia of section about neutral axis formula is defined as the quantity expressed by the body resisting angular acceleration. Here the moment of inertia of section is second moment of area. 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 (S), Area of Section above Considered Level (A_abv), Distance of CG of Area from NA (ȳ), Shear stress at section (𝜏_section) & 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 -> 0.001651 = (4900*0.0064*0.082)/(5000*0.095).

FAQ

What is Moment of Inertia of Section about Neutral Axis?

The Moment of inertia of section about neutral axis formula is defined as the quantity expressed by the body resisting angular acceleration. Here the moment of inertia of section is second moment of area and is represented as I = (S*A_abv*ȳ)/(𝜏_section*w) or Moment of Inertia of Area of Section = (Shear Force at Section*Area of Section above Considered Level*Distance of CG of Area from NA)/(Shear stress at section*Beam Width at Considered Level). Shear Force at Section is the force that causes shear deformation to occur in the shear plane, Area of Section above Considered Level can be defined as the space occupied by a flat shape or the surface of an object, Distance of CG of area from NA is a numerical measurement of how far apart objects or points are, Shear stress at section is a force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress & Beam Width at Considered Level is the description of how wide the beam is at that level.

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

The Moment of inertia of section about neutral axis formula is defined as the quantity expressed by the body resisting angular acceleration. Here the moment of inertia of section is second moment of area is calculated using Moment of Inertia of Area of Section = (Shear Force at Section*Area of Section above Considered Level*Distance of 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 (S), Area of Section above Considered Level (A_abv), Distance of CG of Area from NA (ȳ), Shear stress at section (𝜏_section) & 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 of 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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